go Deeper

Formative Assessment Strategies

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.

Choose your Color

Each student uses a different color pen/pencil when working on a group problem. Students can use poster paper or larger than normal paper, so that everyone has physical access to the paper.

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.

Fishbowl

During class discussions, split the group in half. Have one half sit together so they can see each other, and the other half sit in a circle around them. The inner group talks for a certain amount of time (3 minutes, 5 minutes) with minimal input from you. The outer group writes what they heard during the discussion. Collect their notes; switch groups on different days.

Group Questions

The teacher only answers group questions (questions that have been agreed upon by all group members). One student raises their hand when the group has a question. The teacher asks a different student in the group what the question is and only answers the question if all group members agree it’s a question.

Idea Melting Pot

After a do-now, rather than having students raise their hands to share how they solved a problem, have them turn in their work to you without their names on it. Randomly pick one of the papers and choose a student to present the solution written there. The class can work together to understand what was done.

Name It

When a student shares an idea, write their name on the board next to it when you record it. Refer to that idea as “so-and-so’s idea” or “so-and-so’s strategy”. Keep track of whose ideas have been highlighted from class to class.

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.

Shady Bar

For the key ideas in a unit, have students keep a page in their notebook with each idea listed and an empty thermometer/bar drawn. Before you’re ready to move on to a new unit or give a test, have students shade in the bar according to how comfortable they feel with the idea and give the page to you. You can also have a class discussion in which students share how they feel and give each other tips for how to study the ideas.

Share Wrong Answers Like They’re Right Answers

Share an incorrect solution to a problem, saying “another student solved the problem this way. Identify similarities and differences between this solution and the solution you have. What makes sense to you? W hat questions do you have?” Encourage students to share their thinking in a whole class discussion or in small groups about their own solution to the problem as it relates to the incorrect solution the teacher provides. If possible, let the students come to the decision that the provided solution is incorrect and encourage them to justify their thinking.

“Spy” on Another Group

During groupwork, have one member of each team “spy” on another team. Or encourage students to go to a different group and ask questions. Encourage students to build from ideas they heard at another group.

Start with the End

Start a unit with a rich problem that draws out ideas that will be useful throughout the unit. This helps motivate for students why they’re learning the things they are. Ideally, such a problem can allow students to develop the big mathematical ideas (rather than be told them).

Turn it Back to the Students

The teacher does not say correct or incorrect, but rather shifts the authority back to the class as a whole. “What do you all think?” “What questions do you have for [student’s name]?” “Is that an answer that makes sense for this problem? How do you know?” Note down the challenges that you encounter, and bring them back to the group.

Turn-and-talk about a lower-stakes question

Ask students: What is confusing/tricky about this problem? What are three things you know about this problem? With your partner, summarize what we have done so far. Ask your partner: Why did we multiply there?

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.