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Instruction often employs visual representations to support deep understanding. However, students " prior misconceptions may override the meaning in these scaffolds. We investigate fraction bars, a common representation intended to promote sense-making. Our prior work found that students often did not use the fraction bars effectively. This difficulty… (More)

In STEM domains, robust learning includes not only fluency with procedures, but also recognition and application of the conceptual principles that underlie them. Grounded feedback is one instructional approach proposed to help students integrate conceptual knowledge into their learning of procedures. Grounded feedback functions primarily by having students… (More)

What types of scaffolds support sense making in mathematics? Prior work has shown that grounded representations such as diagrams can support sense making and enhance student performance relative to analogous tasks presented with more abstract, symbolic representations. For grounded representations to support students' learning of symbolic representations,… (More)

In order to better understand how humans acquire knowledge, one of the essential goals in cognitive science is to build a cognitive model of human learning. Moreover, a cognitive model that better matches student behavior will often yield better instruction in intelligent tutoring systems. However, manual construction of such cognitive models is time… (More)

Can experimenting with three-dimensional (3D) physical objects in mixed-reality environments produce better learning and enjoyment than flat-screen two-dimensional (2D) interaction? We explored this question with EarthShake: a mixed-reality game bridging physical and virtual worlds via depth-camera sensing, designed to help children learn basic physics… (More)

Empirical results from a fraction addition task reveal a surprising gap in prior knowledge: difficulty applying the transitive property of equality in a symbolic context. 13 out of the 182 4 th and 5 th graders (7%) correctly applied the transitive property of equality to identify the sum of two fractions in a step-by-step worked example. This difficulty… (More)

Problems with many solutions and solution paths are on the frontier of what non-programmers can author with existing tutor au-thoring tools. Popular approaches such as Example Tracing, which allow authors to build tutors by demonstrating steps directly in the tutor interface. This approach encounters difficulties for problems with more complex solution… (More)

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