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?

The Number Sense: How the Mind Creates Mathematics

I just discovered this book from +Liz Krane on Google+.  It is going to the top of my reading list!

 

Here's what Liz had to say about the The Number Sense: How the Mind Creates Mathematics:

I'm just blazing through this book, The Number Sense by Stanislas Dehaene. It's fascinating!

Here's a tidbit I just picked up:

Have you heard that people can generally only remember up to 7 digits? Well, throw that out the window.

This "magical number seven" is derived from the population "on which more than 90% of psychological studies happen to be focused, the American undergraduate!" (p. 103)

Because Chinese uses single-syllable words for numbers, Chinese speakers can easily remember 9 digits, whereas English speakers can only remember 7.

The oral numeral system in Chinese is also much simpler than ours; instead of memorizing separate words for 0 all the way to 19 and then special words for 20, 30, etc., Chinese speakers simply have to say, for example, "one ten two" for twelve or "three ten five" for 35. An experiment found that at age four, American children can count up to about 15, whereas Chinese children can already count up to 40.

I don't need to remind you that China is WAY ahead of the U.S. in math. So, that's one of the main reasons: their spoken numeral system perfectly matches the written system, making counting easier and making the concept of base-10 much easier to grasp.

So, maybe a simple solution to improving U.S. math education is to teach kids to count the way the Chinese do, at least at first. They can memorize the words for 11 to 19 and 20, 30, and so on when they're older, AFTER they've mastered the decimal system. Or, y'know, we could just change the English language. =P It sucks anyway, am I right?

I'm not sure that I agree with the assessment about the Chinese language and math instruction in the US.  But, I'm anxious to read the book and develop a more informed opinion on the matter.  Regardless, it sounds like this book will be worth reading.

If you've read the book, tell us your opinion of it.  What insights did you take away from this book?  Did it change the way you approach math instruction?  

If you decide to read the book after reading this post, come back and comment as you make your way through the book.  Let us know if this book will impact your teaching in any way.  I'll do the same.

Happy Reading!

Seven Ways to Go from On-Task to Engaged

Guest Post by Bryan Harris:  This post was written by a friend and colleague of mine.  It was originally posted on the ASCD blog.  Bryan Harris is the Director of Professional Development for the Casa Grande Elementary School District in Arizona.  He's also the author of Battling Boredom, published by Eye On Education.  

His new book, 75 Quick and Easy Solutions to Common Classroom Disruptions, will also be published by Eye On Education and is scheduled to be released January 2012. You can learn more about Bryan and his work at http://www.bryan-harris.com/.

 
Bryan's Post:

We know that engagement is the key to learning, but we also know that many of our students are bored with the curriculum and activities being offered in classrooms. To battle this problem, much focus and attention has been placed on getting students to be "on-task." Indeed, the link between on-task behavior and student achievement is strong. However, just as a worker at a company can be busy without being productive, a student can be on-task without actually being engaged in the learning. True, long-lasting learning comes not merely as a result of being on-task, but being deeply engaged in meaningful, relevant, and important tasks. 

We see examples of on-task but disengaged behavior every day: students mindlessly copying notes from a screen, listening to a lecture but daydreaming about what to do after school, robotically completing a worksheet. Some students, particularly older ones, have become masters at what Bishop and Pflaum (2005) refer to as "pretend-attend." They've mastered the ability to look busy, focused, and on-task, but in reality they are disengaged in the actual learning.

So, how do we ramp up both on-task behavior and real, meaningful engagement for our students? Here are seven easy ways to increase the likelihood that students are both engaged and on-task:

1. Teach students about the process of focus, attention, and engagement. Tell them about how the brain works and help them to recognize the characteristics of real engagement.


2. When designing objectives, lessons, and activities, consider the task students are being asked to complete. Is the task, behavior, or activity one that is relevant, interactive, and meaningful, or is it primarily designed to keep kids busy and quiet?


3. Ask your students about their perspectives, ideas, and experiences. What do they find engaging, real, and meaningful? 


4. Create authentic reasons for learning activities. Connect the objectives, activities, and tasks to those things that are interesting and related to student experiences.


5. Provide choice in the way students learn information and express their knowledge.
6. Incorporate positive emotions including curiosity, humor, age-appropriate controversy, and inconsequential competition. (Inconsequential competition is described by Marzano [2007] as competition in the spirit of fun with no rewards, punishments or anything of "consequence" attached.)


7. Allow for creativity and multisensory stimulation (think art, drama, role play, and movement).

Have you noticed that on-task does not always mean engaged? How do you achieve both?

Royal Lessons: Powerful Teaching Strategies Seen in the Royal Wedding

Okay, I admit it!  Like 2 billion other people across the world, I tuned in to the Royal Wedding last Friday.  Well, I recorded it since it took place at 2:00 a.m. Alaska time!

As I watched the Royal Wedding, I was struck by some Powerful Teaching Strategies that were on display.  I know, it seems odd, the Royal Wedding showcasing Powerful Teaching Strategies! 


The First Powerful Teaching Strategy Seen in the Royal Wedding:


The Power of a Common Experience

While watching the Royal Wedding, I saw people from around the world who had gone to London just to participate in this experience.  I also knew that at the moment of the wedding, a few billion people were all sitting somewhere watching the very same thing.  With all of the turmoil that is currently taking place around the world, it's amazing that so many people across the globe could be brought together for one event...the Royal Wedding.  

This one event brought together everyone who was watching by giving them a Common Experience. No matter where you're from, if you watched the Royal Wedding, you have something in common with people you may never otherwise associate with.  We may not be from the same Country, Religion,  or Social Class, but we now have something in common that could bring us together.


So how does this impact teaching?

Providing Common Experiences in a classroom setting does 2 very important things:

• Builds Community

• Levels the Playing Field 

 Building Community With Common Experiences

In the classroom, we see diversity all the time.  Students enter our classrooms with various interests and backgrounds.  We need to find ways to bring them together.  Every time we provide some type of Common Experience for the class, we accomplish this goal. Students who may never speak to each other, now have something in common. This is one reason it's important to regularly do Ice Breaker and Brain Break activities with our students.  


When you do Ice Breaker and Brain Break activities, you can just do them for fun or you can include content.  You should use these activities both ways.  For the sake of building community, it's important to have times where you do things just for fun.  Doing activities like this also help students view the teacher in a different way.  It shows that you care about and want to learn more about your students and their interests.  It also shows that you know learning is about more than Content!  Yes, I said it!!!  Learning is about more than Content!  However, it's equally important to use these types of activities with Content.  This shows students that you believe learning should be an enjoyable experience.  These activities can also serve as a means to gather valuable information about student's knowledge and understanding and/or to consolidate learning.
 
When I was in the classroom, a favorite activity of my students was Which Would You Rather?.  

Here's how you play Which Would You Rather?:

• students begin by standing in the center of the room
• the teacher asks a question like "Would you rather eat a worm or stand next to a snake for 5 minutes?"
• the teacher designates a side of the room for eating worms and a side of the room for standing next to a snake
• students move to the side of the room to show their answer

Note:  Sometimes, you can have a student ask the questions.  They LOVE that!  Just give a list of questions to the designated student.  This also frees you up to either play with your students or to question students about their thinking.


As you see, this activity can be very fun!  You can also use it with math content.  When including content, Would You Rather can be used to:

• assess prior knowledge

• conduct formative assessments during teaching

• review previous learning

Here are few ideas for incorporating math content into Would You Rather (or a variation of it):

• Would you rather be get a quarter of million dollars or half of $750,000?

• The right side of the room represents 1/4, the left side of the room represents 1/3.  Which one is larger?

• The right side of the room represents a circle with a radius of 5 meters, the left side of the room represents a circle with a Circumference of 20 meters.  Which one has the smaller Circumference?

• The right side of the room represents Area, the left side of the room represents Volume.  Which one of these would be used to find the amount of water in a fish tank?

 When doing this activity with math content, you could pause in between and do the following:

• have students share their thinking with someone standing next to them

• call on students to explain their choice to the class

• have students on each side of the room debate their choices

Note:  Some students may just follow others in the class because they are not sure of the answer.  As long as you have students discuss their thinking, everyone in the room still benefits form the activity.  If you choose not to have students explain their thinking during the activity, you could have them do some type of reflective activity later.


Leveling the Playing Field with Common Experiences


As mentioned above, our classrooms can be very diverse.  We learn by making meaning.  Prior experiences are key to making meaning of new learning.  So the more diverse your classroom, the more difficult it becomes to reach ALL learners. 

When teaching we may use vocabulary and examples that have no meaning to some students.  This is especially true in math.  Most of our students don't come to us with the background they need to be successful in math.  It's up to us to Create Common Experiences that give students a basis for their learning.  

Each time we create a Common Experience for students, we're putting them on equal footing by providing all students with the same foundation on which they can make meaning.  The final Circumference Activity referenced in my previous post Circumference:  The Evolution of a Lesson is an example of how a common experience gives all students the same background knowledge in which they can build further understandings.  By having all of the students measure the hula hoops, they all had a basis for understanding Pi and Circumference.  We were also able to reference the activity throughout the year because everyone had participated in the Common Experience.

You can find more examples of Creating Common Experiences with Math Content in IGNITE Student Engagement in Math:  3 Simple Strategies for Making Content Memorable.

This is the first in a series of posts titled Royal Learning.  In the next post of the series, we'll explore another Powerful Teaching Strategy that was evident in the Royal Wedding.

Leave a comment.  We'd love to hear what you think of this article or how you use Common Experiences in your classroom.

Circumference: The Evolution of a Lesson

In this post, I'd like to share how I was able to transform the way I taught Circumference in order to make it more Memorable for students.  This transition took place over several years of my teaching career.  It is important to note that I made these transitions while teaching students in Title I schools.  

The ideas presented in this lesson transformation can and should be applied to other topics and concepts in order to make content more memorable for students.

 
Scenario 1:  Rote Learning (Not Memorable!)

When I first started teaching, I pretty much taught everything in a rote and abstract manner.  So to teach Circumference I would just tell my students the formula for Circumference, show them how to input the variables, and finally I’d show them how to solve the equation.  We would do several guided practice problems and they were let loose to practice about 20 problems on their own.  There was no meaning associated with the learning at all!  There was no Novelty involved in the way I taught the lesson.

Scenario 2:  A Discovery Lesson (Somewhat Memorable!)

After a few years of teaching, I learned how to teach math conceptually. This was HUGE for me since I had not learned math this way!  I immediately began to implement Conceptual Development of mathematical concepts into my teaching. 

Once I had this enlightenment, I began to teach Circumference differently.  Here’s how I taught Circumference:

•           I would bring in different sized circular objects and string.

•           Students would use the string to compare the diameter of the circle to the Circumference of the circle. 

•           Students would measure the string used for the diameter of the circle and the string used for the Circumference of the circle.  They would record their findings in a table.

	Diameter in inches (d) Process Circumference in inches (C)

We would then repeat this process with the radius.

The point was to get students to see the relationship between the diameter and Circumference of the circle.  This would lead to the discovery of Pi and the Circumference formula. 

Teaching the lesson this way was much more memorable for several reasons.

•           Students were engaged in the learning process by having to actually measure and compare the diameter to the circumference.

•          By discovering the formula, Circumference had much more meaning to students.  

•          We had incorporated some Novelty because it wasn’t just another worksheet.  It was also different to have to measure the various circular objects.

After teaching the lesson this way, I definitely noticed an improvement in understanding and retention rates.  If students did forget things about Circumference, I could jog their memories by just reminding them about when we measured the circular objects with string.

Scenario 3:  Adding in Some Novelty (Now it’s Memorable!)

Several years later after learning about Brain-Based Learning, I decided that I could make this lesson even more Memorable for my students by adding some Novelty.

We basically did the same lesson as described in Scenario 2 with these variations. 

•            Instead of just bringing in basic circular objects like paper plates and container lids, I decided to use different sized hula hoops. 

•          I made more of a production about introducing the lesson. 

Introducing the Lesson:

In order to build curiosity and anticipation, I would place hula hoops at the front of room.  I wanted to make sure that they were seen when students entered the room.  As you can imagine, they were!  The hula hoops definitely created a buzz, which was exactly what I wanted.

Just by the sight of the hula hoops, my students were being “hooked”.  They wanted to know what was going to happen.  In fact, they could hardly make it through the” Warm Up” because they were so curious about the hula hoops.

When it was time to start the lesson, I would choose a hula hoop and attempt to use it.  After the laughter subsided, I would ask the class these questions.

             Does it matter what size hula hoop you use?  Why?

             Is it easier to use a large hula hoop or a small hula hoop? 

           

We would spend a few minutes debating these questions.  Based on their prior experience, they tended to agree that the larger hula hoops were easier to use. 

Next, I would ask students what “Math” word could be used to describe the size of a Hula Hoop. These were 7^th graders so they had prior exposure to the term Circumference.  It sometimes took a few prompts, but someone would eventually get the correct word.

After discussing the vocabulary related to circles, I would explain that we were going to compare the relationship between the diameter and the Circumference and the relationship between the radius and the Circumference.  I would have them make predictions about the following.

•          How many diameters will it take to equal the Circumference of the hula hoop?

•        How many radii will it take to equal the Circumference of the hula hoop?

•      Will these relationships change based on the size of the hula hoop?

The Lesson:

I would give students the instructions for the activity and get them started.  While doing the activity, they would complete the recording sheet (see below) where they filled in the tables and graphs.  I changed the activity by not having them measure the string.  This time, they were just noticing that the Circumference was a little more than 3 times the diameter.

Circumference Introduction (Hula Hoop Lesson)

The Result:

After teaching the lesson this way, I noticed marked improvements in understanding and retention rates!  This time even my weakest students and my ELL seemed to be able to grasp the concepts of Circumference and Pi.  Overall, my students rarely had trouble remembering that the Circumference is a little more than 3 times the diameter and that it’s a little more than 6 times the radius.  (We did transition to Pi is approximately 3.14.)  Throughout the year if it had been a while since we had done anything with Circumference, it might seem like they had forgotten.  I would just remind students about the activity we did with hula hoops and it would come right back to them.

So, what made the difference?

There are actually several reasons this lesson became more memorable, but Novelty is definitely one of the big reasons students were able to better recall what they had learned.  By bringing in Novelty with the hula hoops, students were interested in and curious about what they were about to learn.  They were more attentive to the learning because it was something different and fun.  When students needed to remember things about Pi and Circumference later, it was easier to recall because it was the only time they’d ever seen hula hoops in a math class.

Relevance and emotions also played a part in making this lesson more memorable.  Students were interested in the hula hoops, they had prior experience with the hula hoops, and they enjoyed seeing me “try” to hula hoop.  Along with the Novelty of the lesson, these things really made a huge impact on student’s understanding and retention rates.

 

If you want to make learning more memorable, Novelty should be a regular part of your daily lessons.  As you begin to include more Novelty into your lessons, you’ll notice that retention rates are not the only benefit.  You’ll also notice that attention and motivation are positively affected!

Remember, something is only novel for a short time, so we have to continually find new ways to introduce novelty into our lessons. 

If you like this post, you may also like these:

Hand-on Lesson for Area of Circles

Did you say Movement in the Math Classroom?!

Looking Beyond the Obvious to Deepen Understanding

Now that's a Novel Idea!

Did You Say Movement in the Math Classroom?!

When is the last time you had your students moving around during your math class?  With all of the pressures we face to teach the standards and improve student achievement in math, we often overlook and under utilize teaching strategies that would actually help to improve achievement. Incorporating movement into lessons is one teaching strategy that is usually absent in many math classes.

Movement is an essential element for optimal learning. When you incorporate movement into lessons students are less bored, more engaged in the learning experience, and they have a better chance of remembering what they're learning.

Here are a few reasons we need to incorporate movement into our math classes:

• Movement increases blood flow in the brain.

•  Movement increases glucose in the brain. (The process of learning drains glucose, which fuels the brain.)

•  "Human beings are designed to recall better what we do actively than what we do passively." (Jensen, 2005)

• Movement has positive effects on attention.

There are many ways that you can incorporate movement into your classes. One of my favorite ways to get students up and moving is to use stations. My students always liked stations too! They enjoyed moving around the classroom and working together. Stations can be activities that students do, problems they work, or a combination. Many times, I'd just create 10 - 15 problems on whatever topic we were learning. We'd put the desks in groups and I'd give each group one or two problems. I'd give them about 3 - 5 minutes per problem. Once the time was up, they would get up and move to the next station. When doing stations with students, you always want to leave time for debriefing. Debriefing is actually when a lot of the learning takes place. During the debrief you want students to reflect on what they did at each station, what they were learning at each station, what they had trouble with, which strategies for solving problems are most efficient, etc.

Rather than just having students work problems on a worksheet, you can get them moving. Another one of my student's favorite activities is a Measures of Central Tendency Activity.

Measures of Central Tendency Activity

I've used this activity with my students as a way to practice finding the mean, median, mode, and range of a set of data.  My students have always loved this one!  They liked getting to interact and learn things about their classmates while practicing their math skills.

I always introduced this activity with a personal story about sending/receiving text messages.  This always grabbed student's attention before introducing the activity.  I've used this activity with my students as a way to practice finding the mean, median, mode, and range of a set of data.  My students have always loved this one!  They liked getting to interact and learn things about their classmates while practicing their math skills.

Procedures for the Activity:

• Pass out Measures of Central Tendency Activity Sheets

• Students will go around the room having various classmates answer the questions on the top of the Activity Sheet.

• Each student can only answer 3 questions (fill in 3 squares) on a classmate's Activity Sheet.  (This is so they will get responses from more students in the class.  Depending on your class size, you may want to increase or decrease the number of times each person can sign one Activity Sheet.)

• Limit the time students have to get their Activity Cards filled out.  Give about 10 minutes for this part of the activity.  That is enough time for most students to get it done. 

• Have students calculate the mean, median, mode, and range for each column on their Activity Sheet.

• Have students answer follow-up questions.

Central Tendency Activity Recording Sheets

You can download the activity recording sheets from Scribd.
Central Tendency BINGO Card Activity

You could add choice to this activity by putting a list of questions on the board and having students choose their own 5 questions.



If you have some ideas or favorite activities for getting students up and moving during math, please leave a comment and share with us.

About Mirror Neurons

via publicwords.typepad.com

Learn a little about mirror neurons in 51 secs.

Brain-Based Learning Teaching Stategy: Respecting Attentional Limitations

Do you often have trouble getting students to pay attention?  There's a very good reason for this!

Our brains have limitations on how long we can maintain focused attention.  The number of minutes a person can maintain focus is usually equivalent to their age in minutes.  So, if you teach 12 year olds, 12 minutes is about how long they can maintain focused attention.  However, this formula does max out at about 15 - 20 minutes. 

So, what can we do about these attentional limitations?

Knowing these natural limitations, there are several things we can do to keep students focused on the task at hand.  Here are a few strategies for helping students focus.

• Always be mindful of the attention limitations and break teaching into smaller segments.  If you have a lesson that you know is going to take longer than 12 - 15 minutes, break it into chunks.  In between chunks of information, have students do a Think-Pair-Share or something similar to give the brain a break and allow time to process new learning.

• Give Cues as a way to let students know that something important is coming.  For example, say things like, "If you don't hear anything else today, make sure you hear this."

• Use physical actions to get student's attention when you are ready to move on to something else.  For example, say to the class, "join me when you can" and start clapping your hands in some type of pattern.  Students would then repeat the pattern of claps.  Keep doing this until everyone has joined in the clapping, and then go right into the next segment of the lesson.

New Brain Discovery: Superior Autobiographical Memory

Last Sunday, 60 Minutes had a story about a new discovery in brain science.  It's called superior autobiographical memory.   The subjects of this story have the ability to recall all the events of their life.  It  was a very interesting story.  I'll be exciting to see what happens with this discovery in the future of Neuroscience and Brain-Based Learning.  I'm attending an Eric Jensen workshop in January, and I can't wait to get his take on this news!


60 Minutes Episode  (Go to the 15:50 mark on the video to see the Lesley Stahl story.  You'll have to watch a commercial before the story clip.)

Lesley Stahl interviews the handful of individuals known to possess the skill of near endless memory.

Extra Clips from story:

Marilu Henner, who has what is called superior autobiographical memory, tells Lesley Stahl how she uses her extensive memory to "time travel" and recall moments of her childhood.

Lesley Stahl puts Louise Owen's memory to the test. Owen has superior autobiographical memory.

New Brain Discovery: Superior Autobiographical Memory by Love of Learning Educational Services, LLC is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.