1. Targeting points of high working memory load: Expertise reversal effects Paul Ayres (p.ayres@unsw.edu.au) School of Education, University of New South Wales 3rd International CLT Conference Heerlen, NL 2 March 2009

2. The trouble with brackets Ayres (2001) -3(-4 - 5x) - 3(-3x - 4) Op 1 Op 2 Op 3 Op 4 –3(–4) -3(–5x) -3(-3x) -3(-4) Op-2 > Op-1, Op-4 > Op-3, Br-2 > Br-1

3. Evidence of WM load causing errors Verbal protocols (Ayres, 2001) Dual tasks (Ayres, 2001) Subjective measures within problems (Ayres, 2006: L & I)

4. What would be helpful instruction? For novices this is fairly complex domain- high in element interactivity Need to deal with Intrinsic CL Isolating elements (Pollock, Chandler & Sweller, 2002) Pollock et al. proposed a two stage learning experience. During the first phase, learning is conducted element-by-element, leading to some partial schemas being acquired.

5. Ayres (2006 Appl. Cog. Psych.) Complete Group 5 (3x - 4) - 2 (4x - 7) = 5 * 3x + 5 * -4 - 2 * 4x - 2 * -7 = 15 x - 20 - 8x + 14 Single (isolated) Group -5 (3x - 4) - 2 (4x - 7) = -5 * 3x = - 15x

6. Results Expertise reversal effect For students with below mathematical ability the isolated strategy was effective. For students with above average mathematical ability it was not effective- CL measures suggested low engagement. However, the error profiles remained Hypothesis: extra practice at points of greatest WM load will lead to greater learning.

7. The present study: Targeting strategy 90 grade 8 students: 47 above average in math ability, 43 below average. Equal group:Isolated single calculations equally distributed over four operations during acquisition Targeted group: Isolated single calculations : three times as many on operations 2 and 4 compared with 1 and 3. Design Acquisition phase: 4 pairs of worked examples (16 calculations). Study one- complete one alternation. A nine-point self-rating scale ( see van Gog & Paas, 2008 ) Test phase: 8 complete bracket expansion tasks.

8. Means from Exp. 1 High AbilityLow Ability EqualTargetEqualTarget Acq.(36)31.131.431.530.8 CL (9)2.52.72.32.5 Test (8)6.46.86.45.5 Effic.0.060.130.21-0.34

9. Statistical tests Acquisition: Ability F < 1 ; Strategy: F < 1 Interaction: F= 4.0, p < 0.05; no simple effects CL measures: All F < 1 Test scores: Ability F=5.0, p < 0.03; Strategy F < 1 Interaction F = 4.4, p < 0.04 Simple effects High ability t < 1; Low ability t = 1.97, p = 0.055 Efficiency: All F < 1

10. Summary Expertise reversal effects present again Students with above average mathematical ability benefited from a targeting approach, but students below average didn’t. For the latter it is plausible that the targeting format was too far removed from the full problems to be meaningful.

11. Exp 2 Exact test of relevant mathematical ability (2 groups) Full worked example group added (3 x 2 Design) Transfer questions Same design –Acquisition –CL measures (Difficulty- see van Gog & Paas) –Test –Transfer

12. Means from Exp. 2 Low AbilityHigh Ability TotalSingleTargTotalSingleTarg Acq.(32)23.317.118.328.429.828.4 CL (9)4.52.63.02.11.6 Test (16)10.69.310.315.214.915.2 Trans (12)4.95.13.910.59.310.1

13. Analysis Acquisition: Strategy F < 1 ; Interaction: F < 1 Ability: F= 15.5, p < 0.001 CL measures: Ability F = 15.6, p <0.001 Strategy: F = 3.7, p Isolated groups Interaction, F < 1. Test scores: Ability F = 22.4, p < 0.001; Strategy F < 1 Interaction F < 1

14. Transfer Ability F = 42.7, p < 0.001 Strategy: F < 1 Interaction F = 4.0, p < 0.05, Simple Effects –High Ability, F < 1.5 –Low Ability; Isolated > Targeted Efficiency (transfer) Ability; F = 29.5, p Low Strategy: F = 3.3, p < 0.05, Combined ability: Targeted > Total worked example Interaction, F < 1

15. Efficiency (Test) Ability; F = 19.0, p Low Strategy: F = 4.3, p < 0.02, Combined ability: Targeted > Total worked example Interaction, F < 1

16. Summary Low ability students –Single isolated > targeted on test scores (Exp. 1) –Single isolated > targeted on transfer scores (Exp. 2) High Ability Students –No differences between groups Overall ability effects –CL measures: full worked examples had greatest CL measures –Both efficiency measures (Targeted > full worked examples)