This study shares two frameworks for analyzing teacher actions that support students in generalizing and examines how those frameworks align with teacher questioning. One classroom teaching episode focused on the mathematical activity of generalizing is shared to illustrate effective generalizing promoting practices. We found several patterns of…

High school calculus has become indispensable for students seeking a college degree in a STEM field. However, in the present study, we argue that the mathematics opportunities that students seize (when afforded) in middle grades are the key to earning calculus credit in high school. To take calculus in high school, students usually need to take…

Decades after the 1954 "Brown v. Board of Education of Topeka" unanimous decision to desegregate schools, the ideology of Black people having equal educational opportunities has not been realized; Black people continue to lag in educational attainment. However, the inequalities in life experiences between Black and White people limit the…

Two set of studies were conducted to better understand grades and grading practices in physics courses, and how these might influence demographic representational disparities in physics. The first study investigates the relationships between grades and the student-level factors of standardized test scores, (binary) gender, underrepresented…

In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners' learning and a teacher's beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…

Corequisite remediation involves placing students who have been designated as underprepared directly into college-level courses with concurrent supports--such as in-class tutoring, online learning labs, or a supplemental class--rather than making them take non-credit-bearing developmental courses first. Despite the growing number of studies on…

The Education Week Spotlight on Improving Math Fluency is a collection of articles hand-picked by editors for their insights on the importance of math fact fluency, the challenges students face with word problems, how teachers can optimize how they introduce math facts and better support students, how early math supports help vulnerable students,…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

The identification of students at risk for academic failure in undergraduate chemistry courses has been heavily addressed in the literature. Arguably one of the strongest and most well-supported predictors of undergraduate success in chemistry is the mathematics portion of the SAT (SAT-M), a college-entrance, standardized test administered by the…

In this paper I analyze students' conceptual understanding of the quality of polynomial approximation. In particular, I analyze to what extent the interactive play with various methods of interpolation enables the students to build visual pictures that help understanding the formal mathematical statements. The role of the Mathematica software in…

In this Research Commentary, the author explores what is meant by "teaching for understanding" and delves into these questions: How does teaching for understanding interact with the backgrounds of the students who experience it or the attributes of the contexts in which they learn? Which empirical findings are context dependent, and…

Many high schools use online courses to allow students to retake failed classes in an effort to help get students back on track and graduate. However, there is limited evidence available on the effectiveness of online credit recovery in improving students' long-term outcomes compared with traditional face-to-face credit recovery courses. In this…

A web-based education system was designed within the scope of a project to ensure the professional development of middle school mathematics teachers. This system was designed in a way to allow teachers to prepare a Hypothetical Learning Trajectory and lesson plan related to the algebra learning content and also to give feedback to these contents…

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students' (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early…