When do you use problem-based tasks? |
We use problem-based tasks to develop students' conceptual understandings.
To that end, we use problem-based tasks to introduce new concepts and before teaching students a particular method to solve a type of problem. This type of lesson occurs about once a week. On other days, lessons focus on building students’ fluency and efficiency in mathematics. |
What is the structure of a problem-based task lesson? |
We use three simple components adapted from John Van de Walle’s Teaching Student-Centered Mathematics in our problem-based task lessons: Before Problem Solving, During Problem Solving, and After Problem Solving.
Before Problem Solving: Understanding the Problem (no more than 15 minutes): During this portion of the lesson, introduce the problem to students. We use an anchor chart called a KWI to help students unpack the problem and ensure that they share a common understanding of the problem before engaging in it. The “K” stands for “What do you Know about the problem?” Students identify the information stated explicitly in the problem and activate their prior knowledge about the situation and any relevant mathematics. The “W” stands for “What do you need to find out?” Students explore what the problem is asking. In addition, you can clear up any confusion and answer questions to ensure that students can productively engage in the math. The “I” stands for “What Ideas do you have for solving the problem?” Students explore possible pathways to solving the problem. By asking students to explicitly unpack and explore the problem before solving, you help avoid any comprehension challenges that may distract students from the math and assess whether students are prepared to solve the problem. Students can unpack the problem in several ways, and the videos showcase a couple of these. In general, students can take a first pass individually or in pairs before you bring the class back together to make sure that the whole class understands the problem before beginning to solve it. During Problem Solving: The Grapple (15 to 45 minutes): During this portion of the lesson, students actively grapple with the mathematics as they attempt to solve the problem. While they work, circulate, listen to students, and ask probing questions to keep them thinking without providing too much information. This is also a time to identify one to three students to share at the end of the class. Students can work in several groupings, including individually, in pairs, or in small groups. Most teachers find that pairing students works well, but small groups can be helpful for younger students early in the school year or for older students grappling with more complex problems. After Problem Solving: Share and Debrief (at least 5 minutes): The lesson ends with students sharing and debriefing to synthesize their learning. In the During Problem Solving portion of the lesson, you selected one to three students to share based on who had an instructive solution, made a discovery that might benefit the rest of the class, or got stuck in a place that highlights the lesson’s targeted concept. The students who share must help everyone understand the mathematics better, though this doesn’t always mean that a student who shares must have solved the problem correctly. |
|
Can I have a list of all the problems Two Rivers has used for problem-based tasks?
|
We are more than happy to share lesson plans with problem-based tasks. However, the best problem-based tasks are crafted with a specific class of students in mind. Tailoring tasks to students’ interests and their current levels of knowledge and skills is essential to ensuring that every student will grapple constructively with the concepts. This also helps teachers become intimately familiar with problems, which is essential for any problem they plan to use with students. In our experience, finding, solving, and adapting problems from a variety of sources, including textbooks and websites, is the best way to meet the unique needs of a given class of students.
|
|
How do I find the problems? Where do I go to find problems?
|
While there isn’t a single source, we do rely heavily on certain resources to help us find and create rich problems for students. Teaching Student-Centered Mathematics by John Van de Walle et al., any of the many books from Marilyn Burns’ Math Solutions Publications, and Cathy Fosnot’s Context for Learning Mathematics are all great text resources with rich problems and foundational information about the mathematics. In addition, the following websites are great collections of problems that are searchable by area of mathematics and age range:
|
|
How do I find a problem that will meet the needs of all the students in my class? I have some students who are several grade levels below everyone else and few who are several levels above.
|
Differentiation in diverse classrooms is certainly challenging. Luckily, problem-based tasks offer several possible ways to engage all students in developing deep conceptual knowledge of the mathematics. First, it is often possible to find or craft problems that allow for multiple pathways to solutions. Allow some students to draw or act out a problem while encouraging other students to write out standard algorithms. This enables all students to engage in the problem solving and helps them understand the math more deeply as they find connections between different models of the problem.
However, when it isn’t possible to find or revise a problem so that all students can engage with it, it can be equally productive to have students work on similar problems that work with the same basic concepts. You can simply change the numbers or add complexity for more advanced students. Often, it is possible to give students choice over which level of problem they want to engage in. The easiest problems available to students should be at grade level, and the scaffolding should change how students approach the problem, not the actual mathematics students grapple with. |
|
I watched the videos, and I'm amazed at how your students are productively struggling while solving the problem. How do you get your students to do this?
|
Thank you! Our students definitely did not come to school knowing how to grapple productively with mathematics. Throughout the school year, we explicitly name the expectations for work and share times, practice the expected behaviors, and debrief and assess students’ ability to meet the expectations. We spend much more time norming classroom behaviors in the first six weeks of school, but students still need regular reminders all year round.
One technique we use is to share a few of the Standards for Mathematical Practice from the Common Core State Standards. This helps us name important expectations, such as making sense of problems, persevering, and effectively critiquing one another’s reasoning. |
