Abstract
This study aimed to characterize Chinese teachers’ expertise in mathematics instruction through analyzing five selected expert teachers’ video-taped lessons, their lesson designs and reflections. A prototype view of teaching expertise was adopted and used to identify similarity-based central tendencies that are shared among these expert teachers. Data analyses revealed six central tendencies of these teachers’ lesson instruction and thinking. The case analysis of one expert teacher’s lesson instruction was also used to provide rich descriptions and illustrations of the prototype of these teachers’ teaching expertise. The findings help us to develop a better understanding of the complexity of teaching expertise valued in China, and are important to teacher educators in their efforts to improve professional development for teachers.
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Appendices
Appendix 1: The Categories and Examples of Teachers’ Comments and Reflections
Categories | Sub-categories | Examples |
|---|---|---|
Teacher knowledge | Content knowledge | Knowing the connection and differences between percentage and fraction, mastering the conversion between percentage, fraction, decimals and fraction (T1) |
Students’ learning difficulties and treatment | The teacher appropriately anticipated students’ difficulties when learning system of linear equations, and designed the strategies to overcome the difficulties (T3) | |
Developing mathematical thinking methods and abilities | I implicitly introduced the transformation thinking method, the method of integrating numerical and pictorial representations, and the thinking method of using function and equation (T4) | |
Developing mathematical application | To help students get an experience in solving contextual problems by using function and its graphs, and develop their mathematical application ability (T4) | |
Instructional process | Student-centered activities | Through participating in various learning activities, students are motivated to explore, collaborate and develop their affective experience in learning mathematics (T1) |
Teacher-directed activities | I believe that in this lesson it would be much better if the teacher directly explained the concept. Because the definition is rigorous, the teacher should help students understand the rigor of the definition (T3) | |
Contextual learning | Knowing how to use mathematics language to express real life situations concisely through exposing various real life examples of using percentage (T1) | |
Learning motivation | Motivating students to learn through exploratory activities from concrete to abstract cases (T2) | |
Teaching skills and teacher characteristics | Basic teaching skills | Board writing is good, teaching language is concise (T3) |
Use of multiple media | Using colorful pictures to present real life situations, using multiple media to teach (T1) | |
Improvisational ability | For teacher, the highest teaching ability should be reflected in improvisational ability in classrooms (T1) |
Appendix 2: Frequencies of the Codes Appeared in the Five Teachers’ Comments and Reflections
Sub-categories | T1 | T2 | T3 | T4 | T5 |
|---|---|---|---|---|---|
Content knowledge | 6 | 6 | 5 | 5 | 5 |
Students’ learning difficulties and treatment | 1 | 9 | 2 | 2 | 1 |
Developing mathematics thinking methods and abilities | 6 | 4 | 4 | 8 | 9 |
Developing mathematics application | 12 | 1 | 5 | 3 | 4 |
Student-centered activities | 6 | 9 | 6 | 7 | 5 |
Teacher-directed activities | 1 | 7 | 0 | 0 | 3 |
Contextual learning | 10 | 2 | 1 | 3 | 1 |
Learning motivation | 2 | 3 | 2 | 5 | 4 |
Basic teaching skills | 0 | 0 | 2 | 3 | 3 |
Use of multiple media | 1 | 0 | 0 | 1 | 1 |
Improvisational ability | 1 | 0 | 0 | 0 | 1 |
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Li, Y., Huang, R., Yang, Y. (2011). Characterizing Expert Teaching in School Mathematics in China – A Prototype of Expertise in Teaching Mathematics. In: Li, Y., Kaiser, G. (eds) Expertise in Mathematics Instruction. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7707-6_9
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