Tips for Making the Most of MathByExample

Review the Features of the Assignments with Students Early in the Year.

These assignments are likely to look strange and unfamiliar to students, so reviewing the format of the assignments early in the year is important to ensure students are aware of expectations. You may also choose to take this opportunity to frame a growth mindset around making mistakes in math class, and how analyzing mistakes can help us all become better learners. 

Some prompts for discussion may include:

What can we learn from looking at a student’s incorrect work?

Why do you think it’s important to explain your reasoning in math class?

What can we learn from other students’ work before completing a problem on our own?

Why is it helpful to sometimes make mistakes? 

The More Exposure to Worked Examples, the Better.

Our experience has shown that the more students are exposed to worked examples, the better. However, there’s no set frequency that we recommend. Use as many or as few assignments as you like. You may decide to use an assignment over two days or to use two assignments in one day. There may be weeks where none of the assignments align to what you’re teaching, but other weeks when many of the assignments will fit well. On average, completing two to three assignments per week throughout the year would allow you to use all of the assignments with your students.

Allow Students to Work in Partners or Groups.

Many teachers have reported that they find the assignments most beneficial when students work through the assignments together, rather than individually, since students often discuss the mathematics. Students begin to reason through mathematics content and deepen their understanding, especially when given the opportunity to explain to a peer who is having trouble understanding the problem or how to answer the questions. Mathematics discourse has been shown to improve student understanding and is strongly promoted by 21st century standards. It is important to note, however, that setting norms for partner and group work is necessary in order to avoid students relying on higher-performing or more vocal students to find the answers. 

Review Assignments as a Class.

Though we recommend against completing the problem-sets as a class, it is useful to review assignments as a class once students have had a chance to work through the assignments themselves. Research has shown, in fact, that students who review the assignments as a class learn more than those who do not. By doing so, students are exposed to a range of thinking from other students. Critiquing the reasoning of others is another Common Core practice standard.

Avoid Limiting GeometryByExample to Being Only a Whole Class Activity.

Research demonstrates that students must reason through the problem and analyze the steps and strategies used in order to confront common errors and dislodge misconceptions. It is likely that not all students would be actively engaged when answering them as a class, and there is a strong likelihood that the students who are more likely to benefit from the assignments (students who do not yet understand the concept) would be the first to disengage in a full-class read through. There are exceptions to this. For instance, as mentioned above, going through the first one or two assignments of the year together can be beneficial, so you are able to help students understand the format of the assignments and set expectations for completion and written responses.

Encourage Students to Complete the Self-Explanation Prompts.

We understand that some of the questions may be more challenging, especially for students who do not have experience explaining their thinking in written form and for students who are not English proficient. However, we strongly recommend encouraging students to at least try to answer each self-explanation prompt. Research shows that at least attempting to answer the questions improves learning, even if students use informal language.