Using Online Error Analysis Items to Support Preservice Teachers’ Pedagogical Content Knowledge in Mathematics

May. 01, 2013

Source: Contemporary Issues in Technology and Teacher Education, 13(3), p.207-218. (2013).
(reviewed by the Portal Team)

This article describes an online tutoring system that was used to give preservice teachers an opportunity to analyze and remediate student work.

The participants were preservice teacher candidates from two separate mathematics courses enrolled at a midsized, suburban university in central Colorado.
They completed the error analysis items in this tutoring system, ASSISTment.
The ASSISTment system was designed to blend tutoring and testing effectively, an outcome achieved by providing users with a combination of scaffolding questions, hints, and error messages.


As preservice teachers completed the online error analysis problem sets, the ASSISTment system automatically tracked their responses at each level of the problem.
Using this system function, the instructor was able to review quickly all preservice teacher responses and then select a subset of responses to display anonymously to the class.
Displaying preservice teachers’ answers in class provided an incentive for all students to submit high-quality answers, because they wanted their response to be selected as examples.
It also provided a variety of remediation strategies for each problem, thus encouraging a higher level of dialogical discourse.

Through a careful analysis and rich discussion about different suggested remediation strategies, preservice teachers were exposed to a variety of techniques that could be used to help correct student errors (e.g., using concrete manipulatives, pictorial representations, real life connections, and graphic organizers).
Finally, these rich discussions around common mathematical error patterns also directly informed preservice teachers’ subsequent lesson and activity designs for the courses.

Mathematics methods instructors working with preservice teachers at the university level or professional development coordinators working with in-service teachers at the district level may find these ideas useful.
Clearly, preservice mathematics teachers cannot be expected to learn all there is to know about student thinking in all areas of mathematics.
However, by exploring online error analysis problems and engaging in dialogical discourse about effective remediation strategies, preservice teachers can become equipped with a better understanding of why analyzing students’ thinking is important in key areas of mathematics and how they can effectively remediate.
Through this process, preservice teachers will more clearly see a direct link between students’ understanding and the implications this insight has on the teaching and learning of mathematics. The author argues that this online error analysis items challenged preservice teachers to analyze, diagnose, and provide targeted instructional remediation intended to help mock students overcome common error patterns and misconceptions.

Updated: Mar. 30, 2015