All students want to talk about ideas that interest them, but often, multilingual learners are not offered high-challenge, high-support opportunities to connect everyday experiences to mathematical ideas. We describe a single class period that connects students' everyday opinions with two-way tables and notions of independence.

Previous research has shown that students form fragmented understandings about variability even after instruction and that these primitive notions function as obstacles to a robust understanding of variability. To investigate the effect of disruptions to students' primitive notions of variability, we examined undergraduate students' reasoning…

Caregiver involvement in homework is a key contributor to student success, yet its interaction with intelligent tutoring systems remains underexamined. To address this gap, we conducted a technology probe study exploring how a conversational support tool might enhance caregiver assistance during remote math homework within tutoring systems.…

Several publishing companies now offer competing brands of online homework (OHW) software. Students rarely have a voice in choosing their required course materials, even though, ultimately, they will be asked to use and pay for these systems. In this study, Calculus I students each tested three different OHW systems. The students were then asked…

Prior studies identified effective, but mainly non-digital, homework aids. This research involved 18 middle school students in a lo-fi prototyping study to integrate traditional homework support tools with intelligent tutoring systems (ITS), leveraging rich log data for personalized learning. Feature investigations in standardized diaries, goal…

Previous research on how UK schools can meet the needs of refugee students has not focused on Ukrainian refugee students' learning of mathematics. This group faces specific challenges, simultaneously studying different mathematics curricula, face-to-face in the UK and by distance in Ukraine. We examine the experiences of Ukrainian refugees in UK…

In an online asynchronous vector calculus course, we observed exam answers solved with a formula from online homework instead of the formula from lecture. Our exploratory study investigated (1) why students learned from homework instead of lecture for this topic and (2) their epistemological frames (e-frames) for lecture and homework. Per (1),…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

The present study used a multilevel approach to investigate the influence of four clusters of variables (i.e., demographic, homework, teacher, and parent) on three types of math homework purposes (i.e., academic, self-regulatory, or approval-seeking) perceived by 3,018 8th graders in China. Results revealed that each of the three math homework…

Mathematically gifted students have skills that may help to improve the country. However, those gifted students attend to regular mathematics classes and undertake the same curriculum at the same pace with other students. Their cognitive or psychosocial needs may go undetected in these classrooms. Thus, the aim of this study is to explore…

How can teachers encourage productive struggle in mathematics and yet minimize the exposure to shame often associated with struggle? In this article, the authors offer constructive ways to position struggle in the classroom to minimize shame and promote doers of mathematics.

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

The purpose of this article was to identify the mechanism of bilateral feedback on Mathematics homework and to determine its impact on the success of schoolchildren learning. The following were used as the main research methods: the study and generalization of pedagogical experience which helped to consider possible ways of providing feedback on…

Online software systems are extensively used to give students practice on course content, especially in mathematics and physics courses. They offer instant feedback, and several of these systems are open source or very economical compared with hiring graders for traditional paper-and-pencil-based homework (PPH). In this article, the authors…