Competence and hindrances: How do we support all students to meaningful mathematics learning Edda Óskarsdóttir, Jónína Vala Kristinsdóttir, Dóróþea Reimarsdóttir og Hafdís Einarsdóttir Ráðstefna um sérkennslu 10. Sept. 2016
Inclusion as a system
Based on Florian & Black-Hawkins, 2011 Anderson, Boyle & Deppeler, 2014
Inclusive education
Inclusive practice
Thinking about disability - model
Medical 1
Medical 2
Characteristics
Form of education
Focus on what disabled person cannot do. Attempt to normalize or, if they cannot fit into things as they are, keep them separate.
Segregation: Institutions/hospitals. Special schools (with expert special educators).
Person can be supported by minor adjustment and support, to function normally and minimize their impairment. Continuum of provision based on severity and type of impairment.
Integration in mainstream: At same location but in separate class/units Socially in some activities, e.g. meals, assembly or art In the class with support, but teaching and learning remain the same. What you cannot do determines which form of education you receive.
Thinking about disability - Model
Social
Characteristics
Form of education
Barriers identified – solutions found to minimize them. Barriers of attitude, environment and organization are seen as what disables, and are removed to maximize potential of all. Disabled person welcomed. Relations are intentionally built. Disabled person achieves their potential. Personcentred approach.
Inclusive – schools where all are welcomed, and staff, parents and pupils value diversity. Support is provided so all can be successful academically and socially. This requires reorganizing teaching, learning and assessment. Peer support is encouraged. Focus on what you can do. Rieser, 2011
There are and always will be differences between learners. The key question we have to ask is to what extent are learner differences in mathematics education a result of such natural variation or to what extent are they �spoken into reality� - a social creation? Askew, M., 2016
Diversity in mathematics classrooms • Western-type approach to education and current schooling and classroom structures where one teacher is expected to bring groups of students to one-size-fits-all outcomes turns diversity into a problem. • Achieving the equitable goal of removing ‘barriers to learning whilst challenging each student take risks and responsibility for learning’ is achieved through creating collective classroom cultures that support the individual learner. Askew, M. (2015). Diversity, inclusion and equity in mathematics classrooms: From individual problems to collective possibility. Í A. Bishop, H. Tan, & T. N. Barkatsas (ritstj.), Diversity in mathematics education: Towards inclusive practices (bls. 129–145).
Inquiry into mathematics • Inquiry problems have the potential to promote mathematical activity and thinking and stimulate collaboration where discussions and sharing thinking is meaningful. • Curriculum as inquiry takes a stance towards knowledge as coconstructed and emerging through interaction with others. • The focus shifts away from the individual learner and onto the activity of the collective. • This shift means that while there are still learning gains for the individual these go beyond acquiring knowledge: through becoming part of a community (knowing), learners also learn to learn. Askew, M. (2015).
What companies value most in new employees 1970 1999
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Writing Computational skills Reading skills Oral communications Listening skills Personal career development Creative thinking Leadership Goal setting/Motivation Teamwork Organizational Effectiveness Problem solving Interpersonal skills
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Teamwork Problem solving Interpersonal skills Oral communications Listening skills Personal career development Creative thinking Leadership Goal setting/Motivation Writing Organizational Effectiveness Computational skills Reading skills
The Understanding of Numbers and Operations when Children Starts Elementary School Assessment and Intervention Based on Early Numeracy- Assessment for teaching & intervention by Robert J. Wright, Jim Martland, Ann K. Stafford (2006)
Dóróþea Reimarsdóttir special teacher and educational consultant at Dalvíkurbyggð
Our aims at the elementary school in Dalvík is: • That the classroom teacher knows as early as possible the pupils counting skills and how they perform operations. • To know as soon as possible what pupils need intervention. • To provide support to pupils who have low counting skills and low flexibility in calcultaion when they arrive elementary school. • To involve parents in their children´s learning.
The Assessment • Obtained from the Mathematics Recovery Programme (MRP) which is a project from New South Wales in Australia, developed from 1992 to 1995. • The whole tasks assess how pupils in 1. and 2. class understand numbers and operations. The assessment is published in the book Early Numeracy-Assessment for teaching & intervention by Wright, Martland og Stafford (2006). • We use the first part, which is submitted to pupils in 1. class after one month of school (sept/okt), in interview that takes 30-45 minutes .
The Process • Best of all is that the classroom teacher observes the children´s strategies, if not a special teacher does. • The strategies in MRP is used to classify the depth of childrens understanding. • A special teacher supports the classroom teacher to find out the results for each student. • An overview is made to make easier to see the overall in a brief way.
The ideal Intervention • Meeting, for all parents of the first class, where the development of childs mathematical thinking is presented (in okt). • (Intervention at school, organized by a special teacher (MPR at least 4 x 20-30 min.pr. day 10-20 weeks)). • Special made homeworks in cooperation with parents of child that needs intervention.
The Process in Dalvíkurskóli Mathematics in 1. class Period
What to do
Who
Responsibility
september
All students
The classroom teacher and a special teacher
oktober to january
The assessment MRP 1.1 submitted, author Wright and more Intervention at school and at home
Students that don´t reach criteria
The classroom teacher and a special teacher
january
status DR
All students
The classroom teacher and a special teacher
february to april Intervention at school and at Students that don´t The classroom teacher and home reach criteria when they a special teacher were assessed april
Status DR
may
Asessment for the whole class
The students that got intervention All students
A special teacher The classroom teacher
Does it work? • We don´t have tools to assess the results of the intervention but the year we ..... • All the students who got intervention raised their capability at least 2 steps in counting and reading numbers. • These students were happy, positive and enjoyed the mathematics lessons. • Excellent homeworks with parents gave good performance.
Material • Dóróþea Reimarsdóttir (2015). Þróun talna- og aðgerðaskilnings og mat við upphaf grunnskólagöngu. Glæður, 25 (1): s. 25-34´. • Kristinsdóttir, Jónína V., Reimarsdóttir, D. and Guðjónsdóttir, H. (2016). „There is Always Something New After Nine“ in CURSIV. Special Needs in Mathematics Education, edited by Lindenskov, L. Aarhus: Aarhus University. Er á slóðinni http://edu.au.dk/fileadmin/edu/Cursiv/CURSIV_18__Udgivet_version.pdf • Wright, R.J., Martland, J. og Stafford, A. K. (2006) Early Numeracy: Assessment for teaching & intervention (2. ed,). London: Paul Chapman. • Wright, R.J., Martland, J., Stafford, A.K. og Stanger, G. (2006). Teaching number. Advancing Children´s skills and strategis (2. ed.). London: SAGE. • Wright, R.J., Stanger, G., Stafford, A.K. og Martland, J. (2006). Teaching number in the classroom with 4-8 year-olds. London: SAGE.
Mathematical difficulties Feelings of students - how can we support them? HafdĂs EinarsdĂłttir
Background Started as an teacher assister 2005 Teacher from 2007 B.Ed. 2009 Diplรณma in learning and teaching, mathematic, 2012 M.Ed. in inclusive education, 2013 Teacher in 9th. grade and specialist in math in the school
Mathematic Mathematical difficulties
Mathematical disabilities
Other reasons in a bigger common
Feelings of students with learning difficulties Do often feel stress and depressed Have low self-confidence Feel like nobody understand them Sometimes get bullied Feel disrespect from others Bad feelings and anxiety
The one who is not able to do math must be stupid Research for my Master Degree - 2013 Main results Bad feelings Not enough self-confidence Cowork not good Tests and homework difficult Felt like other didn’t understand their difficulties
Self-confidence Broken Feel like they are stupid Often gets better when they grow More open today
Feelings Do often feel really bad Anxiety Often “sick”
Undarstanding from others
Learning and teaching methods Cooperation, working with others What they learn, the same as others or something different
Groups
Student’s future From elementary school to highschool From the safe environment to open school Negative feelings From school to the life
Daily life
Solutions Talking to students Thinking and talking about their own learning progress FAIL - First Attemp In Learning Screening for difficulties Intervention Putting a clear goals To build new knowledge from the knowledge that already existrs
My experience Talking to students Show them understanding and respect Cooperation with their homes Make them feel good and give them project that they can handle Every one is a single one