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Understanding of Linear Function in Secondary School Students: a Comparative Study Between Shanghai and England

Yuqian Wang

Patrick Barmby

David Bolden

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Content

• Background/Rationale

• Research Questions

• Theoretical Framework

• Results

• Conclusion

• Implication

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Background: Textbooks policy

• Commercial / Compulsory

• Two Levels / Uniform Level

• School / Home

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Rationale

• England-East Asia Gap in mathematics (Jerrim & Choi, 2013)

• Textbooks from Top 30% Ranking State Schools

• Topic: Function to Linear Function

Countries Topic

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1. Does this topic have similar importance between the two countries' textbooks?

2. What is the background context for the two countries' textbooks respectively?

3. What emphases do the selected textbooks have in terms of the model of understanding function?

4. What approach do the selected textbooks use in terms of application?

Research Questions

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Theoretical Framework

At the macro level (Li, Chen & An, 2009)1. General arrangement of the topic in terms of percentage of

pages allocated; 2. Background context of this topic

At the micro level:1. Understanding levels in examples and exercises on basic

knowledge. 2. Application would be analysed based on two aspects: (a) how problems are presented (b) how to resolve them using three main representations

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Results at the macro level:Content Placement:

Textbooks Average Pages (%)

Foundation Level in English textbooks 1.84%

Higher Level in English textbooks 2.53%

Shanghai compulsory textbook 2.16%

Background Context in linear function:

England: straight-line graphs

Shanghai: concept of function, proportional function, inverse proportional function

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Model for Understanding Function

Level 1: Variable perspectiveLevel 2: Dependent relationship Level 3: Translating representationsLevel 4: Property noticingLevel 5: Object analysis Level 6: Inventising

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Results at the Micro Level:Basic KnowledgeThe Percentage of Example/Exercise at Each Level

  Level 3: Translating representations

Level 4: Property noticing

Level 5: Object analysis

Level 6: Inventising

Higher level

13.6%/32.8% 45.4%/41.2% 36.4%/16.0% 4.5%/10.1%

Foundation level 22.2%/45.5% 77.8%/43.2% 0/6.8% 0/4.6%

Shanghai 18.2%/6.3% 9.1%/18.8% 63.6%/50.0% 9.1%/25.5%

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Results at the Micro Level:The Content of Application

Types of Examples/ExercisesEnglish higher level textbooks: Using graph

Shanghai textbook: Word problem

Main Type of SolutionEnglish higher level textbooks: Equation

Shanghai textbook: Mix-method

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Real-life situationGraphic approach

Algebraic approach English textbooks

Definition Algebraic approach combined with graph

More abstract algebraic approach combined with graphReal-life situation

Shanghai textbook

Conclusion

How knowledge is presented

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Implication

For comparative study

• Student assessments

• How to borrow

For real-field area

• Teachers: the disadvantage of each approach

• Schools: teacher’s professional development

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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