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The merits of a general numeracy test as a predictor of statistics exam performance

The merits of a general numeracy test as a predictor of statistics exam performance. Alistair J. Harvey University of Winchester. The importance of numeracy in psychology. Quantitative methods central to study of psychology.

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The merits of a general numeracy test as a predictor of statistics exam performance

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  1. The merits of a general numeracy test as a predictor of statistics exam performance Alistair J. Harvey University of Winchester

  2. The importance of numeracy in psychology • Quantitative methods central to study of psychology. • BA/BSc Psychology Entry criteria includes GCSE Maths Grade C (or equivalent). • Mulhern & Wylie (2006) obtained numeracy baselines from about 1000 psychology students across a range of HE institutions. • Identified students’ conceptual difficulties in mathematical thinking.

  3. Possible implications of poor numeracy for learning statistics • Arithmetic calculation: • Basic skills should not be assumed. • If r=.3, then r²=.09 (not .9!). • Algebraic reasoning • Difficulties distinguishing between variant and invariant formulas [e.g. for (a+b)/(a-b), doubling a and b leads to same solution]. • Suggests some may have problems reasoning with transformed or rescaled variables and their changing effects on mean, sd, distributions, etc.

  4. Possible implications of poor numeracy for learning statistics • Graphical interpretation: • Few would argue that this is one of the most important skills required for psychology; yet less than half the students made the correct correspondence.

  5. Does numeracy ability predict statistics performance? • Gnaldi (2006) investigated this relationship on an undergraduate introductory statistics course (University of Glasgow). • Stepwise regression showed Numeracy Test A* (fractions, proportions, percentages) and Test B** (descriptive statistics, data displays) explained 25% of the variance in Introductory Stats Exam scores. • But found no difference between statistics exam scores and maths entry grades (GCSE, A level, etc). Note *p<.05; **p<.001

  6. Does general numeracy ability predict statistics performance in psychology? • Despite the GCSE Maths prerequisite, many students still perform badly in this core module (British Psychology Society, 2003). • BPS QE quantitative methods syllabus requires little manual number manipulation. • Students are not required to learn formulae. • Perform minimal calculations by hand with analyses performed using SPSS, SAS, Minitab, etc. • Students must interpret computer-generated output correctly. • Raises questions over predictive validity of general numeracy skills/GCSE Maths performance.

  7. Does GCSE Maths predict psychology degree success? • Huws, Reddy, Talcott (2006): 1st Year 2nd Year FYP Final degree Maths GCSE .15 .12 .07 .19 English GCSE .12 .14 .10 .29* Science GCSE .27 .23 .35* .38** Note: **p<.01; *p<.05; n=56. A stepwise regression found GCSE science to be the single best predictor.

  8. The Winchester Numeracy Diagnostic • To what extent does the Winchester numeracy ‘diagnostic’ predict undergraduate statistics (exam) performance? • Diagnostic is a one hour test based on GCSE level maths questions. • Comprised of four sections: • Arithmetic (e.g. 0.25 <= 25% > 0.1) • Fractions/Decimals/Percentages (e.g. convert 1/5; 1/6; 3/20) • Statistics/Graphs (e.g. descriptive stats, graph interpretation) • Algebra (e.g. remove brackets and simplify: 5(2x + y) = 3(4x – 7y)

  9. Statistics Exam Content • Year 1: • Data to be entered into SPSS appropriately. • Data types, variables (IVs and DVs) and experimental designs to be identified. • Appropriate hypotheses to be evaluated/suggested. • Appropriate descriptive statistics, tables, graphs to be produced and interpreted. • Students to identify, conduct and report appropriate analysis to test given hypotheses (and check test assumptions). • Draw sensible conclusions and identify design flaws. • Year 2: • As Year 1 but with more complex experimental designs (e.g. mixed designs, factorial ANOVA). • Greater levels of critical analysis required. • Planned and post-hoc comparisons, tests of association/correlation, and data transformations also included.

  10. Fig. 1. All scores for Oct 2006 intake, by gender (10 males; 64 females).

  11. 2006 Intake (Y1 Stats Exam)Correlations: Arithmetic Stats F/D Algebra Stats Exam (Year 1) .46** .34** .12 .26* Table 1. Correlation coefficients between numeracy subcomponents (IVs) and Y1 stats exam (DV) Note n=74; **p<.01; *p<.05.

  12. Forced Entry (Enter) Regression: 2006 Intake (Y1 Stats Exam) Variable BSE Bβ Constant 28.89 11.24 Arithmetic .50 .16 .40** Statistics .12 .12 .14 Algebra .01 .08 .01 Fractions/Decimals -.04 .09 -.05 Note R² = .23; **p<.01.

  13. 2006 Intake (Y2 Stats Exam)Correlations: Arithmetic Stats F/D Algebra Stats Exam (Year 2) .23* .24* .21* .20* Table 1. Correlation coefficients between numeracy subcomponents (IVs) and Y2 stats exam (DV) Note n=74; *p<.05.

  14. Forced Entry (Enter) Regression: 2006 Intake (Y2 Stats Exam) Variable BSE Bβ Constant 19.98 15.27 Arithmetic .18 .22 .12 Statistics .08 .17 .08 Algebra .04 .11 .05 Fractions/Decimals .15 .12 .16 Note R² = .09.

  15. * Fig. 2. All scores for Oct 2007 intake, by gender (19 males; 72 females); *p<.05.

  16. 2007 Intake (Y1 Stats Exam)Correlations: Arithmetic Stats F/D Algebra Stats Exam (Year 1) -.01 .05 -.06 -.20 Table 1. Correlation coefficients between numeracy subcomponents (IVs) and Y1 stats exam (DV) Note n=91.

  17. Forced Entry (Enter) Regression: 2007 Intake (Y1 Stats Exam) Variable BSE Bβ Constant 60.02 9.35 Arithmetic .06 .16 .05 Statistics -.05 .10 -.06 Algebra -.24 .10 .30 Fractions/Decimals .15 .11 .19 Note R² = .07.

  18. Discussion • No major gender differences in numeracy and stats performance found. • Numeracy ‘diagnostic’ not successful at predicting performance on Year 1 and 2 Stats Exams. • Only the Arithmetic sub-component was a significant predictor, but accounts for only 23% of the variance for Year 1 Stats Exam in 2006 cohort only. • Gnaldi (2006) found descriptive stats numeracy sub-component accounted for most of the 25% of undergrad stats exam variance (followed by Fractions/Decimals/Percentages). • Results lend some support to Gnaldi’s (2006) finding of no relationship between entry maths qualification (e.g. GCSE, A level) and stats test performance. • And raise doubts over Mulhern and Wylie’s (2006) claim of an important relationship between general numeracy ability and stats performance.

  19. Conclusions • Important difference between numeracy ability and “mathematical literacy” (Hoyles et al., 2002). • Numeracy refers to abstract number manipulation and calculations, which are now usually performed by computers. • Mathematical literacy refers to the application of maths to real data outputs, work situations and practices (Hoyles et al., 2002). • Mathematical literacy (Hoyles, et al., 2002): • Systematic and precise data-entry techniques and monitoring. • Context-dependent, multi-step calculations and estimations (esp. with IT). • Modelling of variables/relationships. • Interpreting/transforming graphical/symbolic data. • Extrapolating results/trends across different domains. • Recognising anomalous/erroneous results/effects. • Concise clear communication of judgements. • These skills are more important for learning quantitative methods but are not well tested by the general numeracy tests (e.g. GCSE Maths).

  20. Conclusions and Future Directions • Is GCSE Maths a necessary pre-requisite for Psychology degree enrolment? • Follow-up paper to include all GCSE grades as predictors. • Other factors may also be worth exploring: • Cognitive style • Learning approach • Motivation/interest in subject • Personality/confidence • Emotional intelligence • Competitiveness

  21. Overall numeracy and stats exam performance (%) – 2006 intake* *n=74 (64 females; 10 males)

  22. Overall numeracy and stats exam performance (%) – 2007 intake* *n=91 (72 females; 19 males)

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