Five Benefits of Brainstorming in the Math Classroom

Brainstorming is an excellent teaching strategy that many math teachers neglect to incorporate into their regular classroom practices.  Some teachers don't think they have time, some teachers don't recognize the value of it, and some teachers have never even thought about having students brainstorm.

Brainstorming can be done at various times throughout a unit of study or lesson.  It serves a slightly different purpose and has different benefits depending on when you use it in the course of a lesson or unit.  In this post we'll examine some benefits of brainstorming before a lesson or unit of study.

Brainstorming before a lesson:

• Activates schema --- Our brains love to make associations.  We learn and recall information best when we're able to connect it other things we already know.  Having students brainstorm before you begin a lesson or unit allows their brains to activate things they already know about the topic.  So when students begin to acquire new learning on the topic, they are able to associate it with their prior knowledge. By creating these associations, the connections in the brain will be stronger making it easier to recall the information later.

• Helps set a baseline for learning ---  Brainstorming prior to a lesson or unit of study allows both teachers (and students) to get an idea of how much a student knows about the topic.  As you move through the unit of study, have students revisit their brainstorming tools (where they recorded their ideas) and either add new ideas to the list or correct misconceptions.  Doing this gives students a sense of what they know.  It's also a motivator because it allows students to see progress in their understanding.

• Helps identify misconceptions that students already have about a topic  ---  Students bring misconceptions to the classroom everyday.  Misconceptions are a part of learning.  Brainstorming before a lesson shines a light on any misconceptions that students bring to the discussion.  Identifying misconceptions before you begin the lesson allows you to address ideas that will get in the way of new learning.  For example, if students begin a unit on integers believing that you can only subtract a smaller number from a larger number, they will have trouble grasping the concept of subtracting integers.  If you know that students have this belief, you can make sure you approach subtracting integers in a way that will correct this misconception.  When we don't know about these types of misconceptions before teaching a new topic, we often add to student's confusion rather than helping them learn what we intend.

• Helps guide teaching and differentiation ---  Brainstorming lets you see who has no prior knowledge or understanding, who has a little prior knowledge, and who already knows a lot about the topic.   For example, if you have students brainstorm the topic Volume, you can see exactly what ideas students already have about volume.  Do they know that volume relates to capacity?  Do they know that volume relates to 3-dimensional shapes?  Do they know that we can use a formula to calculate volume?  This type of information helps you decide where to start the lesson, how to group students, which students need remediation, which students are already beyond the lesson you had planned, etc.

• Improve student's perception about their level of mathematical understanding --- Many students have a very low perception of their math abilities because they associate math with computation.  Most students don't realize that they know much more about math than they think.  If you ask 6th grade students what they know about adding fractions, many would tell you they don't know how to add fractions.  This is usually because they have trouble remembering and applying the algorithm for adding fractions.  But if you delve deeper, students might discover that they actually know a lot about adding fractions.  They might know situations where you would need to add fractions, how to estimate an answer, that the steps for adding and subtracting fractions are similar, how to represent adding fractions visually, that you need to find a common denominator when adding fractions, etc.  Once you see what students do know about a topic, you can point out exactly what and how much they already know.  Recognizing what they know about math helps students build confidence and changes perceptions about their abilities. 

There are also other benefits for brainstorming during and after a lesson.  We'll explore these reasons for brainstorming in Parts 2 and 3 of this series.  In part 4 of the series, I'll share some ideas and resources for brainstorming in the math classroom.

Do you incorporate brainstorming?  If so, how?  How has brainstorming benefited your students?

Differentiation Tip: Using Technology to Differentiate According to Student Interests

Current and emerging technology gives us many ways to differentiate according to student interests.  Most students these days are interested in technology, and they use technology to navigate their world. They use it to play games, watch TV and movies, communicate with friends, etc.  Just by using technology in school, we're probably tapping into an interest of most students.  At the very least, we are connecting students with their world.

 Ideas for Using Technology to Differentiate According to Student Interests:

• Keep student interests in mind when searching for videos to use with students.  If you know that many of your students like sports, try to find sports videos that go along with math concepts you're teaching.  If many of your students enjoy watching movies, try to find movie clips where math is being used.  

• Create a classroom blog, website, and/or Social Network (ex. Ning, Social Go).  These days Social Media is everywhere.  Today's students are used to being part of a social community.  Creating classroom blogs or websites is another way to help build and extend the community you create with students in the classroom.  Blogs and websites also allow you to involve parents in your classroom activities.  If you're worried about what students will post, most blogging and Social Network platforms give you the ability to monitor content.

• When having students create a product to demonstrate learning, allow them to choose a format for creating the product.  For example, students could create a GlogPrezi (zooming presentation editor), make a video about the concept, write a song about the topic, create a Voice Thread about the topic.  This list could go on for a while.  There are so many new Web Applications that allow students to create amazing products.  The idea here is to allow students to choose which type of the product they'd like to create based on their particular interest.  (interactive poster), create a

• Create a Live Binder based on the math topic you're teaching.  Fill the binder with websites, videos, images, and documents that students can use to learn about and practice the math concept.  You could require that some resources be used by all students, but then allow students to choose other resources which are helpful to them.  For example, some students may want to watch a video of someone demonstrating how to work out a problem, some students may want to play a game to practice their skill at solving problems, or some students may want to use virtual manipulatives to help them understand the math concept.  The added benefit to creating a Live Binder like this, is that students can access it from home! 

These are just a few ideas for Using Technology to Differentiate According to Student Interests.  We'll explore more ways to do this in upcoming Differentiation Tips.

Do you have any suggestions for using technology as a way to differentiate instruction?  If so, please leave a comment and tell us your ideas.

Differentiation Tip: Questioning Strategies

Varying your questioning and targeting specific questions to specific students is a great way to differentiate instruction.  During the course of a class, you can ask higher level or more open questions to students are at a higher level of readiness.  You can direct lower level or more closed questions to students who have a lower level of readiness for the skill or concept being taught.

If you're doing a lesson that involves manipulatives or problem solving, you can provide more or less scaffolding depending on the needs of the student.  Many times opening (providing few parameters) or closing tasks (providing more parameters) can be an easy way to differentiate.

Example of Differentiating by Opening or Closing a Task:

Lesson:  Exploring Fractions with Multilink Cubes

Students are shown an example of a fraction tower made with multilink cubes.  They are then given tasks to create their own fraction towers.

This is a fraction tower that has one-half red cubes.

Task A:  Build a fraction tower that is made up of two-thirds red cubes. 

(This task is completely open.  The only parameter is that is must have two-thirds red cubes.  Students have to decide how many total cubes to use.  Some students might use 2 different colors and some students may use more than 2 colors to build their towers.)


Task B:  Build a fraction tower with 9 total cubes and is made up of two-thirds red cubes.

(This task is now somewhat closed because you have stated how many total cubes to use for the tower.  If students were having trouble with the Task A because it was too open, this would be one way to make it easier.  It does still have an open element to it because you haven't stated if the tower has to have exactly 2 colors or more than 2 colors.)


Task C:  Using 3 different colors, build a tower that represents two-thirds.

(This task is mostly open with 2 parameters:  3 colors and represents two-thirds.)


Task D:  Using 3 different colors and 6 total cubes, build a tower that represents two-thirds.

(This task is completely closed.  Since you are using 6 total cubes and representing two-thirds, you would not be able to create a tower with more than 3 colors.  If you had specified a value greater than 6 for the total cubes, there would still be an open element to the task.)

Task E:  Build a tower that is one-half red, one-third green, and one-sixth blue.

(This task has 3 parameters, but is open in respect to the total number of cubes used to build the tower.  If students were struggling with this task, it could be made easier by giving a total number of cubes or by scaling back on the given parameters.  For example, you could just say to build a tower that represents one-sixth.)

Adjusting questions and tasks can be a quick and easy way to differentiate instruction, but it does take some practice.  The great thing about this strategy for differentiation is that you have plenty opportunities to practice and fine tune it!

Differentiation Tip: Think-Pair-Share

Think-Pair-Share is a quick and easy way to tap into student's prior knowledge or to allow students time to process information.  Think-Pair-Share can be used at any point during a lesson.  

Think-Pair-Share Procedure:

• Give a question or vocabulary word to think about

• Allow a few moments (usually about 30 sec to a minute or so) for students to think about the question or problem

• Have students share their thoughts with a partner.  They should also come to an agreement about what they want to share with the class

• Have pairs of students share their thoughts on the question or problem

 Using Think-Pair-Share before a lesson:

• allows students to tap into their prior knowledge.

• allows you to gather formative data about what students already know about a topic before starting instruction.  You can adjust instruction based on student responses.  For example, you may discover that students already know a lot about this topic and only need a short review rather than a complete lesson.  Or,  you may notice that students have some misconceptions about the topic that need to be addressed during instruction. 

Using Think-Pair-Share during a lesson:

• allows students time to process their learning.

• allows you to gather formative data about what students are getting from the lesson.  You can then adjust instruction based on what you see.  If students seem to understand what they've just learned, you can move on.  If they seem to have some misconceptions, you can address them when instruction continues.  This could also be a perfect time to break students into groups based on understanding of the concept.

  Using Think-Pair-Share at the end of a lesson:

• allows students time to process and reflect on their learning.

• allows you to gather formative data about what students got from the lesson.  You can then adjust instruction for the next based on what you learn.  You could use this information to assign small groups the next day.  Some groups may be ready to practice the skills being learned and others may need more small group instruction.

Think-Pair-Share Graphic Organizer:

Think-Pair-Share Graphic Organizer  - This graphic organizer will help students keep track of their thoughts during a Think-Pair-Share.  They could keep it in their binders and keep adding to it each time you do Think-Pair-Shares.

Differentiation Tip: Providing Choices

Allowing students to make choices is one of the most effective and easiest ways to differentiate.  There are many ways to provide students with choices.  One way is to give them choice about which problems they want to work.  You could even have the problems marked as easy, medium, and hard.  You can either allow free choice by just saying each student has to work 10 of the given problems, or you could set more parameters.  Such as,  you have to work 4 easy problems, 4 medium problems, and 2 hard problems. 

Unit Rate Stations Activity:

A favorite activity of my students, was when I made problems into stations and let them choose which ones to work.  I might make 20 problems and tape them on the walls around the room.  (Each problem was a station.)  My students would have to work 10 of the 20 problems. 

One year for Halloween we were learning about unit rates.  I went to the Oriental Trading website and downloaded pictures and prices of various items.  I made 25 stations with one picture per page.  My students had to choose 15 items and calculate the unit rate of each.  I had purposely chosen gross items or items that I thought they would like.  They had more fun with this activity than I had even expected.

You could even have students make up their own stations.  Have each student go to a site like Oriental Trading and make and solve 2 problems of their own.  Then combine the problems made and use these as your stations. 

Added Benefit of Using Stations:  Stations get students out of their seats which gets oxygen flowing to the brain.