Abstract
Attempts to understand what contributes to teaching quality have been channeled in different directions, with two main research streams focusing on either teacher knowledge or teacher beliefs. Few are the studies that have attended to both the cognitive and the affective domain simultaneously, trying to unpack how both jointly contribute to teaching quality. Situated at the nexus of these two domains, this study aims to understand how teachers’ mathematical knowledge for teaching and their pedagogical beliefs contribute to their performance in providing explanations and selecting and using tasks, as studied in a teaching simulation. Using a multiple-case approach and examining the development of three prospective teachers’ knowledge and beliefs over a content-and-methods course sequence, the study documents how limitations in either knowledge or beliefs can mediate the effect of the other component on prospective teachers’ performance. Implications for teacher preparation and in-service education are drawn and directions for future studies are offered.
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Notes
A more detailed account of all three PSTs’ performance in both practices is outlined in Charalambous (2013).
Although we focus on only three PSTs and consider their work in a limited set of teaching practices, the results considered in this section are largely typical of the work of the entire group of 20 PSTs on five teaching practices: providing explanations, using representations, analyzing student work, selecting and using tasks, and responding to students’ request for help (cf. Charalambous 2008).
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Appendix 1
Appendix 1
The survey statements used to explore PSTs’ pedagogical beliefs
1. | It is confusing to see many different methods and explanations for the same idea |
2. | A good mathematics teacher is someone who explains clearly and completely how each problem should be solved |
3. | Teachers should not necessarily answer students’ questions but let them puzzle things out themselves |
4. | Students learn mathematics best if they have to figure things out for themselves instead of being told or shown |
5. | When students can’t solve problems, it is usually because they can’t remember the right formula or rule |
6. | When students solve the same mathematics problem using two or more different strategies, the teacher should have them share their solutions |
7. | It is important for students to master the basic computational skills before they tackle complex problems |
8. | If students are having difficulty in mathematics, a good approach is to give them more practice in the skills they lack |
9. | To do well, students must learn facts, principles, and formulas in mathematics |
10. | In learning mathematics, students must master topics and skills at one level before going on |
11. | Doing mathematics allows room for original thinking and creativity |
12. | The most important issue is not whether the answer to any mathematics problem is correct, but whether students can explain their answers |
13. | Basic computational skill and a lot of patience are sufficient for teaching elementary school mathematics |
14. | Teachers should try to avoid telling |
15. | Doing mathematics is usually a matter of working logically in a step-by-step fashion |
16. | A lot of things in mathematics must simply be accepted as true and remembered |
17. | Students should never leave mathematics class (or end the mathematics period) feeling confused or stuck |
18. | If students have unanswered questions or confusions when they leave class, they will be frustrated by the homework |
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Charalambous, C.Y. Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: a multiple-case study. J Math Teacher Educ 18, 427–445 (2015). https://doi.org/10.1007/s10857-015-9318-7
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DOI: https://doi.org/10.1007/s10857-015-9318-7