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To check understanding, ask students to write three different summaries: One in 10-15 words; One in 30-50 words; One in 75-100 words.  The different lengths require different attention to details. Compare/ contrast with peers/ look at teacher model (via document camera.) What might you ask your students to summarize? Example:  How can you solve for the missing parts of a right triangle?

List 3 things that a fellow student might misunderstand about the topic. What topic might you use? Example: Solving exponential equations such as 6x-1 = 32x.

Ask students questions, have them respond on notebook paper anonymously. Students then hand their papers in. Teacher immediately, randomly passes out the papers to students for grading. Students get practice grading others work, but shouldn't know who is who. Teacher then takes informal poll about how many questions students answered correctly. What is a problem that you could give your students? Example: Use Cramer’s Rule to solve a system of equations

Have students build/create something that requires that they apply what they have learned. What might you ask your students to do? Example:  Create a real-world problem requiring the cosine law to solve.

Have students use manipulatives (physical objects) to illustrate and discover mathematical concepts, whether made specifically for mathematics (e.g., connecting cubes) or for other purposes. What might you ask your students to do? Example:  Use algebra tiles to visually see how to factor trinomials.

Metacognition allows for the students to process what they did in class and why it was done. At the end of class have students complete a table similar to the one below. Collect and provide feedback. What did we do? Why did we do it? What did I learn today? How can I apply it? What questions do I still have about it?

Hand out a short quiz or a few simple questions, and students give them to you as they leave your class (Exit slip: 3-2-1!). 3 things I learned today; 2 things I found interesting; 1 Question I still have.

Preset questions in Google Forms. Students who normally would not participate in class will participate virtually. What might you ask your students?  Example:  Go to https://docs.google.com/forms/d/1n3N9FV9xd-VkOcO63YY8FGldpsfCf6NE5DxLs_W1DCU/edit

Give each student a student response system (or clicker) or Plickers (cards) or use a service like Survey Monkey, Poll Anywhere, or Google Docs and ask questions during class, and have students respond individually (or in groups) to the questions. What questions might you ask your students?

Students are able to summarize what is learned from a lesson within a short sentence on Twitter. What might you ask your students? Example:  What are the 3 components of robust learning environments?

Students create short videos or screen-casts where they explain their reasoning. You can then watch what they create and see what they are able to explain, what they omit, and what they may not understand. What might you ask your students to do? Example:  Your assignment is to create a story, song/rap, or video about the quadratic formula.  The formula must be presented in its correct form, with every variable used, in your final project.  If you decide to create a story, make sure you highlight the quadratic formula in your story, and at the end of your story write out the quadratic formula.  See a College Algebra class presentation at UCA https://www.youtube.com/watch?v=E-Eam865X3Y