This article investigates the potential mathematical learning opportunities arising from a digital activity designed to enhance students' comprehension of equations. Employing a commognitive-oriented lens, the analysis explores the potential mathematical discourses that could emerge from students' interactions with a digital scale inspired by the…

Developmental mathematics courses play a critical role in ensuring that students have the foundational mathematical skills necessary to succeed in higher educational mathematics coursework. With the introduction of the corequisite format in recent educational reforms, there has been a growing trend towards transferring developmental mathematics…

Today math teachers can best reach their students and show them how math surrounds us by using manipulatives, children's literature, and GeoGebra while teaching mathematics. These are some of the best pedagogical practices for teaching mathematics today. In our high-tech world, students need to be proficient in science, technology, engineering,…

This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…

This is one of the first studies to evaluate the impact of computer-based individualized instruction in a developing country. We randomly assigned 1,528 students in grades 6-8 in 15 "model" public schools in Rajasthan, India who were using a computer-adaptive learning software to: a control group, in which they were only able to access…

Designers of educational modules for conceptual learning often rely on procedural frameworks to chart out interaction mechanics through which users will develop target understandings. To date, however, there has been no systematic comparative evaluation of such frameworks in terms of their consequences for learning. This lack of empirical…

In this article we analyze how students reason about linear combinations across multiple digital environments. We present the work of three groups of undergraduate students in the Southeast United States (US) who were considered ready to take linear algebra. The students played the game "Vector Unknown," reflected upon aspects of their…

An allegorical thought experiment occurring in a pseudo Huxleyean world in the future is conducted, in which "Euclidean" geometry has been forgotten and can only be retrieved by traversing backward in time, physically and virtually by two protagonists, Alpha and Beta, inspired by the challenge issued by their teacher Aleph 1. In the year…

Community colleges continue to increase their efforts to better serve students who enter their institutions with limited basic math, reading, or writing skills. In 2015, MDRC partnered with the Texas Coordinating Higher Education Board on a study to examine how colleges implemented state guidelines for students scoring below ninth-grade…

"I CAN Learn"® is a computer-based math curriculum for students in middle school, high school, and college. It provides math instruction through a series of interactive lessons that students work on individually at their own computers. Students move at their own pace and must demonstrate mastery of each concept before progressing to the…

"I CAN Learn"® is a computer-based math curriculum for students in middle school, high school, and college. It provides math instruction through a series of interactive lessons that students work on individually at their own computers. Students move at their own pace and must demonstrate mastery of each concept before progressing to the…

Networked computers can potentially support classrooms to be more interactive. It can help students share representations amongst themselves and work together on a shared virtual activity space. In research on the role of shared screens or shared virtual workspace in learning settings, there has been less attention paid to contexts where learners…

In the teaching of math-fact automaticity, most classroom teachers are unaware of research-based practices such as the use of a controlled response time, the scaffolded teaching of individual math facts, the limiting of exposure to new math facts, the separation of math facts with common operands, and even the definition of automaticity. As a…

"Cognitive Tutor"® is a secondary mathematics curriculum developed by Carnegie Learning that focuses on how students think about and learn mathematics. Teachers facilitate student learning as students acquire and apply new information and discuss their work. The curriculum can be implemented using a textbook, adaptive software, or…

Solving systems of equations at school, at least in Argentina, is usually a task that students are given as a series of techniques that "allow" them to find a solution. How to overcome educational obstacles that are generated from a fragmented approach of knowledge? What can DGS do, in particular the CAS environment? What epistemic and…