Adult Mathematics and Numeracy as Emotional Activities: How can this be?!

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Adult Mathematics and Numeracy as Emotional
Activities How can this be?!

• Jeff Evans
• Middlesex University
• London
• J.Evans_at_mdx.ac.uk
• EMMA Clustering Conference
• Bucharest, 26-27 October 2006

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Mathematical Thinking is Hot!

• Emotions, Feelings about Mathematics, reported by
  adults
• Liking or disliking
• I dropped maths with a sigh of relief, for I
  had always loathed it, always felt
  uncomprehending even while getting tolerable
  marks, didn't like subjects I wasn't good at, and
  had no notion of this subject's appeal or
  significance....
• (Margaret Drabble, writer, The Guardian, 5.8.75)
  

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Feelings about Mathematics, reported

• Fear / anxiety or confidence
• Question What do you dread as you open your
  eyes in the morning?
• Answer That I'm still at school and it's double
  maths! two periods of mathematics in a
  row....
• (Shona MacDonald, 26, promotions manager, in
  City Limits, 23-30 May 1991)

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Feelings about Mathematics, reported

• Valuing maths, perceiving it as useful, worth
  it
• Enjoyment, excitement, finding it cool or
• boredom
• and what else ?

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Researchers' Concepts

• Beliefs confidence,
• self-concept,
• self-efficacy, or 'learned helplessness' ....
• Emotion frustration, confidence
• Motivation desire to understand, perform well

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A brief history of the study of affect and
emotions in mathematics education

• Background post-World War II studies of anxiety,
• especially in US Psychology
• 1. Early focus on maths anxiety / fear in
  feminist
• explanations of girls performance deficit
• Gender Performance
• Maths Anxiety Avoidance Course- taking
• Sheila Tobias (1978), Overcoming Math Anxiety
• Laurie Buxton (1981), Do you panic about maths?

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A brief history (contd)

• 2. Surveys gender differences
• dimensionality
• models of influence
• Richardson Suinn (1972) Math Anxiety Rating
  Scale (MARS), for adults
• Fennema Sherman (1976) Math Attitude Scales

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Attitudes to Math (Fennema Sherman)

• Attitude to Success in Math
• Effectance Motivation problem-solving attitude
• Confidence in Learning Mathematics
• Usefulness of Mathematics
• Math as a Male Domain
• Mothers ) Attitudes towards oneself
• Fathers ) as perceived
• Teachers) as a learner of mathematics

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A brief history (contd)

• 3. Move to Process, e.g. of problem solving
• Emotion, rather than Attitudes, Beliefs
• Qualitative Methods observation, interviews,
• rather than (or along with) questionnaires
• focus on positive emotion (not only negative)
• AND feelings of experts, not only novice
  learners
• McLeod Adams (eds.) (1989) Affect and
  Mathematical Problem Solving

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Types of Affect (McLeod, 1992)

• Beliefs Attitudes Emotion
• lt-------------------------------------------------
  ------------gt
• More stable, durable More volatile
• More intense
• More cognitive reflective, More affective
• but not nec. rational charged
• ADD Values Mood
• Sources DeBellis and Goldin (1997)
• M. Roth (2007)

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Types of Affect Research Methods

• Beliefs Attitudes Emotion
• lt-------------------------------------------------
  ------------gt
• Values Mood
• course evaluation // informal interviews //
• self-completion semi-structured
• questionnaires interviews
• BUT standard learning contracts //
• learning diaries

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A brief history (contd)

• 4. Studies with Adults
• D. Coben (2000) life histories of adult students
  of arts and social sciences at London college
• J. Evans (2000) life histories and problem
  solving of social sciences undergraduates
• S. Hale (2002) diaries of adult basic skills
  learners
• J. Swain et al. (2005) interviews with adult
  numeracy learners

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Issues for Research and Practice

• 1. Relation between Affect and Mathematical
  Thinking
• / Problem Solving / College Performance
• (affect and cognition)
• Obvious ??
• Volatile aspects emotions describing problem
  solving
• episodes with experiences of blockage,
  frustrations
• ? vivid descriptions
• (McLeod Adams, 1989)
• (Evans, 2000)
• (Op t Eynde et al., 2006)
• Stable aspects attitudes, beliefs
  investigating relations with measures of
  performance, using meta-analysis
• ? only weak general relationships found so
  far (Ma Kishnor, 1997)
• (Hannula, 2006)

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Issues for Research and Practice

• 2. Where do emotions, attitudes, beliefs come
  from?
• Experiences at school, college (one-off or
  repeated) as interpreted by the learner
• Interactions with significant others Teachers
• Parents / elders
• Siblings / peers
• (Fennema Sherman, 1976)
• Cultural representations films, advertisements
• (Evans, 2003, 2004)

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Issues for Research and Practice

• 2. Example Origins of Maths Anxiety
• Tobias (1978) a problem of beliefs
• interviews focussing on critical incidents
• myths about maths e.g. one right answer
• only one right way to get the answer
• myths about learning maths
• e.g. dropped stitch- once lost, no catchup
• mathematical mind either have it, or you
  dont
• language ambiguous or misleading
• e.g. least common denominator

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Issues for Research and Practice

• 2. Example Origins of Maths Anxiety
• Buxton (1981) group interviews problem solving
• time pressure in the classroom
• unpleasurant or distressing feedback
• apparently arbitrary rules (- times - )
• ambiguity of jargon (e.g. x is unknown)
• moral connotations of right wrong answers
  and especially
• early unhappy encounters around mathematics with
  authority figures - teachers or parents -
  linked with the threat of disapproval

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Issues for Research and Practice

• What social differences can be found in affect,
  feelings towards mathematics?
• Gender formidable literature on school age
• see also e.g. Henningsen (2004)
• Ethnic, cultural group, e.g. Civil (2003)
• Age, or adulthood, e.g. Coben et al. (2003)
• Social Class

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Issues for Research and Practice

• 4. Relationship between Beliefs, Attitudes and
  Emotions
• Qu. repetition of more transitory experiences /
  emotions tends to establish more durable beliefs
  / attitudes ?
• Semi-structured interviews, including
• (a) real-time problem solving observations /
  self-reports of feeling
• (b) remembered experiences
• Self-completion Questionnaires (reported)
  behaviour, attitudes, beliefs
• Op t Eynde et al. (2006), Evans (2000)

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Conclusions

• Mathematics is hot, the object of feelings,
  often negative, but they can be positive - or
  even sometimes ambivalent / fluid. They can be
  made more positive (cf. Women and Maths
  movement).
• 2. The relationship between mathematical
  thinking and emotion is not always interfering,
  but ... it often is, in the current cultural
  conditions.

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Conclusions

• Many feelings about mathematics originate in
  early schooling experiences, or in interaction
  with significant others and are still felt and
  have their effects in adulthood however, adults
  are open to further ideas, beliefs and feelings
  about maths.
• 3a. Other feelings my be influenced by the images
  of mathematics and mathematicians in the media,
  and in popular culture generally.
• Nonetheless, this may offer a way forward in
  terms of repositioning mathematics.

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Conclusions

• 5. Different persons and groups may be
  differently positioned vis-à-vis mathematics and
  numeracy.
• 6. Critical incidents (emotional) may tend to
  lead to relatively stable affective
  orientations (attitudes, beliefs), especially if
  they are repeated.

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Conclusions

• Basic conceptual map for this area
• Social Influences ? Affective Variables ?
  Mediating Learning
• Activities
• gender maths anxiety perseverance in
• social class confidence problem solving
• age liking taking maths
• perceiving as useful courses
• etc.
• Mathematical Outcomes school performance
• (inter)national test
• performance
• Source Fennema (1989), Evans (2000)

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Conclusions and Further Research

• Development of the idea of motivation
• Swain et al. (2005)
• Evans and Wedege (2004)
• Exploration of the public image of mathematics,
  and the role of popular culture in its formation
• FitzSimons (2002)

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Conclusions and Further Research

• Psychoanalytic insights can be explored to
  suggest
• - how the play of desire and fantasies may
  invest mathematics and mathematical objects with
  strong emotional meaning
• - that certain mathematics-related beliefs and
  behaviours are defensive (against anxiety and
  conflict)
• - possible explanations for sometimes surprising
  cognitive slips.

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Conclusions and Further Research

• Need to consider the difference in emotional
  expression and experience between children and
  adults
• Broadening the evidential basis for work in this
  field, especially with adults, beyond the
  currently research-rich countries!

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Issues for Practice and Policy

• 1. How to work on / with negative feelings about
  mathematics?
• 2. What are practical implications of the
  suggested influences on mathematical feelings
  classroom experiences, significant others,
  popular culture representations for each of the
  following?
• Training of teachers
• Engagement of Parents (Civil, 2003)
• Public Understanding / Popularisation /
  'Repositioning of Mathematics / Mathematicians
  (e.g. Simon Singh.net)

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Issues for Practice and Policy

• 3. Should an explicit goal of curricula and
  teaching practice be to develop enjoyment,
  liking,
• engagement with mathematics ?
• 3a. Do the current curriculum / arrangements do
  this?
• 4. How to mount a campaign to improve the
  attitudes and motivations of specific groups of
  learners (e.g. girls, adults) to take appropriate
  mathematics courses and to do well?
• NB Tremendous success of Women Maths
  movement, since mid-1970s in many countries

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Full references

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