Navigating the Seas of Mathematics Education: New Waves in Research to Improve Student Learning

This issue focuses on research in the domain of mathematics education. Although mathematics has been a subject of study for many centuries, mathematics education is a relatively new field of scholarly inquiry, having been established as an independent field of research only in the early twentieth century. The most significant milestone was the establishment of the International Commission on Mathematical Instruction (ICMI) in 1908. Since 1969, ICMI has organized the International Congress on Mathematical Education, a quadrennial international meeting whose aim is to present the current states and trends in mathematics education research and in the practice of mathematics teaching at all levels

Mathematical Problem Posing as a Measure of Curricular Effect on Students\u27 Learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students\u27 learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students\u27 responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed

Impact of Curriculum Reform: Evidence of Change in Classroom Instruction in the United States

The purpose of the study reported in this article is to examine the impact of curriculum on instruction. Over a three-year period, we observed 579 algebra-related lessons in grades 6–8. Approximately half the lessons were taught in schools that had adopted a Standards-based mathematics curriculum called the Connected Mathematics Program (CMP), and the remainder of the lessons were taught in schools that used more traditional curricula (non-CMP). We found many significant differences between the CMP and non-CMP lessons. The CMP lessons, emphasized the conceptual aspects of instruction to a greater extent than the non-CMP lessons and the non-CMP lessons emphasized the procedural aspects of instruction to a greater extent than the CMP lessons. About twice as many CMP lessons as non-CMP lessons were structured to use group work as a method of instruction. During lessons, non-CMP students worked individually on homework about three times as often as CMP students. When it came to text usage, CMP teachers were more likely than non-CMP teachers to work problems from the text and to follow lessons as laid out in the text. However, non-CMP students and teachers were more likely than CMP students and teachers to review examples or find formulas in the text. Surprisingly, only small proportions of the CMP lessons utilized calculators (16%) or manipulatives (11%)

International Comparative Studies in Mathematics: Lessons for Improving Students’ Learning

Mathematics Education; International and Comparative Education; Learning and Instructio

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.

Mathematical problem posing: task variables, processes, and products

Mathematical problem posing (MPP) has been at the forefront of discussion for the past few decades, and a wide range of problem-posing topics have been studied. However, problem posing is still not a widespread activity in mathematics classrooms, and there is not yet a general problem-posing analogue to well-established frameworks for problem solving. This paper presents the state of the art on the effort to understand the cognitive and affective processes of problem posing as well as task variables of problem posing at the individual, group, and classroom levels. We end this paper by proposing a number of research questions for future studies related to task variables and processes of problem posing.Jinfa Cai would like to acknowledge the support of a grant from the USA National Science Foundation (NSF; Award #2101552)

Doing Research: A New Researcher’s Guide

This book is about scientific inquiry. Designed for early and mid-career researchers, it is a practical manual for conducting and communicating high-quality research in (mathematics) education. Based on the authors’ extensive experience as researchers, as mentors, and as members of the editorial team for the Journal for Research in Mathematics Education (JRME), this book directly speaks to researchers and their communities about each phase of the process for conceptualizing, conducting, and communicating high-quality research in (mathematics) education. In the late 2010s, both JRME and Educational Studies in Mathematics celebrated 50 years of publishing high-quality research in mathematics education. Many advances in the field have occurred since the establishment of these journals, and these anniversaries marked a milestone in research in mathematics education. Indeed, fifty years represents a small step for human history but a giant leap for mathematics education. The educational research community in general (and the mathematics education community in particular) has strongly advocated for original research, placing great emphasis on building knowledge and capacity in the field. Because it is an interdisciplinary field, mathematics education has integrated means and methods for scientific inquiry from multiple disciplines. Now that the field is gaining maturity, it is a good time to take a step back and systematically consider how mathematics education researchers can engage in significant, impactful scientific inquiry

An Investigation of Teachers\u27 Intentions and Reflections About Using Standards-Based and Traditional Textbooks in the Classroom

This study analyzed teachers’ intentions for and reflections on their use of Standards-based [Connected Mathematics Program (CMP)] textbooks and traditional (non-CMP) mathematics textbooks to guide instruction. In this investigation of the interplay between textbooks and instruction, we focused on learning goals, instructional tasks, teachers’ anticipation of students’ difficulties, and their perceptions of students’ achievement of learning goals. All of these are aspects of teachers’ intentions and reflections that have proved fruitful in comparing the roles of the CMP and non-CMP mathematics textbooks in our Longitudinal Investigation of the Effect of Curriculum on Algebra Learning project. Whereas the cognitive level of the teachers’ intended learning goals appeared generally to reflect the emphases of their respective textbooks, we found that the CMP teachers’ intended learning goals were not as well aligned with the CMP textbooks as the non-CMP teachers’ learning goals were aligned with their non-CMP textbooks. The CMP and non-CMP teachers’ implementations of the lessons seemed to reduce the degree of difference between the cognitive levels of their intended goals. Even so, we found that significantly more CMP lessons than non-CMP lessons were implemented at a high level of cognitive demand. Although the non-CMP teachers’ intended learning goals were better aligned with their textbook’s learning goals, we found that the CMP teachers were more likely than the non-CMP teachers to follow the guidance of their textbooks in designing and selecting instructional tasks for a lesson. Future research should consider other aspects of teachers’ intentions and reflections that may shed a broader light on the role of textbooks and curriculum materials in teachers’ crafting of instructional experiences for their students

Doing Research: A New Researcher’s Guide

This book is about scientific inquiry. Designed for early and mid-career researchers, it is a practical manual for conducting and communicating high-quality research in (mathematics) education. Based on the authors’ extensive experience as researchers, as mentors, and as members of the editorial team for the Journal for Research in Mathematics Education (JRME), this book directly speaks to researchers and their communities about each phase of the process for conceptualizing, conducting, and communicating high-quality research in (mathematics) education. In the late 2010s, both JRME and Educational Studies in Mathematics celebrated 50 years of publishing high-quality research in mathematics education. Many advances in the field have occurred since the establishment of these journals, and these anniversaries marked a milestone in research in mathematics education. Indeed, fifty years represents a small step for human history but a giant leap for mathematics education. The educational research community in general (and the mathematics education community in particular) has strongly advocated for original research, placing great emphasis on building knowledge and capacity in the field. Because it is an interdisciplinary field, mathematics education has integrated means and methods for scientific inquiry from multiple disciplines. Now that the field is gaining maturity, it is a good time to take a step back and systematically consider how mathematics education researchers can engage in significant, impactful scientific inquiry