A Case Study on an Experienced Elementary Teacher’s Teaching Strategies and Teaching Reflection in Mathematical Classroom Feng-Kuang Chiang
Su-Hsiang Chung
Department of Industrial Technology Education,
Graduate Institute of Education
National Kaohsiung Normal University, Taiwan, R.O.C.
National Sun Yat-sen University, Taiwan, R.O.C.
forite@gmail.com
suchung@mail.nsysu.edu.tw
Abstract: The purpose of this research is to investigate teaching strategies and teaching reflections of an experienced elementary teacher in the mathematical classroom. This study explored the changing process of students’ learning attitudes toward mathematics. This research adopted qualitative research methods as a main means of inquiry and used quantitative questionnaires as a supplement means of inquiry. Researcher had inquired by observations, in-depth interviews, video recordings, document data collections and the pre-post questionnaire survey during one semester. This research used triangulation methods to analysize the data. Finally, the conclusion was proposed.
1. Introduction The purpose of the Trends in Mathematics and Science Study [TIMSS] offering the achievement of the long-term studies on students ’ trends to learn mathematics and science hold by the International Association for the Evaluation of Educational Achievement [IEA] is to promote the learning efficiency of students . TIMSS (2003) research report pointed out 34 % of the fourth grade students in primary school, above the average 22 %, disagreed to “I like learning math,” and merely 41 % of students achieved the high index, below the average 55 %, in the Index of Students’ Self-Confidence in learning math[SCM].
Furthermore, the outcomes of Chang’s
(2004) study on TIMSS cited comparing 1999 the percentage of disagreement to “I like learning math” increased 16 percent in the questionnaires. Thus, how to promote students ’ learning motive and interest in learning math is the main problem in Taiwan. Ball (1990, 1996) cited the math content knowledge of pre-service teachers is rather weak and segmented resulting from memorizing the formulas; meanwhile unlike experienced teachers teaching math by conceptive realization let the students do the complex mathematical logic.
Hembree (1990), according to the 151 studies
did meta-analysis, finding the pre-service teachers have higher anxious on math subject. In addition to that, Tobin and Fraster (1989) thought studying on the executions of the practician sets an effective teaching sample and improves the skills of other teachers. From researchers own learning and teaching experiences, we can understand the great differences in teaching skills between experienced teachers and novice ones. Also lots of researches indicated the experienced teacher have the great teaching efficiency. Their teaching skills increased year by year are worthy to learn, but less people record the abundant teaching experiences. Shulman, early in 1987 supposed it is the the important direction for study on teachers’ teaching to systematic interpretation and represent the executions of the experienced teacher. Many scholars (Elbaz, 1991; Tobin and Fraster, 1989)
encouraged to study on teaching experiences of the experiend teacher, for they regard the great teaching examples as references for others. The studies in Taiwan on elementary school’s math experienced teacher are quite few and on teaching strategies and teaching reflections in teaching executions are much less. amount of teaching experiences affects teaching performance.
The
The deeper the teachers understand the students
the better teaching arrangements and strategies for students. As a result the differences exist in not only the teaching experiences but in strategies, skills.
2. The propose of the study Due to the statement mentioned above, this study focused on an experienced elementary school teacher. The researcher observed the teaching process, interviewed deeply with the case teacher to explore the teaching strategies and reflections. So that the researcher could learn the practical knowledge in teaching and exhibit the study for teachers as reference.
The purposes of the study as follows:
1.
To explore the instructional strategies of the experienced teacher in the math classroom
2.
To explore the way, the content, and the level of the experienced teacher reflected.
3.
To realize the change of the students’ math learning attitudes.
3. Literature review 3.1 Mathematical instructional strategies Gagne (1985) thought the teaching strategies are the ways improve their own teachings, guide students how they improve their own learning to achieve the best efficiency. teachers (teaching) and the actions of the students (learning).
Instruction includes the actions of the
Thus, there are two paradigms during teacher’s
teaching; one is teacher-centered, and the other is pupil-centered.
Karp and Voltz (2000) also divided teaching
strategies into two parts likewise, and they exhibited the continuum of instructional strategies ( see Figure 1).
Teacher-center
Student-center Explicit Instruction Apprentice Approach Constructivist Approach Figure 1. The continuum of instructional strategies Figure 1. The continuum of instructional strategies
Source: Karp & Voltz. (2000)
After reading the studies on the math teaching practices, the researcher found the action of the teacher and of the students is the center of teaching model. Therefore, researcher adopted the mathematical instructional strategies of Koehler and Grouws (1992) as the foundation theory in this study.
3.2 Teaching reflections Dewey (1916) mentioned the most important literacy of a teacher is critical thinking, and early in 1904 had mentioned three attitudes of reflective action: open-mindedness, responsibility, and wholeheartness. Schon (1983) mentioned two concepts of reflection including reflection-in -action, reflection-on-action, and
identified the reflective practitioner a professional practitioner solving problems in certain situation. Through the reflection the teacher performed the ability of criticism and comprehension, and through these uncertainties or unique experiences, the teacher did the meaningful interpretation of these situations. Henderson (1998) cited offten reflections can result in some practical ideas.
The orientation of the teacher’s reflection would
fulfill the ability of solving problems, of dealing with students ’ needs, and development of a study on new knowledge. (Dilwotrh & Imig, 1995) The relations between reflections and teachings, and the meaning of reflections in education.
The views
of are followings: Day (1993) supposed reflection plays an important role in teaching as a helpable means to the professional growth.
Yost, Senteer and Forlenza -Bailey (2000) though to face the educational challenge in
next century, the teacher must have three main characters: intellectual, moral, and critical thinking. Decision-making may be identified the access to think of educational issue, the decision made to solve the teaching problem, and the responsibility to the imposed issue (Goodman, 1984; Schon, 1983; Zeichner& Liston, 1987).
Calderhead (1988) pointed out the four items of the reflections to teachers’ growth: 1. promote
the professional growth of elf-oriented 2. connect teaching theory and teaching executions 3. assist to explain the critics and evaluation of the experienced teacher 4. promote the role of his own professional growth.
3.3 Reflective content and reflective level Reflective content means the reflective subjects and the objects. reflective content.
Reflective level means the level of
Wu (1999) divided reflective content into eight items: teaching, pupils, teachers,
management of the class, environment of the campus, reflection of one’s own, system, and strategy& study. The reflective level divided in four: description, intelligence of skill, real action, and critical reflection.
Van
Manen (1977) studied on teaching reflections of pre-service teachers, dividing in three: technical, practical, and critical reflection.
The pre -service teachers focused on the technical level.
Cheng (2003) categorized
different divisions of reflective levels in four main items: descriptive level, technical level, practical level, and critical level. Thus, after investigating the reflective contents, reflective level of studies, the researcher arranges, categorizes, corrects, and interprets them as follows.
Based on above literature, we will reflective
content divides in seven in this study. (1) Students: students are the main objects. (2) Teaching: reflect the first part, the middle part, and the last part of teaching. (3) Colleague: coworkers and trainees are the main objects. (4) Classroom management: the way of class management or teaching strategies. (5) Environment of the campus: system, affairs of the school. (6) The teacher himself: the emotion of the case teacher. (7) Other: none of the six items mentioned above. Reflective level divides in four: (1) Level 1: describe; only describe the affair without any reflections. (2) Level 2: technical level; think of the strategies without real actions.
(3) Level 3: practical level; face, investigate, analyze the question and take action to solve it. (4) Level 4: critical level; criticize the property behind the question.
4. Design of the study 4.1. Case study The study adopts the case study due to the concerns as follows. 1. This study focus on the teaching strategies and teaching reflections used by the experienced teacher in math class in elementary school.
2. The
researcher hopes to do observation and interview without disturbance to record the reality. 3. To get the unique qualities, large and deep information of the class, avoiding the different teaching background, personalities, teaching style, and teaching concepts of the teachers. 4.2 The experienced teacher The case teacher, graduated from one National Normal collage, also the founder of the teachers’ association, has been serving in one elementary school for 13 years in Taiwan.
The case teacher is the
recruiter of the mathematical field in the Association for the Development of Course.
From the teacher’s
experiences most students lack of the confidence and motif to learn math since math is the biggest obstacle to students. Knowing this, the case teacher often participates the conferences on math teaching such as K12 working house, etc. to improve the professional skills. Concentrate himself to math teaching, going on new teaching strategies to remove the obstacles of the students in learning, to increase the confidence of the students. The case teacher is rather famous in the district for his enthusiasm and concentration. 4.3 Data collection and analysis The data collection of this study includes the four parts: observation (the note taken in class, video observation), interviews (formal and informal), Document collection (text books, and notes of the students, the reflections of the teacher on net) The data analysis includes quantitative ones and qualitative ones. (1)Quantitative analysis: the researcher adopted the paired-sample t-test of Sheu’s mathematical learning attitude questionnaires (2000) to explore the effects of the strategies and reflections of the case teacher to students through the suitcase programs of SPSS11.5 for windows. (2)Qualitative analysis: 1.organize the data. 2. Establish code number and classify 3. Check the credit.
5. Conclusions 5.1 Result 1. The case teacher delivered the class mainly by lectures and questions, and other multi-teaching strategies in accordance to the contents of the courses. The main ways of the case teacher to teach math are teacher-centered, to lecture and ask questions. In the process of teaching the case teacher control the learning reactions at ease, giving the skills to answer the questions, and he ways to learn math to them, asking students work together.
The researcher regarded the
teaching strategies the case teacher used, calm down before per class, picture memory, group discussion, questions and answers, multi-evaluation, read speedly, teaching assistant, summarize the points, review in minutes, play math games, as the teacher-leading strategy and construction of teachers and students.
2. Steps in teaching. The case teacher has formed the specific teaching system. The researcher found the teacher asked students calm down, table clear before class, and reviewed the key points of the last class. Following is read through the content and added many skills such as group discussion, multi-grade, and math games, etc. Finally the teaching assistant came to the students ’ aids conducting remedial instruction and summarized the points.
The experienced teacher has specific steps in mathematical classes as follows: help students calm
down à review à read through the contents (of new unit) à question and answer( as ways to figure out the structure of the contents) àlecture the contents and concept à mix with multi-teaching strategies àconduct remedial instruction (peer and teacher) àsummarize the key points of the unit.
3. The reflective contents of the experienced teacher focused on “students”, and the reflective level of the experienced teacher tended to be the “descriptive level.” The ways for the case teacher to reflect in teaching are followings:
1.Impromptu reflection in class. 2.
To keep the diary on net. 3. The reflections dialogue in the e-community of classroom management.
4.
Deliver the teaching e-newspaper. Students are the main issue in teaching reflection (table 1) and the reflective level (table 2) tends to be descriptive level.
Though the case teacher described pure events in class, he took
action in dealing with students ’ learning and in the improvement of teaching practice with many critics to the events at school. Table 1: The contents of the case teacher’s teaching reflection Reflection
Students
Teaching
Colleague
contents
Classroom
Environment of
Teacher
Management
the campus
himself
Others
Total
Frequency
78
27
37
21
40
29
12
244
Percentage
32%
11%
15%
9%
16%
12%
5%
100%
Table 2: The level of the case teacher’s teaching reflection Level of reflection
Describe
Technical
Practical
Critical
Frequency
97
23
36
53
Percentage
47 %
11 %
17 %
25 %
4. Students’ learning attitude toward mathematics has a significant increase. After analyzing the pre-post test, the researcher found that students ’ math learning attitude toward mathematics has a significant increase (table 3) also in “confidence in learning math, communication with math,” agreement to the practicability of math among the eight tends in questionnaires. Thus, the researcher supposed the teaching strategies the case teacher used improved the efficiency in students ’ learning.
Table 3. The result pre-post t-test of students' math learning attitude Paired Differences
Pair 1
pre - post
Mean
Std. Deviation
Std. Error Mean
-4.970
10.36667
1.80461
95% Confidence Interval of the Difference Lower -8.6456
Upper
t
df
Sig. (2-tailed)
-1.2938
-2.754
32
.010
5. The study of teacher’s teaching practices can promote his professional growth. The researcher found when there are two more eyes (the researcher) and a digital video in the class, the case teacher would pay much attention to the teachings and teach students with all the efforts. The reflection notes promote the case teacher’s thinking and professional growth.
The case teacher realized what explored in
the study, so that he would be more careful and enthusiastic; also the case teacher quite agreed to the idea, the study on teaching execution would promote the professional teaching sense. 5.2 Suggestions The suggestions for the case teacher: 1.Check the efficiency of teaching strategies. 2. Deeper reflections in the content of teaching subject in reflection notes. 3. Encourage the students with low learning attitude. In addition to suggestions for the future study, inculing to go on trace the teaching and learning, and the inside and outside factors in confidences of learning math would be the study issues.
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