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Proceedings of the Fourth Annual Teachers College Educational ...

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Derived Facts 0 1<br />

Quick 88** 164**<br />

Note. The strategies are listed in <strong>the</strong> order <strong>of</strong> typical development.<br />

**significant at p < .001<br />

Table 2: Strategy Use by Condition for Low Block (n = 23)<br />

Looking at <strong>the</strong> participants’ strategy use helps indicate why <strong>the</strong>y are less accurate. Participants in <strong>the</strong> lowblock<br />

multiple-character condition are more likely to be using an advanced strategy (see Table 2). Given<br />

that <strong>the</strong>y use an advanced strategy, <strong>the</strong>y are not more likely to be accurate, but <strong>the</strong>y are more likely to be<br />

near <strong>the</strong> answer on <strong>the</strong>ir first or second attempt (see Table 3).<br />

Score<br />

Exact Answer<br />

(on first attempt)<br />

Near Answer<br />

(+ or – 1 on first attempt)<br />

3<br />

Near on ei<strong>the</strong>r attempt<br />

Single Multiple Single Multiple Single Multiple<br />

0 841 877 830* 831* 815* 813*<br />

1 148 178 159* 224* 174* 242*<br />

Note. A score <strong>of</strong> 1 indicates both use <strong>of</strong> an advanced strategy and meeting <strong>the</strong> column<br />

criteria, whereas 0 indicates a non-advanced strategy and/or not meeting <strong>the</strong> column criteria.<br />

* significant at p < .05<br />

Table 3: Effective Use <strong>of</strong> Advanced Strategies by Condition for Low Block (n = 23)<br />

Discussion<br />

Improved performance on addition tasks should not be judged based on accuracy alone. A careful<br />

analysis <strong>of</strong> strategy use in conjunction with exact accurate and near accurate answers gives a more<br />

complete picture <strong>of</strong> children’s development. Looking at accuracy alone, <strong>the</strong> hypo<strong>the</strong>sis that multiple<br />

characters improve addition performance would be rejected, especially for lower performing students. Yet<br />

also analyzing strategy and near accuracy reveals that multiple characters may be helping <strong>the</strong>se lower<br />

performing students to take more risks and try out new, more advanced strategies. More research is<br />

needed to determine if taking risks in trying out new strategies helps students to become more accurate<br />

over time and to investigate why <strong>the</strong> multiple characters encourage <strong>the</strong>se risks.<br />

References<br />

Baylor, A. L., & Ebbers, S. (2003). The pedagogical agent split-persona effect: When two agents are<br />

better than one. ED-MEDIA (pp. 1-5). Honululu, Hawaii.<br />

Carpenter, T. P., & Moser, J. M. (1984). The acquisition <strong>of</strong> addition and subtraction concepts in grades<br />

one through three. Journal for Research in Ma<strong>the</strong>matics Education, 15(3), 179-202.<br />

Moreno, R., Mayer, R. E., Spires, H. A., & Lester, J. C. (2001). The case for social agency in computerbased<br />

teaching: Do students learn more deeply when <strong>the</strong>y interact with animated pedagogical<br />

agents? Cognition and Instruction, 19(2), 177-213.<br />

Piaget, J. (1929). Introduction: Problems and Methods. The Childʼs Conception <strong>of</strong> <strong>the</strong> World. London:<br />

Routledge and Kegan Paul.<br />

Siegler, R. S. (1987). The Perils <strong>of</strong> Averaging Data Over Strategies : An Example From Children's<br />

Addition. Journal <strong>of</strong> Experimental Psychology, 116(3).<br />

White, B. Y., Shimoda, T. A., & Fredericksen, J. R. (2000). Facilitating students inquiry learning and<br />

metacognitive development through modifiable s<strong>of</strong>tware advisers. In S. Lajoie (Ed.), Computers as<br />

cognitive tools vol 2: No more walls (pp. 97-132). Mahwah, NJ: Lawrence Earlbaum.

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