Learner Centered Math Lesson Breakdown

December 14, 2021

Learner Centered Math Lesson Breakdown

December 14, 2021

As a secondary math teacher, understanding the content is the easy part, but how to teach it in a meaningful way is a whole other ball game. Thinking about our learners intentionally before each lesson is the most valuable, yet complex thing we could do.

  • What do they already know, and how will it connect to the previous unit?
  • Will I make small groups or teach whole-group?
  • What resources might I need to provide my learners? 
  • Should I get out those math manipulatives for my hands-on learners?
  • How much will I be talking today, and how can I maximize the learner’s voice?

Some of these questions need to be answered a few days in advance, while others can be answered on the fly or right before the learner-centered lesson begins.

Planning for a Learner Centered Lesson

Start with Pre-Assessments

When I start a new math unit, I like to think of the previous unit and how it can flow into the upcoming one. What natural connections can I make, or how can I guide my learners to make those connections? What was the energy and engagement level like within the last unit?

In addition to the culture of learning, I like to also know what my learners know coming into our next unit. I develop a pre-assessment with proficient-level questions to see their readiness level. Depending on the unit and the vertical alignment of skills, I’ll add questions for the grades above and below the current grade level, as well.

I do this to see what gaps need to be filled, and who is capable of being pushed. Sometimes, depending on the unit, I’ll allow learners to be exempt from parts of a unit or even a whole unit if they demonstrate mastery on the pre-assessment. 

Incorporate Grouping

When I am looking at the bigger picture of the unit, I like to identify the concepts that would lend well to whole group vs small group instruction. Whole group instruction has learner-centered opportunities just as much as small group instruction. 

They both offer opportunities for discussion between learners, sharing their mathematical thinking, and listening to others’ perspectives. This is where you have to put on your learner-centered lens: which learner[s] might get bored/lost during this whole group lesson, and would benefit from a smaller group? 

I also make the decision to do a whole or small group based on the results of the pre-assessment. If there is a wide range of readiness levels, and kids are ready to move on, or some kids really need to take time to fill those gaps, honor those results.

That’s where you’ll see more engagement because you’re closing that gap and pushing kids to extend themselves! It’s okay to be flexible with your grouping, as long as you’re intentional with your choice and it’s benefiting all learners. 

Include Lesson Resources

I am a big believer in guided notes. They are a great way to encourage learners to follow along with a lesson, it’s an accommodation in some learner’s IEPs and 504s, and it’s a great resource for future access when studying or when a learner might need help. 

When I develop guided notes, I like to make sure the order of the content, questions, and scaffolding makes sense for my learner population. Sometimes I need to tweak my notes from one year to the next because my population of kids changes. 

Since we all went virtual for a short time, we made video lessons as well to correlate with these guided notes. These video lessons have really allowed learners to work ahead, or revisit a concept when they need or want to. 

Within my guided notes, I like to plan for the different entry levels of my learners. Some kids are ready to move into a proficient level question, while others are just dipping their toe into the water.

Look at the example in the graphic below. This is what a part of my guided notes looks like when I teach the distributive property. 

Some kids aren’t ready for the variables so I provide an example with whole numbers. Other kids are ready for integers and variables so I give them a tougher example. I also know that some learners are visual learners, so I make sure to provide a concrete strategy to bridge the connection to the more abstract strategy. 

Use Math Manipulatives

Math manipulatives are a great tool to promote learning and engagement if used correctly. Not every unit lends itself to a math manipulative, but they’re great to have on hand to reach learners who have a hard time understanding the more abstract content.

Algebra tiles are great when working within Expressions and Equations. Black and red chips are great when working with rational numbers, specifically when introducing positive and negative numbers. Dice are awesome during probability and 3D nets for volume and surface are golden when working within a geometry unit!

Level of Communication 

One of my favorite mathematical practices is constructing viable arguments and critiquing the reasoning of others and how well it ties with the other mathematical practice of looking for and making sense of structure. 

To discuss how these two relate to communication, I want you to read and respond to these questions: 

  • How much are you talking vs. the learners? 
  • What kind of talking are you facilitating? (Open-ended, sharing the process, yes/no questions)
  • How often are you encouraging learners to make predictions and hear each other’s perspectives? 
  • Are you encouraging them to listen and regurgitate aloud what they hear from their peers? 
  • How often are you pushing your learners to use higher levels of mathematical vocabulary? 

These questions are sometimes uncomfortable to answer, but when you take the time to honestly reflect, you are pushing yourself towards a learner-centered mindset. 

When learners are doing more of the talking and discovering, they’re owning their learning. When learners are correcting each other’s vocabulary, they’re doing the learning!

“Turn-and-Talks” or as I like to call them more recently, “turn-and-listens” are a great way to maximize engagement and participation, and develop relationships amongst the learners. 

Float around the classroom when you initiate a turn-and-listen, and listen to what the learners are actually communicating. Push them to dig deeper when you hear a lack-luster response. 

It’s a lower risk to share your mathematical thinking with a single peer instead of a whole class. This simple choice of a turn-and-listen can make a learner feel more connected to the lesson, therefore increasing their understanding of the content.  

Next steps in Developing Learner Centered Lessons

If your goal is to continue developing learner centered lessons, then I would suggest creating a whole unit this way.

How do you know if it’s working?

Push out a mini-check or some kind of exit slip with the intention of breaking down the data into groups of learners to see what they’re comprehending.

Let them know the purpose of this mini-check to reduce the risk or anxiety that might ensue. Once you have the data, you can create flexible grouping based on who did well or who needs enrichment.

The learners who did well can maybe work on one rich task to extend themselves while others close the gaps with you, or clear up some misconceptions of the content thus far.

A learner-centered lesson can have many moving parts. If you’re not quite ready to dive into pre-assessments, the level of communication is a great entry point.

Guided notes would be another low-risk way to enter into a learner centered environment, but does take some preparation. Once you have one or two pieces mastered, take that risk to know what your learners know. It’s fascinating to see what some learners already know or do not know before starting a unit, and it is a powerful tool that can change your practice entirely. 

Feel free to leave a comment for what you have already tried, and share your success in designing a learner-centered lesson!


Bryn Grosskopf is a secondary math teacher in Waukesha, Wisconsin. Bryn earned her Masters of Education at Carroll University focusing on Personalized Learning and Teacher Leadership. She has worked at the Waukesha STEM Academy for eight years, developing a community of empowered learners and pushing her colleagues to do the same.  Teacher leader, innovator, and a learner centered educator are just a few ways to describe how Bryn pushes the envelope on implementing personalized learning strategies and creating life-long learners.

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