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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