Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle.…

Self-efficacy, the beliefs learners hold about what they can do, develops largely from whether learners perceive and interpret their experiences as successful (i.e., perceived mastery). In mathematics, the relationship between perceived mastery and self-efficacy has been well established. Less is known about the factors that may influence…

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of…

We compared self-regulatory processes and mathematics achievement with 138 elementary students across three conditions: learning by actually teaching (LAT), learning by preparing to teach (LPT), and learning for learning (LL). Students completed concept maps and then solved the problem. Students in the LAT condition created a teaching video, while…

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

Prerequisite skill structures have been closely studied in past years leading to many data-intensive methods aimed at refining such structures. While many of these proposed methods have yielded success, defining and refining hierarchies of skill relationships are often difficult tasks. The relationship between skills in a graph could either be…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…

With careful consideration given to task selection, students can construct their own solution strategies to solve complex proportional reasoning tasks while the teacher's instructional goals are still met. Several aspects of the tasks should be considered including their numerical structure, context, difficulty level, and the strategies they are…

This paper reports on a design experiment within a professional development context purposefully planned to teach teachers about students' mathematics thinking and learning. We examine the factors to which participating elementary teachers attributed student mathematics success or failure when engaging with the projects' professional learning…

This study examined the effects of task difficulty on on-task behavior for four students exhibiting low levels of math performance and on-task behavior. Curriculum-based assessments were conducted with each student to define the difficulty level of math tasks for each student based on the individual's rate of accurate performance on computational…