Ideas for Differentiation in Math Class

Differentiation. I probably don't need to say this, because you already know, but I want to acknowledge just how tricky differentiation can be. There are several reasons:
1. Different kids need different things
2. Different kids like different things
3. Not everyone has the same background knowledge
4. Everyone has different misconceptions or misunderstandings

With all of these factors, in each kid, there is actually no way that two kids can be alike! Each kid is unique in their way or learning and seeing the world! There are infinite combinations in how those above factors play out in kids brains. How amazing!

But also, how hard for teachers! No two kids are alike, but somehow we are supposed to differentiate?? Teachers ask me all the time, "Annie, I know you aren't a fan of tracking, but then how do we reach our top kids? Or struggling kids?" Here's the thing, even if we did have "tracking" and kids were perfectly placed (which we know they aren't) you would still have to differentiate because there are so many different factors at play even if they are more homogeneously grouped! Grouping kids "by ability" is not differentiation.

What can we do?
I am a problem solver, and while I do like a good education rant, in the end I am optimistic that there are solutions to even our toughest problems. When it comes to how to differentiate for different ability levels, I have some ideas. I have tried these in my own work with middle schoolers. For most of my 12 years in the classroom, I had students with IEPs, emergent bilinguals, and high ability. Not every idea will work in every situation. I also can't promise that any of these will be perfect, but hopefully you will find something here to help you and, ultimately, help your students!

Idea 1: Challenge our own beliefs
We need to start here. Everyone can learn mathematics. Many of us say this, but do we truly believe it? Math is not just for "gifted" students and there is no such thing as a "math person." As Jo Boaler says, "Our conversations and work with students need to reflect the new science of the brain and communicate to all that everyone can learn math well, not only those believed to hold a “gift”. This could well be the key to unlocking a different future – one in which math trauma is a thing of the past and students from all backgrounds are given access to high quality mathematics learning opportunities."

Idea 2: Problem Based Approach
Parallel Tasks, Open Middle Problem, Open Ended Problems! Yes to all of these. Read Mark's post because he explains them so well. You can also read more about non-routine problems here.

If the task is interesting, students of all levels will be engaged. Listen, I've been teaching middle school math for over 12 years and I still can get excited or interested in a math task about the content. How can this be? Obviously the math content is "easy" for me. However, I am still making connections and seeing things in new ways. So, if your more accelerated students are bored, ask yourself, "is this an interesting task?" Imagine yourself seeing a task for the first time. What make it interesting to you? What makes you want to solve a math problem or be authentically interested in thinking about it? (for my answer to this, check out idea 5)

Idea 3: Anticipate Student Thinking
This skill is something that you will get better at the longer you teach. To look at a problem and predict the ways students might solve it and where their misconceptions might be is not something that comes without experience.  However, there are curriculums that provide this insight in the teacher resources. There are also tasks that provide pretty good teacher notes that you can use while you are working on building your own skill.

I borrowed this slide from my teacher friend, Leah. She suggested this sentence stem. Ask yourself this as you plan each lesson.

Idea 4: The Notecard Strategy
This will not be one of my most elegant suggestions, but it's pretty practical and quick, so I wanted to share. When I would ask myself the question from "Idea 3," I would often anticipate some students that needed something extra, either more advanced or extra support. 

If it was a way to make a kid think deeper about something, I would write it down on an index card. I made a few of them and just had them ready. If a student, or pair of students, moved through an activity or task quickly, I would have the notecard ready to hand to them to help them go deeper. 

If I was using the notecard strategy as a support for a struggling student, I just made sure that the "help" didn't over-scaffold or take away from the learning I wanted to take place. Instead, it might be a visual. Or, perhaps it was a simpler problem to solve first, so students could look for a pattern that they then could apply to the task at hand (again, not giving away anything from the actual task).

Idea 5: The Ramp

Having a low floor and high ceiling ensures that every student has access to the mathematical idea, but can go deeper as their understanding let them. Think about using tasks from youcubed or a problem of the month. MARS tasks are also designed in this ramp-type structure.

Other tasks I love for their structure of allowing everyone access are 3-Act Math Tasks by Dan Meyer. Here is one of my favorites because it was the first one I ever tried. 

Finally, here are some MARS tasks that are great for middle and high school that you can use for an activity, small group, formative, or summative assessment.

Once you get used to these types of tasks, you can begin using your own curriculum and turning them into this type of task!

Idea 6: Re-engagment Lessons
The idea behind a re-engagement lesson is to use student thinking to plan a lesson that engages all learners to make connections. I'm not going to go into all the details here, but check out this resource for more explanations and videos to learn more about this powerful type of math lesson.

Idea 7: Tech Tools

If you are fortunate enough to have access to technology in your classroom, there are some tools you can use to help with differentiation. Let me be clear that I am not advocating for each student to be silent, on their own device, learning about different content, with no interaction with peers. While some edtech programs might promise differentiation, and they might be good for some practice, that is not the answer I propose here. I also strongly believe in the importance of class discussions, re-engagement lessons, and other class structures that draw on the strength of a community of learners.

However, it is important to use multiple strategies in a math classroom. So, for the times when you have students doing individual or partner type work, I'm suggesting that you use something like ClassKick. It is a way to give students a task, and in real-time you can see their work and give feedback.

From the teacher dashboard, you can see all the students' work. I use this to then look for similarities in misconceptions, as they are working, and pulling that small group of kids to work with them on that particular struggle. I used a flexible grouping strategy. The group is simply formed by a common misconception on that particular content/task.

The other thing you can do with a tool like ClassKick, is to create slides that follow the ramp, from "Idea 5." Create slides that go progressively deeper. You might want all of your students to, let's say,  the content/work on slides 3-8, but you create slides 1-2 as an entry level to the task and you create slides 9 and 10 with conceptually deeper content that goes beyond the standard. So all students will start on slide 1, have access to the content, and then work at their own pace through the slides. More advanced students will get to the conceptually deeper content on slides 9 and 10, but many or most will be able to at least complete slides 3-8.

All students deserve a high quality, rigorous math education. I hope some of these ideas will help you find ways to differentiate to meet the needs of the learners in front of you!


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