Guide Students to Think Like Mathematicians with the BEAR Worksheet

There are many reasons why teachers can be overwhelmed in the math classroom. Students have differentiated needs, can be apathetic to their own learning, or simply struggle with the critical thinking skills required to tackle math problems. When students have the right tools, and those tools teach them inquiry-based learning, they require less hand holding and build confidence in their ability to learn independently. This enables the teacher to focus on other priorities.

The BEAR worksheet is part of MathTrack Pedagogy and was developed by the MathTrack team in order to guide learners through the process of solving math problems, especially for individual work time. This is part important for several reasons. It enhances self-guided learning for students by providing a framework for the critical thinking involved in tackling a problem successfully. It also provides a way for teachers to hold students accountable to the learning process, including questioning, showing their work, and reflection. All of these benefits are also why we use this tool to train teachers, including those pursuing licensure, a bachelor's degree, or professional development. 

BEAR stands for:

• Begin
• Explore
• Attempt
• Reflect

Each section has prompts that a student should be able to fill out independently through the use of designated resources. 

The BEAR worksheet

There are many applications of the BEAR worksheet and it can be adapted in several ways to fit the unique needs of you and your students. Let’s explore each of the sections in further detail.

Begin - Start a math problem by writing it down

Before we can tackle a math problem we have to know what it is. Having students copy down the problem is a low-lift way to get them started, and there are a lot of benefits to writing out math by hand to enhance learning. The BEAR worksheet can also be used as an assignment so for grading purposes it should be clear what the problem is from the worksheet alone. 

Explore - Understand what is included in the math problem and what it is asking us to do

In mathematics it can be tempting to jump right to the algorithm or set of steps for solving a specific type of problem. However, when we are learning something new, or struggling with a tough problem, we should take our time to fully understand it before we attempt to solve it. This is really where we practice critical thinking skills and take ownership of the problem solving process. 

The prompts in this section guide students to explore:

• What information is provided in the problem?
• What key words are present in the problem, and what do they mean?
• What should the answer look like? 
• What information is unknown that we need to figure out?

Within this section there is also a checklist for resources to use for support. For example, key words can be defined using their textbook or students can ask for help from their peers.

Even students who are struggling can work through these prompts independently, and the benefit of exploring the problem this way is that it helps the student better understand where they are getting stuck. Instead of "I don't understand this" we can help students ask more specific questions like "I don't know what this word means" or "does this picture look right?". Asking good questions is an essential skill for self-guided learning.

Attempt - Try to find the solution to the math problem

In this section students take the information they collected in the Explore phase, and actually find the solution. If this area is not big enough to work out the problem, whiteboards or scratch paper are great options. 

The goal of this section is not necessarily to get the right answer every time. Mistakes can be incredible learning opportunities and students should be encouraged to preserve their work, even if they got the incorrect answer. There is a separate box for the correct answer so students can reflect both on their actual work and the correct result.

Reflect - Celebrate and consider what we have learned

It is tempting to stop working on a math problem once we get the correct answer, but there is still a lot to learn through analyzing our work and reflecting on our result. In this section we answer another set of prompts which are expanded on below:

• Does the answer make sense? Why or why not?
  • If a student really understands a specific type of problem, they should be able to use their intuition to judge whether or not their answer makes sense. This depth of knowledge helps us transfer our learning to everyday life. 
• What resources really helped you the most with this problem?
  • Acknowledging what resources were most useful helps students become autonomous learners.
• Did you learn anything new while tackling this problem?
  • This prompt is all about the aha moments students may have had. This can be treated as data for the teacher so they better understand where students are at. 
• Could you explain your process back to someone else?
  • Being able to teach something is one of the highest degrees of understanding someone can have. Teachers can use this information to identify students that might make good peer tutors.
• What mistakes did you make along the way?
  • In a growth mindset oriented classroom mistakes should always be framed as learning moments, and these are worth celebrating. Having students identify mistakes is the first step to understanding why they happened and what they can do differently next time. 

Implementation Suggestions and Recommendations

• The BEAR worksheet is intentionally 2 pages long, making it possible to print it out on one double sided sheet of paper. Students can fill this out on paper using a pencil, or if the sheet is laminated or placed in a plastic sleeve, they can be filled out and reused using dry erase markers. 
• The BEAR worksheet is a great tool for demonstrating problems within each of the 3 MTSS tiers of support, including large group demonstrations, small group instruction, and individual interventions. 
• Setting boundaries for how many, and what, resources should be used before asking the teacher can help students work independently for longer. This frees up the teacher for whatever else they need to be doing in the classroom. 
• Challenge yourself and your students to fill out every prompt for every problem. You may be surprised how even the simplest problems can be drawn out or analyzed deeply. 
• Peer to peer learning can be difficult to implement and advanced students may not know how to tutor others without just giving their tutee the answer. The BEAR worksheet is the perfect guide for helping students collaborate effectively. 

The BEAR worksheet can also be adapted to fit the individual needs and resources of your students, and teachers are encouraged to make this method their own. For example, adding additional Explore and Reflect prompts can enhance learning for specific types of problems. You can also name the specific resources you have available in the resource list.

Ready to try out the BEAR worksheet yourself?