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A wise person (probably a teacher) once said, “What’s equal is not always fair. What’s fair is not always equal.” This certainly goes for teaching. Middle school math differentiation of instruction is a key to meeting the individual needs of students and helping ensure their success in learning. We asked a few top middle school math teachers, math coaches, and curriculum specialists to weigh in on common questions middle school math teachers have about differentiating instruction.

- What will get my students to use what they know in order to problem solve?
- Can I make sure all of my students get the lesson they need?
- How do I re-engage a student in understanding why math patterns matter?
- Is it possible to accommodate and assist a student with perceptual problems?
- Show me how to help my students understand why the physical drawing of circles helps them understand the math.
- What do I need to do to organize my instruction based on a pre-assessment?
- Is it OK to let students try work above their skill level?
**Coach’s Corner:**How can I help teachers effectively and efficiently review math data?

## “I have several students who are very good with computation and mathematical procedures, but who struggle in applying what they know in problem-solving situations. My other students are not as skilled with procedures, but they can problem-solve. What can I do to help each group?”

We asked two veteran middle school math teachers from Princeton Junction, NJ for their best advice. Mike Delasandro recommends putting your students into mixed school groups. He says, “Start with an assignment that involves both mathematical procedures and problem solving. Make pairs or groups that have both your strong problem solvers and your procedural thinkers. Encourage them to collaboratively solve the problems. Linda Scanlon added, “Try pairing students up to work on problems together, but assign one the role of recorder and the other, the coach. This can help the student who can problem solve formalize and organize their work. It will also help the student who needs help with problem solving as the thinking is explained out loud.”

Margaret Bowman, a math academic designer with McGraw Hill, agrees and further explains. “Encourage your problem solvers to use their strong reasoning skills and conceptual knowledge to help them identify the conceptual components of the procedures that they’re struggling to memorize. Give them the background they need to contextualize those procedures, commit them to memory, and apply them. For your group that is still building their problem-solving skills but has memorization and computation down, they may need some of the same work developing conceptual understanding of what they’ve already memorized. Help students to first make sense of the problem and the context in which the procedures are being applied. Additionally, they may also need time with practice, mathematical discourse, and plenty of math positivity to overcome any fears of activities that require higher-order thinking.”

## “We’ve just started a unit on computation with fractions. I’m seeing that about half my class still does not have a good foundational understanding of fractions. The rest of the kids are solid and ready to start computation. How do I accommodate all of my students?”

Math coach Linda Scanlan thinks centers are a good way to go here. “To accommodate all students in this case, a choice of centers can be given. These can incorporate both foundational understanding of fractions and computation. As students are collaboratively working on the centers, some groups of students can be pulled for small group instruction to work on building understanding of fractions using manipulatives and diagrams. Using small groups in this way, you can individualize instruction and clarify misconceptions more easily.”

Margaret Bowman, McGraw Hill, reminds us that this could be a good opportunity to use technology as well as hands-on learning with manipulatives. “So many teachers face the challenge of moving too quickly or moving too slowly, both of which lose some student engagement. If you use any adaptive learning technologies, this is a great opportunity to dedicate time to individual work that addresses gaps in learning. Technology that acts as a 1:1 tutor is truly invaluable. If technology isn’t available, you might consider middle school math differentiation through homework assignments. In addition, providing all students with manipulatives—physical or virtual—that demonstrate and reinforce the conceptual foundation of fractions is a great way to support students. Ask students to show their reasoning, which supports their ability to apply their knowledge of fractions in real-life situations.”

## “One of my students says she is bored with the pattern work we are doing to begin our unit on algebra. The rest of the class loves it and finds it fun and motivating. Any suggestions on how I can make it more interesting and challenging for her?”

Mike Delasandro says, “Patterns are the basis of all algebra, so it is important for students to find value in seeing and analyzing patterns. Assuming she is bored because she thinks the pattern work is too easy, I would try to find more challenging patterns for her. I would also challenge her to use variables and equations to model the patterns.” Scanlan also suggests that “Students should be able to recognize and analyze patterns from multiple representations. It’s a great idea to encourage students to develop patterns with different kinds of representations or media; that kind of fluency and flexibility can be quite powerful. This helps students to become more self-aware.”

David Hatfield, a lead learning scientist with McGraw Hill recommends looking at technology as a resource. “This is where digital learning can have such an impact on students—when learners need additional rigor, a different mode of instruction, or simply a fresh approach to a challenge, the right online game, assignment, or lesson can really fill that gap, even for a single student. Finding another game-based activity that appeals to her might prove equally interesting for the rest of your learners, too.”

## “We are working on graphing, and things are going pretty well, except for one student who I know has perceptual problems. I think he understands the concepts, but he struggles to actually draw the graphs. Should I still require him to do this? What’s a good alternative?”

Math coach Linda Scanlan recommends using technology for graphing with this student. “Many apps make graphing easier for students but are also accurate and exploratory. Students can explore how changing parameters of a graph changes the shape of the graph, and they can make connections between representations of the graph in table or equation form. Another option would be to provide this student with the graph already completed, and ask them to interpret the meaning of the graph and write the information in another representation such as a table, equation, or word description.”

## “Our unit on geometry involves lots of work with circles and finding circumference and surface area of three-dimensional objects. We have been drawing circles and measuring the surface area of actual objects. Some of my class says this is too slow, and they want to just do the calculations on paper to figure it out. I think it’s important that they physically experience this to truly understand it. How do I explain this to them and get them on board?”

David Hatfield, McGraw Hill explains that student agency—students taking ownership of their learning—is incredibly important. “Kudos to you for recognizing the importance of getting your students on board for a learning experience! Fostering student agency can be a bit overwhelming. Start small and build towards greater agency based on your comfort level. For the situation you described, you might try connecting the objectives for the lesson with some real-world applications of the skills you’re hoping to foster. Perhaps asking students to find their own real-world applications to increase their ownership of the challenge. Working out calculations on paper obviously isn’t a bad thing. However, it might be useful to create individual and/or small group challenges that require both measurement and calculations to reinforce the usefulness of combining these skills in real-world situations.”

Linda Scanlan, Math Coach, also emphasizes student involvement in creating learning. “It is important for students to understand both the calculations on paper and what they represent in real-world contexts. Try to involve students in creating a learning experience that meets their creativity, pace, and learning needs. Have students develop a performance-based assessment. This will be a task or a project that applies the skill, concept, and standard. The teacher and students together can find a real-world application problem that would require students to demonstrate knowledge of the objectives. If students develop their own learning experience, it will give them a felt need to find a solution to the problem.”

## “I just pre-assessed my class on our next unit on probability. About a third have very little knowledge, another third understands about half the material, and another third could take the final test today and pass. How should I organize my instruction to accommodate them all?”

### Analyze assessment data

Margaret Bowman, McGraw Hill, likes letting analysis of assessment data guide the next move. “It will be helpful for instruction to pull some additional insights. Of those with very little knowledge, is it in all elements of the unit? Are there specific skills that are truly fundamental that they’re missing, where you might want to focus first? Of those that understand some, are there any trends that will allow you to focus on gaps? Of those who could pass the test today, do they have similar skill sets outside of this unit that will guide differentiated activities? This is a challenge, but pulling out these trends might help you to spend your precious and limited time addressing the gaps that matter most. Ideally, you’re looking for a level of differentiation that addresses the fundamental gaps to get your lower proficiency students up to speed and challenge your higher proficiency students.”

### Identify smaller learning groups

Linda Scanlan, Math Coach, sees grouping as the way to go, also. In this case, students could be organized into groups according to like knowledge for differentiation to be effective. Depending on class size, this may be three groups (one of each knowledge base) or six groups (two of each knowledge base). Students who have been identified through pre-assessment as having mastered the required material can work on an in-depth challenge of the material such as a performance task, with a low-floor high-ceiling or an application problem that requires a deeper understanding of the material beyond what was pre-assessed. You can check in with these students and provide support, but they can be self-directed for most of their learning.

### Create a choice menu

Mike Delasandro, Math Teacher, adds, “I like to create an entire differentiated assignment based on the unit objectives. I often use an assignment called a Totally 10. Some teachers call this a menu. Students are given a variety of choices for each objective that are worth different point values. Choices include worksheets, puzzles, videos, online quizzes, small groups, online tutorials, and enrichment. As students are working, their goal is to get 10 points. Based on the pre-assessment, you can help students make ‘just right’ choices that help them achieve the objectives. You can also call small groups to work with students at different levels. You should remind students that their ultimate goal is to build their brain, and that looks different for each student.”

## “I have a small group of students that I have doing some very complex project-type problems because they already understand the material the rest of the class is still working on. A few of the other students asked to try these problems as well. I don’t think they’re ready for this level of work. Should I let them try it anyway?”

Both Mike Delasandro and Linda Scanlan agreed that every student should have an opportunity to attempt challenging and complex problems. Delasandro said, “I would never tell students that they can’t do an assignment other students are working on. What I would do is let them know that some of the problems require certain prerequisite skills to complete. If the students are really motivated, I give them the ‘project-type’ problems to look at and ask them to identify the skills and/or operations needed to solve the problems. Then I provide them resources (such as tutorial videos) to learn the skills. Once they have a better understanding of the basics, they can come back to the problem solving.”

David Hatfield, McGraw Hill, was excited by the enthusiasm of students to seek the challenge. “First of all, what a testament to your teaching to have a group of students eager to tackle challenges outside of their comfort zone! Now the challenge is to work with that engagement and enthusiasm while avoiding overwhelming students. Your work has created a great opening to build on your already established culture of student agency. Perhaps begin by having a conversation with each of them about where they think their specific strengths are in math and where they think they can grow. Offering access to the project work might motivate some students to really push themselves.”

## “Some of the teachers I support in my role as a math coach tell me it is difficult to find time or even know where to begin to review all the student performance data they receive. What are some specific suggestions and strategies I can share with them to help?”

Linda Scanlan explains, “As a coach, I set up a meeting with teachers to review student performance data together. We review some independently and then together and discuss our findings. This session clarifies why the data was collected. We also talk about what the teacher was hoping to find. When looking at a quick formative assessment, like an exit card, we separate results into three piles. The piles will include students who demonstrate advanced proficiency, proficiency, and partial proficiency. Based on these proficiency levels, differentiated lessons and materials can be created. For a more in-depth assessment, analysis based on meeting standards and the learning continuum needs to take place. A rubric or checklist may be helpful. Developing a long-term plan to move all students forward in their learning journey would be the final step.”

David Hatfield, McGraw Hill, agreed with this coaching plan. “Many schools struggle to navigate the student learning data available to them in a way that informs instruction. The sheer amount of data can be overwhelming. Particularly when it’s collected from various sources, such as homework assignments, standardized tests, and in-class work. It’s also important to recognize that most teachers are already integrating other signals that are central to teaching. Set realistic expectations and start small. Encourage your teachers to pick a topic on which students have scored unusually low. Then, dig into the data just for that unit. Help them uncover the specific knowledge gaps within that space. Map out a differentiation plan just for that unit, using adaptive technology as a way to scale instruction. Framing those questions is a critical first step.

### Want more math expert advice? Check out Ask the Experts: Assessment in Middle School Math

Illustration: Jennifer Jamieson