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S. S. Karunakaran, & A. (Ed.)In this paper, we introduce an RMEbased (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a wholeclass setting.

S. S. Karunakaran, & A. (Ed.)In this paper, we introduce an RMEbased (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a wholeclass setting.

Karunakaran, S. ; Higgins, A. (Ed.)In this paper, we introduce an RMEbased (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a wholeclass setting.

Karunakaran, S. ; Reed, Z. ; Higgins, A. (Ed.)We present results of a grounded analysis of individual interviews in which students play Vector Unknown  a video game designed to support students who are taking their first semester of linear algebra. We categorized strategies students employed while playing the game. These strategies range from lessanticipatory buttonpushing to more sophisticated strategies based on approximating solutions and choosing vectors based on their direction. We also found that students focus on numeric and geometric aspects of the game interface, which provides additional insight into their strategies. These results have informed revisions to the game and also inform our team's plan formore »

The results we report are a product of the first iteration of a designbased study that uses a game, Vector Unknown, to support students in learning about vector equations in both algebraic and geometric contexts. While playing the game, students employed various numeric and geometric strategies that reflect differing levels of mathematical sophistication. Additionally, results indicate that students developed connections between the algebraic and geometric contexts during gameplay. The game’s design was a collaborative effort between mathematics educators and computer scientists and was based on a framework that integrates inquiryoriented instruction and inquirybased learning (IO/IBL), gamebased learning (GBL), realistic mathematicsmore »

Demands in undergraduate education are shifting to reach larger student populations  especially learners beyond the brickandmortar classroom  which has led to more pressing demands to incorporate technologies that afford such learners access to highquality, research based, digital instructional materials. In this article, we explore three theoretical perspectives that inform the development of such instructional materials. In our team’s efforts to develop a gamebased learning applet for an existing inquiryoriented curriculum, we have sought to theoretically frame our approach so that we can draw on the corpus of researcher knowledge from multiple disciplines. Accordingly, we will discuss three bodiesmore »