Doing some learning tonight. Notice and wonder seems to be a theme recently, most recently at Educating Grace. Things:

I was reading Fawn Nguyen. She’s amazing. Her posts on deconstructing a lesson are solid gold. Seriously, go read them. They’re way better than anything I write.

Fawn advocates for two approaches to introducing a task. Approach A:

- What are we trying to solve for in this problem?
- What information do we know?
- Is there information that you wished you knew? Why is it not given then?
- What’s the first strategy you have in mind that might help you attack this problem? And why did you say ‘do a simpler problem’?

Or** **Approach B

- What do you notice?
- What do you wonder?

**I teach almost entirely through Approach A.** I’ve used the notice & wonder protocol, and I enjoy it, but it also scares me a little bit. Fundamentally, I am a teacher who wants students to learn specific skills and concepts on a given day, and then move on to the next concept. I set aside time for problem solving, and these are the places I am most comfortable using notice & wonder, but it’s a small part of what I do in the classroom.

My basic issue is that if I have a specific goal for where I want my students to get by the end of the lesson, I also have specific questions in mind to get them there. Using notice & wonder — pushing authority to the students, giving them control of the lesson — is scary. What if we don’t finish, and this class falls behind the other sections? What if they decide they don’t care about this question?

**There are tons of great thoughts out there about the value of giving students this freedom. **These two Ignite talks (5 minutes each) by Annie Fetter (referenced by Fawn), and the unbelievable Max Ray illustrate the power of letting students wonder and harnessing that engagement for learning.

**So I’ve got this puzzle. **Notice & wonder vs more directive forms of problem solving (vs traditional teacher-led instruction). Notice & wonder seems to have higher potential for engagement, traded for a less predictable classroom.

Two more thoughts helping me to sort this out:

Dan posted this week on the idea of **developing the question. **He describes it this way:

If I do a good job developing a question, my students and I take a little longer to reach it but we reach it with a greater ability to answer it and more interest in that answer.

Dan gets at a key aspect of great math questions. I think a more directive framework is what students need to develop the question. If all of my students are noticing and wondering, inevitable they are noticing and wondering different things. Some are easy to answer, some are impossible, some are more or less interesting. Developing the question requires knowing what that question will be, and for me that means that I have it planned in advance, and I am using each question I ask to move my students toward it.

Finally, **experts vs novices**. There’s tons of great literature out there — this is a fun sample. Here’s a quote:

- Experts notice features and meaningful patterns of information that are not noticed by

novices.- Experts have acquired a great deal of content knowledge that is organized in ways

that reflect a deep understanding of their subject matter.- Experts’ knowledge cannot be reduced to sets of isolated facts or propositions but,

instead, reflects contexts of applicability: that is, the knowledge is “conditionalized”

on a set of circumstances.- Experts are able to flexibly retrieve important aspects of their knowledge with little

attentional effort.

Seems to me like novices, while they may be engaged by noticing and wondering, will always struggle to notice and wonder mathematically meaningful things that motivate learning connected to prior knowledge. However, by the same token, once students have gained familiarity and fluency in a concept, they’re noticing and wonderings will reflect the deeper ideas of that concept, and promote further learning — learning connected to prior knowledge, that students will retain and be able to apply in the future.

**So that’s my grand theory of noticing and wondering.** I’ll be experimenting with it more this year, as a tool for connecting knowledge and deepening understanding once students are familiar with a concept. I think in a master teacher’s hands, notice and wonder will absolutely be more versatile, but for me, this is where it fits into my students’ learning, and I’m excited to learn more about it.

Howard PhillipsAbout your approach, described in paragraph 2.

What if you get to the end of the lesson, all the stuff has been presented, the kids do some work, and half or more go away with no clue as to what you were talking about?

Math is one of the few subjects in which one’s sense of great achievement can be based on test results alone.

The blog post here

http://gowers.wordpress.com/2012/11/20/what-maths-a-level-doesnt-necessarily-give-you/

is about The UK course equivalent to AP Calculus, but it is relevant at all levels.

Pingback: How do we get better at researching online? | Learning Reflections