Effective professional learning is engaging, relevant, connected to long-term goals, and involves participants in interactively constructing understanding. Because thinking routines (especially like those described in Making Thinking Visible by Ritchhart, Church, and Morrison) are tools, structures, and patterns of behavior that are used to initiate, explore, discuss, document, and manage thinking, they can be used by educators during professional development to help actively become engaged in constructing understanding. Furthermore, since they're experienced themselves, those educators are more likely to use those thinking routines with their students, a vital part of creating a culture of thinking in their own classrooms.

Therefore, at a recent pedagogical leadership team meeting, when one of the leaders asked other teams how they guided their students through solving mathematical word problems, I knew that using a thinking routine would help guide us through that exploration.

Here is that story:

**Start with a concept.**

We started with the timeless, abstract, universal, and transferable idea that

*solving problems independently is made easier by following a set protocol*.

**Pick a specific, concrete example of a person, place, situation, or thing that illustrates that concept.**

In order to gain an understanding of that abstract idea, we explored different protocols used by teachers throughout our building to help their students solve mathematical problems independently.

**Create an opportunity for participants to explore that concrete example.**

During this phase of the conversation, we agreed to dialogue and suspend judgement. For more information about dialogue, discussion, and how both can be used to transform conversations we have in schools into meaningful communication, see "Teacher Talk That Makes a Difference" by Robert Garmston and Bruce Wellman.

To guide our dialogue, we followed the thinking routine See-Think-Wonder from Making Thinking Visible by Ritchhart, Church, and Morrison (p. 55).

*See: What do we see?*During this phase of the dialogue, team members shared the protocols they use with their students to solve mathematical word problems. Comments and crosstalk were discouraged.

1st protocol shared:

- What are you trying to find?
- What numbers will you use?
- Open number sentence - using a variable for the unknown
- Decide what to do with a remainder

2nd protocol shared: (students don’t have to follow these in order)

3rd protocol shared: U.P.S. Check- Make a prediction
- Answer
- Number sentence
- Strategy
- Show your thinking

- Understand: look at the problem and understand what it is asking us to do. What are we trying to find out?
- Plan: What do we need in the number story to solve the problem? Circle the important points.
- Solve, using different strategies.
- Check: Solve it a different way, using another strategy to see if you get the same result.

4th protocol shared: (for behavior problem-solving)

- What are you doing that I can’t allow?
- Why can’t I allow you to do that?
- What will you do instead, next time?

- Objective: What do we know about this?
- Reflective: How do we feel about this?
- Interpretive: What does this mean for us?
- Decisional: What are we going to do?

- Equation
- Representation (including acting it out), to check for understanding
- 1st step
- Next step
- Answer with a label

- What do you want to find out?
- What do you know?
- What will you do?

- Read the problem.
- What do I know?
- What is the question?
- What strategy will I use?
- Organize my thinking so others can understand what I did.
- Answer the question in a complete thought.

- Understand the problem
- Devise a plan
- Carry out the plan
- Look back

*Think: What do we think?***Next, leaders were invited to comment on what they had just heard, noting any "big ideas" that surfaced during the sharing period.**

- There is more than one way to solve problems.
- There are a lot of similarities, but in different language.
- Protocols range from a lot of steps to a few steps.
- Lots of visual aids, graphic organizers
- Acting out and using manipulatives helps.

*Wonder: What does this make us wonder?*- Do we all have to be doing the same thing?
- Would this be a site-based decision or district-wide?
- Using the various protocols, what’s the level of independent use?
- Can students name the strategy they’re using?
- Do the protocols we’re using lead to innate problem-solving (are students internalizing the steps)?
- Can kids explain why they’re using a particular strategy?
- Does the district math coordinator have any insight?
- What do math experts have to say?
- What language constructs need to be supported?
- How much of this is a vocabulary issue and not a math issue?
- Could the vocab piece be consistent throughout the grades?
- Does our curriculum use the same language as the standardized tests that our students take?
- Should protocols be teacher-given or student-created?
- If protocols are student-created, how can teachers support students? Is this the right way to go?
- Can we use prompts like “show me your thinking” and “did anyone solve this in a different way?” along with these protocols?

**Check for understanding by having them write a concept statement.**

After our discussion, leaders were asked to respond to this question: "What can you tell me about how we can make solving problems independently easier for our students?"

**Reflect on their thinking and decide next steps.**

After analyzing and reflecting on the responses above, here are the big ideas I see surfacing.

__What do you see?__

A protocol for solving problems in math should:

- require students to make their thinking visible (or verbal).
- require students to show different strategies to solve the problem.
- help students identify vocabulary that is essential to understand the problem.
- help students visualize the problem.
- have few steps so students can use it independently.
- be universal so it can be used at all ability levels.
- be transferable to all settings where problems need to be solved.
- be student-created (at least partially).
- help students develop PYP attitudes like creativity, commitment (persistence/grit), independence.

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