What is Sensemaking in Math, and Why is it Important?
By now, many educators are familiar with this oft-cited experiment in math education: Ruesser (2000) asked students: ‘There are 125 sheep and 5 dogs in a flock. How old is the shepherd?’ (p. 23), to which many students presented various answers that represented some relationship between the two numbers in the sentence. Why is this happening? Why would students come up with answers to questions designed to have no answer?
Sensemaking in Math Education
Educators have attributed this phenomenon to a lack of “sensemaking” in mathematics, or “non-sense making.” Essentially, students aren’t assigning adequate meaning to the elements of math problems as they navigate numbers, words, and symbols to find an answer — they’re simply applying familiar operations to numbers in a way that generates another number in the end.
The National Council of Teachers of Mathematics (NCTM) defines sensemaking as:
“…the process of understanding ideas and concepts in order to correctly identify, describe, explain, and apply them. Genuine sense making makes mathematical ideas “feel” clear, logical, valid, or obvious.” (Battista, 2017, p.1)
Annie Fetter, a founding staff member of the Math Forum and mathematical consultant, frames sensemaking as the antithesis of “answer-getting.” She writes:
“Many students believe that the goal of math is to get answers really fast. They don’t believe that doing math means thinking about situations, pondering different ideas, or even taking time to understand a story before trying to calculate anything.” (Fetter, p. 2)
Math teachers can take steps to foster sensemaking habits in students at all grade levels. In addition to improved mastery of critical math concepts, an emphasis on sensemaking in the classroom may also lead to increased student agency, engagement, and even equitable opportunities.
How to Encourage Sensemaking in Math
In her whitepaper, “Four Ways to Encourage Sensemaking in Math,” Annie Fetter outlines a few instructional strategies math teachers can use to encourage students to practice sensemaking:
- Get Rid of the Question: This strategy calls for educators to present information about a scenario (perhaps a graph, or a few sentences — think, the beginning of a classic math word problem without the actual question). Instructors allow students to make observations and verbalize or document what they know. For more on the process of making observations, see the full white paper.
- Get Rid of the Question and the Numbers: This approach is similar to the first but goes a step further by first framing the scenario to students without any numbers. The scenario may include words, images, or diagrams — but requires students to begin to make sense of the “story” being told, or the foundation of the math problem.
- Give Students the Answer: This strategy directly addresses the issue of “answer-getting”, because it shifts the unknown element to the process, not the outcome. Examples of this strategy include “In and Out” boxes, where students have a series of numbers to start and a series of corresponding numbers that “came out of the box” and must determine the function that would produce that series of number transformations.
- Ask About Ideas, Not Answers: To elicit ideas from students about math problems rather than answers, Annie Fetter suggests the phrase “Tell me something about…” in reference to a scenario. There’s an element of inclusivity and empowerment to this strategy — rather than implying that someone in the class has the correct answer to the problem, the teacher is implying that everyone in the class has valuable observations about the problem.
For detailed examples of each strategy, see the full whitepaper.
Why Sensemaking in Math is Important
Arming students with the skills to make sense of math problems is clearly intended to boost mastery, fluency, and overall mathematical competence — the ultimate goal is simply to help students understand math. But some researchers connect sensemaking in math to other critical elements of students’ relationship to math education that are all too often in short supply: including agency, engagement, and even equity.
Sensemaking is tied to student agency. Annie Fetter’s strategies for sensemaking illustrate this connection clearly: empowering students to take the time to make observations and tell a story gives them ownership over the problem-solving process. Mathematics scholar Piera Biccard frames agency and sensemaking as the “opportunity that learners will have to see themselves as mathematical thinkers” (Biccard, 2018, p. 4). In order to make sense of math, students must make choices about how to exercise mathematical thinking.
Sensemaking can boost student engagement. Again, the examples from Annie Fetter’s paper make this connection intuitive: giving students the room to make decisions about problem-solving also empowers them to stay engaged even when they’re struggling. Mathematics educator and researcher Michael Battista reminds educators that math should be an “intellectually satisfying experience” for students, and students who continually come to new understandings about math and believe that they are capable of math are much more likely to stay engaged. Those who continue to fail to understand (let alone produce the “right answer”) are more likely to disengage. (Battista, 2017).
Encouraging sensemaking may create a more equitable learning environment. Placing value on the process of understanding math rather than simply producing the right answer is a strong foundation for a more equitable math classroom. In Annie Fetter’s “tell me something about…” strategy, all students have the opportunity to share observations and thoughts about mathematics, before anyone has the opportunity to make it to the “answer.” Michael Battista points out that sensemaking can align to all three Response to Intervention (RTI) tiers, because teachers can monitor Tier 2 and 3 students’ mathematical learning by observing their reasoning through observation and formative assessment (Battista, 2017).
For more on the how and why of sensemaking in math, check out this interview with Annie Fetter:
Battista, M. T. (2017). Reasoning and sense making in the mathematics classroom, grades 6–8. The National Council of Teachers of Mathematics, Inc.
Biccard, P. (2018). Mathematical sense-making through learner choice. Pythagoras, 39(1). https://doi.org/10.4102/pythagoras.v39i1.424
Fetter, A. (n.d.). Four Ways to Encourage Sensemaking in Math. mheducation.com. https://s3.amazonaws.com/ecommerce-prod.mheducation.com/unitas/school/explore/sites/reveal-math/white-paper-four-ways-to-encourage-sensemaking-in-math.pdf
Reusser, K. (2000). Success and failure in school mathematics: Effects of instruction and school environment. European Child and Adolescent Psychiatry, 9(2), 17–26. https://doi.org/10.1007/s007870070006