Why Students Deserve to Know the “Why, How, and What” of Math
Finding Opportunities to Notice and Wonder About Mathematics
At the grocery store with her family, a child watches her mother pick up 1, 2, 3, 4, and then 5 apples. The cashier scans each of their items, puts them in bags, and the numbers on the cash register rise until Mom counts out bills and change to pay. On the way home, Mom says she can go ahead and have a bag of chocolate candies — but only if she splits half with her little brother! While eating the candies she has just sorted (keeping as many of the colors she likes for herself without shorting her brother) she watches out the car window as clouds of different shapes and sizes float overhead. Later at the park, she picks up a pinecone and runs her fingers over its sharp, carefully arranged seed pods, slipping it into her pocket to add to her collection of outdoor treasures with pretty patterns. Before bed, she does a puzzle with her brother, counts to 60 while she brushes her teeth, and dreams of skipping on the playground.
What is Sensemaking in Math?
What this child is doing, whether she realizes it or not, is making sense of mathematics through the interactions in her everyday life. Children (and adults!) use math every day, making sense of the world around them through a mathematical lens. That skill can be taught and is important to foster in the classroom. Sensemaking is a critical part of inquiry-driven math instruction because it encourages a deeper understanding of math. 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, math education expert and Reveal Math contributing author, frames sensemaking this way: “… noticing and wondering about situations, being curious, pondering different ideas, or even taking time to understand a story before trying to calculate anything.”
Why is sensemaking in math so important?
Math is more than just delivering the right answer or an exercise in using procedures. Math is a way of thinking, a universal human language, and even a natural map leading to new discoveries. So many students don’t see themselves as capable of math because of preconceived notions that math is only about coming up with the right answer. But teachers know that the journey to the answer is just as important!
Shifting instruction to focus on that journey is a way to not only practice important math skills but also to help students see themselves as “doers” of mathematics. Any student can — and deserves the opportunity to — be curious, explore, and make discoveries about math.
How Can Teachers Encourage Sensemaking in Math?
In the classroom, sensemaking activities are an excellent exercise in mathematical thinking. They make math more accessible to all students and provide valuable formative assessment opportunities to teachers by exposing students’ reasoning skills and prior knowledge. In her white paper Four Ways to Encourage Sensemaking in Math, Annie Fetter provides the following examples of sensemaking exercises:
Remove the Question (and the Numbers!)
Annie says: “If you don’t want students focusing on answers, then don’t include the questions.” Instead, present a mathematical scenario, graph, or the first part of a word problem. Here’s more from Annie’s white paper:
“Present each of these scenarios to students and ask them what they Notice and Wonder © (a strategy we first developed at The Math Forum for use with teachers in a protocol for looking at student work in 2005 and formalized as an approach for problem-solving with our Problems of the Week in 2007). The work that students now do is focused on making sense of the situation, not answering a specific question.”
Activities like these are a great way to begin a lesson and collect information on students’ prior knowledge.
To push students even further, teachers can also remove the numbers from a problem. Annie notes that when presented with a numberless problem, many students may claim that they can’t do anything with it at all, but in a scenario with a picture, some may begin to make mathematical observations about the image.
Provide Students with the Answer
One way to redirect students from focusing on “answer getting” is to give them the answer in the first place. For example, Annie suggests providing students with a classic “in out” table, like the one below, and having them describe everything they notice about it.
Annie says, “The point is to have the students do the work of making sense of the situation.”
Ask for Ideas Instead of Answers
Finally, Annie suggests simply switching question framing from, “What is the answer to this problem?” to “What can you tell me about this problem?” Student responses will of course vary widely, but that’s okay! Annie says,
“When we ask for the answer to question number 7, we already know that there are students in the room who can’t tell us. We’re almost telling some students they can’t do math, which is not the message we want to be sending when we know everyone CAN do math! But in asking more broadly about question 7, we fully expect that every student could tell us something and are sending a message that everyone has math ideas to contribute to our learning community.”
To read more about each sensemaking strategy and for more detailed examples with images, read Annie Fetter’s full whitepaper.
Spotlight on California
California’s new math framework prioritizes helping students understand the “what, why, and how” of math. The state’s inquiry-based approach is focused on the big ideas of math highlighting the interconnectedness of math concepts and supporting sense-making. Instruction includes open and engaging tasks to invite students to ask questions and think critically about math — which means sensemaking will be a valuable tool for California teachers. Here’s more from the framework:
“This framework lays out an approach to curriculum and instruction that harnesses and builds on students’ curiosity and sense of wonder about the mathematics they see around them. Students learn that math enriches life and that the ability to use mathematics fluently — flexibly, efficiently and accurately — empowers people to influence their lives, communities, careers, and the larger world in important ways.”
Sensemaking activities can help teachers address the framework’s three Drivers of Investigation (DIs), which provide the “why” of learning mathematics, and Content Connections (CCs), which provide the “how and what” of mathematics. One of the key Drivers of Investigation for the California Math Framework is D1: Make Sense of the World (Understand and Explain). The others are D2: Predict What Could Happen (Predict) and D3: Impact the Future (Affect). The framework encourages students to wonder, make connections, understand relationships across mathematical ideas, and do far more than simply “calculate.” Sensemaking activities, like those in Anne Fetter’s white paper, are engaging and equitable options for teachers looking to help their students make sense of the world through mathematics.
Annie Fetter, a contributing author of Reveal Math, is currently working on the development of the new California Reveal Math © 2026 curriculum. Annie’s expertise will help teachers foster sensemaking, pique students’ curiosity, connect learning to the “real world” through authentic examples, and encourage inquiry, problem-solving, and deep learning.
The Reveal Math and California Reveal Math curricula are designed to support sensemaking, curiosity, and authentic, open-ended tasks through features such as:
- Sensemaking Routines, including: Be Curious: Notice and Wonder; How Are They the Same? How Are They Different?; Which Doesn’t Belong?; Is It Always True?; Numberless Word Problems
- Mathematical Modeling Tasks
- Activity-Based Explorations and Guided Explorations that can be accessed in print and digitally, independently or guided by the teacher.
To support the California Framework’s call for embedded teacher support for cultivating curiosity and meaningful discourse, California Reveal Math will also include:
- Strategies to Support Students in Accessing Content that can be found in the Teacher Editions in every lesson level. This supports teachers in ensuring all students can make sense of and connect to the content no matter their background or personal experience.
- NCTM’s Effective Teaching Practices are embedded throughout the Teacher Edition to help them elicit, make sense of, and respond to student thinking. These practices include Pose Purposeful Questions and Facilitate Mathematical Discourse with a “Listen to” feature and Common Errors and Misconceptions with support to respond appropriately.
For teachers of early learners, the California Reveal Math TK curriculum coming soon in 2026 is built on an instructional design that harnesses the power of imagination and curiosity with a strong focus on sensemaking, exploration, and discourse to bridge the transition to Kindergarten.
For more on California Reveal Math, see: https://www.mheducation.com/prek-12/explore/states/california.html
For more resources for California math teachers, see:
References
Battista, M. T. (2017). Reasoning and sense making in the mathematics classroom, grades 6–8. The National Council of Teachers of Mathematics, Inc.
