What does it mean to engage students in learning mathematics? When asked, teachers often respond that it means students can’t wait for math each day or that students are self-motivated to learn or that it just means students *want *to do mathematics.

Who would not want to hear a student share in delight, “Yay, it is time to do math!” or, “Please, teach me more about ratios!”? These types of statements are exciting for any mathematics teacher to hear because they describe a learner passionate about mathematics and motivated to keep trying. But what if a student does not have innate passion for the subject? Can he or she still be engaged in learning mathematics every day? Thankfully, the answer is Yes!

So, what does it mean to engage students in mathematics? When students are engaged in learning mathematics, they:

- strive toward a solution without giving up
- believe, with effort, they can learn and solve problems
- make connections between previously learned content and new content
- recognize patterns and apply mathematics to describe them
- choose between a variety of strategies and tools to solve problems, often using more than one
- apply mathematical models to patterns and real-world situations
- use precise language and notation

Now the question becomes: **How can a teacher engage all students in learning mathematics** – whether the student is passionate about learning mathematics or not?

Below are a few ideas to consider when working to engage all students in learning mathematics. Each is tied to a daily lesson, intentionally planned, with thought given to the time students will spend doing mathematics and the instructional strategies that can be used to grow mathematical reasoning and application.

**Time**

For a student to be engaged in learning, the lesson must include time – time for students to think and attempt solutions, time to talk with others and correct any errors or misconceptions, and time to learn a variety of strategies shared by other students. Time also allows the teacher an opportunity to give specific feedback to students recognizing their successes and areas to improve. In each part of the lesson consider what the teacher is doing, but more importantly, what the students are doing and learning from any activity. The choice of tasks used in a lesson allow for this type of quality learning time. Consider high-level cognitive tasks used in groups that promote student discourse and allow for different solution pathways.

**Culture**

The culture of a classroom influences the willingness of a student to try, to admit mistakes, and to learn with a growth mindset, believing that learning is possible with focused effort. How well do students respect and learn from one another? How are mistakes seen as opportunities to learn? How are students listened to and their work honored in class? The culture of a classroom reflects the attitudes and beliefs of those inside.

**Strategies**

There are many different strategies that can be used in a lesson regardless of the curriculum materials used in class. A few are listed below:

Want to have students solve a high-level cognitive task? | Consider “chunking” the task. Have students read it once and share with one another a summary of the task while restating the question. Next give students two minutes to start the task. Have them share their “starts” with a partner and choose one before finishing the task together.
Consider having students work on a large piece of chart paper, each writing his or her solution in a corner and then choosing the “best” (their opinion) to place in the middle of the paper to share in a gallery walk with the class. |

Want students to talk with one another about mathematics? | Consider using sentence frames and creating a bookmark of questions to use when asking another student for help. (e.g., What is this problem asking us to solve? Why did you start with a picture – can you explain it to me?) |

Want students to use precise language and notation? | Have students trade papers and read one another’s work. Ask them to give feedback to the author related to not just the content, but the language and notation used to communicate the thinking in the solution pathway.
Consider sharing work from a problem that includes an error and ask students to identify the mistake in thinking.
Have students sit back-to-back and explain their solution pathway using correct mathematics vocabulary. Can the other student critique the reasoning and give feedback? |

Want students to choose from a variety of strategies and tools? | Ask students to choose the tool they need to solve a problem.
Have students share on posters or under a document camera their different strategies and help them make connections between them. Ask students which strategy is easy, effective, and efficient so they begin to make choices themselves about strategies to use. |

Each of these strategies contributes to an engaged student, one developing the habits of mind in the mathematical practices and productively struggling toward a solution.

Whether a student is in kindergarten or calculus, when he or she is engaged in learning mathematics, opportunities for rich conversations and deep understanding with flexible thinking abound.

Can all students be engaged in learning mathematics? Yes! How can they all be engaged? Consider the roles that time, culture, and intentional strategies play throughout a lesson plan in growing the young mathematicians in your class.

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