Volume 1, 2016
The professional journal of International Grammar School International Grammar School
Purpose of iNK: iNK is the professional journal of International Grammar School. It's purpose is to promote professional discussion and debate within and beyond the IGS community.
Volume 1, 2016 Editor: David Hamper Design and Production Editor: Kristel Montarde Design, production and editorial conducted by International Grammar School Staff Services
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Notice ÂŠ Copyright. No part of this publication can be used or reproduced in any format without express permission in writing from International Grammar School. The mention of a product, person or service in this publication does not indicate an endorsement from International Grammar School. The views expressed in this publication do not necessarily represent the opinion of International Grammar School, its agents, company officers or employees. However, they are published in iNK in the spirit of promoting discussion and debate on matters of professional interest.
Contents Editorial 4 David Hamper
Parent Volunteers: maximising impact and building mathematical 5 vocabulary in the Kindergarten classroom Jessica Slater
Pushing Buttons: learning on demand with Tuts & LMS's
Harvard with Passion 28 Alison Housley
What happens to students' mathematics achievement levels and 34 engagement, in a Year 5 class, when they are grouped homogenously based on assessment? David Engelbert
Studying at the Feet of Masters 47 Michele Ellis
Editorial David Hamper, iNK Editor
Welcome to the second edition of iNK – the professional journal of International Grammar School. The concept of iNK is to provide a place for professional discourse for not just the staff of the School but the wider community.
David Engelbert was the School’s second candidate for Experienced Teacher. David’s presentation at the Symposium was likewise acclaimed by his colleagues from I hope that you will enjoy the across the independent sector. 2016 edition of iNK and we look David’s research into how to forward to the 2017 edition! make better use of assessment This edition has a focus on methodologies to inform practice professional reflection with a view is an important piece of practical of enhancing professional practice. research that is already being In 2016 two of the School’s implemented into the School. We candidate’s for Experienced live in a data rich world and as Teacher accreditation with the teachers there is a wealth of data Independent School Teacher available. However, using data to Accreditation Authority (ISTAA) make decisions about how best completed their accreditation to assist students learn is the key. through the new action research David’s work deals with this issue pathway. I am very pleased that and provides excellent advice. we are able to publish the results of their research here in iNK. The Graham Clarkson, IGS High notion of teachers as researchers School Digital Innovator, provides is an important concept and one an insight into the School’s use that is a key objective iNK hopes of new technology and how to foster. these technologies are enhancing learning opportunities. From Jessica Slater’s research into the School’s Music Department the power of training parental Alison Housley – Director of volunteers in mathematical Music writes of her experiences vocabulary in improving student on a recent professional learning outcomes is an example of opportunity to Harvard. While on thorough and comprehensive the other side of the USA Michele research. Building confidence in Ellis – Head of Primary Music mathematical concepts is crucial writes of her time at the famed San to improving student outcomes Fransisco School. in Mathematics. Jessica’s work demonstrates that starting this in I would like to take this the first year of formal schooling opportunity to thank iNK’s Design and involving parents is highly and Production Editor – Kristel effective. Jessica’s research was Montarde. Kristel has again presented at the recent Association produced a visually stimulating of Independent Schools Research journal. Symposium to wide acclaim.
Parent Volunteers: maximising impact and building mathematical vocabulary in the Kindergarten classroom Jessica Slater
Abstract This action research study was conducted in a Kindergarten classroom involving 25 students, 6 parent volunteers, Year 6 student buddies and a teacher as researcher. The investigation was intended to examine the effects of using a Parent Volunteer Training Program (PVTP) to improve student mathematical vocabulary use as well as increase student understanding of geometry concepts. Parent volunteers worked with small groups to deliver geometry specific activities within the kindergarten classroom. The parents did not receive training before the first activity. Prior to administering the second activity, volunteers participated in a 5-10 minute training program. This process was repeated with different learning outcomes the following week. Frequency of Vocabulary Use tables, Socrative surveys and student work samples provided comparative data. An age appropriate online geometry assessment before the interventions provided baseline data. The results obtained indicate that children can be enabled to use topic specific mathematical vocabulary as a tool for describing geometric concepts; and that increasing mathematical vocabulary use can help the development of studentsâ€™ mathematical understanding of geometry. The results also encourage the view that the PVTP is a good model in the development of childrenâ€™s learning. Introduction vocabulary has been well documented, yet how to introduce the vocabulary has received far less consideration. This literature review discusses the importance of mathematical vocabulary and its central function in communicating and comprehending mathematical
Mathematics can be thought of as a visual language of conventions, symbols and numbers that must be meaningful (Kovarik, 2010). If students are to comprehend Mathematics, communicate mathematically and apply Mathematics effectively, they must comprehend and apply the necessary vocabulary. Therefore, vocabulary training is just as critical in Mathematics as it is in reading comprehension (Monroe & Orme, 2002). The importance of explicitly teaching mathematical
concepts. Furthermore, the discussion turns to how the tuition of mathematical vocabulary can be administered by parent volunteers in a kindergarten classroom. The review is organised and sequenced around these key themes and ideas.
Mathematics can be thought of as a visual language (Kovarik, 2010).
The Importance of Mathematical Vocabulary Vocabulary knowledge is a chief contributor to overall understanding in many curriculum areas, including Mathematics. Effective methods for teaching vocabulary in all areas are varied. (Riccomini, Smith, Hughesand Fries, 2015). A Vygotskian, sociocultural perspective sees language as important social tool, which can promote intellectual development (Vygotsky, 1978). Cognitive psychologist, Lev Vygotsky concluded that a child’s understanding of the world is a consequence of interacting with others through language (Monroe and Orme, 2002).
in their study of preschool aged children and their teachers, found that the amount of the teacher’s mathematical related talk was significantly related to their mathematical knowledge over the school year. Anthony and Walshaw (2007), also highlight the importance of explicit instruction of mathematical language. They point to a range of research that has shown that all students, in particular those from diverse language or cultural backgrounds, need to be ‘explicitly taught the conventions and meanings associated with mathematical discourse, representation, and forms of argument.’ (2007, p.69)
A review of the literature around language input and general vocabulary growth reveals that the overall amount of language input children receive is related to their general vocabulary growth. Weizman and Snow, (2001) found that early exposure to sophisticated vocabulary demonstrated greater gains for word development. Similarly, Marzano (2004) found that teaching academic vocabulary could positively influence standardized test scores by as much as 33%.
Moving from a largely American research base to a more relevant Australian context, the implementation of a new mathematics syllabus in 2015 saw mathematical language kept as a key focus in each stage and sub strand (NSW, 2015). The Mathematics Education Research Group of Australia in their response to the first full version of the mathematics curriculum published in 2011 recognise that language can provide a barrier to the understanding of mathematics' concepts and to assessment aimed at eliciting mathematical understandings (Lowrie, Logan & Scriven, 2012). It is much better to encourage the use of precise mathematical terminology with children from an early age to avoid misconceptions as they progress through the curriculum (Lowrie et al., 2012).
Although Mathematics is a graphical language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in Mathematics, they must recognise, comprehend and apply the necessary vocabulary (Kovarik, 2010). Because of the high incidence of unfamiliar vocabulary in Mathematics teaching unknown words become central to mathematical literacy (Monroe and Orme, 2002 p.1). Klibanoff, Levine, Huttenlocher, Vasilyeva and Hedges, (2006)
Pegg, (2010), a former primary and secondary school mathematics teacher turned researcher, also offers an Australian perspective. He describes mathematical language 6
development as important in building students’ understanding and reducing working memory demands, allowing more capacity for other mathematical actions. Sullivan (2011) explains this idea further in his paper for the Educational Research Council of Australia. “If students do not know what is meant by terms such as ‘parallel’, ‘right angle’, ‘index’, ‘remainder’, ‘average’, then instruction using those terms will be confusing and ineffective since so much of students’ working memory will be utilised trying to seek clues for the meaning of the relevant terminology.” (Sullivan, 2011, p. 13). Students, in finding, clarifying and using appropriate language, can then focus on conceptual understanding, and then transfer this understanding to many other content areas in mathematics. The evidence clearly supports teaching and learning the language of Mathematics, for the development of mathematical proficiency but could mathematics be understood as a language in itself? Kenney, (2015) proposes that many educators have referred to mathematics as a special language where the process of learning the language of Mathematics is similar to that of learning any other second language. International Grammar School was founded on the principle that every child should have a second language and that learning is better when immersed in another language. Thinking of Mathematics as a language with it’s own conventions, representations and most importantly to this study, vocabulary, fits perfectly with the ethos and aims of our school.
Examining Pedagogy: What is best practice for delivering the vocabulary? The importance of explicit vocabulary instruction has been well highlighted thus far but how should the instruction be delivered to kindergarten students?
this action research study as well as the pedagogical approach in their delivery. Educational and developmental researchers Piaget, Inhelder, & Szeminska, (1960) explain that students construct their internal representation of Kovarik, (2010) examines direct space by active manipulation of and indirect instructional methods their environment. This means for teaching mathematical that this is not just a ‘reading off ’ vocabulary. She promotes a of the spatial world but results combination of both methods from active interaction with it. for fostering mathematical Children begin their geometric vocabulary development. Indirect understandings visually ("First methods focus on studentSteps Mathematics - Steps centered inquiry and discovery Resources - The Department of based learning. Direct instruction Education", 2016). At the visual takes a “systematic, goal-oriented, level, they judge a 2 dimensional teacher-directed approach to (2D) shape or 3 dimensional learning” (Kovarik, 2010, p.6). (3D) object by its appearance as a whole. Geometric knowledge Indirect instructional strategies gained at the visual level is then for teaching vocabulary are extended to the verbal level at diverse and can include puzzles which children begin to focus and games, movement activities, on the specific attributes of the problem solving, creative 2D and 3D shapes and learn the and visual activities. In direct language important in describing instruction, the focus is on shapes according to their particular words and studying properties (Flanagan, 2012). their parts, word relationships, visual and phonological The implication for teaching representations and through is that it is not enough to just games (Marzano, 2004). show students a triangle, for instance, but rather that students The childhood development of will learn more about triangles geometric ideas is discussed here if they pick one up and explore to give background to the tasks and play with it. Furthermore, designed to collect the data for
use of manipulatives (objects that are used as teaching tools) in mathematical instruction has been well documented. “In order to have opportunities to learn mathematics, children need firsthand experiences related to mathematics, interaction with other children and adults concerning these experiences and time to reflect on the experiences” (Seefeldt & Wasik, 2006, p. 250). In this action research, the teaching and learning around geometric mathematical vocabulary included both direct and indirect instructional methods within small collaborative groups where children manipulated objects and communicated using the vocabulary with their peers. These methods compliment the constructivist pedagogy I espouse where physical engagement and communication play an important role in helping young children construct links between their perceptions and the abstract language and symbolism of mathematics. It also plays a key function in helping children make connections about representations of mathematical ideas (Lowrie et al., 2012).
Parental Involvement in Schools Positive associations between parent involvement and academic achievement have been demonstrated repeatedly in the literature. (Nokali, Bachman, and Votruba-Drzal, 2010). Whilst most of the research focuses on engaging low SES and culturally diverse American families, The Australian organisation, The
Family-School & Community Partnerships Bureau offer an Australian educational view stating that parent involvement significantly contributes to improved academic achievement, wellbeing and productivity (Emerson, Fear, Fox and Sanders, 2012). That is, Australian children, regardless of culture or economic 7
status tend to do better in their primary school years if their parents participate in activities within the school, and develop relationships with their teachers (Henderson and Berla 1994). In a study of the literature around parental involvement in schools, Emerson et al., (2012) found that parents’ engagement in
their children’s schools and their general education has shown to have a positive impact on student academic, social and emotional outcomes. Furthermore, parents’ involvement in their children’s education is influenced by a school culture that values relationships with families that are respectful and reciprocal (Child Trends, 2012). Parents develop a connection to an educational community in a way that is empowering (Hoover‐Dempsey, Walker, Sandler, Whetsel, Green, Wilkins and Closson , 2005). Consistent with the literature and relevant to the context of this action research, parents
with higher levels of education are more likely to be involved in their children’s schools (Emerson et al.,2012). The kindergarten classroom at International Grammar School has traditionally been the source of the most volunteerism in the Primary School. Our school database confirms that a large majority of our parent body holds a tertiary and postgraduate qualification. I had a wonderful opportunity to capitalise on an increasing pool of highly educated and motivated parent talent at the time when parents are most willing and motivated. Evidence suggests that parental involvement tends to decline in student’s high school
years (Hoover‐Dempsey et al., 2005). In the International Grammar School context, parents, as a whole, want their children to succeed in school and understand the importance of family participation in their children’s education. They report social and school factors influence their involvement and that volunteering in the classroom gives them a chance to socialise with other parents. However, anecdotally, parents have often questioned how much they can offer as they often feel “left out” of the teacher’s plan.
Maximising the Impact of Parent Volunteers on Kindergarten Student Learning Outcomes In a less recent study but contextually relevant in age of children to this action research, an administrator in an American elementary school established a volunteer training program to increase the efficiency of the volunteer staff in the school. The intervention was designed to help 6 volunteers better perform their volunteer work within a kindergarten classroom. The intervention involved a series of training sessions for volunteers which had unanimous support from parents for the program and its benefits. The study also revealed that teachers felt volunteers were better prepared for their volunteer work as a result of the intervention (Bailey, 1992). More recently in another Kindergarten classroom parent volunteers were trained to support literacy development, (Porter DeCusati & Johnson, 2004). The school in this study recognised the busy lives of successful working parents so the training
was a flexible and easily accessible 15-minute workshops prior to the volunteering sessions. Children in the parent volunteer groups received more individual attention and had their efforts validated by adults other than their teacher or parents. The findings also report that beside the help the teachers received, the parents learnt more about the classroom and the process of education (Porter DeCusati & Johnson, 2004). The Center for Mental Health in Schools at UCLA (2007) in their technical pack on volunteers in the classroom, suggest that the key to a successful volunteer program is to make the ongoing, training, and daily maintenance of the volunteers part of the everyday agenda in the classroom. The aim of parent volunteer training should be to develop skills appropriate to the tasks set by the teacher and all classroom volunteers should have a clear orientation about what is expected in order to understand the 8
teacher's objective (The Center for Mental Health in Schools at UCLA, 2007). The literature around parental involvement and engagement in their children’s education centres around what it looks like and its importance to student outcomes. The few articles that discuss the classroom systems and specifics of classroom volunteerism suggest that efficacy is determined by the training, and daily maintenance of the volunteers as part of the everyday agenda in the classroom. If the kindergarten parents were trained prior to volunteering, in topic specific mathematical vocabulary, would the students make greater gains in mathematical understanding? Would a training program for parent volunteers impact student use of mathematical language in kindergarten students? Consequently the key aims of the research were: • What happens to kindergarten
studentâ€™s mathematical understanding of geometry when parents deliver geometry specific mathematical vocabulary during small group learning activities in a kindergarten classroom? In addition to responding to this
main question, I also investigated: â€˘ Whether the parent volunteer program is a good model and guide for student learning?â€¨ I hypothesised that with the instruction of geometry specific mathematical vocabulary by
parent volunteers in small groups, kindergarten children will use more mathematical vocabulary when explaining their investigations and improve their understanding of the mathematical sub strands taught.
Clarifying the Action Research Project
Who are we? Six parents, a Year 6 class and 25 kindergarteners participated in this study with myself, their teacher, (author) as researcher. There are 12 boys and 13 girls in my class of 25. From my observations this group was a cohesive one. The youngest student is 5.1 years and the eldest student is 6.5 years. Most students lived with both parents with the exception of 5 students. One male student had same sex parents and one student has a father only. About a quarter of students speak another language at home; Spanish, Russian, German, and Cantonese. About one half of the class have parents born overseas. Children willingly shared their cultural and familial background
with their peers. Four students attended learning support classes for reading. In mathematics, 3 students are performing significantly below their peers. Two students are performing well above their peers in literacy and attend an enrichment writing session twice weekly. 2 students have mathematics skills at least 2 to 3 years above their peers and are extended within the classroom environment.
Hollingshead (1975) Four Factor Index of Social Status. The 6 parents who participated in this study included 5 mothers and 1 father.
The other participants in this group were the Year Six Buddies. The buddy program connects a year six class with a kindergarten class for one 40-minute oneto-one session per week. The program is believed to foster social relationships between the students The parent sample was and to enhance a cooperative homogenous with respect environment of citizenship educational and occupational among students. Their role was background with 100% of the sample had a tertiary qualification, to complete the Frequency of Vocabulary Use tables with their occupied managerial positions or buddy after each intervention. equivalent as estimated with the
Data Collection Parent volunteers worked for four 60-minute sessions, two sessions in one week and two sessions in the following week providing geometry activities with a focus on language delivery. Each group worked with a different volunteer at each intervention so that no group saw the same volunteer
more than once. One week prior to, and one week after the volunteer intervention, pre and post-test data was collected. A variety of methods were used to collect data regarding what effect the implementation of a PVTP would have on kindergarteners use of mathematical vocabulary
and understanding content. Quantitative methods included a shape content knowledge pretest, student surveys and vocabulary frequency tables. Teacher observations and student work samples provided qualitative data.
My Action Research Journey I used the first term of the 2016 school year to informally observe the consistency, and frequency of parent volunteers in my classroom. I spent time observing interactions between students and volunteers and between volunteers and teachers. In our fortnightly team meeting my teacher colleagues provided some insights into how they manage parent volunteers and their thoughts on a parent volunteer training program. The academic and emotional benefits of volunteerism on student outcomes have been well documented and highlighted in the literature review. Thus my observational attention was directed away from student satisfaction and focused ways to maximise student learning during the volunteer/student interactions. My observations and informal conversations with parents revealed that the parent volunteers are keen to add value to the classroom-learning environment but often feel confused about the teacher’s goals. One parent was often worried if she was doing the “right thing” but didn’t feel like she could clarify learning goals with the teacher who during peak periods of volunteerism was busy managing students and parents. The teachers echoed these concerns stating time constraints and behavior management as main concerns. During this phase I carefully considered which area of mathematics to focus on for the intervention. I finally decided on the mathematical sub strand of Geometry as the words and symbols of geometry are used to describe specific spatial ideas and relationships accurately
and succinctly. For many young students, the words of geometry are either new to them or are familiar words used in unfamiliar ways. This provides a perfect environment to measure vocabulary use when students practise saying the words aloud and when sharing their ideas. On a more practical level, in a kindergarten classroom where mathematical concepts may only be taught over a single week, the geometry unit covered two weeks giving more opportunities for data collection.
This test revealed that the average score for the class was 92% with just under half the class scoring 100% and only four children scoring below 80%. Of those three children, one child had taken the Year One level test and scored 60%. These results, combined with my classroom observations, revealed that all children had already mastered the Early Stage One (ES1) Shape and Geometry outcomes with 80% of children scoring above 85%. These results encouraged me to rethink my grouping strategy as well as the vocabulary I emailed parents to recruit them introduced during the sessions. for the study and timetabled their The pretest results confirmed that attendance. in order for the learning activities to be challenging and within During this observational phase of the students’ Zone of Proximal the research study I administered Development, the activities and the kindergarten Mathletics shape vocabulary would have to be pretest to determine what the guided by the BOSTES Stage One students already understood about (S1) (grades one and two in the shapes, which language they were primary school) outcomes for already familiar with and how Measurement and Geometry with they would be ability peer grouped more sophisticated geometrical for the intervention activities. vocabulary and concepts. ZPD (Appendix A) can be described as "the distance between the actual developmental The Mathletics site is an level as determined by educational e-learning application independent problem solving and or website aligned with the the level of potential development Australian Curriculum for the as determined through problem Board of Studies Outcomes. I solving under adult guidance, or used the Mathletics shape pretest in collaboration with more capable for two reasons. Firstly, all the peers" (Vygotsky, 1997, p. 86). kindergarten children have a subscription to Mathletics and The two lowest scoring children secondly, the test is available with on the Mathletics pre-test (both at audio support so the children 66%) received extra training and can listen to the questions rather assessment of ES1 measurement than read them. The limitation of and geometry outcomes by the testing kindergarteners is that only classroom-teaching assistant a few children can read and write before the interventions. enough to be given a pen and paper test. This makes whole class testing labour intensive and time consuming. 10
The Learning Activities and PVTP The 25 children were divided into 6 groups. Five groups had four children and one group had five children. The children were grouped in heterogeneous gender groups the only consideration being academic ability as determined by the Mathletics shape pretest. The volunteers worked for four 60-minute sessions, two sessions in one week and two sessions in the following week. There was no consistency in terms of volunteerism. Each group worked with a different volunteer at each intervention so that no group saw the same volunteer more than once. One week prior to and one week post the volunteer intervention, pre and post-test data was collected. There were two intervention weeks. The first week focused on 3D shape and the Second week focused on 2D shape. The geometry activities I developed for the kindergarten children during the intervention took a great deal of working and reworking. I needed the two learning tasks within each of two the interventions, firstly 3D shape and secondly 2D shape, to allow the students to construct their own mathematical knowledge by
representing and manipulating shapes as well as reasoning geometrically. After much experimenting with similar aged children from my neighbourhood, I developed four learning tasks. The Monday 3D shape activity used grocery boxes alongside commercially made geoconstruction materials to enable children to identify, describe and represent 3 dimensional shapes. The parents did not participate in a training program prior to this activity but they did receive a lesson plan. On Wednesday, during the 3D shape activity the children worked with grocery boxes as well as straws and play dough to identify, describe and represent 3D shapes. The parents arrived 5-10 minutes before the lesson to participate in a threepart training program. The program included: A three minute YouTube clip highlighting the vocabulary I wanted the parents to focus on and encourage the students to use, some tips on behavior management, stickers to reward student behaviour and a detailed lesson plan which I discussed with parents during training. In the second week, The Monday 2D shape activity saw children
working with commercial geoboards to identify, describe and represent 2D shapes. During the Wednesday 2D shape activity the children explored the same learning goal but this time with toothpicks instead of geoboards. Again, the Monday volunteers received a lesson plan only and the Wednesday group received the three-part training program including a YouTube clip highlighting the 2D shape vocabulary that I wanted them to use during the task, tips on behaviour management and a detailed lesson plan which was discussed prior to the lesson. The explicit vocabulary input by parent volunteers during the activities provided the scaffold for the concepts taught. Sperry and Smith, (2001) maintain that when children are given access to conventional words we use to talk about shapes and an understanding of the way we classify them using conventional geometric criteria, they move from concrete experiences to abstract reasoning Importantly to this study, it was not enough to simply present the activities and resources to the children but to support their concept development with correct vocabulary and conventions.
The Learning Activities and PVTP The first method of data collection was the Socrative student surveys. Socrative is a web-based application used as a tool for assessment, quizzing and engaging children in learning activities. A teacher can create questions that reflect the
learning content of a particular topic, in this case, geometry, and question the children in a controlled and engaging way. The application enables you to ask a mixture of ‘multiple choice’, ‘true or false’ and ‘short answer’ questions. This opens up the 11
scope for the line of questioning. Socrative automatically collects the assessment data and emails you a report when the test is finished. I developed the student survey questions based on the BOSTES Stage One Geometry and Measurement outcomes to
gather information about student understanding about shapes. Throughout the first training program, parents were asked to use vocabulary, which included words such as prisms, pyramids, edges, vertices and faces when administering the three dimensional learning activities. During the 2D training program, parents were asked to explicitly use words such as angles, right angle, rectangle, square, straight lines, parallel lines, vertical, horizontal and curved when administering the 2D shape activities. After each intervention, students completed an understanding survey, which provided comparative data. In both the 3D shape interventions and the 2D shape interventions the survey was administered after the first intervention where the parent volunteers did not receive training program and then again after the parent training program.
With the main focus of the study being mathematical vocabulary use, the vocabulary presented during the parent volunteer activities was tallied using a Frequency of Vocabulary Use Table. The Kindergarten children were asked to respond to geometry problems after each 2D and 3D activity similar to those encountered during the interventions. As the children verbally responded to the problem, Year 6 buddies kept a tally of each time they used the specified vocabulary during their responses. The frequency of use measure was administered after each of the 4 interventions and provided comparative data. As the researcher-teacher in this action research project, I kept detailed observations of the interventions. I recorded conversations between students and students as well as conversations between students
and parent volunteers. I took photographs of the learning and student work samples were analysed using a rubric-based grading system. Educators tend to define the word â€˜rubricâ€™ in slightly different ways. A commonly used definition is a document that states the expectations for a learning task by listing the criteria and describing levels of quality from exceptional to poor (Stiggins, 2001). Children, in their first year of school are just learning to read and write and therefore, written messages from teachers on their work or even a numerical grade are a superfluous strategy. I developed this visual rubric to inform children of the success criteria for mathematical problem solving tasks. This proficiency scale based marking system also provided data as to student success with the geometry activities.
What the Data Revealed Students completed The Socrative Student 3D Shape Survey after the first 3D shape activity where the parent volunteers received no training and again after the second 3D shape survey where the parent volunteers received training before the activity. All 25 students in the kindergarten class participated in the survey. All the children completed the survey with a privacy screen. The questions were read aloud twice by myself, the teacher researcher and technical support was offered to students by a classroom assistant and a preservice teacher. These surveys provided information about student understanding of 3D shapes before and after the PVTP and the results are displayed on
STUDENT KNOWLEDGE OF 3 DIMENSIONAL SHAPE SOCRATIVE SURVEY
Pre parent training program
Post parent training program
Percentage of corrent student responses
Figure 1 and Figure 2. The analysis consisted of comparing the two sets of results. Figure 1 shows a 20% increase in correct responses of 3D shapes after the parents received the 12
training program with a focus on 3D shape vocabulary. The Socrative Survey Data shows more correct answers for the physical characteristics of a 3D shape such as the faces, edges and vertices with 39.5% of students able to
answer how many edges a square based pyramid has. Likewise with the question about a rectangular prism, which asked students to select the how many faces and edges a rectangular prism has, 28% of students answered the question correctly in the first surv ey whereas 84% of students were able to answer the question correctly after the second survey. The survey revealed little or no improvement around shape names, comparing shapes to everyday objects and how shapes move. These questions showed student knowledge between 90% and 100% after both the first and second intervention with only one or two children answering incorrectly on any one question. My observations during the interventions and student work samples revealed that students were quick to recognise and name 3D shapes in the environment and were quick to be able to name shapes prior to the PVTP. After the parents received training in 3D shape vocabulary, they were able to explicitly instruct the students to use and rehearse the terminology. Consequently, students had the tools to accurately and confidently describe shape properties and better understand its physical characteristics. Figure 2 shows the results from the Socrative Student Survey of the 2D shape unit. Again, the survey was administered twice; once after the first 2D shape activity where the parents did not receive a training program and then again after the parent volunteer activity where parents received a training program. As in the 3D shape survey, the children were supplied the questions orally by myself and the classroom assistants offered technical
STUDENT KNOWLEDGE OF 2 DIMENSIONAL SHAPE SOCRATIVE SURVEY
Pre parent training
Post parent training
Percentage of corrent student responses
support such as how to use the response keys. The Socrative data set revealed that more students answered more questions correctly after the parents received training than before parents received training. There was a 13% increase in student understanding between the pre and post parent training interventions. The increase in correct answers was not as significant as in the 3D shape survey. Most notably, after the parent training program 11% more students than before training were able to identify right angles in a square and 32% more students were able to identify the angles in a triangle correctly. Before parent training, only 28% of students were able to offer a correct answer to the question, “How many sides does a pentagon have?” compared to 78% of students after parent training. Interestingly, when the students were asked a similar question with a true or false answer, “Does a pentagon have five sides?” 88% of students answered correctly before training whereas after training only 78% of students gave a correct response. Another incongruity in the data collected surfaced around 13
squares and rectangles. Children gave a true or false answer to the question “Is a square a rectangle?” 14.2% fewer students answered correctly after the PVTP than before parents receiving training. After the parents participated in training 30 % more students responded correctly to the true or false question, “Are these all rectangles?” This anomaly in the data may have been in the wording and type of question as well as the developmental stage of the students. Survey questionnaires require care and attention to the design and wording, as well as to the means of administering the survey (Lobe, Livingstone, Olafsson, Simoes, & Aristodemou, 2008). Although a square is a special type of rectangle, asking whether a figure or object, is something else may be too complex for young children to reason with. Jean Piaget the well respected cognitive theorist, called the period from around 2-7 years of age, the Preoperational Stage where logical thinking is still not present, so children cannot rationalise or understand more complex ideas ("Piaget's Stages of Cognitive Development", 2016). The idea that something, for example a square, can be something else at the same time, for example a rectangle may
After the parent training, 100% of students correctly called a quadrilateral a four-sided shape. Only 84% of students answered this question correctly before training. The most confusion in the data set was around naming and identifying types of lines. Whilst 96% of students could identify parallel lines before parent training, only 54% answered correctly after parent training. When asked about horizontal lines within a shape, only one student answered correctly prior to training compared to 25% of correct student responses after parent training. Although those figures represent a 21% increase in correct student responses, three quarters of the class still cannot identify horizontal lines within a regular polygon. Similarly, when asked about vertical lines, three students before training recognised these lines within a closed shape compared to one quarter of the class who answered correctly after parent volunteers had training. That leaves 75% of students in the kindergarten class who cannot identify vertical lines after the 2D shape unit. If we look again to Piaget, this evidence suggests that this 75% of children, still in preoperational stage of development, were not ready to understand and retain complex knowledge around linear connections. The 25% of children who answered the question correctly may have already moved from the pre-operational stage
children were asked by the Year Six students,“ Tell me some things which are the same and different about these two shapes.” double the amount of children were able to use the correct term, edge, which describes where two flat faces of a solid shape meet.
of development into the next cognitive phase of development, the Concrete Operational Stage of development. During this phase, children are more able to apply projective geometry in their thinking and can further understand the placement of objects in relation to each other and take into account vertical and horizontal relationships (McLeod, 2016).
I observed many children incorrectly calling an edge a side during the interventions. After parent training where parents were introduced to the vocabulary to describe the properties of 3D shape, the parent volunteers more frequently corrected children when they used the term side in place of the term edge, which could possible account for the 22 out of 25 children able to use the term correctly after parent participated in the PVTP.
Students completed the Frequency of Vocabulary Use Survey four times after each of the four interventions. The Year 6 Buddies interviewed a Kindergarten after the first three interventions and then a Year 6 Enrichment Maths group, which consisted of six students, interviewed two or three kindergarten students after the last intervention. These surveys provided information about how frequently students used the topic specific mathematical vocabulary when asked to respond to a shape problem. Figure 3 provides results of vocabulary use for 2D shape. Figure 4 provides results of vocabulary use for 3D problems.
“Sometimes I feel like I’m telling the kids the wrong thing. It was really helpful to know exactly what the teacher wanted me to teach the kids and how to phrase it so that I felt confident when I was correcting or praising them.” (Parent volunteer, 2016). When parent volunteers know the teacher's plan for student learning, they feel they can play a positive role in carrying out that plan. It is
Figure 3 demonstrates an increased use of all the 3D vocabulary except for the term square. When kindergarten
Mathematical Vocabulary Usage 3 Dimensional Shape Pre and Post Parent Training 30
Number of Children
have been too much of a leap in thinking for these 5 to 6 year olds. The second question asked children to classify a group of objects, a well-practiced skill for these kindergarten children.
25 20 15 10 5 0
Vocabulary Used Pre parent training
Post parent training
important for them to feel they are part of the teaching team working collaboratively with the teacher. (The Center for Mental Health in Schools at UCLA, 2007).
Prism is still a term children in the kindergarten class are not frequently using with only four children saying the word when answering the problem. Pleasingly, 13 children compared with only one prior to training used the term equal when answering the problem.
a relational meaning to allow children more flexibility and a broader base of understanding as they progress through their mathematics learning (Baroody & Ginsburg, 1983).
Number of Children
The BOSTES ES1 Measurement and Geometry Outcomes for 3D Figure 4 tells a slightly different Shape, advise the word corner to story. When children were ask describe a vertex at this stage of to describe similarities and learning. Prior to parent volunteer It is inconclusive which way the differences between 2 regular training, 9 children used the word children were using the word polygons, children did not use 2D corner compared to 6 children prism as the frequency table shape vocabulary as frequently as who were able to use the technical only measures the amount of they used 3D shape vocabulary term vertex, for the point where use and does not describe the and there were fewer significant the edges of a solid shape meet. context of its use. If the children differences in the amount of After training more children were in this class used the term to children using particular words able to use between the both these pre and post terms with training data. Mathematical Vocabulary Usage 2 Dimensional Shape Pre and Post Parent Training 13 children The terms preferring to 30 square and 25 use vertex/ rectangle 20 vertices to 12 15 were used children who 10 by most preferred the 5 children term corner. 0 in the class Both these e e e le le r l de r l l i e g g g S prior to ra ua ng rn terms are an An te An ia Sq ct Co ila Tr ht r Re g d training correct and Ri ua Q when therefore responding 100% of the Pre parent Post parent Figure 4 training training to the class using problem mathematical proposed by the Year 6 students vocabulary correctly to describe a describe equality within a shape and by all children in the class property of shape. or between two shapes, it would post training program. be an unexpected gain from this The term face, which describes action research project. Baroody 18 children were able to correctly the flat area of a solid shape, saw & Ginsburg, (1983) advocate using name the side of a closed shape a 52% increase in its usage after equals in this relational context compared to only 12 children parent training compared to prior more often in mathematics prior to training. During my to parent training. instruction. Children may come observations of the parent lead to school viewing the equals sign learning tasks, parents were The entire kindergarten class used as an operator symbol because of more likely to correct studentsâ€™ the term square and rectangle their informal experience with incorrect usage of terms such during the frequency use adding. They suggest much early as edge for a two dimensional assessment, post parent training. mathematics instruction required shape after the training program The term square was known and children to compute an expression than prior to training. Likewise used by all children both prior on each side of an equation in for the terms angle and corner. to and post training but the term order to establish equality. They Only two children used the term rectangle was used by 9 more do not advocate eliminating this angle prior to training, where 13 children post training as opposed operator view of the equals sign children favoured the term corner to prior to training. but broaden this view to include to describe where two sides of a 15
closed shape meet. Interestingly, 20 students, 5 more than prior to parent training, were able to name this property with one quarter of the class using the term angle rather than corner. The terms corner and angle are both acceptable at this level according to BOSTES ES1 Measurement and Geometry outcomes with the latter encouraged from Stage One. None of the kindergarten children used the term right angle at any time. The term triangle only occurred in the data five times after training compared to no usage prior to training. During the PVTP, parents were encouraged to use the term quadrilateral to describe a foursided shape. No children used the term prior to training and less than a quarter of the class used the term after the parents received training when responding to the problem posed by their buddies. Looking back to the data from the Socrative 2D Shape Survey, at the end of the 2D Shape Unit, 100% of students correctly identified a Quadrilateral as a four-sided shape. This variance appears to stem from the ability to know something but the inability to express something (McLeod, 2016). During my observation rounds, I noticed children having great difficulty in using this five-syllable word. When I asked children if they know how to classify a group of 2D shapes, many children indicated that they knew but could not remember how to pronounce the word. When presented with the question and the term quadrilateral in the Socrative survey question, “How many sides does a quadrilateral have?” all children answered correctly.
Why was student understanding and frequency of vocabulary use more significant for 3D shape concepts and vocabulary than for 2D shape? We live in an obviously three-dimensional world that we walk through, explore and use every minute of every day. Children develop a system and vocabulary for with which they can talk about the space that they occupy and the properties that this space has perhaps before they develop a system for classifying 2 dimensions. Purely by more experience, children are cognitively more able to process the properties of three dimensional objects, which they have probably already noticed but have previously lacked the correct terminology to describe (Piaget, Inhelder, & Szeminska, 1960). Clements (1998) suggests that young children may form misconceptions around 2 dimensional shapes due to certain shapes having cultural preference. In his examination of materials that teach children about shapes, he found that many of these materials teach children concepts of two-dimensional shapes in rigid ways. Most triangles were isosceles or equilateral with a horizontal base; rectangles were usually horizontally orientated and usually twice as long as they are wide and square were usually represented in the one orientation. Clements (1998) maintains that these visual prototypes can rule children’s thinking. Relative to this study, and as explored in the review of the literature, if these kindergarten children were spending much of their learning time familiarizing themselves with these 2D shapes presented in different orientations and therefore unfamiliar, the children’s cognitive capacity was overloaded 16
with no more room for complex thought and technical vocabulary to describe shape properties (Pegg, 2010). The rubric grading system (Appendix B), indicated how they well they performed on the problems presented during the interventions. Student work samples showed that there was no significant increase or decrease in the amount of stars awarded to students before or after any of the interventions. While this rubric enabled students to become more thoughtful judges of the quality of their own work, the rubric measured the process of problem solving, not the use of vocabulary or student understanding of geometry. The mathematical problem-solving rubric used in this kindergarten classroom is what Mertler (2003) describes as a holistic rubric where the focus of the score is on the overall quality, proficiency, or understanding of the content, and skills-it involves. In this situation the rubric measured the students proficiency at problem solving as well as the quality of their responses rather than student knowledge of geometry. An analytic rubric identifies specific observable attributes and may have been a better scoring instrument to evaluate student geometric knowledge in this study (Nitko, 2001).
What are the implications for my classroom teaching practice? The data presented here, demonstrates that this kindergarten class did improve both their mathematical understanding of geometry concepts and use of mathematical vocabulary after parents delivered geometry specific mathematical vocabulary during small group learning activities. Although the data showed more significant gains in both knowledge as well as frequency of vocabulary use for 3D shape than for 2D shape, children did seem to improve enough to implement the PVTP as a regular part of mathematics instruction in this kindergarten classroom. The importance of mathematical vocabulary for student understanding This research project confirmed that for students to understand Mathematics, they must comprehend and apply the necessary vocabulary. Thus, vocabulary instruction is as important in mathematical understanding as it is in language learning. With the belief that the fluent use of terminology is necessary, explicitly introducing the mathematical vocabulary and encouraging students to use it fluently is one aspect of mathematical instruction I will continue to promote in my classroom. Parent volunteers and other classroom visitors were surprised by the complexity of the mathematical vocabulary being introduced to these kindergarten children. Many of the kindergarten students already had a good understanding of 3D shape as demonstrated by the Mathletics shape pre-test. However, the data demonstrated the significant improvement in both mathematical vocabulary use and improved geometric knowledge after parents explicitly introduced geometric mathematical terminology. Providing students with the mathematical vocabulary to describe what they know, allowed them to express understanding articulately, freeing up cognitive space for deeper understanding of the shape concepts being taught and making connections with other mathematical concepts (Pegg 2010). The PVTP as a model for student learning The PVTP does require more planning prior to the lesson but benefits for student learning outcomes were significant in this kindergarten class. Because children make such good gains in the learning during these sessions, training the parent volunteers prior to the lesson, allows for more content to be covered and understood in less amount of time. The PVTP can provide a simple way to give children more targeted instruction. Unexpectedly, the small amount of extra time I spent engaging with the parent volunteers prior to the lesson discussing my pedagogical aims seemed to foster a mutually reinforcing and respectful relationship. Linking the parents to the learning outcomes reinforced that shared responsibility for the childrenâ€™s education and learning outcomes. As I move forward with the PVTP in the classroom for mathematics vocabulary instruction, it is important to continue to monitor the results and continue to assess its efficacy through student assessment. The participating volunteers in this study offer another dimension to evaluating the success of the PVTP as a maintainable classroom practice and should be explored further. Limitations of the Action Research Model with very young students Conducting action research with very young students with the teacher as researcher has limitations. In this action research project the major limitation was the age of the children. Instruments to measure student understanding in older children usually incorporate pen and paper tests and surveys. In order to fully understand what a kindergarten student knows and understands, they need to hear and respond to questions verbally. Educational research with very young children usually involves interviews, which are time intensive for a single teacher as researcher. Children in Kindergarten for the most part have not learnt to read and write at a level at which a traditional pen and paper or even online assessment could measure student 17
understanding. The Socrative surveys did provide some sort solution to the problem however each of these surveys required three adults in the room to administer them and could only provide limited data. The time required to collect usable data from very young children limited the amount of data that I could collect and analyse within the time frame. Improving the grading systems The rubric grading system did provide some important data for this action research project and is a useful tool in helping children to become master problem solvers. However, the student work samples could be analysed and explored further. This study highlighted the importance of the degree of feedback offered to students as well as to teachers is significant. In the future, I will aim to develop grading systems where students receive specific feedback on their performance with respect to topic specific learning outcomes as well as the processes- to then create a "profile" of specific student strengths and weaknesses (Mertler, 2001). Exploring parental perceptions further This action research put the student and student understanding at the core of the investigation. Additional questions around parental perceptions of their involvement in this type of training still exist for me. I would like to further investigate what type of impact a training program has on their participation levels and their attitudes to classroom volunteerism. In Conclusion Action research is demanding and time consuming and requires a great commitment from teachers (Hendricks, 2006). This one study does not solve all issues around parent volunteerism and mathematical vocabulary instruction but seeing the usefulness and relevance of the action research to student outcomes was critical in motivating me to revaluate my practice and ask further questions. Given the clear benefits in this study of positive parental engagement on student learning, by way of improved mathematics achievement and productivity, the PVTP could be broadened into other grades and other areas of curriculum. The idea that learning the vocabulary of mathematics may have the potential to increase childrenâ€™s understanding of mathematics is a simple one but one that holds promise for increasing the readiness of young children for the challenges they will face in primary school and beyond.
Jessica Slater, BEd (ECE), has been a member of the IGS Primary Department since 2004. Jessica has a keen interest in developing strong working relationships with parents. Jessica also works as a seasonal lecturer at the University of Notre Dame. Jessica recently completed the Action Research stream for her Experienced Teacher accreditation with the Independent Schools Teacher Accreditation Authority. This paper is written based on this research project.
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Appendix A 3D shape Frequency of Vocabulary Use Checklist which was given after both the 3D shape interventions.
Frequency of Geometric Language Usage Checklist Kindergarten Blue 2016 Action Research Project Name of Assessor: _____________________________________________ Name of Child: _______________________________________________ Tell me 5 things which are the same about these shapes? Tell me 5 things which are different about these shapes? (Show children a trinagular prism, a rectangular prism and a cube)
Vocabulary Tally Vocabulary Edge Vertex/vertices Triangle Square Rectangle face Equal
2D shape Frequency of Vocabulary Use Checklist which was given after both the 2D shape interventions.
Frequency of Geometric Language Usage Checklist Kindergarten Blue 2016 Action Research Project Name of Assessor: _____________________________________________ Name of Child: _______________________________________________ Tell me 5 things which are the same about these shapes? Tell me 5 things which are different about these shapes?
Vocabulary Tally Vocabulary Side Angle Rectangle Square Right Angle Quadrilateral Corner Triangle
Appendix B The Mathematical Solving Rubric which was used to assess children's written responses to the geometry problems presented during the 4 shape interventions.
Kindy Maths Rubric 2016
I worked through the problem by myself with a partner. I have clear and organised drawings which are labelled with both numbers and words. I explained my work using mathematical vocabulary
I worked through the problem by myself with a partner. I have clear and organised drawings which are labelled. I explained my work.
I worked through the problem with my teacher. I have clear and organised drawings. My teacher helped me to explain my work
I worked through the problem with my teacher. I have a drawing. My teacher helped me to explain my work.
Pushing Buttons: learning on demand with Tuts & LMS's Graham Clarkson
As many know, IGS has chosen to use Canvas as our new learning management system. This has brought about a lot of excitement around the possibilities teachers will have to communicate, deliver lessons, and provide resources for students. While there is excitement for most, for some the prospect sense of creates a sense fear and anxiety. Partly, this is partly due to change, but it can also come from the same place of anxieties that make people suspect that “robots are taking
are jobs”. The actual fact in this case is that they do, but at the same time create new industries and new jobs. Likewise, it can be imagined that LMS’s are there to replace teachers. In actuality, Online Learning is giving teachers more time to do what they do best: teach. Teachers who would
The face of education is changing with the advancement of technology. There is a saying “a teacher is only as good as their resources”. While there is much more to great teaching, this sentiment aims to describe that the more ways one has of showing and sharing ideas, the broader reach one can have in the classroom with new possibilities for teaching and learning. While curriculum may remain static by comparison, it is the delivery that evolves rapidly. This rate of change has led to a "resources boom" in the sector (so to speak). With the advent of learning management systems, video tutorial culture and the rise of Virtual reality, comes a richness in education that will see students engaged like never before.
communication and project-based learning that sees learning happen on the devices that are built into our lives; computers, tablets, and mobile phones. Yes, teachers can live the dream of marking essays on the beach providing real feedback at the click of a button, but students will also be able to
With the advent of learning management systems, video tutorial culture and the rise of Virtual reality, comes a richness in education that will see students engaged like never before.
otherwise spend their time photocopying, gathering resources and performing administrative tasks will be able to focus on teaching and providing students with an interactive and engaging forum of ideas and creativity. LMS’s and Canvas, in particular allow for students to move at their own pace whether it is the keener accelerating ahead to unlock lessons that have not yet been taught or the student who always needs time to catch up and for whom tomorrow is the best time to start projects. Assignments, discussion, learning games and collaborative education is the nature of the beast that is Canvas. The learning platform, we have carefully chosen is built for 24
pull out their mobile phones while they are travelling and download the resources the teacher has given them and receive reminder by a message (at the same time as their parents) in their inbox that they have homework that is due. In some cases submitting this homework that is as simple as pushing a button on their phone and recording a current account of holidays, spoken in Japanese, Italian, Spanish, French, German or Chinese that they then upload from their phone to their teacher. by way of example I recently used Canvas to create an in-class assignment for my HSC Design Technology class. Using our LMS I was able to give my students an assignment that consisted of
going to a web-site of weird and wonderful Japanese inventions (such as the Butter Stick, think role-on deodorant the you smear on your toast). Students had the link inside their task sheet online and were asked to pick an invention and perform a needs analysis and advertisement in the form of an online presentation. Students were able to find their resources, create a recording, put all of their information, upload a link to their presentations (Prezi. com) to me in the span of a single lesson. I was able to access the link, see who submitted and when and give the students feedback the following day. This condensed a regular week of class into two days. The reason for its success is not just because of the function of our LMS, but as Marshall Mcluhan says “The Message is The Medium”. It is therefore not only the content, but the context
and act of using fast and effective technology that matches the speed and familiarity of the delivery of information. Like modern entertainment media, it is all there ‘on-demand’, lightning speed and created by a series of clicks. An LMS is also helpful for students who regularly have organisational challenges. It is almost tailored for those students who lose, forget, can’t find homework. It is a scientific fact that dogs can’t eat the internet, so homework is safe from the proverbial worksheet munching canine forever more. LMS and technology are not the future, they are happening now across the world at all learning levels. Will they change the way things are done and the goals of education? Yes they will. As the goals of education evolve with the changing world, it is our responsibility as teachers 25
to answer the call. It is okay to fear change. There is a place for tradionalists and technophobes. As teachers in a digital age we don’t have to worry about those who are trailing behind because when they are ready to catch up, they can do so at the click of a mouse or the push of a button. Faster than they you can say “A robot stole my job”. Another trend currently in education is tutorials. We are now able to go online and get a tutorial on anything from making robots to using rapid 3D printers to print in chocolate. If you can imagine it, Google has probably already thought of it. Jung’s collective unconscious is a manifesting reality, day by day with the growing collective that is the Internet. Of course it is more like a ‘collective conscious’ than an ‘unconscious or like a big brain that we all tap into. Trends are determined by what is produced
and posted by people who are experts in a field of their own proclamation. Once upon a time, you would a need a producer to produce, a director to direct or a publisher to publish. As David Gaunlett points out in his work “Making is Connecting”, since the advent of Web 2.0 (the Internet as we know it), creativity has hit an all time high. As such, experts and entertainers are born and die by public ‘liking’. This has given us the tutorial or "tut" as they are better known. This has seen the rise of resources like Kahn
Academy, Video Co-Pilot and a whole world of ‘Self-teaching’. The ability for teachers to record lessons and perform screen capture means that we can now deliver lessons and post them for students for them to be able to have immediate recall once again ‘at the click of a button’. To keep up with this trend and to begin to build up resources, teachers can also be producers and publishers of lessons and tutorials. To respond to this, IGS will be providing and training
Future implications could see high school classes offered to students at a distance who live or have gone overseas. This would allow International Grammar to become even more international and world-ready.
teachers to use software like Camtasia so that in tandem with the arrival of Canvas we can begin to create a ‘bank’ of tutorials and documentation for current and future students and staff to use. Camtasia allows the user to screen record, annotate, animate and edit a complete lesson in simple steps. Currently, I use it to make tutorials for my students and create the “Canvas Nugget’ series that I have been distributing to teachers as a way of navigating our new LMS. Video captured lessons and tuts again allow learning to happen at individual paces and in the comfort of their own homes, on their own time. In fact the first professional development session I did this year was while the
Languages Faculty and other staff were away. With the help of Camtasia, it was made available to staff to view later. It is this digital, broadening of the net that will allow us to catch a broader audience and give people the opportunity to choose the context of the delivery of lessons.
gone overseas. This would allow International Grammar to become even more international and world-ready. At the very least, for the moment it will give parents, students and teachers a new context and possibilities to create richer content for the quality lessons they are already delivering. Platforms like Camtasia and Canvas will help give students a clearer path for an ever evolving landscape of new technology in a time when the very nature of things is becoming more elastic and organic as we try to create changes to keep up change.
The implications of the combination of Camtasia and Canvas is immediately beneficial in giving teachers the tools to do what they do best and a new way for students to interact with and receive information. Future implications could see high school classes offered to students at a distance who live or have
Graham Clarkson, GradDipEd, MVA, joined IGS in 2016 as the High School Digital Innovator. He has worked as a commercial designer working in new technologies and has a Masters of Visual arts. He has worked extensively at Independent schools in Canada and Australia. Graham has lectured at Charles Darwin University in Creative Practice and has worked as an instructor in Graphic and 3D design at UNSW Art and Design.
Harvard with Passion Alison Housley As I stood in the Harvard Graduate School of Education (HGSE) courtyard I was at once taken aback by the striking display in front of me; a plethora of crimson silk banners that hung fluttering in the breeze, forming a dramatic contrast against the brick and mortar ivy classicism backdrop that they framed. This was the reason why I was here, to take advantage of a once-in-a-lifetime opportunity to collaborate with the Silkroad Ensemble, one of the most inspirational and acclaimed groups of our time, under the guidance of the renowned musician and educator Yo-Yo Ma. Our goal was ambitious to say the least; I was here to â€œLearn to Change the Worldâ€?, the mission statement of this institution, appropriately reflecting the work of this faculty as they tirelessly strive to provide each other and their students with the tools and opportunities to facilitate self-improvement, maximise personal attainment, and promote engagement with their community. I had arrived at Cambridge, the Harvard University suburb of Boston, along with 109 other delegates from all over the world as part of a diverse group, consisting of approximately one
third classroom teachers, one third fine-arts directors and arts coordinators, with independent artists and art organization administrators making up the remainder. We had made the journey to attend the Arts and Passion Driven Learning Institute as part of a unique collaboration with Yo-Yo Ma and the Silkroad Ensemble to ask ourselves some fundamental questions underlying our work; How can we, as artists and educators, cultivate a practice of listening? and, how can listening to ourselves and our students support the development of passion-driven learning/learners? It became rapidly apparent that Passion was the answer to these ambitions and aspirations, a term that initially seemed an 28
unconventional focus when considering the fundamental design of an educational system. However, as Yo-Yo Ma explained, when educators focus on their passion, they are empowered through deep listening, heart, and imagination to instill a similar passion within their students, driving them to make creative decisions and constructive choices, despite potential conflict and confusion, challenges, difficulty or discouragement. Passion Driven Learning is an educational philosophy underpinned by the belief that learning is motivated by insatiable curiosity and the desire to make sense of the world AND involves asking questions, finding patterns, making connections, building theories and taking actions in
On each day of the Arts and Passion-Driven Learning program delegates met in seminar groups to discuss focus areas: 1. Curiosity – exploring approaches and strategies for using the Arts to spark curiosity, Passion-driven learning and meaningful connection-making for students.
The goal of the Silk Road Project itself is to bring together musicians from all over the world so that they can collaborate on
and teach multicultural music while exploring the intersection of the Arts. These musician educators representing dozens of nationalities and musical traditions, model new forms of cultural understanding through performances, workshops and residencies. The forum they foster has established a new crosscultural conversation through musical collaboration, that effectively enables globalization of impassioned education based on communication through collaborative arts practice.
3. Visibility/Audibility – to consider the role of seeing and listening (to our students and ourselves) and how it can support Passion-Driven Learning. 4. Learning Community – to foster a learning community in which we can explore questions about Passion-driven learning with faculty and fellow participants and how teachers and artists can continue to inspire and sustain their work over the long haul.
the world. This understanding forms the core of the Silkroad ensemble’s education programs, using the exquisite ability of the Arts to inspire learning and to help teachers and students make meaningful connections to themselves, one another and the world around them. The Silkroad focuses on three areas: musical performance, learning programs and cultural entrepreneurship.
2. Inspiration – finding inspiration (or reinspiration) for our work as educators about the power of the Arts to engage learners in deep and powerful learning
It became apparent that Passion was the answer.
Over the following days workshops focused on these key areas:
The Language of Music: Learning to Communicate Across Cultures This workshop made it clear that while the Arts may indeed comprise a universal language, different cultural beliefs, values, reference points, and world views can make communication across cultures challenging. During this exchange we discussed some of these challenges that we had experienced within our own
lives, and were able to engage with Sandeep Das (Indian Tabla player), Jeff Beecher (Double Bass trained in the Western classical tradition) and Cristina Pato (Galician tradition bagpipes and classically trained concert pianist) as they demonstrated some of the unique musical, philosophical and educational dimensions of their
respective cultural backgrounds. We discussed ways to foster intercultural communication, to both fellow musicians and audiences with different backgrounds and musical traditions.
Silkroad ensemble at the end of their concert Models of Excellence: Ron Berger The structure and operations of the Expeditionary Learning School Network, which works to provide free curriculum, resources, and videos for schools in collaboration with Project Zero and the HGSE, was described by the Chief Academic officer Ron Berger. Ron has spent many years drawing together Models of Excellence, the nation’s largest collection of ‘beautiful’ exemplary student work produced at these schools. This collection of
collaborative inter-disciplinary projects is a vital resource for students and teachers and serves as exemplars and inspiration for future projects, often providing a major focus of learning for significant periods of time each year. We were given the opportunity to view a variety of works that created a fusion between the visual arts and other disciplines which included several e-books.
All of these projects and their associated materials can be downloaded free by clicking
Unfolding Practice: Todd Elkin and Arzu Mistry At the start of the course, we were introduced to the concept of the Accordion book by Todd Elkin and Arzu Mistry from the Harvard Graduate School of Education. This is a hybrid medium occupying the aesthetic space between that of a sketchbook, a process journal, a scientific field notebook, and a site for data visualization, with space to record and revisit thinking, an effective tool to prompt analytical and investigative thinking. We were all encouraged to create one of these fantastic books and develop it throughout the course, resulting in the book becoming a handmade map of our changing thought patterns and thinking styles. Accordion Books facilitate multifaceted reflection, connection and inquiry simultaneously, and are never
Accordion Book finished, just as learning and reflection are never finished, with the recorded ideas, thoughts, and visual expressions continually revisited and refined. Accordion Books can be shared between individuals to encourage discussion and learning, providing a great opportunity to engage and reflect on other people’s ideas.
Fu rth er inform ation s u rrounding th ese fantastic tools can be found
The Pedagogy of Listening: Professor Carlina Rinaldi
Italian Professor Rinaldi from Reggio Emilia, is one of the 21st Century’s leading pedagogical thinkers. Her Early Childhood program is acclaimed to be one of the best education systems in the world. Her lecture gave us an insight into her educational philosophy where she believes that “children trust us from the first moment and we have to trust them. The teacher is there to observe and play the wonderful game of learning. School can kill creativity”.
The cornerstone of our experience, based on practice, theory, and research, is the image of the child as rich, strong, and powerful. The emphasis is placed on seeing the children as unique subjects with rights rather than simply needs. They have potential, plasticity, the desire to grow, curiosity, the ability to be amazed, and the desire to relate to other people and to communicate.
– Carla Rinaldi
workshop with three members of silkroad The last day of the Institute coincided with the launch of a new free curriculum resource based on the recently released film The Music of Strangers featuring Yo-Yo Ma.
Access the resource by clicking here This resource was produced by ‘Educating for Global Understanding’, a group who believe that film is a highly effective medium to prepare students to live and work successfully in the 21st century as informed and globally competent citizens. This resource via its lesson plans promotes the widespread use of film as a window to the world to help students to mitigate existing attitudes of cultural bias,
cultivate empathy, develop a richer understanding of global issues, and prepare for effective participation in an increasingly interdependent multicultural world. Selected films act as springboards for lesson plans in subjects ranging from music, maths, science, languages, arts, and social studies and include topics such as environmental sustainability, poverty and hunger, global health, diversity and immigration. My journey to the Harvard Centre of Excellence allowed me to showcase the ethos of the IGS community and contribute as part of a diverse and engaged supportive global community of educators, united by a passion for improving lives and making a difference in education today. After arriving back at IGS following this fantastic
experience I realised just how fortunate we are to be a part of the IGS community, with staff and students that are so passionate and innovative about driving learning and personal development. For example, our SAGE and STEAM programs which allow students to engage enthusiastically in inspirational real world projects which build their love of learning. I think the words of Professor Fernando Reimers, from the HGSE, are well-matched to the culture of the IGS learning environment. He said, “the magic of this place is the result of the many voices that contribute to a conversation about what it means to educate in our time and how best to support the opportunities to be educated for each student”; this has never been more applicable.
Alison Housley, BA, DipTeach, LTCL, was appointed as the IGS Director of Music in 2008 after migrating to Australia from New Zealand. Alison has extensive experience in Music education. Alison is a highly skilled Musician and has a reputation internationally for her work in adjudicating large music festivals.
alison and yo-yo ma 33
What happens to students' mathematics achievement levels and engagement, in a Year 5 class, when they are grouped homogenously based on assessment? David Engelbert
LITERATURE REVIEW: When considering this question, one must consider the function of assessment and how it is used as tool to develop an understanding of student achievement. The literature reviewed explores the different formats of assessment and how tracking student achievement can provide educators with a basis for implementing change in the classroom to meet student needs. The literature also delves into the reliability and validity of different forms of data collection methods of student achievement in primary Mathematics. The NSW syllabus for the Australian curriculum identifies effective assessment in Mathematics as a process that; provides teachers with opportunities to gather evidence about student achievement in relation to the syllabus outcomes; enables students to demonstrate what they know and can do; clarifies student understanding of concepts and promotes deeper understanding; provides evidence that current understanding is a suitable basis for future learning (Syllabus.bos.nsw.edu.au). With this in mind, it becomes evident that the collection of evidence
on student achievement should come from a range of assessment practices. What first needs to be considered is the different types of assessment that exist in primary education and what the research suggests is the most effective practice to raise student outcomes. Black and William (2010) are lead researchers in the field of formative assessment and base their research on the underlying principle that when teachers assess formatively they adapt their teaching practice to meet pupilsâ€™ needs in a response to student results. They also acknowledge that part of the role of the teacher is to provide summative assessment data to parents and other stakeholders about the progress of their pupils (Black and William, 2010). They argue that the information a teacher gathers for formative assessment purposes should provide a strong position, with selection and reinterpretation, to contribute to a fair summative report on each pupil (William and Black, 1996). Referring to the action research question, the process of 34
systematically collecting data on student achievement formatively, essentially contributed to the overall summative assessment, that is reports. The regular routine of measuring student progress is an important step in the formative and summative assessment process. With teachers becoming more accountable for their studentsâ€™ achievement levels at a school, state and national level, the need for a systematic, reliable and valid data collection method becomes increasingly important. In an attempt to increase reliability and validity of assessment, the practice of curriculum-based measurement (CBM) was established. The research on CBM is comprehensive but mainly focuses on the implementation of the assessment procedures in English and Mathematics. For the purpose of this review, and the action research, the focus was on Mathematics. As explained by Deno â€œCBM is a set of procedures for formulating assessments by sampling the local curriculum, for administering and scoring assessment, and for integrating
the data with instructional decisions” (cited in Fuchs et al., 1994, p. 25). Weekly or bi-weekly tests are administered, usually consisting of 25 questions, with a time limit of no longer than 10 minutes. Data collected from these tests are aggregated and organized into progress graphs using computer software (Fuchs, Fuchs and Courey, 2005). Initially, CBM had system limitations, in that it only addressed portions of the curriculum by sampling mathematical facts and/or operations (i.e., adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals) (Fuchs et al., 1994). More recent developments in CBM evaluate students’ skill development across the entire curriculum including math computation (CBM-COMP), mathematical concepts & applications (CBM APP) and maths problem solving (CBMRLM), providing greater scope and validity to the process (Fuchs et al., 2005). However, research conducted by Christ, Scullin, Tolbize and Jiban concluded that “CBM scores should not be interpreted to represent math achievement generally and instead represent a subset of skills within the domain of math (cited in Methe, Briesch and Hulac, 2014, p. 204). This conclusion is based on the fact that CBM collects data on student achievement predominately through arithmetic-based tests. Fuchs and Fuchs have examined the effects of systematic formative evaluation by teachers and found that this technique increased achievement for students with mild learning disabilities (cited in Hattie, 2008, p. 181). They also discovered that when teachers
were required to use data and evidence based models, student outcomes were higher than when data were evaluated by teacher judgment. In addition, when data was graphed, effect sizes were higher than when data was simply recorded (cited in Hattie, 2008, p. 181). Fuchs, Deno and Merkin support this notion and prove that systematic, formative evaluation models of assessment can improve student achievement: This systematic approach to setting goals, monitoring growth, changing programs, and evaluating the effects of changes is the formative evaluation model. Research on the achievement effects of using this approach has revealed that the students of teachers who use systematic formative evaluation based on CBM have greater achievement rates (cited in Deno, 2003, P. 187). In response to the No Child Left Behind Act (2001) in the United States, Van Der Heyden and Burns (2005) conducted research into whether curriculum-based assessment (CBA) and CBM would lead to improved student outcomes. CBA data was used daily to track mastery of skill level and CBM data was used to track progress. Results suggested that children made significant progress within one school year, contributing the success to the program implemented (Van Der Heyden and Burns, 2005, p. 27). The success of using the CBM program relies heavily on the assumption that teachers are implementing appropriate measures in response to student achievement data. In research conducted by Fuchs, Hamlett and Stecker (1991), they compared two groups of teachers implementing 35
the CBM program. The first was provided with consultation on strategies to adjust teaching programs and the other was provided with no consultation after student achievement data was collected. They concluded that the teachers who received consultation relied on a more varied set of instructional design features to adjust student programs (Fuchs et al., p. 636). Baker, Gersten and Lee (2002) conducted similar research in an attempt to synthesize research on the effects of interventions to improve the mathematics achievement of students considered low achieving or at risk (p. 51). In their study, one group of teachers graphed information for themselves and (low-achieving) students and found slight increases in results. The second group had strategies and groupings that could be implemented in response to the data (p. 60). The conclusion was that the second group of students demonstrated a higher rate of achievement due to the implementation of purposedriven strategies. Barker et al. (2002) concluded that “merely providing teachers with data on student performance may not be as beneficial as the combination of providing data and then making specific instructional recommendations to address problem areas identified in current student performance” (p. 61). Fullan, Hill and Crevola (2006) support the conclusions of the discussed research. They believe that “the key to transformation in academic achievement lies in the smart use of data to drive instruction” (p. xvi). They make note of how school systems collect data and feed it back to districts and schools, but do not know how
to translate the information into powerful, focused instruction that responds to individual needs (p.xvi). Similarly, Black and William (2011) explain how teachers collect marks to fill up records with little analysis of pupils’ work to discern learning needs (p. 4). It is clear that systematic data collection methods on student achievement is only the first step in the formative assessment process. It is imperative that teachers use data effectively to adjust teaching and learning programs to meet the needs of their students with the purpose of improving student outcomes. When looking at what makes summative assessment valid and reliable, one must look at ways to reduce subjectivity. Linn and Miller argue that multiple-choice style questions are probably the most objective test questions (cited in Frey and Fisher, 2007, p. 103), which increases reliability and validity of the assessment practice. To further increase validity and reliability, the design and construction of common assessment practices across a year group is essential. With common assessments, comes the ability to consensus score and item analyse (Frey & Fisher, 2007, p. 122). Shinn explains that “the process of standardization allows individual and group comparisons across time and enables the summarization of group data for developing local norms and for general description of program effects across students” (cited in Deno, 2003, p. 185). Frey and Fisher (2007) also highlight how incorrect responses in multiplechoice tests can be clustered as percentages, providing teachers with the opportunity to identify areas of weakness across a cohort, consequently providing direction
for future planning and revising (p. 128).
mathematics (Syllabus.bos.nsw. edu.au).
Often multiple-choice tests are criticized because they assess only lower-order skills such as factual recall or application of standard algorithm (William, 2011, p.102). Contrary to this perception, multiple-choice questions, if carefully designed, can address higher-order skills (Williams, 2011). Thompson and Kaur (2011) have demonstrated how a single question can be re-designed for the purpose of assessing a more robust understanding of the underlying principles and uses of a concept (p. 21-25). Multiplechoice tests also prove to be an efficient method of collecting data on student achievement and provide an opportunity to gauge students’ understanding in a fairly quick and efficient manner (Frey and Fisher, 2007, p. 103).
If the aim is to develop students who are proficient users of Mathematics, assessment practices need to provide teachers with opportunities to gather evidence about student achievement that goes beyond just the application of algorithms. Students need to be provided with opportunities to demonstrate their mathematical understanding, reasoning skills, problem solving capabilities, communication skills and mathematical fluency.
This format of a ‘paper-and-pencil test’ in Mathematics has been seen to have limited capabilities for assessing students’ complete understanding. Webb claims that “tests are an important quantitative assessment tool, but they do not constitute the totality of assessment. Thus in this age of accountability, teachers need more varied information about their pupils mathematical understanding and competence” (cited in Yeo, 2011, p. 117). Both CBM and ‘paper-and-pencil tests’ have the potential to be used only to assess students’ skills in arithmetic and computation. As outlined by the NSW syllabus for the Australian curriculum, working mathematically is an essential part of the learning process as it provides students with the opportunity to engage in genuine mathematical activity and develop the skills to become flexible and creative users of 36
Thompson and Kaur (2011) use a multi-dimensional approach to understanding, to assess students’ mathematical knowledge. They believe that “if teaching material reflects a multidimensional perspective then assessment needs to reflect this perspective as well as in order for teaching and assessment to align” (p. 19). In response to this need, Thompson and Kaur have developed four domains (S-P-U-R) with a purpose of assessing students’ ability to be robust and flexible users of mathematics. They include: skills (procedures and application of algorithms); properties (principles underlying the mathematics); uses (application of problems to the real world); and representations (using graphs pictures and other visual representations) (p. 20). Their research tested over 1000 primary aged children over a seven year period and discovered their abilities were not consistent across the four domains (p. 2630). This suggests that teaching, learning and assessment in Mathematics was not effective in developing well-rounded numerate students. It becomes apparent that
reliable formats of assessment in Mathematics are needed to allow students to demonstrate what the know and can do across the working mathematically strands and content strands within the NSW syllabus for the Australian curriculum. Jin and Wong’s (2011) approach to assessing conceptual understanding, is through the use of concept mapping. This strategy provides students with the opportunity to demonstrate their understanding of links between related concepts. As explained by Jin and Wong (2011) “it can provide a visual representation
express ideas about what has been learnt (p. 119-126). It becomes evident that a balanced approach to assessment is important if educators are to gather a full understanding of a pupil’s mathematical capabilities. When considering the array of alternate assessment measures available to teachers, one must question how to reduce subjectivity of these practices. The implementation of rubrics and checklists that match directly with the appropriate outcomes, provides a step in the right direction.
during the early stages of the project, the focus of the research shifted to a more student-centred study where by data was collected about student achievement and engagement rather than on the processes and systems surrounding assessment.
Although the focus had shifted, the assessment systems put in place were a necessary part of the data collection process. Throughout implementation I adopted Kemis and McTaggart’s action research framework which is cyclical in nature and moves between planning, action, observation and reflection Kemis and McTaggart’s framework allowed (1988). Kemis and McTaggart’s me to reflect at pivotal stages of the research, framework allowed me to reflect at pivotal stages of the research, consequently providing me with the consequently providing me opportunity to modify direction as needed. with the opportunity to modify direction as needed. Throughout of the interconnected properties On reflection of the literature implementation I collected both of the concepts held by the reviewed, it becomes apparent that qualitative and quantitative data student” (p. 96). An approach in order to produce reliable and over 25 weeks to help provide to assessing students’ ability to valid data on student achievement some insight into the revised problem solving was constructed in Primary Mathematics, one must question. The quantitative data by Toh, Quek Leong, Dindyal and gather student results from a range was collected in the form of Tay (2011). The approach moves of assessment strategies. These student achievement scores, while away from assessing the products strategies should be closely looked the qualitative data collected of problem solving and towards at before implementation to were from work samples as well emphasizing the importance of the ensure they meet the appropriate as a student survey, which was process. The questions are created syllabus outcomes but are also analysed thematically. following the Polya’s problem designed to allow teachers to solving method and responses make well-informed inferences marked using a rubric created about their students’ learning. The around the method (p. 35). literature reviewed also made it clear that collecting and tracking Other alternate methods of data on student achievement assessment explored by Yeo (2001) contributes to an increase in move away from ‘paper-andoutcomes, only if the information pencil tests’ and focus on how gathered is used to adapt teaching open-ended questions can provide practices to address student needs. a window into students’ relational understanding. Other formats for The initial focus of the research testing students understanding looked specifically at different outlined by Yeo include: practical methods of data collection as a tests using manipulatives; oral means of gathering information presentations demonstrating on student understanding in students’ abilities to justify and Mathematics. In response to a reflect and; journal writings to sequence of actions and reflections
RESEARCH IMPLEMENTATION AND RESULTS Cycle 1 Planning and initial action With the initial question focusing on consistent and systematic data collection in Mathematics, (Can consistent and systematic data collection methods of student achievement in primary mathematics increase the validity and reliability of summative assessment measures and raise student outcomes?) I began by researching how other primary schools in NSW collected data on student achievement and how they used this data in an effort to improve student outcomes. A meeting was set up with the Mathematics Coordinator at a Catholic school in Sydney. The school was in its second year of maths profiling in which the academic growth of each student from Years 3-6 was tracked using pre and post-tests for each sub-strand taught. Each child was represented on a data wall (see figures 1.1, 1.2 and 1.3) and grouped according to their level of understanding and ability for that particular sub-strand. Streaming of these groups occurred every time a new sub-strand was taught. The streaming also occurred across grades and stages.
The results of the tests that students undertook were shared with students, who recorded their results on a growth chart. The coordinator explained that the purpose of using maths profiling was to:
track student development in mathematics ensure teaching and learning was targeted at the necessary level for each child ensure report grading was standardized provide valuable evidence and information about students who required extra support make students accountable for their learning in mathematics.
To gather a greater understanding of whether maths profiling or some elements of the process would be suitable for implementation at IGS, I organized semi-structured interviews with the other Year 5 teachers at IGS. The teachers were questioned about their understanding of the current assessment procedure and how useful it was to their teaching. Observation and reflection Some of the core themes that arose from the interviews with the Year 5 teachers were as follows: • • •
The current assessment process at the school was not used to inform teaching Units of work, assessments and reporting was not aligned There were too many content descriptors that required assessing
The tracking of student data did not provide enough detail Assessment and report grading was not standardized
Data from cycle one revealed a need for a more aligned assessment procedure across the grade, which informs teaching and learning. It highlighted the need for a process to be implemented in which data could be collected on student achievement and engagement to modify teaching practice.
Cycle 2 Planning and initial action Having reflected on the process of maths profiling and the responses from the other IGS teachers, I decided to implement a similar process to what was experienced at the school I had researched. In week 4 of Term 1, I constructed a sub-strand pre-test on fractions (MA3-7NA), which was aligned with the outcomes and content from the Mathematics unit of work for the following two weeks. This was administered across the grade in preparation for teaching in weeks 5 and 6 of Term 1. Students received their test results and recorded them on a growth Figure 2.1 chart (see figure 2.1). On the chart they also indicated areas for development (What I would like to improve). Studentâ€™s raw scores were also placed into a data tracking excel spreadsheet. These results then informed student grouping in class as well as across the grade. Students were placed into 5 ability groups within my class (see figure 2.2). Figure 2.3 shows the differentiated activities in which each group would be engaged in for that week. Four ability groups were created across the grade ready for streaming. An 80-minute lesson was carried out on one morning of week 5 in which students were streamed across the grade. I took the highest group. Teaching was modified by each teacher to meet the needs of the group they were teaching.
Student names have been blocked out for privacy reasons
Figure 2.3 39
Observation Observing the streaming across grade, it was evident that some children who were placed in the top group were not keeping up. Their knowledge of content was sufficient, however, some of the students did not have the necessary skills to apply their understanding to more conceptual tasks (working mathematically). As this time during the week constitutes 'enrichment' and 'support' sessions for Mathematics in Year 5, the groups had to stay relatively fixed. This did not allow for my original plan of streaming across grade each time a new sub-strand was taught. When grouping students within my class, my observation was that children were engaged in the differentiated content and demonstrated an improved understanding and knowledge Reflection It became evident that streaming Mathematics groups, across the grade, based on standardised tests would not be possible, due to the complex timetabling experienced at the school. Therefore, I decided to only focus on the students in my class. On reflection, the aim of the research also needed to be adjusted to focus on student engagement and achievement, rather than on assessment procedures. Consequently, the question needed to be modified.
Cycle 3 Revised planning and action I could still see the value in streaming children based on ability, so decided to continue this practice in my own class. This required the revision of my research question to have a greater focus on student engagement and achievement. This led to the revised question â€“ What happens to studentâ€™s maths achievement levels and engagement, in a Year 5 class, when they are grouped homogenously based on assessment? The action that followed this revised plan was implemented on a smaller scale to test its methodology and to inform the next cycle of the action research. As students had already been homogenously grouped on their knowledge of fractions, they stayed in these groups for the following week (week 6 of term 1). In its entirety, students were grouped and worked in rotations with differentiated activities on fractions for two weeks. The lessons were developed in alignment with the outcomes and content from the pre-test and unit of work. On completion, students sat a post-test, which was also aligned with the pre-test and outcomes and content from the unit. Students were given their test papers back and asked to identify areas of improvement to be recorded on their growth chart (Letâ€™s celebrate!) (see figure 2.1). Student achievement scores were placed into the data tracking excel. The raw scores were aggregated and generated a comparison between the pre and post-test scores. Growth in student achievement was also calculated as a percentage for each student. Observation and Reflection 88% of students showed positive growth with just over half the class achieving 100% or more growth in scores (see Table 1 and Graph 1 on the following page). From a combination of work samples over the two weeks, achievement scores and my own teacher observation, it was clear that grouping students homogenously, using assessment data for grouping, had a positive impact on student achievement scores. It was also evident that students had a positive level of engagement with the process. On reflection, a more tangible measure of student engagement was needed to develop a greater sense of how engaged students were in the process. It was also evident that students needed more guidance with how to identify areas for improvement when analyzing their results from the pre-test. Achievement Scores The achievement scores in this document have been grouped according to strand. There is a combination of data that has been input into an excel spreadsheet (tables), as well as graphs which clearly demonstrate the comparison of students pre and post-tests scores as a percentage. Tables show the raw scores as well as the corresponding percentage for both the pre-test and post-test that each student completed. The growth from pre to post-test has been calculated for each student as well. Names of each student have been changed to a number to protect privacy. Total number of students contributing to the data = 25. 40
The results in Table 1 and Graph 1 show 22 students achieving positive growth. 2 students showed negative growth and 1 students stayed the same. Those students who scored lowest on the pre-test seemed to have had a greater growth rate percentage. This is due to the fact they had more potential to build on their grade. Those students who had a higher percentage score in their pre-test found it more difficult to build on their post-test scores. This is specifically evident for S21 who had a 3% negative growth.
Cycle 4 Final planning and action Large scale implementation was undergone in cycle 4 after cycle 3 confirmed the methodology was sound. For the remainder of Term 1, all of Term 2 and the first 2 weeks of Term 3 the process from cycle 3 was repeated. The following steps were taken: 1. Students sat pre-tests for the focus sub-strand. Scores were placed into the data tracking excel spreadsheet. 2. Students identified areas for improvement from the pre-test and recorded this on their growth chart. Their mark was also recorded as a percentage on their chart. 3. Students were homogenously grouped into 5 groups, based on their test results. 4. Students participated in differentiated exercises and tasks for the period of time in which the particular sub-strand was taught. 5. Students sat a post-test and recorded areas of improvement, as well as, their overall mark on their growth chart. Post-test results were input into the data tracking excel spreadsheet. It is important to note that not every week students would be engaged in a maths rotation set up. This was due to some teaching weeks being shorter in length. Reasons for this included extra-curricular activities (e.g. sports carnivals, music events, etc.). It is also important to note that students sat their pre-tests the week before the content was taught. This was necessary to ensure there was enough time to mark, group and organise appropriate lesson material. Over the remaining period in which student achievement scores were collected, six more sub-strands were covered. For detail of student achievement scores for each sub-strand see the Achievement Scores document in the Analysis of Data section. Sub-strands covered include: 1. Addition and subtraction MA3-5NA (Number and Algebra) â€“ See Table 2 and Graph 2 2. Length MA3-9MG (Measurement and Geometry) â€“ See Table 4 and Graph 4 41
3. 4. 5. 6.
Time MA3-13MG (Measurement and Geometry) – See Table 5 and Graph 5 Chance MA3-19SP (Statistics and Probability) – See Table 6 and Graph 6 Data MA3-18SP (Statistics and Probability) – See Table 6 and Graph 6 Multiplication MA3-6NA (Number and Algebra) – See Table 3 and Graph 3
When creating the pre and post-tests for these sub-strands, the outcomes and content were more clearly labelled, from that in the first cycle, to assist students in identifying areas for improvement and areas of improvement. More time was also spent on coaching students on how to identify areas for and of improvement. To gather a greater sense of student engagement a student survey was also administered in week 7 of term 2. This survey was thematically analysed. Table 2
Table 2 and Graph 2 shows 19 students achieving positive growth in scores. 3 students stayed the same and 3 students demonstrated negative growth. There was significantly less growth across the class in the addition and subtraction sub-strand when compared with the fractions sub-strand. This could be due to a number of factors including more difficult content and longer tests. Further investigation would be required to gather a more comprehensive understanding into why this was the case. S24 achieved no movement in grade for fractions and addition and subtraction. This flagged some necessary remedial work and a review of the students personalised learning plan. Table 3
Table 3 and Graph 3 represent the percentage scores for the multiplication sub-strand. S2 was not present for the week of school the pre-test was administered, so there was not sufficient time for the student to complete it. S23 was away for an extended period of time and was not present for either of the tests. Although 42
multiplication was planned for Term 2, it was tested and taught in Term 3 due to time restraints in term 2. 22 of the 23 students who took part in the tests and participated in all learning opportunities for this substrand achieved a positive growth in achievement scores. There was only one student who stayed the same. No student displayed negative growth. This overall improvement in achievement compared with the other number and algebra strands could have been put down to a number of reasons: 1. As this was the last test in the research project, students were more familiar with the process. 2. The construction of the tests had greater clarity in its questions. 3. Teaching and learning tasks were more logically aligned to the outcomes and content of the unit of work and assessment tasks. Table 4
Table 4 and Graph 4 display student achievement scores from the unit on length. 13 students in the class performed worse on the post-test, therefore achieving negative growth. There were a number of reasons this could have been the case: 1. The construction of the post-test. One of the questions required an understanding of decimals to be able to convert between units of measurement. This skill was not required in the pre-test. Many students were unable to answer this correctly. 2. The teaching of this unit spread across Term 1 and Term 2 with a break for 2 weeks holiday. The students sat their pre-test in Term 1 and their post-test in Term 2. 3. Students did not participate in a maths rotation set-up but were provided with differentiated work as a whole class. Table 5
Table 5 and Graph 5 display student achievement scores for the sub-strand time. Students’ background knowledge and initial understanding on time was much greater than the other sub-strands that were assessed. This was reflected through their pre-test scores. 5 students had negative growth, with the remaining students showing positive growth. The percentage of positive growth was not as dramatic when compared to the growth percentages in the number and algebra strand. This was due to the students’ comparatively higher scores in the pre-test. Table 6
Chance and data were taught simultaneously to allow for more authentic learning opportunities to occur. The raw scores from the chance test were combined with the raw scores from the data test giving an overall mark out of 52. This can be seen in Table 6. S23 was away for an extended period of time and was not present for the post-tests. 7 students had negative growth, with the remaining students showing positive growth. The reason for this could have been due to the fact that students did not participate in a maths rotation set-up but were provided with differentiated work as a whole class instead. The percentage of positive growth was not as dramatic when compared to the growth percentages in the number and algebra strand. This was due to the students’ comparatively higher scores in the pre-test. Observation and reflection The majority of the class improved in their achievement scores. My main observation when analyzing student growth percentages, was that some students who had proven capable of meeting certain outcomes were not showing this through their test results. This arose as one child in particular who excels in Mathematics performed poorly when presented with a pen and paper test. He had, however, demonstrated an ability to communicate his understanding verbally when in small groups. It highlighted the idea that pen and paper tests should only constitute part of a child’s overall achievement. The results from the survey provided a valuable insight into student’s perceptions and ideas about the process they had been part of for nearly 2 terms. Some of the common themes included: • •
Majority of students surveyed preferred working in ability-based groups because the content/work provided was specific to their needs. All children in the class liked working in groups for a number of reasons. These included; variety of tasks, student interaction and their learning was occurring at the appropriate level.
EVALUATION To gain an insight and to begin finding answers to the research question, data was collected using a combination of achievement scores, student work samples and a student survey. The overall findings of the project are as follows: 1. On average, students showed improvement in their achievement levels when grouped homogenously based on ability. 2. The majority of students preferred being grouped homogenously as they were more engaged in the differentiated and varied content. Students demonstrated their levels of achievement through test scores and work samples. When students were not grouped by ability, their growth percentages were lower than when grouped by ability. This suggests that students’ levels of achievement are increased when grouped homogenously. When being grouped homogenously based on ability, students were provided with the opportunity to work on content that was specific to their learning needs. They were also able to work with other students who required the same level of work, which enabled them to develop knowledge and understanding together. This was also reflected in their responses when surveyed about their engagement in ability-based maths groups. The majority of students surveyed preferred working in ability-based groups because the content and work provided was specific to their learning needs. All students in the class liked working in groups for a number of reasons. These included; variety of tasks, student interaction and their learning was occurring at the appropriate level. The project raised some important questions which would need further attention if the research was to continue. One of these was how students could be assessed using a range of assessment strategies instead of just a ‘paper-and-pencil test’. It became evident during the research that not every student could demonstrate their understanding of a concept due to learning difficulties and different learning styles experienced by students in the class. One student in particular was diagnosed with dyslexia during the course of the year. To provide them with the best opportunities to show their understanding, reading of the questions by an adult was required. This occurred during the later stages of the research. Other students in the class were also more suited to demonstrating their understanding though communicating their ideas verbally or through the use of concrete materials. This highlighted the need for a variety of assessment strategies to gather a more comprehensive picture of students understanding. Other limitations of just using a ‘paper-and-pencil test’ was that it did not allow students to demonstrate their ability in more practical situation. This was most evident in the measurement and geometry strand where much of the content in the syllabus requires students to show their understanding through doing. Minimal student growth percentages in the measurement and geometry sub-strands reflected this. A large challenge that was faced during the process of my research was having to adjust the focus of my question. The initial focus of the research looked specifically at different methods of data collection as a means of gathering information on student understanding in Mathematics. Although the systems created to collect data were necessary tools, the shift in focus meant there was a greater emphasis on students, rather than on the processes and systems surrounding assessment. Although this change was initially daunting, the nature of the action research provided me with the ability to be flexible and adaptive. Another challenge faced during the project included the everyday disruption that occurs during the life of a school. For example, extra-curricular activities including sporting carnivals, music events and school excursions as well as extra holidays. These interruptions made teaching weeks shorter in length and reduced the learning time with some of the sub-strands taught. On reflection, the research provided me with valuable insights into best teaching practice. It promoted risk-taking and important reflective practices, which are all important to developing as a teacher. If there 45
was more time and resources to implement further initiatives, I would apply a variety of assessment strategies, including practical assessments, and test their capability at capturing student understanding more thoroughly.
References Baker, S., Gersten, R., & Lee, D. (2002). A Synthesis of Empirical Research on Teaching Mathematics to Low-Achieving Students. ELEM SCHOOL J, 103(1), 51. http://dx.doi.org/10.1086/499715 Black, P., & Wiliam, D. (2010). Inside the Black Box: Raising Standards through Classroom Assessment. Phi Delta Kappan, 92(1), 81-90. http://dx.doi.org/10.1177/003172171009200119 Deno, S. (2003). Developments in Curriculum-Based Measurement. The Journal Of Special Education,37(3), 184-192. http://dx.doi.org/10.1177/00224669030370030801 Fisher, D., & Frey, N. (2007). Checking for understanding. Alexandria, Va.: Association for Supervision and Curriculum Development. Fuchs, L., Fuchs, D., & Courey, S. (2005). Curriculum-Based Measurement of Mathematics Competence: From Computation to Concepts and Applications to Real-Life Problem Solving. Assessment For Effective Intervention, 30(2), 33-46. http://dx.doi.org/10.1177/073724770503000204 Fuchs, L., Fuchs, D., Hamlett, C., Thompson, A., Roberts, P., Kubek, P., & Stecker, P. (1994). Technical Features of a Mathematics Concepts and Applications Curriculum-Based Measurement System. Assessment For Effective Intervention, 19(4), 23-49. http://dx.doi.org/10.1177/073724779401900403 Fuchs, L., Hamlett, D., & Stecker, P. (1991). Effects of Curriculum-Based Measurement and Consultation on Teacher Planning and Student Achievement in Mathematics Operations. American Educational Research Journal, 28(3), 617-641. http://dx.doi.org/10.3102/00028312028003617 Fullan, M., Hill, P., & CrĂŠvola, C. (2006). Breakthrough. Thousand Oaks, Calif.: Corwin Press. Hattie, J. (2008). Visible learning. London: New York. Kaur, B., & Wong, K. (2011). Assessment in the mathematics classroom. Singapore: World Scientific. Kemmis, S. & McTaggart, R. 1988. The action research planner. Geelong: Deakin University Press. Methe, S., Briesch, A., & Hulac, D. (2014). Evaluating Procedures for Reducing Measurement Error in Math Curriculum-Based Measurement Probes. Assessment For Effective Intervention, 40(2), 99-113. http://dx.doi. org/10.1177/1534508414553295 Syllabus.bos.nsw.edu.au,. (2015). Mathematics Kâ€“10. Retrieved 29 November 2015, from http://syllabus.bos.nsw.edu. au/mathematics/mathematics-k10/ VanDerHeyden, A., & Burns, M. (2005). Using Curriculum-Based Assessment and Curriculum-Based Measurement to Guide Elementary Mathematics Instruction: Effect on Individual and Group Accountability Scores. Assessment For Effective Intervention, 30(3), 15-31. http://dx.doi.org/10.1177/073724770503000302 Wiliam, D., & Black, P. (1996). Meanings and Consequences: a basis for distinguishing formative and summative functions of assessment? British Educational Research Journal, 22(5), 537-548. http://dx.doi. org/10.1080/0141192960220502 Wiliam, D. (2011) Embedded formative assessment. Australia: Hawker Brownlow Education
David Engelbert, BEd, joined the IGS Primary Department in 2011. He has considerable teaching experience having worked in independent schools in Australia and the UK. David also has experience in the tertiary sector working as a seasonal tutor for the University of Notre Dame. David recently completed the Action Research stream for his Experienced Teacher accreditation with the Independent Schools Teacher Accreditation Authority. This paper is written based on this research project.
Studying at the Feet of Masters Michele Ellis
In 2002, I met Doug Goodkin in Brisbane at a national conference and was introduced to Orff Schulwerk, a holistic approach to music education grounded in movement, dance, speech and music. It was created by Carl Orff (composer) and Gunild Keetman (dancer/musician) who believed music education starts with the body and that exploration and the creation of music is fundamental to learning this art form. Since that day I have been a disciple, studying all four levels of the teacher training in Australia, attending the International Summer School in Salzburg Austria in 2015, and presenting at conferences and teacher training events over the past few years. Having exhausted my learning opportunities in Australia I began seeking further ways I could deepen my understanding, to drink at the font, be connected to the source and to seek the expertise of those who have walked this path before me. Doug returned to Australia earlier this year. The entire International Grammar School (IGS) Music Department attended a three-day workshop and were immersed in uncovering the sequence and possible teaching/ learning experiences a child could encounter from preschool to Year 8 with an Orff specialist. Pens
could not write these pearls of wisdom fast enough, nor could the collective memories reliably recall the magic experienced. There was a thirst for more. However, these three days did have a lasting impact and storytelling, movement and mystery became part of teaching music at IGS. This was extended to whole staff PD where dances were created without talking, unity was experienced in song, and communally the staff embraced each other in movement. A brief conversation with Doug at this time led to an application for the International Intern Program at the San Francisco School (SFS). I was fortunate to be accepted following the support and encouragement offered by Shauna Colnan, Principal at IGS and the New South Wales Orff Schulwerk Association. I am the first Australian to participate in this program. The internship has several components including observing, team teaching, devising and delivering didactic units, reflections, readings and growing alongside the masters as a unified team. This has included social events such as sight-seeing, square dancing, pumpkin carving, processing like minstrels, sea shanties and sharing our cultures. I share this experience with 47
students from Finland, Spain and the US. James Harding, Sofia Lรณpez-Ibor and Doug Goodkin are the master teachers who give the interns access to their space each and every lesson, uncensored, raw and real. They have been an inseparable unit at SFS for the past 20 years. Each one has a unique style and present their ideas worldwide through conferences and workshops as well as their publications. They are fondly referred to as the Three Musketeers and their chemistry reflects that of skilled musicians, respected fellows, family members and best friends. I am privileged to witness and be part of this very unique setting every day. While I am honing my teaching skills and am considering what I will transfer to an Australian context, it has become clear that the learning of specific music skills is a small portion of the delivery of this subject area. The SFS students are given a rich grounding in humanity in which they can explore this art form, allowing them to reflect on their modern culture and to question the values they currently hold. Every grade has been challenged, adored, loved unconditionally, guided and enlightened while enjoying the success of music making and performance since the commencement of the school
year. On the right is a poem used for a composition project for the seventh grade. Preceding this task was an exploration of authentic instruments and performance of traditional music, studying art works and recreating aspects of them in period costumes, producing an art work, performing period dances, identifying various religious and secular music through movement, the reading of ancient texts and a discussion of how Muslims, Jews and Christians lived harmoniously in Medieval Spain in both Music and History classes. I was moved to tears as the students earnestly presented the poem and instrumental accompaniment. The empathy was obvious, the students felt the isolation of the subject using sparse instrumentation, the
A palm tree stands in the middle of Rusafa, Born in the West, far from the land of palms. I said to it: How like me you are, far away and in exile, In long separation from family and friend. You have sprung from soil in which you are a stranger; And I, like you and far from home. This poem was written by Abd al-Rahman, founder of the Umayyad Emirate of Cordoba, who lived from 731 to 788.
yearning of home sensed through an ancient modal scale and the acceptance of the situation through the vocal tones of the reciter as well as the unspoken communication of the ensemble musicians. The sounds of the xylophone, rain stick, psaltery and recorder echoed this earlier time which seems so relevant now as global community witnesses some of the greatest migration in human history. These creations exposed the sadness and despair of displacement. This sentiment is omnipresent in the Grade 8 Jazz History course where the pupils explore, discuss and personally relate to the exploitation of blacks from the past to the present
alongside performing, with great joy, the classics of this genre. My experience with the masters has given me the opportunity to gather new teaching ideas specifically related to music but more importantly to confirm that our time with students is brief, memorable and life changing for better or worse. Everyone can reflect on their own school experience to recall both sides of this coin. Music is the sounds of the soul and we are entrusted to assist young people find their voice and to walk beside them on their path. We can assist a student to unfurl, mature and blossom if we tend and nurture well. Our teaching landscape must be fertile, hand crafted and turned with love. This is the premise of the Orff Schulwerkâ€”spiritual nourishment through the exploration and creation of elemental music, music for children. I too feel like the palm, blossoming in a foreign soil far from home. I am eager to share the fruits of this experience with my IGS and Orff families when I return.
Michele Ellis, BMusEd, joined IGS in 1999 and has held roles as the Director of Music and more recently as the Head of Primary Music. She is one of Australiaâ€™s leading practitioners of the Orff Schulwerk approach of music instruction. Michele was awarded an internship at the prestigious San Francisco School in Term 4 2016 and will be returning to IGS in 2017.
Volume 1, 2016