For many math teachers, the single most difficult issue they face on a daily basis is how to meet the needs of so many students that vary greatly in terms of what they currently know, what they can do, their motivation, their personalities… While there are many strategies to help here, most of the strategies used seem to lean in one of two directions:

- Build knowledge together as a group; or
- Provide individualized instruction based on where students currently are

Let’s take a closer look at each of these beliefs:

Those that believe the answer is providing all students with same tasks and experiences often do so because of their focus on their curriculum standards. They believe the teacher’s role is to provide their students with tasks and experiences that will help all of their students learn the material. There are a few potential issues with this approach though (i.e., what to do with students who are struggling, timing the lesson when some students might take much more time than others…).

On the other hand, others believe that the best answer is individualized instruction. They believe that students are in different places in their understand and because of this, the teacher’s role is to continually evaluate students and provide them with opportunities to learn that are “just right” based on those evaluations. It is quite possible that students in these classrooms are doing very different tasks or possibly the same piece of learning, but completely different versions depending on each student’s ability. There are a few difficulties with this approach though (i.e., making sure all students are doing the right tasks, constantly figuring out various tasks each day, the teacher dividing their time between various different groups…).

There are two seemingly opposite educational ideals that some might see as competing when we consider the two approaches above: Differentiated Instruction and Complexity Science. However, I’m actually not sure they are that different at all!

For instance, the term “differentiated instruction” in relation to mathematics can look like different things in different rooms. Rooms that are more traditional or “teacher centered” (let’s call it a “Skills Approach” to teaching) will likely sort students by ability and give different things to different students.

If the focus is on mastery of basic skills, and memorization of facts/procedures… it only makes sense to do Differentiated Instruction this way. DI becomes more like “modifications” in these classrooms (giving different students different work). The problem is, that everyone in the class not on an IEP needs to be doing the current grade’s curriculum. Really though, this isn’t differentiated instruction at all… it is “individualized instruction”. Take a look again at the Monograph: Differentiating Mathematics Instruction.Differentiated instruction is different than this. Instead of US giving different things to different students, a student-centered way of making this make sense is to provide our students with tasks that will allow ALL of our students have success. By understanding Trajectories/Continuum/Landscapes of learning (See Cathy Fosnot for a fractions Landscape), and by providing** OPEN problems** and Parallel Tasks, we can move to a more conceptual/Constructivist model of learning!

Think about Writing for a moment. We are really good at providing Differentiated Instruction in Writing. We start by giving a prompt that allows everyone to be interested in the topic, students then write, we then provide feedback, and students continue to improve! This is how math class can be when we start with problems and investigations that allow students to construct their own understanding with others!

The other theory at play here is Complexity Science. This theory suggest that the best way for us to manage the needs of individual students is to focus on the learning of the class.

The whole article is linked here if you are interested. But basically, it outlines a few principles to help us see how being less prescriptive in our teaching, and being more purposeful in our awareness of the learning that is actually happening in our classrooms will help us improve the learning in our classrooms. Complexity Science tells us to think about how to build **SHARED UNDERSTANDING** as a group through **SHARED EXPERIENCES**. Ideally we should start any new concept with problem solving opportunities so we can have the entire group learn **WITH and FROM** each other. Then we should continue to provide more experiences for the group that will build on these experiences.

Helping all of the students in a mixed ability classroom thrive isn’t about students having choice to do DIFFERENT THINGS all of the time, nor is it about US choosing the learning for them… it should often be about students all doing the SAME THING in DIFFERENT WAYS. When we share our differences, we learn FROM and WITH each other. Learning in the math classroom should be about providing rich learning experiences, where the students are doing the thinking/problem solving. Of course there are opportunities for students to consolidate and practice their learning independently, but that isn’t where we start. We need to start with the ideas from our students. We need to have SHARED EXPERIENCES (rich problems) for us to all learn from.

As always, I leave you with a few questions for you to consider:

- How do you make sure
**all**of your students are learning? - Who makes the decisions about the difficulty or complexity of the work students are doing?
- Are your students learning from each other? How can you capitalize on various students’ strengths and ideas so your students can learn WITH and FROM each other?
- How can we continue to help our students make choices about what they learn and how they demonstrate their understanding?
- Do you see the relationship between Differentiated Instruction and the development of mathematical reasoning / creative thinking? How can we help our students see mathematics as a subject where reasoning is the primary goal?
- How can we foster playful experience for our students to learn important mathematics and effectively help all of our students develop at the same time?
- What is the same for your students? What’s different?

I’d love to continue the conversation. Write a response, or send me a message on Twitter (@markchubb3).

Your writing here really spoke to me. I’ve been trying to wrap my head around a “prescribed” version of math workshop and feeling uneasy. The model is one where students are all doing something different, or at least many are doing something different often in isolation. I’ve not been sold on the idea. I have been exploring parallel task, low floor-high ceiling, and other ways to provide “experiences” in class as opposed to “activities”. I use Context for Learning with great success and am happiest while facilitating in this style. I really appreciate what you have written. Thank you.

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Thank you, Mark, for another thought provoking post. I always stop to think over the questions at the end.

“How do you make sure all of your students are learning?”

I’ve never tried ability grouping, my groups are mixed, but I did have to organize lessons when I had to pull students to work one-on-one or in small setting. I agree with the point that we need to move towards understanding of mathematics as a subject whose primary goal is reasoning. But to reason effectively we need to be able to apply mathematical tools and understandings that are appropriate in the context.

For example, if my students have no understanding of place value, they find it difficult to access many Open Middle problems in a meaningful way. If some students don’t recognize a benchmark of 10, they can’t follow many of the claculation strategies that others share in number talks. I feel like certain benchmark skills and understandings constrain the range which the student is able to work productively, kind of like zone of proximal development.

Now my challenge is that kids come into my classroom in the beginning of the year with the huge range of skills. Elementart curriculum is heavy with skills learning. If someone leaves my classroom this year without having a confident grasp on subtraction, I will feel terrible because I know that this difficulty can snowball into ugly things. I love the joy of mathematical imagination and creativity, the challenges of proofs and arguments, the intuition of estimation, the strategizing and making sense in a mathematical community. Yet it is about three months left of school and I will be losing sleep over my students who still can’t subtract, or tell me that 7+4 =10 and 6+4 is…also 10. We don’t have intervention, the only chance for these kids to get some one-on-one time figuring out what understandings they have and how we can connect them is with me. When the rest of the class in engaged with something else.

There is also often assumption of students’ high degree of independence. While students need to acquire the skills eventually, they are usually in the beginning of this process in early elementary. Some students can’t read and write, some cry when they lose rock paper scissors game and punch when someone touches their pencil. There are a lot of logistical challenges that social-emotional development brings.

I guess, after all this rambling, I am still looking for the ways to consistently create mathematically rich learning experiences that my students can access as a community of diverse learners while making sure they develop their numeracy skills to the grade appropriate level and don’t have too many emotional meltdowns in the process.

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Thanks for the comment! It sounds like some of the ideas here have helped you reflect on your practices. Hopefully I haven’t provided a “here’s how everyone should do things all the time” message, and instead helped us consider other possibilities as well. Of course, there are times when we might give different feedback, or give different next steps… but I’m not sure this is where we should be all the time.

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I jumped to the Math Wars last night, so I thought I should actually read the piece properly, without spinning things my own way. 🙂

I see, if all kids are working on the same task, that there can be subtle variations on the task that give all kids an entry point. Interactions with each kid, and questioning, for me, are a big part of differentiating.

Part of what makes differentiation so angering for more “‘traditional” educators is that they think they are being asked for 30 lesson plans, and that (rightly) offends them. It’s not that- what instructional moves can we make in the moment so each kid has a way in, and stays in the “flow” or zone.

As you point out, thinking developmentally, and tracking on continua, helps a lot.

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Thanks for responding Matthew. I agree that creating different learning paths for each student or groups of students can be overwhelming for us! But I am also not sure it is in the best interest of our students most of the time. You are right though that the way we respond to students, the feedback we give, the ways we can push our students think deeper… is a big part of how we personalize the learning in our classrooms. However, while different students might be getting different things out of a lesson/ problem/ investigation… hopefully all students are still able to learn together through shared experiences!

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