I’ve been thinking a lot about how to meet the various needs of students in our classrooms lately. If we think about it, we are REALLY good at differentiated instruction in subjects like writing, yet, we struggle to do differentiated instruction well in subjects like math. Why is this???

In writing class, everyone seems to have an entry point. The teacher puts a prompt up on the board and everyone writes. Because the prompt is open, every student has something to write about, yet the writing of every student looks completely different. That is, the product, the process and/or the content differs for each student to some degree.

Teachers who are comfortable teaching students how to write know that they start with having students write something, then they provide feedback or other opportunities for them to improve upon. From noticing what students do in their writing, teachers can either ask students to fix or improve upon pieces of their work, or they can ask the class to work on specific skills, or ask students to write something new the next day because of what they have learned. Either way the teacher uses what they noticed from the writing sample and asks students to use what they learned and improve upon it!

In Math class, however, many teachers don’t take the same approach to learning. Some tell every student exactly what to do, how to do it, and share exactly what the finished product should look like. OR… in the name of differentiated instruction, some teachers split their class into different groups, those that are excelling, those that are on track, and those that need remediation. To them, differentiated instruction is about ability grouping – giving everyone different things. The two teachers’ thinking above are very different aren’t they!

Imagine these practices in writing class again. Teacher 1 (everyone does the exact same thing, the exact same way) would show students how to write a journal (let’s say), explain about the topic sentence, state the number of sentences needed per paragraph, walk every student through every step. The end products Teacher 1 would get, would be lifeless replications of the teacher’s thinking! While this might build some competence, it would not be supporting young creative writers.

Teacher 2 (giving different things to different groups) on the other hand would split the class into 3 or 4 groups and give everyone a different prompt. “Some of you aren’t ready for this journal writing topic!!!” Students in the high group would be allowed to be creative… students in the middle group wouldn’t be expected to be creative, but would have to do most of what is expected… and those in the “fix-up” group would be told exactly what to do and how to do it. While this strategy might seem like targeted instruction, sadly those who might need the most help would be missing out on many of the important pieces of developing writers – including allowing them to be engaged and interested in the creative processes.

Teacher 1 might be helpful for some in the class because they are telling specific things that might be helpful for some.

Teacher 2 might be helpful for some of the students in the class too… especially those that might feel like they are the top group.

But something tells me, that neither are allowing their students to reach their potential!!!

Think again to the writing teacher I described at the beginning. They weren’t overly prescriptive at first, but became more focused after they knew more about their students. They provided EVERYONE opportunity to be creative and do the SAME task!

In math, the most effective strategy for differentiating instruction, in my opinion, is using open problems. When a task is open, it allows all students to access the material, and allows all students to share what they currently understand. However, this isn’t enough. We then need to have some students share their thinking in a lesson close (this can include the timely and descriptive feedback everyone in the group needs). Building the knowledge together is how we learn. This also means that future problems / tasks should be built on what was just learned.

We know that to differentiate instruction is to allow for differences in the products, content and/or processes of learning… However, I think what might differ between teacher’s ability to use differentiated instruction strategies is if they are Teacher-Centered… or Student-Centered!

When we are teacher-centered we believe that it is our job to tell which students should be working on which things or aim to control which strategies each student will be learning. However, I’m not convinced that we would ever be able to accurately know which strategies students are ready for (and therefore which ones we wouldn’t want them to hear), nor am I convinced that giving students different things regularly is healthy for our students.

Determining how to place students in groups is an important decision. Avoid continually grouping by ability. **This kind of grouping, although well-intentioned, perpetuates low levels of learning and actually increases the gap between more and less dependent students.** Instead, consider using *flexible grouping* in which the size and makeup of small groups vary in a purposeful and strategic manner. When coupled with the use of differentiation strategies, flexible grouping gives all students the chance to work successfully in groups. Van de Walle – Teaching Student Centered Mathematics

If we were to have students work on a problem in pairs, we need to be aware that grouping by ability as a regular practice can actually lead students to develop fixed mindsets – that is they start to recognize who is and who isn’t a math student.

Obviously there are times when some students need remediation, however, I think we are too quick to jump to remediation of skills instead of attempting to find ways to allow students to make sense of things in their own way followed by bringing the learning / thinking together to learn WITH and FROM each other.

To make these changes, however, I think we need to spend more time thinking about what a good problem or rich task should look like! Maybe something for a future post?

**As always, I want to leave you with a few reflective questions:**

- I chose to compare what differentiated instruction looks like in mathematics to what it looks like in writing class. However, I often hear more comparisons between reading and mathematics. Do you see learning mathematics as an expressive subject like writing or a receptive subject like reading?
- Where do you find tasks / problems that offer all of your students both access and challenge (just like a good writing prompt)? How do these offer opportunities for your students to vary their process, product and/or content?
- Once we provide open problems for our students, how do you leverage the reasoning and representations from some in the room to help others learn and grow?
- Math is very different than Literacy. Reading and writing, for the most part, are skills, while mathematics is content heavy. So how do you balance the need to continually learn new things with the need to continually make connections and build on previous understanding?
- What barriers are there to viewing differentiated instruction like this? How can we help as an online community?

For more on this topic I encourage you to read How do we meet the needs of so many unique students in a mixed-ability classroom? or take a look at our Ontario Ministry’s vision for Differentiated Instruction in math: Differentiating Mathematics Instruction

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

Good post, with some very nice thinking, Mark. As always, there is no easy way to teach math… people who say ‘just use xxx resource’, or ‘just follow these steps’ are missing the point. Math isn’t about teaching stuff… it’s about teaching thinking. And that’s complicated!

I appreciate you sharing your thinking with us … reflecting on ideas is how WE grow! Some afternoon, we need to talk about this for a year or two.

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Absolutely Gerry. You pick the afternoon. I’ll bring the drinks.

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Yesterday I wrote a quick post on a similar theme: http://followinglearning.blogspot.co.uk/2017/07/going-sideways.html

– partly about differentiation.

I like the analogy with writing a lot. It also fits with my post because in a sense each writing lesson goes sideways. Overall we want students to improve their powers of expression, along with knowledge of vocabulary, spelling, sentence and paragraph construction, punctuation. But we find, particular tasks which are at right angles to this. Write a haiku, write an advert for your fruit juice, write an account of our trip to the farm. The students can stretch themselves in these lateral directions, and yet the whole group can stay together in writing about the same thing. It seems a bit like a sail boat tacking against the wind to me, that we make progress, and keep “together” by giving their energies to aspects of the tasks that are not the progress itself.

On another note, this year I’ve been looking to make my maths lessons more like writing and less like reading. Almost all the equations the students came across were ones they had themselves written, and they wrote a lot of them. Often I photographed their books and shared what they’d written, so there was a reading component too. But I sense they found being the producers rather than the processors empowering. Certainly they brought me more in that they’d done at home in previous years. I must blog a reflection on how the year went.

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What a beautiful comment. Thanks Simon for adding your thoughts here! I love your analogy of tacking and sailboats. What I feel like I need doing is to blog about specific lessons and problems, then relate back to why they were so successful for those students who we might be worried about. Can’t wait to read your blog!

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I have been thinking a lot about these topics with my colleagues this summer as we consider topics for next year’s PD. We are trying to encourage teachers to break from a rigid, ability leveled, centers based workshop model, to one in which the focus is on rich tasks and math talk. As an interventionist, I am still trying to reconcile how to meet the needs of the students who need more time with the content at each grade level. I am still trying to figure out where the balance is with working with these students in small groups, and having these students work with their peers on open problems. I think this balance is crucial to closing the gap. Thank you for your thoughtful post, I look forward to sharing it!

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Thanks for the comment Jennifer. Questions that you are asking Drive right at the heart at the problem. On one side we here messages about making sure we are giving students exactly what they need. And on the other, we have messages telling us that we want students to be able to think for themselves and develop mathematical reasoning skills. With so much talk about growth mindset, I wonder how it’s ever possible to help our students have a growth mindset in mathematics when they are put into the ability groups. However, the question still exists, how do we help those who are struggling the most? Is the answer put them in a fix up group and hope to fill gaps? Is the answer provide them with the same work as everyone else and hope that The conversations will help them understand what others are thinking, while helping them Belong in the mathematics community just like everyone else? As an interventionist I would hope that the first few experiences in class included opportunities for all students to participate and construct the learning together in a shared experience. After the first few days, however, you might notice a few that need more time and attention. This wouldn’t be ability grouping, it would be flexible grouping.

Somehow, beliefs about who can learn math needs to change. Providing an open problem tells her students that we value their thinking and believing them as learners. Putting them into groups based on ability send them not so subtle signals as to who is and who is not a math student. What would happen if small group instruction meant everyone is doing the same problem in pairs and you can monitor The learning as needed with which pairs you feel like you need to spend more time with? What are your thoughts?

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Mark, I think your suggestion of pairing and conferring is a great one. I have had, unfortunately for my students, the experience of working with teachers who are either unwilling or unable to do this in an effective way. As the interventionist, I have tried to either assist them in doing this in the classroom with the benefit of a second teacher in the room (me), or I have pulled the students out of the room that are significantly behind and provided them with rich problems in a small group setting that moves at their pace. Sometimes a combination of these two structures works. I think it depends on the teacher and the students. Whatever we do, I think we can agree that it must be flexible and in the interest of developing confident problem solvers.

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Thanks for your blog and the discussion it generates. A lot of this resonates with me and is what I try to achieve in my teaching. In particular I feel learners having “agency” in their learning is a desirable thing to achieve in the classroom. However, I have two continual issues I grapple with when taking a more student-centred approach.

1) It’s unreliable. There is something joyous about having students spend time on an open problem and then as a class bring together that learning through discussion and feedback. But it can go wrong and as a teacher it requires a higher level of skill to make it work. Am I leaving to much to chance? It is an abdication my responsiblties as teacher? And when working with newly qualified teachers, am I asking too much?

2) It’s inequitable. An approach that relies on open problems is likely to favour the students with more knowledge in the first place. They make more progress on the problem so learn more, thus increasing the gap in attainment between groups of learners.

These are not criticisms of the approach nor reasons to abandon it. But they are things we need to be aware of and attempt to address and I offer them to further the debate!

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Thanks Mark for your comments here. I really appreciate some pushback. Some thoughts:

1. When we give open problems we. We’d to know why we are giving that problem. We need to have a goal in mind. This helps us as we are monitoring students’ progress as they work to know what we are looking for, know what to observe, & know what conversations to have /questions to ask. This, in turn, allows us to know which samples we want to choose, and how we want to sequence, in order to have a really rich conversation about what’s mathematically important here. To your point though, The conversation could potentially veer off track if we let it (maybe something important is discussed we didn’t anticipate…) but we need to always know what our goal is! There are a few resources out there that have helped me with making sure these conversations not only help with student agency, but also help us focus on Tye important mathematics at hand – 5 Practices for Orchestrating Productive Mathematics Discussions and Intentional Talk.

2. In my experience, this approach actually allows more students to be part of the conversation. Students feel comfortable asking each other questions as dialogue actually starts to happen! With this approach, students realize that how they learn happens in these conversations. Students learn with and from each other which closes any gaps between less dependent and more dependent learners!

At least these are my experiences…..

I did read your student centered / teacher centered / math centered discussion. To be honest, I’m not sure what “math centered” means. But I am sure that the problems we do, the discussions we have… allow mathematical ideas completely

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…mathematical ideas, thinking & reasoning to be the focus! However, the easiest place to start is with their ideas so I know where to start the conversation and where to take it.

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While I like the comparison to writing, but reading and writing are not “just skills”.

Small groups are not always intervention. It allows that time for teacher to hear the thinking students are doing.

I agree the thinking is the challenge, but that is the problem with all teaching. I feel like the work we are giving is not zone of proximal development plus 1. So the students want just tell me what you want me to do and let me do it. Good questions are critical.

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