Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.

Experiencing Manipulative Material for the Teaching and Learning of Mathematics

This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

Cooperative Learning Groups in the Middle School Mathematics Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the inclusion of cooperative learning groups. Data was collected to see how cooperative learning groups affected oral and written communication, math scores, and attitudes toward mathematics. On the one hand, I discovered that many students enjoyed the opportunity to work within a group. On the other hand, there continues to be a handful of students who would rather work alone. The benefits outweigh the demands. Overall, students benefitted from the inclusion of cooperative learning groups. Oral explanations of solutions and methods improved during the study. Written expression also improved over this time period. As a result of this research, I plan to continue with the incorporation of cooperative learning groups in the middle school math classroom.

Cooperative Learning in Relation to Problem Solving in the Mathematics Classroom

In this action research study of my classroom of 5th grade mathematics, I investigated cooperative learning and how it is related to problem solving as well as written and oral communication. I discovered that cooperative learning has a positive impact on students’ abilities in problem solving and their overall impression of mathematics and group work. I also found that my students’ communication skills improved in oral explanations of their work. As a result of this research I plan to continue my implementation of cooperative learning in my classroom as a general method of teaching. I also plan to continue to use cooperative learning in working with my students to increase their achievement in problem solving and communication of mathematics.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.

Learning and Assessing Competencies: New challenges for Mathematics in Engineering Degrees in Spain.

The introduction of new degrees adapted to the European Area of Higher Education (EAHE) has involved a radically different approach to the curriculum. The new programs are structured around competencies that should be acquired. Considering the competencies, teachers must define and develop learning objectives, design teaching methods and establish appropriate evaluation systems. While most Spanish universities have incorporated methodological innovations and evaluation systems different from traditional exams, there is enough confusion about how to teach and assess competencies and learning outcomes, as traditionally the teaching and assessment have focused on knowledge. In this paper we analyze the state-of-the-art in the mathematical courses of the new engineering degrees in some Spanish universities.

Pursuing excellence : a study of U.S. eighth-grade mathematics and science teaching, learning, curriculum, and achievement in international context /

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