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.
Jon Wetzel
Thank you for checking out the TopoMath project video! We have only just completed our first classroom study and will be improving the design this summer. Questions, suggestion, and other feedback on our work are welcome.
If you are a math teacher with experience teaching high school algebra word problems, we'd love to learn from your experiences as well! In particular, what strategies do you teach your students to help them find the equations to solve?
Nadine Bonda
This is an interesting idea. We certainly need ways to help students understand algebra word problems. Will your next bootcamp also be with college students? Do you have plans for moving it into high school? If so, at which levels would you intend to use it and why?
Kurt VanLehn
Prof
Once we have it working well with College Algebra, then we plan to try it in high school Algebra II.
Brian Drayton
I am interested in your strategy for "chunking" into schemas. This is intuitively appealing, and I wishi I'd had it in my own high school algebra class. I would think that it would give students a sort of vocabulary or set of tell-tales to look for in interpreting word problems — do you have a library of such schemas you are drawing from, or are you identifying the ones relevant to your target students as you go along? Are you asking/challenging students to identify or characterize schemas for themselves, from the problems they have encountered (and solved)?
Kurt VanLehn
Prof
We are drawing our schemas from Rich Mayer's work:
Mayer, R. E. (1981). Frequency norms and structural analysis of algebra story problems into families, categories and templates. Instructional Science, 10(2), 135-175.
When students become fluent at working with the schemas in that we tell them about, then we will have them identify new ones. The students in the first two boot camps did not get that far.
Karen Economopoulos
I'm curious about whether or not students are able to carry forward their experiences with model construction and apply their what they have learned to novel situations outside of the Topomath environment?
Kurt VanLehn
Prof
We use a conventional algebra test as the post-test, but we have not tried further transfer.
Nancy McGowan
Visual learning is a great method of engaging students. I wondered about the success of your Boot Camp students as they moved forward in higher level math. Do you plan to track these students?
Kurt VanLehn
Prof
It's a good idea, and ASU has the data to do so. When we start getting larger numbers of participants in the boot camps, we'll have to look into feasibility with respect to privacy issues.
Mari Strand Cary
Thanks for sharing how student difficulties and teacher successes using their own strategies in the first boot camp led to revisions you're making now. You're working with college students...would this (or your envisioned end-result) work in high school settings or are there things you anticipate would need to be quite different to work with this population?
Kurt VanLehn
Prof
Once we have it working with College Algebra students, we plan to try it with high school Algebra II students. We could use some advice on how to get the 20 hours required for the boot camp given that the curriculum is so packed.
Further posting is closed as the event has ended.