2. GENDER GENDER DIFFERENCES Gender and sex “Disadvantaged groups” Participation rate Achievement

3. Biological Gender-segregated education Teacher expectancy and interaction Cognitive variable Confidence and other affective variables Attribution and fear of success Social shaping: mathematics as a male domain Attempted explanations

4. 1. Females are as good as males in geometry. 2. Studying mathematics is just as appropriate for women as for men. 3. I would trust a woman just as much as I would trust a man to figure out important calculations. 4. Girls can do just as wells as boys in mathematics. 5. Males are not naturally better than females in mathematics. 6. Women certainly are logical enough to do well in mathematics. 7. It’s hard to believe a female could be a genius in mathematics 8. When a woman has to solve a math problem, it is feminine to ask a man for help. 9. I would have more faith in the answer for a math problem solved by a man than a woman. 10. Girls who enjoy studying math are a bit peculiar. 11. Mathematics is for men; arithmetic is for women. 12. I would expect a woman mathematician to be a masculine type of person. Mathematics as a Male Domain

10. ※ males hold more functional beliefs about themselves as learner ※ gender differences more prevalent among older students ※ math viewed as male domain, more so by males ※ confidence is critical in participation ※ females less likely to contribute math success to ability and failure to lack of effort ※ external influence influences students’ beliefs

11. ※ womenless math ※ women in math ※ women as a problem in math ※ women as central to math ※ math reconstructed

12. CONCRETE ABSTRACT SAME PERFORMANCE CONCRETE ABSTRACT SAME PERFORMANCE NOT AS GOOD PERFORMANCE IN HIGHER MATH BETTER PERFORMANCE IN HIGHER MATH CONCRETE ABSTRACT SAME PERFORMANCE NOT AS GOOD PERFORMANCE IN HIGHER MATH BETTER PERFORMANCE IN HIGHER MATH IN-BORN/ SOCIAL SHAPING

13. 「拒絕『成功』」 ？

14. “Fennema & Sherman (1976, 1978) developed their attitude scales for the purpose of research on gender- related differences in mathematics achievement, but their impact has been felt widely in all research on attitudes towards mathematics” (McLeod, 1994) - - attitude towards success - - mathematics as a male domain - - confidence - - motivation - - usefulness AFFECT

15. “… almost reducing it (the concept of attitude) to the pseudo-definition ‘attitude is what attitude questionnaires measure’” (Daskalogianni & Simpson, 2000, p. 217 – see Martino, 2003)

16. Beliefs - - About mathematics - - About self - - About mathematics teaching - - About the social context Attitudes Emotions Self-concept Mathematics anxiety Re-conceptualisation: from “residual” to Mandler’s theory

17. Two basic approaches (Hannula, 2002): - “simple” definition describes it as the degree of affect associated with mathematics - 3-component definition distinguishes emotional response, beliefs, and behaviour as components of attitude

18. Attitude in cognitive-emotional terms (Hannula, 2002) When engaged in doing math: emotion When not engaged: emotional disposition, as measured by questionnaire, base on experiences Respond to questionnaire for a longer period: additional cognitive process In further discussions: based on cognitive analysis Representation

19. Local/global affects and pathways Exploratory Problem-defining heuristics Heuristics for understanding problem Useful problem-solving heuristics Challenge to authority-based problem- solving Insight (imagistic) Acceptance of authority-based problem solving Defense Mechanisms Heuristics of avoidance and denial Concealment of Inadequacies Frustration Anxiety Fear/ Despair Global structures self/mathematics/ science / technology -hatred Curiosity Puzzlement Bewilderment Encouragement Pleasure Elation Satisfaction Global structures specific representation schemata, general self-concept structure Emotion – attitude – beliefs – values Influence of beliefs of others/society, societal belief.

20. 1. Simple definition: attitude is a general emotional disposition toward a certain subject 2. Attitude has three components: an emotional response, the beliefs regarding the subject, the intentional behavior toward the subject 3. Attitude is the pattern of beliefs and emotions regarding a certain subject. “epistemologically correct attitude” – bidimensional definition Martino & Zan (2001a, 2002)

21. Ontology: do people actually possess “things” called beliefs ? Generation: even if people hold and sustain beliefs and attitudes, it is not at all clear that beliefs and attitudes actually generate behaviour. Revelation: whether such things can be externally observable. Belief – behaviour

22. “The student must: understand that the new informations are in contradiction with the belief believe that it’s necessary to overcome the contradiction want to resolve the contradiction.” Change of beliefs (Martino, 2003)

23. Relationship between affects & achievements Other related notions - - confidence - - attribution - - motivation - - locus of control - - fear of success - - engagement

24. Give n Goal Process Open Open Open Cognitive engagement Affective engagement Behavioral engagement Problem solving abilities A priori model for path analyses

26. MODELS OF MATHEMATICS LEARNING Fennema (1985)

27. Eccles (1985)

28. Attitude To Learning Maths (time 1) Subjective Norm For Learning Maths (time 1) Behaviour intention To Learn Maths (Time 1) Maths Learning Behaviour (time 1) Maths Achievement (time 1) Maths Learning (Time 2) Maths Achievement (time 2) Norwich & Jaeger (1989)

29. Haladyna, Shaughnessy, & Shaughnessy (1983)

30. Walberg, 1984

31. Ethington & Wolfle (1986)

32. Reynolds & Walberg (1992)

33. Papanastasiou (2002)