How Does Anxiety Influence Maths Performance and What Can We do About It?

1. How Does Anxiety Influence Maths Performance and What Can We do About It? David Sheffield, Staffordshire University.

2. Acknowledgments • Sheila Ford, Paul Staples, David Clark-Carter. • PhD students: Tom Hunt and Keven Smith. • Undergraduate students: Tim Hobbs, Leah Vanono.

3. Types of Difficulties • Poor experience/ability • Dyscalculia • Dyslexia (Loughborough studies) • Math Anxiety

4. What is Maths Anxiety? • Feelings of tension and anxiety that impair the ability to manipulate numbers and solve mathematical problems (Richardson and Suinn 1972). • Separate from but moderately correlated with other forms of anxiety (Ashcraft, Kirk & Hopko 1998).

5. Some Definitions • “Feelings of tension, apprehension, or even dread that interferes with the ordinary manipulation of number and the solving of mathematical problems” - Ashcraft & Faust (1994) • “The panic, helplessness, paralysis, and mental disorganization that arises among some people when they are required to solve a mathematical problem” - Tobias and Weissbrod (1980)

6. Prevalence • According to Burns (1998) 2/3 of Americans fear and loathe maths. • Jackson and Leffingwell (1999) found that only 7% of Americans have had a positive maths experience. • In a study of over 9000 students, Jones (2001) found that 25.9% had a moderate to high need of help with maths anxiety. • BUT no UK or European studies.

7. Effects of Maths Anxiety • Evidence for performance differences as a function of maths anxiety (Hembree 1990). • Prominent on two column addition problems involving carry operations (e.g. 27+56=?). Ashcraft & Faust (1994).

8. Relationship with working memory. • Intrusive thoughts and worries interfere with working memory (Eysenck & Calvo, 1992; Ashcraft & Kirk, 2001). • In complex addition, working memory may be important for storing information and keeping track of the calculation (Hitch, 1978).

9. 3 Studies • Influence of secondary task on performance of maths anxious vs. non maths anxious individuals. • Neuropsychological correlates of maths anxiety. • Brief intervention for maths anxiety.

10. Study 1: Performance • Investigate errors that anxious vs. non anxious individuals make especially on complex arithmetical tasks (Ashcraft & Kirk, 2001). • Look at the effect of maths anxiety on a secondary task (serial recall of letters). • Coding of item information may be separate from coding of serial order in verbal short term memory (Burgess & Hitch, 1999).

11. Examples of Math Anxiety Questions • “Thinking about an upcoming maths test 5 minutes before”. • “Deciding how much of a tip to leave in a restaurant after a meal”. • “Having someone watch you as you add up a column of numbers”. -Richardson and Suinn (1988)

12. Accuracy (% correct) • Main effect of anxiety (F (2,45)=4.3 p=.02) • High Anxiety = 87.6% (6.0) • Medium Anxiety = 90.9% (4.3) • Low Anxiety = 92.3% (3.2). • Significant 3 way interaction between Task x memory load x anxiety. (F(2,45)=3.9, p=.03).

13. Task x memory load x anxiety (accuracy)

14. Serial Letter Recall (% of items recalled in correct serial order) • No significant main effect of anxiety • Significant 3 way interaction of task x difficulty x anxiety (F(2,90)=2.8 p=.03) • In the letter only condition there was a significant main effect of difficulty (p=<0.01) but no main effect of anxiety and no interaction between difficulty and anxiety. • In dual task condition, there were effects of difficulty (p<.01), anxiety (p<.05) and difficulty x anxiety (p<.05).

15. Difficulty x Anxiety (Serial recall in Dual Task)

16. Discussion: summary • Maths anxiety has an effect on accuracy, particularly when performing a secondary task that puts heavy demands on working memory. • Maths anxiety had no effect on serial recall when there is no maths involved but there is an effect with a concurrent maths task and this effect is stronger with more difficult problems.

17. Discussion: interpretation • Maths anxiety probably affects accuracy because anxious thoughts load working memory resources which may be needed for calculation (counting strategies). • If these strategies are affected this may lead to errors, including losing a running total which results in large errors. • If anxious thoughts disrupt serial order then this would have implications for calculations that require counting strategies.

18. Study 2: EEG Investigation • Electroencephalogram (EEG) measures the activity of populations of neurons firing across the cerebral cortex. • Shows different states of alertness or consciousness. • There are changes in brain activation in response to a specific event.

19. Problem 17

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21. Problem 18

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23. Problem 35

25. Conclusions so far • Large differences within the (left) frontal area • Only in response to carry operations. • Both an initial response difference (perception - oh shit! It’s maths) and later difference in slow (Processing). • Carry operations = increased working memory load. • Also differences in parietal region (for carry and no-carry) - general calculation differences.

26. Study 3: Intervention • 2 types of intervention strategy (Zettle, 2003): • Behavioural approaches - focus directly on emotionality component of mathematics anxiety (first order changes). • Cognitive approaches - focus on altering the negative cognition’s contributing to mathematics anxiety (“I’m terrible at maths”).

27. Efficacy of Interventions • Hembree (1990) comparison of interventions. • Suggests behavioural interventions most effective in reducing math anxiety. • Some cognitive and mixed strategies as good. • Best interventions include systematic desensitization.

28. Procedure

29. Intervention • Modified from Meichenbaum’s (1972) cognitive modification program. • The behavioural component taught • relaxing diaphragmatic breathing, • anxiety reduction through imaginary • in situ desensitization (graded exposure while practicing relaxing breathing).

30. Math Anxiety - Decrease in intervention group

31. Math Performance - Increases in Intervention Group

32. Conclusions • Brief intervention (1 60 minute session) decreased math anxiety. • Maintained at 5 week follow-up. • BUT control group not comparable (less anxious). • Associated increases math performance (at post-task and follow-up) BUT only simple addition. • Anxiety changes impact performance (intrusive thoughts/inhibition model).

33. Future Directions • Measuring Math Anxiety in UK (European) populations. Questionnaires development and prevalence. • Developmental Aspects. • Mechanisms and strategy use. • Interventions for Students.

34. A Couple of Helpful Websites • Systematic Desensitization • http://www.guidetopsychology.com/sysden.htm • Dyscalculia and Dyslexia Interest Group (this site has links to a number of maths-related resouces) • http://ddig.lboro.ac.uk/