Building on Prior Mathematical Knowledge

While the National Council of Teachers of Mathematics (NCTM) and other research studies highlight the importance of engaging students’ prior knowledge in order to build new understandings, the question of what this involves and how educators might approach it remains less certain.

How can students productively return to their initial math understandings? Working in a Grade 12 math class, Werklund’s Dr. Jo Towers  and Dr. Lyndon C. Martin of the Faculty of Education at York University investigated the pedagogies and techniques that might better take up previous understandings.

The researchers emphasize the importance of not just seeing prior understandings as erroneous, or as simply misconceptions. They suggest that earlier understandings need to be collected and engaged in detail – not just overcome. Taking the time to explore existing conceptions, and how and why they might be insufficient in the new context, helps students engage with the new knowledge.

In the study, the researchers explored how a teacher guided students to return to their understandings of the concepts embedded in the equation of a line, before introducing vectors. The teacher drew out students’ knowledge with explicit questioning, diagrams, and instruction based on what they already knew. This purposeful and sustained approach allowed the teacher to engage prior understandings in greater depth.

For Teachers

Rather than quickly skimming over prior knowledge, having students bring their understandings forward and examining them in depth can help teachers to better scaffold learning. Moving more deliberately from prior knowledge to the target idea, by exploring how ideas met before are either still valid or in need of reconceptualization, can lead to a deeper, conceptually-connected understanding.

*This research was funded by the Social Sciences and Humanities Research Council of Canada (SSHRC)*