Introduction

INTRO TO ST MATH SUMMER SCHOOL

Developing a Strong Mathematical Schema

Schema is our brain's way of organizing our thoughts and experiences. It's the way we make sense of the world around us. As students engage in academic discourse during summer school, they're revising, extending and building new schema around mathematics concepts. View this video to learn more about schema.

Academic Discourse: Effective Facilitation Strategies

Facilitation plays a pivotal role in creating a classroom rich with academic discourse. Asking facilitation questions that focus on student thinking helps engage them in deeper learning around the concepts. Click through the slideshow for a few quick strategies.

As facilitators, teachers focus on asking the right questions, instead of telling students how to get the answers.

Click here for a talk moves document to help with student discourse.

When teachers tell students instead of letting them figure it out, the majority of the thinking rests on the teacher.

As facilitators, teachers focus on teaching students how to think instead of what to think.

Facilitation helps students put their thinking into words by making students’ thinking visible. At MIND Research Institute we have a three-step facilitation process to uncover, focus, and extend student thinking.

Step One is Uncover Student Thinking. Probing or clarifying questions should be asked to help get at a student’s understanding. These questions should be open-ended and help the student more clearly explain their thinking.

Some examples of questions to ask students include:

What have you tried?
Why did you. . .?
How did you decide where to begin?

These questions are great to use during math instruction to create academic discourse. Some examples of questions to ask students include:

How are you thinking about starting this problem?
How does this part relate to the problem?
Tell me more about...

Step Two is to Examine the Animation. Ask questions about the feedback to help students examine their thinking and results of their strategy as a visual proof.

Some examples of questions to ask students include:

What did you notice happening in the animation?
Why do you think that happened?
How does that compare to what you thought would happen?

While students may not have animated feedback in everyday instruction, they can examine and learn from their mistakes. Some sample questions could include:

What did you try that did not work? Why didn’t it work?
What did you learn from your mistake? How did it change your thinking?
How are you going to adjust your strategy based on what you learned from your mistake?

Step Three is to Apply the Hypothesis. Students form a hypothesis around what they are learning and how it will apply to future puzzles, communicate their hypothesis, and then test it with new puzzles.

Some examples of questions to ask students include:

What do you think will happen in this new puzzle?
How do you know if this will always work?

Help students gain a strong foundation of the math AND how to apply it in different situations. Some examples of questions to ask help students form and test hypothesis around what they are learning:

What happens if we use different numbers?
What is another way we can represent this?
How did you come up with your hypothesis?

Facilitating in Action: Puzzle Talks

For facilitation to be effective we must purposefully plan the types of questions we are going to ask ahead of time. The types of questions you ask should make students accountable for their thinking. The questions should address thinking that results in correct solution strategies and thinking that results in incorrect thinking strategies. Students should be engaged in processing, communicating, evaluating, considering the thoughts of others, and refining their own thinking.

Problem Solving Discussions: Effective Facilitation Strategies

Engaging students in discussions around the problem solving activities is a great way to explore connections, expand perspectives, and have students check and challenge each other. Have students share strategies, compare, and share their work. Click through the slide deck then watch the video to learn more about sharing student work.

The problem-solving activities provide a great opportunity to facilitate classroom discussions around student work.

Click here for a problem solving document to help with making connections.

Before students begin working on the problem solving activity think about what your students might do to solve the problem, and what mathematics you would want them to be able to see and describe.

What strategies would you want shared?
How would you order the work that is being shared to maximize the learning?
What questions would you ask?

Order the work you selected to share from least sophisticated to most sophisticated. Include some work that has misconceptions and/or errors in reasoning. Discuss both correct and incorrect reasoning.

How would you order these pieces of students' work?

A, B, C, D
C, D, A, B
B, C, A, D

Sharing the pictorial strategies is the easiest way to give all students access to the discussion. As you move from the more visual responses to the more abstract responses ask students to compare the strategies.

How are the strategies similar and how are they different?
Do you agree or disagree with your classmate’s strategy? Why or why not?

When students share work, ask questions like:

What is your level of understanding of your classmate’s strategy?
What questions can you ask to clarify your own understanding of the strategy?
How does your classmate’s strategy compare to your strategy?
Would you change any of your work? Why?

When students share work, ask questions like:

What is your level of understanding of your classmate’s strategy?
What questions can you ask to clarify your own understanding of the strategy?
How does your classmate’s strategy compare to your strategy?
Would you change any of your work? Why?

Facilitating in Action: Thinking and Reflecting Time

Students use their My Thinking Path, exit tickets, student notebooks (including problems of the day, math journal prompt) to review all that they have learned. Engage them in a discussion around what they have learned.

As you discuss focus on:

Unpacking their thinking - how are they thinking about the math they learned this week?
Examining their mistakes - what were their aha’s this week? How did they learn from their mistakes?
Applying their hypothesis - how might they apply this learning to similar problems? What can they connect it to?
Click the image to see the slide deck to get more information about My Thinking Path and Exit Tickets.

Final Week of Summer School Curriculum

Reflection Poster

This poster is completed in the final week of summer school. It is a culmination of the thinking, learning, and growth that students experienced during summer school.

Extending the Learning

This is an opportunity to revisit a problem of the day that has been previously discussed, extend student thinking and ask additional questions to deepen understanding.

Learning Showcase and Celebration

This is a time for students to share what they have learned during summer school. They will create a poster, complete their game and be prepared to give an oral defense of their work.

*Parents, community members, school administrators, teachers, and board members should be invited to this showcase and celebration.