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Yuqian Wang Patrick Barmby David Bolden

Understanding of Linear Function in Secondary School Students : a Comparative Study Between Shanghai and England. Yuqian Wang Patrick Barmby David Bolden. Content. Background/Rationale Research Questions Theoretical Framework Results Conclusion Implication.

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Yuqian Wang Patrick Barmby David Bolden

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  1. Understanding of Linear Function in Secondary School Students: a Comparative Study Between Shanghai and England • Yuqian Wang • Patrick Barmby • David Bolden

  2. Content • Background/Rationale • Research Questions • Theoretical Framework • Results • Conclusion • Implication

  3. Background: Textbooks policy • Commercial / Compulsory • Two Levels / Uniform Level • School / Home

  4. Rationale • England-East Asia Gap in mathematics (Jerrim & Choi, 2013) • Textbooks from Top 30% Ranking State Schools • Topic: Function to Linear Function

  5. Research Questions • Does this topic have similar importance between the two countries' textbooks? • What is the background context for the two countries' textbooks respectively? • What emphases do the selected textbooks have in terms of the model of understanding function? • What approach do the selected textbooks use in terms of application?

  6. Theoretical Framework At the macro level (Li, Chen & An, 2009) General arrangement of the topic in terms of percentage of pages allocated; Background context of this topic • At the micro level: • Understanding levels in examples and exercises on basic knowledge. • Application would be analysed based on two aspects: • (a) how problems are presented • (b) how to resolve them using three main representations

  7. Results at the macro level: Background Context in linear function: England: straight-line graphs Shanghai: concept of function, proportional function, inverse proportional function

  8. Model for Understanding Function Level 1: Variable perspective Level 2: Dependent relationship Level 3: Translating representations Level 4: Property noticing Level 5: Object analysis Level 6: Inventising min

  9. Results at the Micro Level: Basic Knowledge

  10. Results at the Micro Level: The Content of Application Types of Examples/Exercises English higher level textbooks: Using graph Shanghai textbook: Word problem Main Type of Solution English higher level textbooks: Equation Shanghai textbook: Mix-method

  11. Conclusion How knowledge is presented English textbooks • Shanghai textbook

  12. Implication • For comparative study • Student assessments • How to borrow • For real-field area • Teachers: the disadvantage of each approach • Schools: teacher’s professional development

  13. Thanks for listening! Any questions? Reference: Jerrim, J., & Choi, Á. (2013). The mathematics skills of school children: how does England compare to the high-performing East Asian jurisdictions? Journal of Education Policy(ahead-of-print), 1-28. Li, Y., Chen, X., & An, S. (2009), Conceptualizing and Organizing Content for Teaching and Learning in Selected Chinese, Japanese and US Mathematics Textbooks: The case of fraction division, ZDM, 41(6), 809- 826

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