This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

Despite extensive research suggesting the importance of students developing strong foundational math skills during early grades, more than 60% of 4th graders in the United States lack proficiency in mathematics. Such data are influenced by several factors, including summer learning loss in math, negative impacts from the COVID-19 pandemic, and a…

We report on a case study of eight grade 5 to 6 students (ages 12-14) involved in a three-day "digital-making summer camp" focused on mathematical problem-solving through block-based programming combined with programmable electronics. Data analysis focused on the computational thinking (CT), mathematics, and problem-solving challenges…

Rehearsals have become an increasingly popular pedagogy to support preservice teachers in developing competency in enacting challenging instructional practices and communicating associated pedagogical commitments. To understand how best to support learners participating in rehearsals, researchers have begun to analyse the facilitation of teacher…

In this "Perspective on Practice," we describe an application of recommendations made in "Formative Assessment in Secondary ­Mathematics: Moving Theory to Recommendations for Evidence-Based Practice" (Kenney et al., 2022), which was recently published in this journal. The authors made recommendations for mathematics teacher…

Proof is a fundamental aspect of mathematics. However, in the high school curriculum, it often receives uneven attention that is focused on form rather than understanding. One avenue for addressing this issue is to change and strengthen teachers' conceptions of proof. To explore this idea, we followed a group of teachers as they participated in a…

Mathematics educators and researchers have increasingly integrated social justice-oriented tasks into their classrooms. Teaching mathematics for social justice (TMfSJ) aims to help students develop mathematical knowledge in ways that promote students' abilities to critique the communities of which they are members (Ellis & Malloy, 2007;…

Summer bridge programs are the second most common student support program in the United States. Though they vary in design, most are focused on supporting students who are at risk. Programs vary in terms of their curricular offerings as well. This study examined the ex post facto data from a summer bridge program at Manchester Community College in…

Summer numeracy interventions have become standard educational practice across a range of jurisdictions, but there is a paucity of evaluations of those interventions across international settings. We employ a quasi-experimental evaluation of voluntary summer numeracy programs for 569 attendees and 2,193 comparison students in grades 1-3, conducted…

Out-of-school learning opportunities can improve student academic achievement and support social-emotional learning. Such programming is valued by the public and in high demand. Teachers can also benefit from seeing students engage in learning in contexts that promote creativity, safe risk-taking, and a tolerance for ambiguity and failure. This…

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and…

The manuscript describes a community-based mathematical modeling task that was implemented in a Calculus I classroom to engage students in mathematical modeling. Twenty-five undergraduate students engaged in this activity. These students selected a context that they found interesting, posed questions, developed constraints, came up with solution…

Computational thinking (CT) has great potential for enhancing mathematics and science lessons in K-12 education. Numerous studies demonstrate that under the right circumstances, CT integration in math and science can improve student learning and promote deeper understanding. However, teacher education currently does not include preparation for…

Urban school districts have seen low scores on NWEA Map math scores (Education Recovery Scoreboard, 2024). To foster and promote urban youths' capabilities to learn mathematics, a new method to teach, enhance, and remediate understanding of fractions was developed, Fractions and Signed Numbers Workshop (FracSi). It utilizes the approach of an…

Many researchers have debated potential differences between male and female students' mathematical performance. One important factor that can impact performance is perception of the content. The purpose of the study is to investigate factors that impact high-ability male and female students' perspectives of mathematics. Participants (n = 12;…