I Notice I Wonder
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The obstacles: Students don’t know how to begin solving word problems. They don’t trust or make use of their own thinking. They freeze up or do any calculation that pops into their head, without thinking, “does this make sense?” They don’t have ways to check their work or test their assumptions. They miss key information in the problem. They
don’t understand the “story” of the problem.
The solution: Create an safe environment where students focus on sharing their thoughts without any pressure to answer or solve a problem.
The obstacle: Sometimes when we put a problem on the board, students notice the question and go into one of two modes:
This can make it difficult to facilitate a whole-group brainstorm. The first student doesn’t participate and doesn’t connect to his own thinking, losing out on the power of noticing and wondering. The second student doesn’t participate and narrows in too quickly on her own thinking, losing out on the opportunity to surface more interesting
(and more challenging) mathematical questions and ideas.
The solution: Use the basic “I Notice, I Wonder” Brainstorm, but include only the mathematical scenario. Leave out the question, and even some key information for solving the problem. Only after all students have participated and understand the scenario thoroughly do you reveal the question. Or, ask students, “If this story were the beginning of a
math problem, what could the math problem be?” Then solve a problem the students came up with.
Leaving off the question increases participation from struggling students because there’s no right answer and no wrong noticings and wonderings. It keeps speedy students engaged in creative brainstorming rather than closed-ended problem solving. And having a question to solve that students generated increases all students’ understanding of the
task and their engagement.
The obstacle: Some students are shy or hesitant to participate in a brainstorming session.
The solution: Hold all students accountable by giving each a recording sheet.
Noticing and wondering is a tool to help students:
This means that at the end of a noticing and wondering sessions, students should be able to:
If students are not ready to do those things, we recommend any of the following activities:
PoW IQ: Describe the Information and Question. Say what you are being asked to find, and estimate an answer. Give a high and low boundary for the answer, say whether it could be negative, fractional, zero, etc. Tell the key information given in the problem that you think you will use.
Act it Out: Have a group of students act out the problem while the audience looks at their list of noticing and wondering. The audience should be prepared to share new noticings and wonderings, as well as tell if the group missed or changed any noticings.
Draw a Picture: Have each student draw a sketch that they think shows what happens in the problems. They should sketch first and then label their picture. Students can then use their sketches to say the problem in their own words to a partner or small group.
Noticings and wonderings are great tools for checking your work at the end of the problem. Students don’t have to ask, “Am I correct?” They can look at their noticing, wondering, and estimates to make sure they were accountable to all the information in the problem.
And noticing and wondering is a skill students can get better at. That’s why it’s important to look back over your noticings and wonderings and ask, “Are we getting better?” After solving a problem, ask:
After noticing and wondering several times, ask: