It’s fine to work on any problem, so long as it generates interesting mathematics along the way—even if you don’t solve it at the end of the day.

—Andrew Wiles

It seems intuitive that students who are genuinely engaged in a mathematical task will learn the mathematics in a more productive manner than students who are not engaged. In fact, a 2009 Gallup poll found that a one percent increase in student engagement resulted in an eight percent increase in mathematics achievement, and schools in which students were in the top quartile of average engagement were 82 percent more likely to get above the state average for mathematics achievement than schools in the bottom quartile of engagement (Smith, 2017a). Beyond being intuitive, student engagement is a proven factor in mathematics achievement.

Sounds great, doesn’t it? So what can be done to increase the likelihood that students will be engaged with the tasks we ask them to do? Here are ten tips:

**Make It Fun**

Almost any task can be turned into a game to add a sense of fun to a skill that is being practiced. Consider turning number-based problems into a Memory or Matching game simply by making problem cards and answer cards to be flipped over. A rummy-style card game (called Triplets) can be made by creating cards that have the same answers, such as 5 + 6, 12 – 1, 4 + 7, 15 – 4 and 11 + 0 for Kindergarten or First grade, or x + 2 = 9, 2x = 14, –x = –7, 25 = 4x – 3 and 2(x + 1) = 16 for algebraic equations. There are many games that are easily made to turn practice into a collaborative or competitive activity (Smith, 2017b and c).

**Incorporate Activity**

Keep in mind how long students sit. Any activity that provides action and activity is an instant source of energy and requires more engagement. Consider making an “Around the World” or “Treasure Hunt” activity. Display posters of problems around the room or down a hallway. At the top of each poster, post an answer to a different poster’s problem. Students begin the game at various posters. They solve the problem in front of them and then look for their answer at the top of another poster. If they can’t find the answer, they have made an error. When they find the answer, they move on to the problem on the poster where they found it. This continues until students complete all the problems (Smith, 2017a).

Any kind of movement in class fosters engagement for most students. Even having students stand to discuss a question can bring new life rather than turning and talking in their seats. This is also why students may want to work on the floor!

**Change it up!**

Add elements of surprise. Try using playing cards or dice to generate numbers. Change your routine or sequence. Have a variety of partner options. Use extra-large or very small pieces of paper for student work. Have students create skits to teach a concept. Try doing anything out of the ordinary, and see what happens!

**Provide Choice**

Research in motivation has changed over the years. Intrinsic motivation is increasingly attributed to giving students voice and choice. In fact, research suggests that at least 35% of the time students should have cognitive choices to increase intrinsic motivation (Smith, 2017 b and c). Providing choices is a great way to get student buy-in, and thus increase their motivation. Choices can be included by a choice of tasks, a bank of problems from which students choose a certain number or even various methods for students to show their leaning through assessment options.

**Develop Discourse Skills**

Having students participate in robust mathematical conversation develops mathematical concepts as well as increasing engagement. However, many students do not know how to have these conversations and need to be taught how to communicate with one another, and not just answer teacher-directed questions. One way to do this is to provide sentence stems (Smith, 2017b) including:

- I agree with ___ because ____
- Another way to think about this is _______
- I did it a different way. I ________
- I disagree with ___ because ____
- I would like to add on to what ___ said about ____
- Can you explain what you mean by ____
- Can you show ____ in another way
- I think that ________ because ________

**Practice Concept Attainment**

This strategy provides students examples and non-examples for a topic. Students have to determine what makes the topic what it is. For example, consider pictures of many polygons as “Examples”, and pictures of 3-D figures, circles, open shapes, etc. as “Not Examples.” You would then ask students to determine what makes a polygon, a polygon. I’ve also heard of a teacher covering herself with Post-It Notes and asking students what the notes have in common.

**Use Technology**** **

Technology is very engaging for most students. They enjoy mathematics software, and many teachers use Poll Everywhere and other sites to gather data and have students see class results. Have you tried Flipgrid to have students record their thinking in a video for playback?

**Go Deep**

Sometimes the reason students are not engaged with the learning of mathematics is simply because the tasks are low-level and boring. Providing high-level problems (DOK 3 and 4 or Procedures with Connections or Doing Math in Cognitive Demand) can provide the motivation for engagement.

**Establish a Learning Environment **

When a class has a norm where students are sluggish and disengaged, it’s hard to get any engagement going! The classroom environment needs to be built so that collaboration is a norm and there is an expectation of learning. Establishing a learning environment where all students are willing to try, are not afraid to fail, and value both as part of the learning process is foundational to all learning and engagement becomes natural.

**Don’t Let Productive Struggle Cross Over to Frustration**

We expect students to wrestle with math content and not give up. Students should understand that productive struggle is a natural part of learning, and we learn more from mistakes than we do correct answers. However, be very careful to know your students well and monitor their process carefully so that the struggle does not cross over into frustration. Productive struggle when you are making progress is motivating and engaging. Frustration is not.

So, I hope you try something new. Don’t forget – when students are engaged, it is a lot more fun for us as teachers as well.

References

Smith, N.N. (2017a). *A mind for mathematics: Meaningful teaching and learning in elementary classrooms*. Bloomington, IN: Solution Tree.

Smith, N.N. (2017b). *Every math learner: A doable approach to teaching with learning differences in mind K-5.* Thousand Oaks, CA: Corwin

Smith, N.N. (2017c). *Every math learner: A doable approach to teaching with learning differences in mind 6-12.* Thousand Oaks, CA: Corwin

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## Nanci Smith / October 2, 2018

I agree completely. The creativity of Desmos and the technology add a sense of fun and can easily incorporate discussion, problem solving and productive struggle.

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## Nick Corley / September 30, 2018

I think Desmos and it’s activity site teacher.desmos.com could help with several of these ideas. It is an amazing edtech tool.

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