When viewed through a lens of embedded cognition, algorithms may enable aspects of the cognitive work of multi-digit multiplication to be "offloaded" to the environmental structure created by an algorithm. This study analyses four multiplication algorithms by viewing different algorithms as enabling cognitive work to be distributed…

Calculus students' difficulties in understanding integration have been extensively studied. Research shows that the difficulty lies with students understanding of the definition of the definite integral as a limit of a Riemann sum and with the idea of accumulation inherent in integration. We have created a set of manipulatives and activities…

The purpose of the study was to determine if standardized math test scores improve by administering different types of exercise during math instruction. Three sixth grade classes were assessed on the Measures of Academic Progress (MAP) and the Minnesota Comprehensive Assessment (MCA) standardized math tests during the 2012 and 2013 academic year.…

One of the major benefits of the face-to-face teaching environment is that social interaction opportunities are a natural part of the course: Learners meet in the same room for the same allotted period of time each week. This social opportunity is not organic to online courses; therefore, to have this social interaction as a part of online classes…

Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students' achievements of intended instructional outcomes. Formative assessment means assessment embedded in instruction. That definition was adopted in 2006 by the Council of Chief State…

The purpose of this study is to design a modeling task to facilitate students' inquiries into the chain rule in calculus and to analyze the results after implementation of the task. In this study, we take a modeling approach to the teaching and learning of the chain rule by facilitating the generalization of students' models and modeling…

This paper describes an after-school club aimed to engage elementary students in project-based learning by integrating mathematics and literacy connections within a community-based topic. Building on students' backgrounds and interests, researchers created the Community Super Investigators (CSI) Club as part of an after-school program to explore…

Student voice is recently attracting educational researchers' attention for its influence on various aspects of student lives and futures, as well as social life in general. Mobile technologies are proliferating in social and practical life. This article studies student voice in carrying out outdoor activities with mobile phones. Thirty middle…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight…

Many elementary schools across the nation are scaling back or cutting arts curriculum altogether. This article presents classroom teachers with an activity for integrating art with mathematics. Through a three-phase exploration of reasoning with shapes and their attributes, students will get to know a classmate better, work with defining and…

Little research exists on young children's beliefs about mathematics, and current research perspectives on early mathematical activity may overlook a great deal of young children's sophisticated mathematical thinking. We argue this is attributable, in part, to a need for a broader view of what mathematics is, including cultural practices that are…

Teacher telling continues to be poorly understood within inquiry. In this paper I extend prior efforts to reimagine telling within contemporary pedagogical thought. Using a case study, I investigated a well-regarded teacher's use of mathematical telling while supporting groups and individuals working on tasks. The teacher used seven unique types…

This document presents the proceedings of the 27th Annual Research Forum held June 29, 2023, at Wake Forest University in Winston-Salem, North Carolina. Included are the following fifteen action research papers: (1) The Effects of Real-World Mathematics Activities on High School Students' Attitudes (Alexa Altizer); (2) An Investigation of the…

Parents and grandparents are always looking for new ways to engage their kids and grandkids in meaningful, enriching educational activities. While there is evidence that playing games can increase numerical fluency, research also shows that parental involvement outside of school is one of the best predictors of student achievement and that games…