Tuesday / June 25

But They Are All Different: 5 Tips to Differentiate Your Mathematics Classroom

Welcome to school! As teachers, each year and each class brings new joys and challenges as we get to know our students as people and as learners. We are faced with the often-daunting task of designing learning experiences to entice and excite our students to learn rich and rigorous mathematics content.

But they are all different.

There is Maddi who already knows much of what is in our grade level content, and what she doesn’t already know she will learn in less than half the time it takes the rest of the class. There is outgoing Elena who prefers to learn with others, asks for help freely and offers help equally as freely. Judah is a constant bundle of energy and desires to follow directions, even if he usually forgets what the directions were. There is Izzi who prefers to draw and thinks in color and pictures, and Landon who is shyly constant in his learning. There is Alexia who reads voraciously and above grade level, but is less inclined to enjoy math. Sophia is extremely shy, bright and capable but doesn’t want to show it and does not like to do anything in front of the class. And there is Justin who you didn’t even realize was a Special Education student with an IEP until the IEP showed up in your mailbox. We have students from other countries with limited language proficiencies… and we are charged to teach them all in a way that enables them to master the standards and (sigh) be proficient or above on high-stakes tests.

But they are all different.

There is no prescribed method for reaching and teaching all of our students. If that were the case we would not be having the ongoing challenging conversations around how to best teach mathematics to all students. In fact, the reality is that there is no single best method because they are all so different; however, there are ideas and strategies that will help us address the differences.

Tip 1: Clarify Content

Of all the tips, this is the only one that is not about differences. That is because it is about content. Sometimes the page of the resource we have reached defines our lesson content. Instead, the lesson content needs to be explicitly unpacked in terms of what are the conceptual big ideas and skill-based knowledge that students will learn.

In an elementary lesson, the content should not only be “addition of multi-digit numbers and a strategy,” but should also include that you can only add (join, total) things that are alike. When we work with numbers, place value determines what can be added. When developing the strategies for addition, such as base-10 blocks, tally method, partial sums, or others, the methods enforce the role of place value and the meaning of addition as joining and totaling things that are alike.

Likewise in an Algebra class, combining like terms operates in exactly the same way. The only things that can be added are things that are alike, and in algebra that would be like terms.

But they are all different.

Tip 2: Support and Challenge Appropriately

In any mathematics class, hitting exactly the right level of challenge and push can be tricky. The Zone of Proximal Development (ZPD) suggests that appropriate challenge is 10 – 15% beyond where students currently are. That’s the problem! Our students are not currently at the same place with their prior knowledge, speed at which they learn and master skills and concepts, reading ability, and the list goes on. It is tough to appropriately challenge every student in class with a single task. To appropriately challenge each and every student consider:

  • Select tasks that have multiple entry points so every student can begin, have multiple solution paths and possibly multiple answers and representations.
  • Design from top – down to challenge students who learn more quickly or are rarely challenged first, then add other supports such as partial models or hints to engage all students with the task.
  • Offer manipulatives, drawings and other tools to make sense of mathematical processes before showing the symbolic work. Keep these options available for all students as needed.
  • Group students together with the same challenge needs (not mixed groups) on occasion to design appropriate tasks and mini-teaching sessions.

But they are all different.

Tip 3: Offer Choice (As often as possible)

Research suggests that giving students voice and choice a minimum of 35% of the time in class will increase their intrinsic motivation to learn. Often students feel that mathematics class is about passively watching examples and then practicing and memorizing. This takes all voice and choice out of their control. Adding choice to class is actually fairly easy.

There is always more than one way to solve a problem, practice a skill or demonstrate learning. Find multiple methods and activities (colleagues are great for this!) and instead of choosing one that looks best, use them all and offer your students the choice of what they prefer to do to learn, practice, or demonstrate their skill.

But they are all different.

Tip 4: Make It Brain Friendly

We probably all have a story for when learning mathematics really made sense to us, as well as when it didn’t. Part of your story might be due to teacher-student relationship or perhaps inappropriate challenge levels. However, many times it is because we are asked to do something that does not work for how my brain makes sense of learning. For example, many students need to see the big picture before the detail, so explaining steps to a procedure before developing the goal and purpose of the procedure will be frustrating for them. On the other hand, some students learn more part-to-whole, and want the steps first in order to build up to the rest. Some students love graphic organizers and worksheets, and others abhor both. Some students thrive with color-coding, and others see it as tedium. It’s about matching what different brains need in order to connect, makes sense, and move learning into memory.

There are many structures for address learning preferences with which you are probably familiar – Modality (auditory, visual and kinesthetic), Gardner’s Multiple Intelligences, and Sternberg’s Triarchic Theory (Creative, Analytical and Practical) to name a few. Use these structures to design tasks for students to make the learning process more likely to fit your learners’ brains. You can create the tasks as stations or just give choice as described in Tip 3.

But they are all different.

Tip 5: Summarize Often

From cognitive science we have learned the importance of summarization to solidify the connections and memory storage of new learning. This needs to happen throughout a lesson as well as at the end of a lesson with a closure activity. Just how you have students summarize is wide open and can address students’ differences. Some typical ways to provide a summarization activity include:

  • Make a list of steps
  • Use a two-column format to show and explain
  • Reciprocal teaching
  • Draw a picture showing …
  • Demonstrate …
  • Write a letter explaining…
  • Create a rap to tell the steps of ….
  • Use white boards
  • And the list goes on.

But they are all different.

When we think about meeting all of our students’ learning needs alongside our demanding standards, it can seem overwhelming. Not all differentiation requires a lot of extra time and preparation. With some simple design adjustments and additions, all of our students can be successful in learning mathematics in just their own ways.

Written by

Nanci Smith, founder of Effective Classrooms Educational Consulting (E2C2), is currently a full-time consultant in the areas of differentiated instruction, curriculum, Common Core State Standards, and mathematics. Also ASCD faculty in the differentiated instruction cadre, and a Solution Tree consultant and author on two books in press, Nanci has provided professional development in small, large, urban, rural, and suburban districts in 47 states, as well as the Netherlands, Singapore, and Japan. She has presented at conferences and institutes in Southeast Asia, Europe, and the Middle East, and has helped develop high-quality curriculum in the Philippines. Smith is the math consultant and author of the User’s Guide for ASCD’s Meaningful Math: Leading Students Toward Understanding and Application DVD series and has developed a CD/DVD-based professional development series for middle school math teachers. Her classroom was featured in ASCD’s video series At Work in the Differentiated Classroom. She authored a chapter in the ASCD book Differentiation in Practice, Grades 5 – 9, as well as assorted lessons in other ASCD books on differentiation.

Nanci is the author of Every Math Learner, Grades K-5 and Every Math Learner, Grades 6-12, which publish in spring of 2016.

Latest comment

  • I totally agree that one of the things a teacher can do to help the students learn and develop memory retention is by summarizing often. This can be done at the beginning of the lecture and towards the end. Some of the simple ways of providing a good summary are by using whiteboards or by simply making bullet points of the things that were discussed during the day. This should also help promote active participation among the students. If I were a teacher, I would make sure to consider this type of teaching style. Thanks.

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