To date, of the many studies on early algebraic thinking, none, to our knowledge, has examined the relationships between algebraic thinking and negative numbers. Students encounter persistent difficulties in dealing with these numbers, and we believe that these could be addressed through the development of algebraic thinking. We are particularly…

In this article we show how students' productive struggle on a mathematical task can lead to collective mathematical creativity. We use observable (co)actions and interactions from a video record that features three Grade 6 students in a problem-solving session to document the emergence of collective creativity leading to a solution. We discuss…

A challenge in digital learning games is assessing students' learning behaviors, which are often intertwined with game behaviors. How do we know whether students have learned enough or needed more practice at the end of their game play? To answer this question, we performed post hoc analyses on a prior study of the game "Decimal Point,"…

Practicing teachers as well as researchers, mathematicians, and teacher educators have offered opinions and theoretical critiques of the multiple models used to teach integer arithmetic. Few studies, however, have investigated what students learn with models or empirically compared affordances and constraints of integer models. This led me to…

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…

Although students and adults alike are constantly exposed to visuals both online and offline, merely being exposed to visuals does not guarantee visual literacy (Kedra & Zakeviciute, 2019). This study explored K12 teachers' perceptions regarding their personal and instructional use of online images as well as the influence of a visual literacy…

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…

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…