The purpose of this study was to investigate the effects of multiple representations-based instruction on seventh grade students&amp / #8217 / algebra performance, attitudes toward mathematics, and representation preference compared to the conventional teaching. Moreover, it was aimed to find out how students use multiple representations in algebraic situations and the reasons of preferring certain modes of representations. The study was conducted in four seventh grade classes from two public schools in Ankara in the 2003-2004 academic year, lasting eight weeks. For assessing algebra performance, three instruments called algebra achievement test, translations among representations skill test, and Chelsea diagnostic algebra test were used. To assess students&amp / #8217 / attitudes towards mathematics, mathematics attitude scale, to determine students&amp / #8217 / representation preferences before and after the treatment representation preference inventory were administered. Furthermore, as qualitative data, interview task protocol was prepared and interviews were carried out with the students from experimental and control classes. The quantitative analyses were conducted by using multivariate covariance analyses. The results revealed that multiple representations-based instruction had a significant effect on students&amp / #8217 / algebra performance compared to the conventional teaching. There was no significant difference between the experimental and control groups in terms of their attitudes towards mathematics. The chi square analyses revealed that treatment made a significant contribution to the students&amp / #8217 / representation preferences. The results of the interviews indicated that the experimental group students used variety of representations for algebra problems and were capable of using the most appropriate one for the given algebra problems.

The current study assessed an error reflection intervention on Algebra I students’ conceptual and procedural knowledge and sense of belonging to mathematics. Also of interest was whether perceptions of the functionality of errors mediated the effect of condition on learning and sense of belonging to mathematics. Middle school students (N = 207) were randomly assigned within classroom to one of four conditions: 1) a Problem-Solving Control group, 2) a Correct Examples Control group, 3) a Correct Examples Error Reflection condition that promoted reflection on hypothetical errors through self-explanation prompts, or 4) an Incorrect Examples Error Reflection condition that promoted reflection on displayed errors within the example through self-explanation prompts. Conceptual and procedural knowledge, sense of belonging to mathematics and perceived functionality of errors were measured pre- and post-intervention. After controlling for unanticipated clustering effects, results suggest that reflecting on and explaining errors within a worked examples intervention is just as effective at promoting learning as traditional problem solving alone or working with traditional correct worked examples and written self-explanation prompts. Students’ sense of belonging to mathematics or perceived functionality of errors for learning were high at the start of the study and remained so throughout the intervention. Perceptions of the functionality of errors were unrelated to learning and sense of belonging to mathematics. The limited size of the minority population in the sample did not allow for exploration of differential effects of condition for underrepresented minority (URM) students. However, these students reported lower feelings of belonging to mathematics than non-URM students. Implications for theory and practice are discussed. / Educational Psychology