Abstracts - Earli

knowledge about relatively simple mathematics problems are so closely intertwined thatdistinguishing between them is of limited practical value. However, the generalizability of thesefindings is unclear and should be the subject of further research. Implications for cognitivelearning theories, for educational practice, and for future studies are discussed.Contrasting cases in mathematics lessons support: Procedural flexibility and conceptualknowledgeJon Star, Harvard University, USABethany Rittle-Johnson, Vanderbilt University, USAEncouraging students to share and compare solution methods is a key component of reform effortsin mathematics in many countries, but experimental studies that more conclusively demonstratethe benefits of sharing and comparing ideas for student learning are largely absent. In a series ofstudies, we experimentally evaluated a potentially pivotal component of this instructional approachthat is supported by basic research in cognitive science: the value of students comparing multiplesolution methods. Our investigations focused on 10-12 year olds studying computationalestimation (e.g., mentally estimating the product of 23 * 57) and 13-14 year olds studying algebralinear equation solving (e.g., solving equations such as 3(x + 1) = 12). In all studies, studentslearned the mathematical content in one of two conditions (assigned randomly): 1) comparing andcontrasting alternative solution methods (i.e. contrasting cases), where two worked examples werepresented on the same page, accompanied by two reflection questions that asked students tocompare and contrast the two worked examples; or 2) reflecting on the same solution methods oneat a time, where the same worked examples were presented on two separate pages, with a singlereflection question focusing on only one worked example on each page. In both conditions,students worked with a partner in their regular mathematics classrooms to study and explainworked examples. Our results indicate that students in the contrasting cases group were moreaccurate in their performance on procedural knowledge items (including transfer items), showedgreater procedural flexibility, and also showed comparable gains in conceptual knowledge. Inparticular, comparison seemed to facilitate attention to and adoption of non-conventional methods.These findings suggest potential mechanisms behind the benefits of comparing contrastingsolutions and ways to support effective comparison in the classroom. Overall, it seems to pay tocompare.C 229 August 2007 08:30 - 10:30Room: 0.59SIG Invited SymposiumReflections on the "first principles of instruction"Chair: Tamara van Gog, OUNL, NetherlandsOrganiser: Jan Elen, Universiteit Leuven, BelgiumDiscussant: Jeroen van Merriënboer, OUNL, NetherlandsBased on a study of a variety of instructional design theories and models, Merrill (2002) putsforward five ‘first principles of instruction’ which uphold that learning is promoted when: 1.learners are engaged in solving real-world problems, 2. existing knowledge is activated as a– 121 –