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

1. Adult Mathematics and Numeracy as Emotional Activities: How can this be?! Jeff Evans Middlesex University London J.Evans@mdx.ac.uk EMMA Clustering Conference Bucharest, 26-27 October 2006

2. “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)

3. 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)

4. Feelings about Mathematics, reported • Valuing maths, perceiving it as useful, “worth it” • Enjoyment, excitement, finding it “cool” … or boredom • and what else …?

5. Researchers' Concepts • Beliefs: confidence, self-concept, “self-efficacy”, or 'learned helplessness' .... • Emotion: frustration, confidence • Motivation: desire to understand, perform well

6. 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?

7. A brief history (cont’d) 2. Surveys: gender differences dimensionality models of influence Richardson & Suinn (1972): Math Anxiety Rating Scale (MARS), for adults Fennema & Sherman (1976): Math Attitude Scales

8. 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 • Mother’s ) Attitudes towards oneself • Father’s ) [as perceived] • Teacher’s) as a learner of mathematics

9. A brief history (cont’d) 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

10. Types of Affect (McLeod, 1992) Beliefs Attitudes Emotion <-------------------------------------------------------------> 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)

11. Types of Affect & Research Methods Beliefs Attitudes Emotion <-------------------------------------------------------------> Values Mood course evaluation // informal interviews // self-completion semi-structured questionnaires interviews BUT… standard learning contracts // learning diaries

12. A brief history (cont’d) 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

13. 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)

14. 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)

15. 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 don’t • language ambiguous or misleading e.g. ‘least common denominator’

16. 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

17. 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

18. 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)

19. 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.

20. 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.

21. 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.

22. 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)

23. 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)

24. 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”.

25. 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!

26. 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)

27. 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

28. Full references • Click this link for full references