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

An Investigation of Students' Learning of Integral Calculus with Maple Software and Paper-Pencil Strategies in the Western Region of Ghana.

The goal of the research was to look into the impact of Maple software instruction on senior high school students' understanding of integral calculus. The study adopted a mixed-method design comprising qualitative and quantitative research designs. The researcher used both purposive and simple random sampling techniques to select one hundred (100) participants: fifty (50) participants for the control group and fifty (50) participants for the experimental group. The data collection instruments used in the study were an interview, pre-test and post-test. Data analysis was carried out using descriptive statistics and an Independent Samples t-test. The study found that 7(7%) participants found it difficult to execute correct substitution of the lower and upper limits of definite integral questions. Moreover, most of the participants, 35(35%), omitted the constant of integration after responding to the indefinite integral test item of the pre-test. It was noted that 18(18%) of the participants could not correctly integrate the polynomial or quadratic function administered to them. The independent samples t-test analysis of the post-test scores for the experimental and control groups revealed a statistically significant difference between the experimental group (M = 24.80; SD = 9.48) and the control group (M = 20.65; SD = 7.67). The estimated t-statistic was (t = 2.986; p = 0.005). This shows that Maple Software's experimental group outperformed the control group using the paper and pencil strategy. The analysis of the interview data indicated that Maple Software has contributed to the success of students’ achievement in the integral calculus by arousing and sustaining the student’s interest. The Maple Software also made it easier for students to follow the calculus instruction. The findings recommended that technology and mathematical software should be used in the teaching and learning of integration at schools

A case study of collaborative learning among preparatory year students and their teachers at Hail University in Saudi Arabia

The concept of collaborative learning (CL) relates to the educational use of small groups, in which students work together to maximise their learning and to teach and learn from each other as much as possible, after receiving guidelines and instructions from their teachers. Collaborative learning in Saudi higher education (SHE) has been promoted at the government level in recent years as part of a trend to increase the adoption of e-learning. The policy also aligns with educational reforms and the drive to make the Saudi economy more competitive and diverse. Nevertheless, it is still enforcing itself to become a norm in the teaching and learning process as it is a radical shift from the traditional centralised decision making in educational settings and teacher-centred teaching, which indicate a high power distance structure. Therefore, this study investigates the perceptions of preparatory year students and teachers at Hail University regarding the implementation of CL. A qualitative research methodology was adopted. Data were gathered from observations, six focus groups (composed of five students in each group) and individual interviews with 12 teachers on the foundation year. The findings of this study indicated two modalities for deploying CL: traditional CL (TCL/non-computer- supported collaborative learning [CSCL]) and computer-supported CL (CSCL) in Saudi higher Education. Furthermore, the results showed that CL indeed provides personal, social, and academic benefits. It is still, however, marred by challenges such that effective implementation is curtailed and thus does not produce positive learning outcomes among students. Overall, given the cultural background, the preference for retaining a high power distance, and what teachers and students are accustomed to, the study suggests further research be conducted to implement an form of CL adapted to suit Saudi culture

Developmental Students\u27 Perceptions of Unsuccessful and Successful Mathematics Learning

The purpose of this phenomenological study was to describe what experiences, attitudes, and learning strategies developmental mathematics students believed contributed to their failure to gain basic math skill proficiency in the past and what experiences, attitudes, and learning strategies these students now believed were most likely to enhance the successful learning of basic math skills. To gain an understanding of the lived experiences of successful developmental mathematics students who were previously unsuccessful, structured, open-ended interviews were conducted, classroom observations were made, and formative and summative assessments for the students were collected. Fourteen students from a western 4-year college were selected purposefully based on instructor recommendations and preliminary survey results. The students, who were eight males and six females, ranged in age from 19 to 51. Seven were considered traditional students and seven nontraditional. Based on the data analysis, five prevalent themes emerged: turning point, attitude, motivation, learning environment, and learning strategies. Motivation was the most common reason given as the difference between being unsuccessful and successful math skill development. Underlying their motivation were the students\u27 own beliefs. In the unsuccessful period, every student had the fixed mindset of not being capable of learning mathematics. When successful, the students exhibited a growth mindset, believing that if they exerted time and effort, they would be able to learn. This mindset made the difference in their motivation and attitude. Previously they hated mathematics. When successful, students actually enjoyed learning mathematics and expressed confidence that they would be successful in the subsequent course. When unsuccessful, students were field dependent. Most were children or adolescents. They had no control over their learning environment or selection of learning resources. The predominant coping strategy was one of avoidance. When successful, students were more field independent. They could choose their teachers and actively seek learning resources. When asked what changes in their K-12 experience would have helped them be more successful, the students paradoxically suggested that a close monitoring of their progress might have made a difference. However, during their unsuccessful period, students did everything they could to avoid being labeled as needing help