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What Do You Notice? What Do You Wonder? Getting Students Thinking – and Talking – About Math

Adult numeracy expert Connie Rivera is coming to Minnesota for Math Institute in early May! Read on for a preview of Connie’s math teaching tips, and please plan to join her in person on May 5. Registration information can be found at the end of this article.

A recent trend in numeracy instruction is to find ways to engage students in thinking and talking about math, not just computing with a memorized procedure. Such instruction enables our students to think more flexibly about math and prepare them to tackle the math related problems they encounter in their everyday lives.

Image source: bryanmmathers.com

Notice and Wonder is a simple technique that students at any math level can do. First students are presented a problem or task (which could be a situation, image, graph, video, etc.), and they are asked what they notice about the problem. The teacher then records all of the student responses. In this technique there is no wrong way to notice or wonder! Record everything they share, even if it doesn’t appear to be relevant.

You might want to begin with “This is a graph. It is red and blue.” This will provide an entry point for students new to the class, with lower language skills, or who are unfamiliar with the math content used to solve the problem in a traditional way. TIP: Do you have students who need more time to process independently? Provide a few moments of quiet to allow students to jot down a few notes on their own before sharing out to the large group.

Repeat the process with wonders. What do students wonder about the information provided? Such questioning opens doors to solution pathways. Again, there are no wrong wonderings! Students may wonder, “Why are are doing this instead of just solving?” or even something that may seem to be off-task at first, “I wonder how many chips come in that bag?” These conversations are important because it provides the foundation for making sense of a problem or task which is a CCRS Mathematical Practice: MP 1 – Make Sense of Problems and Persevere in Solving Them.

Notice and Wonder steps

  1. Present a problem/task
  2. Record everything students notice
  3. Record everything students wonder
  4. Support students in turning their wonders into mathematical questions
  5. Transition into developing a way to solve the problem
  6. Continue to ask questions and refer back to the created lists while problem solving

When using Notice and Wonder with your students, know that the responses will become richer as students get used to the process. You don’t need a large group for this process to be effective. If you are in a one-room schoolhouse setting, you could create a Problem of the Week board that all students participate in by recording their thoughts on sticky notes and then solve the problem independently the next time they are in class after reviewing other’s contributions. This process could also be a launching point for math classes who use small group time. Students could be presented the same situation, given the opportunity to notice and wonder together, but then be given different problems to solve based on that situation at an appropriate level.

Avoid leading questions

When using this technique it is important to make sure you are not being too helpful. Try to allow students to think, notice, and wonder freely without being directed. It may be a challenge at first not to direct students to a particular pathway by using statements like “What do you wonder about how these lines meet?” Over time the class will learn how to pick up on important details needed to help solve the problems on their own.

Try this strategy with your students. It is an easy way to get learners at a variety of levels engaged together in mathematical thinking. Take some time prior to the lesson to anticipate some of the responses you will get from students and be mindful if some tasks may lend themselves to meatier conversations. Dedicating time to these discussions will pay off as your students become more attuned with problem solving!

Connie Rivera, President of the Adult Numeracy Network, has compiled a list of six strategies, including Notice and Wonder, and accompanying resources to improve the ways word problems are utilized in ABE and ESL classes. In her article, Rivera identifies small strategies to promote deeper and more flexible thinking in level-appropriate ways. To read more, check out her article Changing How Problems are Presented on the Adult Numeracy Center at TERC blog.

Learn more at Math Institute on May 4-5, 2017!

To learn more about word problems and ways to better use them in the CCRS-aligned classroom, join us at Math Institute on May 5! Ms. Rivera will be leading a hands-on workshop designed to empower teachers to evaluate problems in textbooks and identify high-value actions to improve their CCRS alignment and make them truly problems worth solving.

Need an introduction to the CCRS Math standards? We will be offering an all-day CCRS Math Foundations workshop on May 4, similar to what is offered at Summer Institute. During that training you’ll get to learn the basic shifts in math education as identified in the CCRS, how to read the standards and identify the level of standards your students need, and what the Mathematical Practices look like for students at all levels.

Amber Delliger, Numeracy Coordinator ATLAS