Abstracts - Earli

Strategy flexibility in the domain of multi-digit arithmetic: children’s use of compensation andindirect addition strategiesJoke Torbeyns, K.U.Leuven, BelgiumLieven Verschaffel, K.U.Leuven, BelgiumPol Ghesquiere, K.U.Leuven, BelgiumThis study aimed at analyzing the developmental changes in children’s strategy flexibility in thedomain of multi-digit addition and subtraction. Strategy flexibility was defined on the basis of thenumber characteristics of the items, i.e. as using compensation (45+19=45+20-1=65-1=64) andindirect addition (71-69=.; (69), 70, 71; so the answer is 2) strategies on those items that can besolved efficiently with the respective strategies. One-hundred-ninety-five second-, third-, andfourth-graders solved a series of two-digit additions and subtractions twice. In the first task, theywere instructed to solve each item as accurately and as fast as possible with their preferredstrategy. In the second task, they were asked to solve all items with at least two different strategies.Results showed that children hardly used compensation and indirect addition strategiesspontaneously in the first task, and thus did not flexibly apply these strategies on the items that canbe answered efficiently with compensation and indirect addition strategies. Moreover, second- andthird-graders hardly reported compensation and indirect addition as an alternative strategy in thesecond task, indicating that they did not know (and therefore did not spontaneously use) thesestrategies. Fourth-graders reported compensation, but not indirect addition, as an alternativestrategy in the second task, suggesting that they knew the first, but not the second, strategy. Theseresults are interpreted in terms of the viability of different instructional approaches to enhance theacquisition of adaptive expertise.Teaching Mathematics in classes of different levelsRuhama Even, Weizmann Institute of Science, IsraelTova Kvatinsky, Talpiot College of Education, IsraelThis study challenges a commonly held view that teachers tend to adopt a more traditionalteaching method when teaching in classes of lower achieving students. The study comprises twocase studies, each of a teacher who teaches the same syllabus in two classes of different levels.Quantitative and qualitative analyses of observed teaching practices and classroom interactions in46 lessons suggest that one teacher adopts the "transmission of knowledge" approach in both herclasses, emphasizing basic skills and rote learning; whereas the other teacher emphasizes morethinking, understanding and problem solving. Surprisingly, both teaching profiles were enhancedin the lower level class of each teacher. The findings suggest that in her own way, each teacheraimed to help more the students who encountered more difficulties – the lower achieving students– and she did it by using the resources available to her. Theoretical and practical implications willbe discussed.Investigating student learning gains using the Teaching Mathematics Observation Schedule(ToMOS)Sarah Hopkins, University of Western Australia, AustraliaHilary Hollingsworth, Education Consultant, AustraliaWilliam Louden, University of Western Australia, AustraliaThis paper presents the findings from the first phase of a large scale investigation of studentlearning gains and the effective teaching of mathematics. Numeracy achievement scores werecollected for 2864 students (132 classrooms) at the end of Year 7 and Year 8. These scores were– 76 –