1. Kurt VanLehn
  2. http://www.public.asu.edu/~kvanlehn/
  3. Prof
  5. Arizona State University ASU
  1. Jon Wetzel
  2. http://www.public.asu.edu/~jwetzel4/
  3. Research Scientist
  5. Arizona State University ASU


NSF Awards: 1628782

2018 (see original presentation & discussion)

Grades 9-12, Undergraduate

One of the most difficult parts of high-school and pre-calculus mathematics is writing a set of equations that model a given text.  This corresponds to the first half of solving algebra word problems.   (The second half is solving the equations,  which nowadays can be done by computer algebra systems.)  This skill--mathematical model construction--is an essential prerequisite of many STEM topics.  It is notoriously difficult to learn. 

The TopoMath project is developing a short lesson sequence (about 18 hours) and an intelligent tutoring system that are designed to bring most students to mastery of this important skill.  The instruction is based on decades of research in the learning sciences.  Some of the key ideas are (1) to explicitly teach a strategy for decomposing the whole problem into subproblems recursively, (2) to explicitly teach a small set of primitive schemas, such as part-whole and distance-rate-time, (3) to use a graphical notation that makes the meanings of variables highly salient, (4) to adaptively fade from immediate feedback to delayed feedback to no feedback, and (5) to have the computer solve the equations so that students can focus on constructing them. 

TopoMath is being iteratively developed in the context of College Algebra classes at Arizona State University.  Two 18-hour classes have been conducted so far, each resulting in many design changes.  

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