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Abstract
This study examines the mediating role of homework in the daily practice of a middle‐school mathematics teacher and her colleagues in Shanghai. It aims to explore how a system of homework activities mediates and engenders a cultural pedagogy characterized by transforming errors into resources for teaching and learning. The transformation itself embodies teacher learning processes tied up with making sense of errors and providing feedback and pedagogical support to help as many students as possible to ‘get it right’. The findings of the study raise important questions about what teaching entails, and how to organize teachers’ work so that teacher learning occurs in the process of fostering student learning. This requires a reconceptualization of homework to capitalize on its pedagogical potentials.
Acknowledgements
I am thankful for the guidance and encouragement of Lynn Paine, Helen Featherstone, and Gary Sykes in putting together this work. I particularly wish to thank Ian Westbury for bouncing off ideas, providing editorial suggestions, and sharing the final work of editing.
Notes
1. The names of the school, the teachers, and the students are pseudonyms.
2. This is a direct translation from Chinese, jiaoshi ban gong shi; literally, it is a place for teachers to work and interact; however, students are daily participants in the work activities of this teachers’ workspace.
3. I use the abbreviation ‘Tr.’ to refer to ‘Teacher’, the respectful title that Chinese society has traditionally assigned to a teacher. No matter whether it is in the school or in the community, a teacher is always addressed as ‘Teacher Wang’, ‘Teacher Li’, etc.
4. Starting in 2002, with the passing of the baby‐boom era in Shanghai, the number of students enrolled in the first year of junior secondary schools decreased, and the average secondary school class size, as stipulated by Shanghai Municipal government, became no more than 45.
5. There was a higher proportion of mathematically weaker students in Class 2 compared to that of Class 4, but there were mathematically strong students in both classes. Because of this, Class 2 was not called a ‘weak class’ but a ‘parallel class’ to Class 4. There is no tracking in middle schools in Shanghai; all students use the same textbooks and workbooks and are expected to pass the same examinations.
6. Tr. Wang told me that my questions prompted her to think about why she made the adjustments in teaching the next class, something she always did but was not aware of until being asked.
7. Before the fieldwork, I had visited the school for a few times as a part of a large project, ‘Middle grades mathematics and science teacher induction in selected countries’, funded by the US National Science Foundation (1998–2001). The study examined induction and mentoring of mathematics and science teachers in selected countries; see Paine et al. (Citation2003).
8. This is a direct translation from Chinese, jiaoxue cankao ziliao. It is a small and thin volume accompanying a textbook. It offers concise analyses of the teaching content by topics and lessons, student learning difficulties, and teaching suggestions (Shanghai Municipal Education Commission Citation1998b).
9. Student corrections were made in a number of ways: written side‐by‐side of the original work, if there is enough space; written on a Post‐it note stuck on top of the original work; or simply adding corrections to the wrong steps using a differently coloured pen.
10. This is an rank conferred to a very small number of teachers or school leaders for their special contribution to teaching and education.
11. Congruent (equal) chords in the same circle are equidistant from the centre.
12. Unfortunately, the emotional nature of teacher’s work, particularly as it bears on interactions with students and their learning, is under‐studied (Hargreaves Citation2000).
13. That the two sides are equal should be used as the condition to back up the argument that a given triangle is an isosceles triangle. All students used the two equal base angles as the condition.
14. In the textbooks and in teaching of geometry and geometric proofs in China, the idea of ‘congruent angles’ (either independent angles or angles belonging to a shape) is generally referred to as ‘equal angles’; but the term ‘congruence’ (meaning completely equal and overlap) is always used to refer to equal shapes, as with congruent triangles and quadrilaterals.