The Exercise with No Wrong Answer: Notice and Wonder

Guest post by May Mei, Denison University.

How often have your students said nothing rather than risk saying something wrong? And how often in our own writing are we so paralyzed by the fear of imperfection that we end up writing nothing at all? 

Enter Notice and Wonder, the exercise that has no wrong answers. After all, everything you can observe about a problem is a valid thing to notice and every question you can ask about a problem is a valid thing to wonder.

Notice and Wonder is a way for instructors to create a safe place of exploration by allowing students to brainstorm before attempting to solve a problem. It’s a simple process-students are presented with a problem and before attempting to solve it, they are asked what they notice about it. When all students have contributed, or nothing new is being noticed, students can then answer what they wonder.

This provides opportunities to discuss what is still unknown and puts all students on equal ground-everyone can wonder about something. Because there are no wrong answers for either of these questions, all students can participate in the activity.

This handout describes Notice and Wonder as an in-class activity, but I like to use it to review for an exam.

If my students have an upcoming exam, I will use the class period before as review, and sometime before that review period I ask each of my students to email me one thing they noticed and one thing they’re still wondering about. Just before class on the review day, I put all the students’ Notices and Wonders into one document and distribute it to the class. As I'm making this document I'm able to recognize themes and repeated observations or questions and can focus on those during the in-class review.

The purpose of the exercise is to help me see what my students need, but also for the students to take inventory of what content the course has covered and to self-assess their understanding.

Note that a brief discussion about what makes a fruitful Wonder may be needed. Let’s consider an upper level course, such as an introductory course on proof techniques. To help students develop ‘good’ Wonders, I provide them with the following examples and ask about the different levels of self-reflection that they display.

"I wonder in Chapter 6, Exercise 5 in which it asks us to prove 3 is irrational, which definitions to use. Just like the proof we did for2, here I would say suppose 3 is rational so therefore3can be written as a/b where a and b are in Z. But once I squared both sides and did some algebra it does not come out to show a2 is even. Since we haven't done irrational numbers any other way I am confused as to what to do."

3 reasons to consider incorporating this exercise into your math courses:

• Notice and Wonder ingrains good habits of mind. This exercise provides a way for students to engage with material after the initial in-class exposure. The Notice component encourages students to draw connections that may not have been apparent in the first read-through while the Wonder component asks students to evaluate their comprehension of the material.
• Notice and Wonder minimizes instructional prep time. I spend about 20 minutes compiling responses. For a class of 25 students, this generates much more material than I can cover in a 50 minute class. The responses provide students with something to work on after class, when they may feel compelled to study.  The student-generated ideas provide guidance about how and what to study for students who are unsure of how to proceed and need to develop useful study habits.
• Notice and Wonder allows students to gain insight into the thought processes of their peers. How many times have you heard a student say something to the effect of "everyone gets it but me"? Students gain the benefit of seeing that other people have questions, and maybe the same ones as them. Students can also see questions that they may not have thought to ask, and can’t yet answer. 

I'm always impressed with the wonderful gamut of things students notice and wonder.  Thus the practice makes not only supports student learning, it also makes my own teaching more effective and enjoyable.

Design Practices to Maximize Students Learning

By Karen Keene, North Carolina State University, Beth Burroughs, Montana State University, and Hortensia Soto, University of Northern Colorado

This semester Teaching Tidbits continues its posts highlighting the new Instructional Practices Guide (IP Guide) from the Mathematical Association of America (MAA). This evidence-based guide is a complement to the Curriculum Guide published in 2015. The guide provides significant resources for faculty focused on teaching mathematics in evidence-based ways. There are three focus chapters in the guide, Assessment Practices, Design Practices and, Classroom Practices, along with some additional sections that explain the importance of evidence-based instructional practices. Karen Keene and Beth Burroughs served as lead writers for the Design Practices and Hortensia Soto was a project team member and co-editor of the MAA IP Guide.

College professors have been planning for their classroom instruction for as long as universities have existed.  Planning for instruction is one facet of the practice of design. The MAA IP Guide addresses design practices as

“the plans and choices instructors make before they teach and what they do after they teach to modify and revise for the future. Design practices inform the construction of the learning environment and curriculum and support instructors in implementing pedagogies that maximize student learning.”

Design practices include planning for the content, but much more as well.  Designing to maximize student learning requires professors to consider many things as they plan, but also to use the results of teaching to continue to revise and modify teaching in the future. Consideration of what is known about teaching practices and how students learn is necessary for all parts of the design. The design practices chapter of the IP Guide includes questions that instructors could ask themselves while designing instruction (i.e., how can I be sure to be inclusive in my instruction?), as well as many suggestions that focus on designing cognitive and affective learning goals, developing tasks and other ideas for instruction, and creating learning environments. To focus on student learning, instructors need to design the learning environments, the tasks and the homework based on the student learning objectives.

In the design practices chapter, the authors offer design principles and considerations, educational research, and real examples provided by faculty in the field.  Readers can access the chapter for a quick planning idea, or to consider making bigger instructional changes that focus on student learning; both are exciting and possible.