GENDERGENDER

GENDER DIFFERENCESGender and sex“Disadvantaged groups”Participation rateAchievement

BiologicalGender-segregated educationTeacher expectancy and interactionCognitive variableConfidence and other affective variablesAttribution and fear of successSocial shaping: mathematics as a male domain

Attempted explanations

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 mathematics8. 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

※ 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

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

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

「拒絕『成功』」？

“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

AFFECTAFFECT

“… 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)

Beliefs- About mathematics- About self- About mathematics teaching- About the social contextAttitudesEmotionsSelf-conceptMathematics anxiety

Re-conceptualisation: from “residual” to Mandler’s theory

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

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

RepresentationRepresentation

Local/global affects and pathways

Exploratory Problem-defining heuristicsHeuristics for understanding problem

Useful problem-solving heuristicsChallenge to authority-based problem-solving

Insight (imagistic)

Acceptance of authority-based problem solvingDefense MechanismsHeuristics 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 .

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)

• 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

“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)

Relationship between affects & achievements

Other related notions- confidence- attribution- motivation- locus of control- fear of success- engagement

Given

Goal

Process

Open Open Open

Cognitive engagement

Affective engagement

Behavioral engagement

Problem solving abilities

A priori model for path analyses

MODELS OF MATHEMATICS LEARNINGMODELS OF MATHEMATICS LEARNING

Fennema (1985)

Eccles (1985)

Attitude To Learning Maths (time 1)

Subjective Norm For Learning Maths (tim

e 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)

Haladyna, Shaughnessy, & Shaughnessy (1983)

Walberg, 1984

Ethington & Wolfle (1986)

Reynolds & Walberg (1992)

Papanastasiou (2002)