Many students struggle with algebra word problems.  As the students solve these problems, they should produce equations from the text and use them to find the answer.  This process is called model construction, and it is included in new science and math standards because it is a critical skill for working in STEM domains.

At ASU we’ve created an online program called Dragoon, where students can use algebra to build mathematical models of real-world phenomenon.

In our research, all of the students who used Dragoon mastered this model construction skill in 8 hours or less, but these were college students experienced with algebra already.

Using Dragoon as a starting point, we created a new system for high school algebra word problems called “TopoMath”.

TopoMath combines two ideas: first, the model is constructed as a node-link graph that shows the topology of the model.
Second, when teaching with TopoMath, we teach the students to break down the word problem into its smaller subsystems.

Students construct the model using two types of nodes: quantities and equations.  When they finish, they can view the solution as either a table or a set of graphs.

When teaching with TopoMath, instructors teach students to identify subsystems called  “schemas”.  These are relationships between quantities such as d = RT, average, and part-whole.  Each schema is given a specific layout so students can use their visual skills to recognize similarities and differences between problems.

We developed and tested the TopoMath prototype for about a year.  Then, at the start of 2018 we were ready to take TopoMath to boot camp…

We partnered with instructors from ASU’s College Algebra course, which is taken by students who did not achieve mastery of algebra in high school, to create an algebra word problem boot camp.  Students were invited to join if they wanted extra help.

The boot camp was 12 90-minute sessions.  The students were joined by both the instructors and ASU Dragoon Lab researchers for every session.
We encountered three main challenges in this boot camp:

First, students did not think carefully about the names they gave quantities and what they represented.  To help with this, we will simplify the naming system.

Second, our instructor had great success in prompting students to identify the most salient schemas.  So we are revising TopoMath to teach a new strategy, where students first identify all the “main” schemas, then identify “minor” schemas.

Third, we are expanding the set of schemas.  Students had trouble applying Distance Rate Time for rates that didn’t have time in the denominator, and part-whole for differences.  We’ll create more schemas for those cases.

We’ll be improving TopoMath over the summer as we prepare another boot camp for the Fall.  If you would like to see our progress our try out TopoMath yourself, visit our website, topomath.asu.edu . Thanks for watching!