Improving mathematics in key stages two and three:evidence review

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document Improving Mathematics in Key Stages Two and Three (Education Endowment Foundation, 2017). There have been a number of recent narrative and systematic reviews of mathematics education examining how students learn and the implications for teaching (e.g., Anthony & Walshaw, 2009; Conway, 2005; Kilpatrick et al., 2001; Nunes et al., 2010). Although this review builds on these studies, this review has a different purpose and takes a different methodological approach to reviewing and synthesising the literature. The purpose of the review is to synthesise the best available international evidence regarding teaching mathematics to children between the ages of 9 and 14 and to address the question: what is the evidence regarding the effectiveness of different strategies for teaching mathematics? In addition to this broad research question, we were asked to address a set of more detailed topics developed by a group of teachers and related to aspects of pupil learning, pedagogy, the use of resources, the teaching of specific mathematical content, and pupil attitudes and motivation. Using these topics, we derived the 24 research questions that we address in this review. Our aim was to focus primarily on robust, causal evidence of impact, using experimental and quasi-experimental designs. However, there are a very large number of experimental studies relevant to this research question. Hence, rather than identifying and synthesising all these primary studies, we focused instead on working with existing meta-analyses and systematic reviews. This approach has the advantage that we can draw on the findings of a very extensive set of original studies that have already been screened for research quality and undergone some synthesis. Using a systematic literature search strategy, we identified 66 relevant meta-analyses, which synthesise the findings of more than 3000 original studies. However, whilst this corpus of literature is very extensive, there were nevertheless significant gaps. For example, the evidence concerning the teaching of specific mathematical content and topics was limited. In order to address gaps in the meta-analytic literature, we supplemented our main dataset with 22 systematic reviews identified through the same systematic search strategy

Engineering students' actions in a mathematical modelling task: Mediating mathematical understanding in a computer algebra system

Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have challenges pertaining to their mathematical understanding of their actions with a computer algebra system (CAS). We investigated how a mathematical modelling task could mediate varied levels of mathematical understanding. When engineering students are exposed to a CAS environment, they habitually engage in programming activities without considering the computerised outputs. The purpose of this paper was to ascertain South African engineering students’ actions that can mediate broader levels of mathematical understanding in a CAS by utilising the Pirie- Kieren model of growth in mathematical understanding. Thirteen participants agreed to engage collaboratively in a mathematical modelling task. The task was analysed by means of content analysis following a deductive research approach. The findings disclosed that engineering students interdepend on paper-and-pen, computerised and reflective actions in their growth of mathematical understanding. Engineering students can be assisted in mediated and folding-back actions in order to fluctuate back and forth on their way to a more sound mathematical understanding. Explicit planning and sequence of subtasks can support engineering students to merge new levels of mathematics understanding with past comprehensions. Thoroughly planned modelling tasks can mediate novel levels of mathematical understanding when engineering students learn with a CAS

Teacher Perception of Technology as a Conduit to Acquiring Critical Thinking Skills

Seventh-grade and eighth-grade special education students struggle to learn higher-order thinking skills in pre-algebra and algebra that can be addressed by using technology. However, little is known about science, technology, engineering, and math (STEM) teachers\u27 attitudes toward use of and their actual use of calculators and technology to access students\u27 development of higher-order thinking skills. The purpose of this qualitative case study was to explore the perceptions of rural middle school Grade 7 and 8 STEM teachers in one Western state. This study used Gardner\u27s multiple intelligences and Armstrong\u27s neurodiversity theories as a framework. Participants were 10 Grade 7 and 8 STEM teachers in a Western state. Data sources included interviews, surveys, and teacher journals. Open coding allowed the identification of similar threads, common words, or expressions that were then examined for themes and patterns. The emergent themes included a need for training, teachers\u27 technological expectations, and whether teachers could meet grade level standards and students have success. This study assists social change by informing school administrators and teachers how technology is and is not being used in the classroom and how its use can be facilitated in the future

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland