### Differentiation Ideas for Middle School Math

By Teachers.Net Community*Follow along as middle school math teachers share ideas for differentiation of math instruction – from a recent discussion thread on the Math Teachers Chatboard.*

** 2×2 teacher posted:** I have been told that I now have to write and turn in lesson plans showing differentiation in the middle school math classes that I teach. I don’t know where to start. Please help! Thanks!

** Sara’s response:** Are your math classes heterogeneous? I’m guessing so or why would they be asking you for differentiation? So we’re going to differentiate along the lines of varying levels of math ability – and not along other lines? That’s the first question to ask when differentiating – differentiating for what? Learning differences? Reading ability? Attention span? Language differences? Or math ability?

Assuming it’s math ability, I put my kids into three groups (they don’t necessarily like it at first… I take the natural

math kids – they ones who almost don’t need to be taught and put them together. Then I put a ‘low group’ together – the ones who almost don’t get it -or don’t get it – even when you teach them. And the middle group is exactly that.

I use different textbooks – I could actually write the whole plan but before I do it would help to not waste time in case

we’re not differentiating for varying levels of math ability.

What are we differentiating for? What are the differences between them that we’re planning for?

** 2×2 teacher added:** Yes, it is for differences in math ability. I like the idea of three groups. I am already doing that to some extent. I think my biggest problem is how to write it in a lesson plan. I can’t just put “three groups” in my lesson plan every day. They will all be taking a common assessment so my target is the same with all of them. The person reviewing my lesson plans is looking for cute, creative ideas. I really appreciate your help. No one has ever asked what we are differentiating for before.

** Betty Ann posted:** Many math texts have several levels of problems in the problem sets: basic, “regular,” and “challenge.” You can certainly have your various groups working on the same concepts, but with different levels of difficulty.

** Sara added:** I put the easiest questions first on my tests – it boost confidence. I tell them I don’t expect them all to finish every problem but NOT to skip problems – unless they get stuck. I do expect that the ‘top group’ will finish the test and I add a specific challenge section at the end where I pose questions that are more than calculation or harder calculation.

On Mondays, I teach the new operation. On Tuesdays, the top group works on it by themselves in a group off to the side. They consult with each other. I work with the middle and the bottom group going over the operation and doing worksheets together. If any in the middle group think they ‘get it’ , they are welcome to work independently or to join the top group. Wed. I’m still working with the bottom group and I give everyone else the answer sheet to the problems they’ve been doing. (often on Wed. I give the top group and enrichment sheet)

Every Thursday we take a test. Fridays I do enrichment with everybody and I ‘regroup’ them in small groups NOT based on ability. I don’t know how to write it in a lesson plan either but it works well and the parents are very happy with it and everybody can still do well in terms of grades.

I also teach LA and Social Studies and sometimes Science too. We don’t group in Soc.Studies or Science ‘based on ability in science’ – math is something unto itself in my opinion. Kids come with varying levels of ability in math – not necessarily based on learning differences or learning disabilities. There are some kids who have a natural understanding of the social sciences or of science but more often there we differentiate on their presentation of learning differences and we individualize.

I can’t put a group of ADHD kids together …. instead I have to individualize the curriculum, and modify it as well on an individual basis.

** MTA contributed this:** True differentiation is done in curriculum and instruction not in student segregation. It may be easy to be quarantine the poor and enshrine the elite, but triage ultimately does not serve them or those in between.

Students will become who we are. Is this was was meant to be taught? How can teachers, who often don’t have enough time and resources as it is, educate the diverse? Professional development usually is the expression of the administration’s focus – good to bad. Curriculum and instructional excellence takes time, knowledge, and vision.

When you put students in “ability” groups, what do they conclude about their real ability. If I had a perfect solution, I would gladly share it, but we must be very careful of what we do in the name of education that we don’t create larger problems.

One way to look at learning math is that all can do it, but that students construct knowledge at their way and at their own speed.

* Sara addressed MTA’s points with these comments:* I’ve got to guess you’re not a math teacher which is fine but what would your solution be? I read you do not have the perfect one but offer any one – perfect or not.

A grouped class in a linear subject as math is does not allow students to learn at the own speed. I’d fully agree that students learn at their own speed but when half or more of the class has mastered short division, what do I with them while the other half or even a few haven’t?

How do I grade them is an entirely different question but I can grade individually though most teachers feel uncomfortable doing that. So to that I have found a solution though less than perfect.

But I welcome hearing any solution as imperfect as it may be to how students in a math classroom can be left to learn at their own speed when grouped with those whose speed is very different from their own?

In social studies, this is not a problem for me but in math it is given the linear nature of mathematics with one operation building on the next. You can’t skip fractions with students if they’re going to learn decimals.

* MTA’s responds to each of Sara’s points:* I am a math teacher – award-winning for that matter, teacher of the year, educator of the year, department chair, and I have done over a hundred presentations and training sessions on various math education topics. I additional educational certifications, have taught classes from remedial to AP. So what! It does little for me in terms of administrative support.

Documented in the literature is the value of heterogeneous grouping, or groups for that matter. Yet, I seldom use groups, at least physical groups. I do use technology to creat public thought space. I use simple, non-tech, techniques to create real time groups and tutoring, but use low-tech to extend time.

An example, have student write down what they have just learned as an explanation. Rotate papers in a circle of 3-4 students. Have students update what they then know having learned for their peers. Think about how each level student would gain from such an activity.

> A grouped class in a linear subject as math is does not allow students to

> learn at the own speed.

So true, but math is not that linear, except maybe a particular solution

process, which is also subject on conceptual nonlinearity,

> I’d fully agree that students learn at their own

> speed but when half or more of the class has mastered short division, what

> do I with them while the other half or even a few haven’t?

First, if half the class has “mastered” short division, normal variation

means that many of those below that point are close to mastery. Second, if

curriculum and policy permits, move on and outsource the catchup. If not,

move masters to application and the others to mastery. BTW, differentiating

in the first place can reduce the problem dramatically.

>

> How do I grade them is an entirely different question but I can grade

> individually though most teachers feel uncomfortable doing that. So to that

> I have found a solution though less than perfect.

>

> But I welcome hearing any solution as imperfect as it may be to how

> students in a math classroom can be left to learn at their own speed when

> grouped with those whose speed is very different from their own?

>

Speed is a function of time. So, if you learn slower, you need more time

that others to reach the same level. Otherwise, grades (learning) varies if

time is constrained. The problem of “uniform” learning becomes one of time

management. I know this may seem obvious, but I observe teachers too often

try to get (all?) their students to be successful, but define that success

in terms of pass/fail.

> In social studies, this is not a problem for me but in math it is given the

> linear nature of mathematics with one operation building on the next. You

> can’t skip fractions with students if they’re going to learn decimals.

Actually, you can. Both are notation systems. Quantification is the goal. Fractions reach it by a ratio-oriented means, where decimals are addition-oriented. Students end up not liking decimals for a number of reasons like their conceptual extension for the whole number system and its ease of quantification. BTW, fractions should be taught with a teacher thinking about proportions and rationals in algebra and limits in calculus.

An illustration (not example) – Which are more than a half? 2/3, 1/4, 4/5, 4/6, 2/8, 16/20… Skip for later any that take too much time right now. After students figure out a rule (supplement with real and virtual manipulatives), they will get the next task. Make each of the fractions exactly a half by removing sum of the counts in the numerator. Which ones won’t work? Okay, what the fewest number of counts that you can remove to just make the fration be less than one? If you increase the size if the denominator, one-by-one, will all of the fractions eventually become larger or smaller than one? Why do some get there quicker than others?

It’s another way to teach about fractions, but has more differentiability than some.

I still don’t have a perfect solution, but I do suggest putting the learning levels of instruction into teaching instead of the students into groups positioned for uni-level instruction.

** MicB offered:** Check out this website. The way they set up their math program is there are 4 worksheets for every concept. A is the easiest with the least amount of higher level thinking, B has a little bit of higher level thinking, C has more and D they basically make their own worksheet. I have students self evaluate how they feel about the concept and based on how they feel about the concepts depends on which one they do. I really love the incorporation of dice/cards into the lessons and how active the students are in their learning. I usually have to direct a few students to do sheet A. I hope this helps! http://www.bringinglearningalive.com/math.htm

**When I taught middle school a big issue was how well kids knew their multiplication tables. It is a core reason for why differentiation is important, so it makes a good example. The trick is to teach the same core concept in a variety of ways – keep everybody learning at their own level. The songs at Plaid Pancakes are made with middle schoolers in mind as well as elementary. You can use these songs as warm-ups or remediation with small groups or individuals to practice accuracy and speed. Some kids might use them with flash cards while others might write answers. Still others might create their own multiplication table song for that number. The simple act of adding music is a form of differentiation for aural learners.**

*Laura Vickers posted:*That is just one example because I just finished these songs and want to call them to people’s attention (of course!), but you can do this type of thing with any topic.

The bottom line is some kids will need to be remediated in basic information required before even beginning to learn something new while other kids only need to have the new information explained to them once.