An algebraic model uses a set of algebraic equations to describe a situation. Constructing such models is a fundamental skill, but many students still lack the skill, even after taking several algebra courses in high school and college. For such students, we developed instruction that taught students to decompose the to-be-modelled situation into…

Recent research syntheses have identified several potentially high-leverage teaching strategies for improving low-attaining secondary school students' learning of mathematics. These strategies include the structured use of representations and manipulatives and an emphasis on derived facts and estimation. This paper reports on 70 semi-structured…

We collected data on students' self-assessment behavior from four sections of a Calculus II course. Students were asked to write their expected scores on each of the weekly in-class quizzes and problems in the exams, immediately after they completed them. They were then asked to justify their expectation in writing. One-on-one interviews were…

Within scientific debate on post-digital and education, we present a position paper to describe a research project aimed at the design of a predictive model for students' low achievements in mathematics in Italy. The model is based on the INVALSI data set, an Italian large-scale assessment test, and we use decision trees as the classification…

Realistic Mathematics Education (RME) relies on the pedagogy of guided reinvention, in which opportunities for learning are created through the teacher's orchestration of whole-class mathematical discussion towards a specific goal. However, introducing an RME approach to students who are accustomed to traditional teaching requires a substantial…

Background: Past studies clarified the relationship between dimensions of teaching and achievement emotions. However, more information is needed about the underlying process behind this relationship among students with different mathematical abilities. Aims: This study examined the association between students' perceived teaching quality and…

Background/Context: As part of a national movement to eliminate a global tracking system that disproportionately assigned underserved students to low-level math classes, the Chicago Public Schools (CPS) mandated academic algebra for all students entering high school in 1997. The results were disappointing: low-skill students experienced elevated…

Teacher dashboards provide real-time information about students' performance and progress, which help K-12 teachers to adjust feedback to student' specific needs during learning. Prior research indicated two problems with respect to how teachers provide feedback: (i) teachers do not always select the most effective feedback to support student'…

Background: Early numeracy interventions including basic arithmetic are crucial for young students at risk for early mathematics difficulties (MDs), yet few studies have evaluated numeracy interventions in second grade with a randomized controlled design. Aim: This pre- and post-test randomized controlled study evaluated the effects of an…

Running two separate two-stage randomized trials, we implement and test three variants of a small group instruction intervention aimed at improving mathematics competencies for the 20% lowest achievers in mathematics in grades 2 and 8 in Danish public schools. We calculate immediate impacts on math competencies as well as impacts in the medium…

Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

Collaborative problem-solving (CPS) has been widely used in K-12, higher education, and informal learning to enhance the quality of student learning. Understanding the relationship between learning engagement and group performance is crucial for CPS pedagogy and analytics. However, few empirical studies investigated individual engagement role…

The aim of this longitudinal study was to examine the differences between high- and low-performing students' development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n =…

A strong foundation in math is crucial for critical thinking, future careers, and navigating our data-driven world. This Spotlight will help readers identify new initiatives to address gaps in students' math skills; catch up on the debate over the best way to teach math; learn how teachers can build on students' curiosity for math; explore how to…

We investigated the adequacy of the conduct and possible benefits of the use of dynamic maths interviews by 19 fourth grade teachers with students showing low maths achievement to facilitate the identification of maths needs. This study shows the potential of an analytical framework to evaluate the adequacy and benefits of dynamic maths interviews…