Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, and James Hiebert
We use this editorial to propose some ideas for presenting and interpreting results with an eye toward addressing the “so what” question by leveraging the alignment among research questions, theoretical framework, and methods in a well-designed research study. Our aim is to present some practical ideas that could help researchers evaluate their findings with this question in mind.
Juan Pablo Mejía-Ramos and Keith Weber
We report on a study in which we observed 73 mathematics majors completing 7 proof construction tasks in calculus. We use these data to explore the frequency and effec-tiveness with which mathematics majors use diagrams when constructing proofs. At the end of the report, we discuss implications of our 3 key findings for pedagogy and future research.
Mirela Widder, Avi Berman, and Boris Koichu
Aiming to enhance understanding of visual obstacles inherent in two-dimensional (2-D) sketches used in high school spatial geometry instruction, we propose a measure of visual difficulty based on the ratio between 2 attributes of the sketches: potentially misleading geometrical information (PMI) and potentially helpful geometrical information (PHI). Practical, theoretical, and methodological implications are inspected and discussed.
Karisma Morton and Catherine Riegle-Crumb
Using data from a large urban district, this study investigated whether racial inequality in access to eighth-grade algebra is a reproduction of differences in prior opportunities to learn (as evidenced by grades, test scores, and level of prior mathematics course) or whether patterns reflect an increase in inequality such that racial differences in access remain when controlling for academic background. We considered how this varies by the racial composition of the school; further, we examined differences in access between both Black and Hispanic students and their White peers as well as differences between Black and Hispanic students. The results point to patterns of reproduction of inequality in racially integrated schools, with some evidence of increasing inequality in predominantly Hispanic schools.
Shulamit Kapon, Angela Halloun, and Michal Tabach
We compared students’ learning gains in authentic seventh-grade classrooms (N = 144) in 4 different interventions that incorporated a
computer game that aims to teach players to solve linear equations.
Significantly higher learning gains were measured in the implementations that
were specifically designed to mediate the attribution of algebraic meaning to
objects, actions, and rules in the game by engaging students in analogical
mapping between these constructs and their algebraic counterparts and an
exploration of the boundaries of this isomorphism. These findings suggest that
learning disciplinary content and skills from a digital game requires learners
to attribute disciplinary meaning to objects, actions, and rules in the game.
Moreover, this process does not necessarily occur spontaneously and benefits
from instructional mediation.
The editorial team is thanking
individuals who have served as guest editors and reviewers for manuscripts
submitted to the journal in 2018.
Index for
volume 50, covering January–November 2019 issues of JRME.