Why do spatial abilities predict mathematical performance?

Spatial ability predicts performance in mathematics and eventual expertise in science, technology and engineering. Spatial skills have also been shown to rely on neuronal networks partially shared with mathematics. Understanding the nature of this association can inform educational practices and intervention for mathematical underperformance. Using data on two aspects of spatial ability and three domains of mathematical ability from 4174 pairs of 12-year-old twins, we examined the relative genetic and environmental contributions to variation in spatial ability and to its relationship with different aspects of mathematics. Environmental effects explained most of the variation in spatial ability (~70%) and in mathematical ability (~60%) at this age, and the effects were the same for boys and girls. Genetic factors explained about 60% of the observed relationship between spatial ability and mathematics, with a substantial portion of the relationship explained by common environmental influences (26% and 14% by shared and non-shared environments respectively). These findings call for further research aimed at identifying specific environmental mediators of the spatial–mathematics relationship

Building and assessing subject knowledge in mathematics for pre-service students

In planning and teaching curriculum courses for pre-service primary teachers, both within a one-year Post Graduate Certificate of Education (PGCE) programme, and in a four-year undergraduate degree leading to Qualified Teacher Status (QTS), we have always been aware that mathematics presents particular problems because of the experiences and attitudes students bring to the subject. We have always tried to balance students’ learning about how children learn mathematics in school, with reflection on their own experiences as learners, and with understanding of the mathematical content of the curriculum. In the past, mathematical content has generally been approached indirectly through discussion of activities and materials appropriate for the primary classroom. However the recent introduction in the U.K. of a National Curriculum for Primary Mathematics in Initial Teacher Training (ITT) which places considerable emphasis on students’ subject knowledge, has meant that we have had to rethink the balance within courses, and to place much more overt emphasis on developing students’ mathematical knowledge. In this paper we describe the way in which we have approached building and assessing mathematical knowledge during the pilot phase of the ITT National Curriculum, examine some of the students’ responses to our approach, and discuss the issues this has raised

An experience of teacher education on task design in Colombia

We describe an experience in task design within an in-service secondary mathematics teacher education program in Colombia. Following a model known as didactic analysis, a team of researchers, educators, mentors and practicing teachers worked together in designing, implementing, assessing and reformulating secondary school mathematics tasks. We present here the main features of the framework on which the program is based, identify some of the characteristics of the experience lived by trainees, educators and researchers on task design during the first implementation of the program, and analyse the trainees’ assessment on their own proposals of tasks and on the contribution of the program on their task design competencies

On understanding and interpretation in mathematics: An integrative overview

For decades, understanding has been considered as a basic theme of interest and a research object in Mathematics Education. In this theoretical overview paper we present a integrative framework for organizing the diversity of results that emerge from the different studies on mathematical understanding and its interpretation. The proposal is applied onto a representation of relevant literature that has arise in the area over the last two decades. With this overview we seek to provide an useful reference for: (a) advancing towards a better insight of understanding in mathematics, (b) establishing the specific limitations and open questions that demarcate the boundaries of understanding and interpretation in mathematics, and (c) orienting its future study using a shared base of consolidated knowledge