In their position on teaching with high expectations, The National Council of Teachers of Mathematics (NCTM) calls for “design[ing] instruction that builds on students’ prior knowledge and experiences.” In other words, students need to understand the relevance of new information and be encouraged to tap into previously learned skills. NCTM suggests that one way to do this is through 5-10 minute warm-ups, such as a discussion prompt or a mathematical task.
For example, a teacher introducing a new lesson on calculating the area of shapes composed of rectangles could give students a warm-up review question on finding the area of rectangles. This activates students' existing knowledge of rectangles and area so that they are primed to apply these skills to a more complex task.
The Research Behind Building on Prior Knowledge
Building on students’ prior knowledge is rooted in constructivism, which posits that learners have to actively construct their own knowledge rather than passively receive it; they make meaning of new concepts only when they “integrate them into their existing structures of knowledge,” or schemas. This is how long-term memory works: when students process new stimuli, they sort and organize them into long-term schemas based on familiar patterns.
Not only does building on prior knowledge improve students’ conceptual understanding and retention, but it can also foster a positive attitude towards new math challenges by building students’ confidence in their knowledge foundation, which can have a compounding positive effect on future achievement. Education theorist Paulo Friere also argued that building on prior knowledge is what we would call today culturally responsive teaching because it “take(s) the people’s historicity as their starting point”--in other words, it affirms the value of the knowledge and experiences students are bringing to the table.
A Pitfall: Preventing the Misapplication of Prior Knowledge
A study conducted at the University of Wisconsin-Madison found that activating prior knowledge by warming up with related familiar problems before a new lesson could “support spontaneous, correct transfer of children’s prior conceptual knowledge to a novel domain.” However, the researchers did note that teachers should be on the lookout for students applying the wrong strategies to new problems, suggesting that students benefit from explicit guidance on how to make comparisons between similar problems. Another study on common misconceptions in arithmetic highlighted a problem with students incorrectly applying previously learned operational patterns. Both studies affirm the importance of building on prior knowledge in a cumulative subject like math, but caution that educators need to be ready with just-in-time supports so that students do not transfer the wrong approaches.
Yup’s Strategies for Building on Prior Knowledge
Yup’s tutoring rubric is built around the NCTM’s call for equitable, grade-level math instruction that includes building on prior knowledge. When tutors begin a session, they are coached and evaluated on their ability to gauge student understanding and use this as a jumping-off point. The Yup rubric holds tutors accountable to
✅ Assessing prior knowledge. Tutors start by using students’ pre-session responses to the problem to guide their instruction and formulate scaffolding questions.
✅ Guiding the conversation to catch misconceptions. While Yup tutors encourage students to use their existing knowledge, they are also on the lookout for misconceptions and address them with concise explanations or visualizations.
✅ Encouraging students to actively construct their own knowledge. Yup tutors also facilitate productive struggle, pushing students to complete key portions of the work independently so that they will be more likely to retain new skills.