Tuesday, December 11, 2012

Problem-Solving Sharing: Whole Group Area

This week we are excited to add another element to the Math Classroom Challenge on Problem-Solving Sharing. Thinking of classroom space, it is essential to designate a large area of the classroom where students can come together and become mathematicians in a real mathematical community. Take a look at these pictures of Sandy Handrick's 5th grade classroom:

Sandy has a large area for these young mathematicians to come share ideas and strategies that emerge as students do the math and teachers facilitate discussions. Notice that she even has ample space on her white board for student sharing.

What is problem solving?
Problem solving is a process of inquiry where students are investigating mathematical and real-word situations. This could be in the form of a specific problem type in which careful number choices are selected to bring out mathematical relationships, or it could be a problem in which students are applying their mathematical thinking to an authentic, real-life situation such as problem-based learning or performance tasks. Problem solving is NOT giving the students a problem and telling them a certain operation to use and how to solve it step by step. If that's happening, who's doing the problem solving?

How often should students be problem solving?
Every day! Students should have the opportunity to solve a variety of problem types and real-world problems in which they can explore and investigate mathematical relationships. Problem solving every day is critical for a successful math community. For example, if students only have the opportunity to problem solve once a week such as every Friday, that is less than 36 times a school year that they will problem solve. That's not enough! Think of mathematical thinking like a muscle that students must exercise. It takes time and practice for that muscle to get stronger. Making a connection with reading, do you only have your students read once a week and expect fluent readers?

I have so many TEKS to teach, how do I fit in problem solving every day?
One of the biggest misconceptions in mathematics is that skills must be taught in isolation. This is just not true! Our math standards (TEKS) are connected in so many ways. When we only focus on one TEKS or skill in a day or week, this creates a misunderstanding in our students that skills are not connected. One good problem can encompass many TEKS.

How should students share their thinking?
This can be done in many ways! Here are a few examples:

1. Select 2 or 3 students to share to the whole group: We've all had the whole group sharing time where students aren't paying attention. Usually, this is because we select students to randomly share, students don't understand the learning goals, and therefore, they do not make any connections between the student who just shared their strategy and their own ideas about math. Good whole group sharing should only take 5-10 minutes and be focused around a clear instructional goal. Ask yourself, "What is my purpose for these students sharing?" Do you want focus on a big idea, connections between different solutions and strategies, or moving students from less efficient to more efficient strategies?

2. Partner Share: Partner students based on their levels of understanding. Partner a low with a medium and a medium with a high. Be flexible! As students grow in their understanding toward different concepts, partners will need to be changed. The main point here, is if you want to get the most out of sharing time, students should not be partnered randomly.

3. Gallery Walk: Have about half of the students post their strategies so they are visible. This could be done by writing on a chart paper, simply leaving their journal open, or using technology such as the "Show Me" app on the iPad. These students stand by their strategy as the other students walk around and talk, ask questions, collaborate, prove and communicate their thinking to one another. The next day, students can switch roles.

Where do I get problems?
Luckily, LISD's math curriculum is rich with examples of problem types and performance tasks to support this area of instruction. We have several problems and a performance task for each Unit of Study. Please remember that these are problem suggestions and we encourage you to tailor them to fit your student's interest and appropriate number choice.

We would love to hear your questions about this topic! Please share with us your thoughts! Happy problem solving!

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