go Deeper

Dimension 1 Math Strategies

What’s the big picture?

Identify an “essential question” or “big idea” that’s important for the math your students are working on. Share it with students at the beginning of the lesson and find time, especially at the end of the lesson, for students to connect what they’re doing to the big idea. Check in with students about it while they’re working in groups, or have a few students share or lead a class discussion about it at the end of a lesson.

Always, Sometimes, Never

Pose questions that require explanation and are not straight yes/no or one answer solutions. For example, instead of asking, “Is it true or false that when you multiply two numbers, the answer will always be bigger?” ask, “When you multiply two numbers, the answer will be bigger. Is this statement always, sometimes or never true. Explain your reasoning.” This gives students opportunities to explore more possibilities, such as positive / negative numbers and fractions.

Ask for patterns and outliers

To give students something more to think about while they practice similar problems or do problem sets, ask them to describe any mathematical patterns they noticed while working on similar problems. Or, ask them to find problems that seemed like outliers—ones for which the method didn’t work as expected, or with a solution that surprised or confused them. This can be given in addition to a regular homework assignment. Have a few students share their patterns and outliers in class, or have students discuss them in pairs.

Deep Dive Homework

Instead of turning in an entire problem set from homework, students pick some small, reasonable number of problems that they will show work from in detail and then turn in. The goal is to have them make something they want to show the teacher, whether because they’re impressed with what they did, want feedback on that specifically, enjoyed solving it and want to spend more time.

Invent an argument

Come up with some fictional characters who disagree about a math idea you want to teach and ask students how they would resolve the argument. Make sure students also discuss why each side thinks what they do, even if the characters’ arguments aren’t correct.

Make categories

After a long problem set or homework assignment filled with similar problems, ask students to group the problems into categories. They can choose the categories they like, but encourage them to be mathematical. For example, after a homework assignment of solving systems of equations, students might choose to categorize the problems according to those that have solutions and those that do not; those that have solutions in different quadrants when graphed; those that were best solved with different methods; etc. Let students be creative! This gives students opportunities to see the bigger picture after doing detailed problems.

Open it up

Reframe a problem or problem set so that there’s more for students to discover. For example, when doing proofs with students, instead of asking them to “show” something, such as that the diagonals of a rectangle bisect each other (which assumes that it’s already known to be true), pose the thing to be shown as something to discover. Ask, “What do you notice about the diagonals of different quadrilaterals?” and give students time to draw, find patterns, and make claims about what they see.

Reflective Journals

Can begin simply, by asking students to respond to a single question like: What did I learn today? Every day, teachers can choose 3 journal entries to read to everyone at the beginning of the next lesson, that revisit content, embody habits they are trying to build in the whole class, etc. Over a couple weeks, all students’ journals are chosen. Journals can be a place where students write the problem, record their thinking, how it changed, and why, and reflect on what they did not know previously that they know now.

Student-led questioning routine

Establish a routine of student-led questions and challenges after viewing each student presentation or work. For example, students might routinely finish their presentation by asking the class “Do you have comments or questions?” and calling on classmates.

What do you Wish you Knew?

At the end of a test or quiz, ask students to choose at least one problem they aren’t sure they did correctly and write a quick reflection about what they think they’re missing or what tool/method/idea would be useful to solve the problem correctly.