Learning standards such as the "Common Core State Standards for Mathematics" [CCSSM] (NGA Center & CCSSO, 2010) advocate that we develop students' algebraic thinking "beginning in kindergarten." Such a tall order requires innovative approaches that re-imagine what teaching and learning mathematics means for the elementary…

Across multiple age groups and academic disciplines, research has shown that incorporating multimodal signs into instruction can enhance student learning. For instance, gesture might be synchronized with speech or written signs. The present study reports on the semiotic resources used by a teacher-researcher to support kindergarten students'…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons…

Adaptive educational software is likely to better support broader and more diverse sets of learners by considering more comprehensive views (or models) of such learners. For example, recent work proposed making inferences about "non-math" factors like reading comprehension while students used adaptive software for mathematics to better…

Developing and supporting understanding of the meaning of multiplication and multiplicative relationships in students with mathematics learning disabilities requires carefully designed instruction that emphasizes strategic representation use. This article discusses three ways in which teachers can incorporate multiple representations within…

Research and theory indicate that the type and quality of instruction, not the delivery mechanism, are what impact learning. Previous reviews have not systematically explored variations in the instructional strategies, approaches, and designs of educational technology programs and also suffered from lax inclusion criteria, which has been known to…

Understanding equivalence is fundamental to STEM disciplines, but many students struggle with the concept. We present a novel method for students to explore ideas of equivalence where students dynamically transform expressions from initial states to goal states in the web-based app Graspable Math. The structure of the goal state activities implies…

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students…

Prisms VR, a secondary math learning application, allows for users to see, manipulate, and engage with mathematical concepts in an embodied way in Virtual Reality (VR) environment. We examine cases in which mathematics teachers and middle school students worked through Prisms and reflected upon their experiences. Findings indicate that VR…

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students'…

This paper investigates two specific probabilistic biases which middle graders usually exhibit when reasoning about probability and randomness on assessment items. We discuss how students' reasoning about key probability concepts undergirds statistics literacy related to randomness, independence, and the likelihood of future events based on past…

Introduction: Developing graphicacy skills is important for students with visual impairments if they are to succeed in science, technology, engineering, and mathematics (STEM) content. Teachers of students with visual impairments report that they lack resources to use in teaching students graphicacy skills. Methods: Forty-one students with visual…

Assessing students' conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by…

This study investigated the technical characteristics of four early measurement curriculum-based measures (EM-CBMs) designed to assess concepts related to linear measurement and iteration. The sample consisted of 221 first grade students. Data were collected at two time points approximately 10 weeks apart. Reliability and concurrent and predictive…

This pilot study examined the promise of a Tier 2 sixth grade intervention program for students at-risk for difficulties in mathematics. The study utilized a quasi-experimental design. The final sample included 112 students in treatment (Promoting Algebra Readiness) and 86 students in control (standard district practice) conditions. The Promoting…