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. 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).

4. 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)

5. Some More Definitions • “An on-line reduction in the available working-memory capacity” • “Attention to or preoccupation with intrusive thoughts or worry” • “… become confused, are unable to focus on the task at hand, or keep thinking about how poor they are at math” - Ashcraft & Kirk (1999)

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.

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. MethodParticipants • 48 undergraduate students • 19 Men and 29 women • Aged between 18 and 25 years.

12. Tasks • Maths Only • Letter Recall Only • Dual Task • Order of presentation: • Letters presented – 6s read aloud • Sum presented – give answer (timed) • Prompt to recall letters in serial order

13. Tasks cont. • Varied by • Carry status (yes/no); • Difficulty (Basic (1+1 digit), Intermediate (2+1 digit), Complex (2+2 digit)); • Memory Load (2 or 6 letters). • 60 comparable problems for each of 3 task types.

14. Questionnaires • Short Mathematics Anxiety Rating Scale (sMARS; Alexander & Martray, 1989). • 25-item validated version. • Split into TERTILES for analysis

15. Examples of 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)

16. Results

17. 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).

18. Task x memory load x anxiety (accuracy)

19. 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).

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

21. 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.

22. 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.

23. 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 (ERP).

24. Electrode Positions

25. ERPs and Arithmetic • Pauli et al (1994, 1996) found that parietal positivity was unaffected by practice. • In a case study (1997), Whalen et al stimulated a left parietal site of the cortex… performance on simple arithmetic was impaired. • Suggests the importance of the parietal region in relation to fact retrieval. • Frontal region associated with carry operation (working memory used); Kong et al. (1999).

26. Participants • 33 undergraduate initially took part. • 10 men and 23 women. After data screening, data for 22 participants were finally analysed. • Ages ranged from 18 to 45 years, mean = 23.4 years, SD = 6.7 years. • Given MARS (Richardson and Suinn, 1988) • Median split to define anxious from non-math anxious.

27. Experimental Stimuli • Two-digit addends. • 150 problems (75 with carry, 75 with no carry). • First addend taken from a range of 13 to 72. • Second addend randomly taken from a range of 11 to 13 and 17 to 19. • 15 carry and 15 no-carry problems assigned to the false answer condition (plausible but wrong answer). • Data only analysed from responses to 120 true problems.

28. Presentation Order of Stimulus

29. Problem 17

30. Problem +

31. Problem 18

32. Problem =

33. Problem 35

34. Results

39. 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.

40. Intrusive Thoughts • Processing Efficiency Theory (Eysenck & Calvo, 1992) • Anxiety hinders task efficiency • Not related to individual ability • Worry pre-empts task processing • Inhibits effectiveness of working memory.

41. Inhibition Theory • Connelly, Hasher & Zacks, (1991) • Failure to inhibit task-irrelevant information • Leads to consumption of working memory processes. • Maths anxiety as a distractor (Ashcraft, 2002) and inability to inhibit it.

42. 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.

43. 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.

44. Aims • Develop brief behavioural intervention. • For primary school-aged children. • Evaluate effectiveness in reducing anxiety and increase math performance.

45. Participants • Three primary schools in the West-Midlands volunteered to take part in the study, consisting of 7 maths classes. • 154 participants took part in the study. • The experimental group contained 33 boys and 49 girls (4 classes). • The control group contained 35 boys and 37 girls (3 classes). • All participants were between the ages of 10 and 11 years old, in the final year of primary school (year six).

46. Pre-, Post- and Follow-Up Measures • Maths Anxiety Rating Scale for Children (MASC; Chiu & Henry, 1990). • This is a 4-point Likert scale consisting of 22 items. • Minor changes were made to the scale in order to reflect the UK population.

47. Pre-, Post- and Follow-Up Measures • Simple Addition Problems for two minutes. • Participants were presented with 4 sets of mathematics questions. • Each set contained 180 simple addition problems, including an equal number of basic fact, medium and large problems, presented as both carry and non-carry types (Ashcraft & Kirk, 2001).

48. Procedure

49. 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).

50. Control Group • The control group did not receive an intervention in second session. • Instead, participants were involved in a neutral control session consisting of classroom games • After 5 week follow-up taught intervention.