Wednesday, October 12, 2011

Mathematics Glossary

This is one of the best math dictionaries I've ever come across (thanks to Glen Holmes!). The  glossary is hosted by Alberta Learning (Alberta, Canada).  

The beauty of this glossary of math terms is that the terms are often accompanied by "real-world" visuals and applets that students can manipulate to reinforce the point/term. 

Tuesday, October 11, 2011

The Best Technology Tools for Teaching Math

There are many excellent technology tools available today, but a lot of them are not really applicable to the math classroom.  That's why I started The Best Technology Tools for Teaching Math on  This site is dedicated to the best technology resources for math teachers and students.  

Click on tags to see a list of topics.  When you choose a tag, you'll see everything related to that topic.  Some topics that will be included are:
  • YouTube --- sites that help teachers incorporate YouTube videos in the classroom
  • Multimedia 
  • Reflection Tools --- applications that help students reflect on their learning
  •  Student Engagement --- applications that help students become engaged in the learning process
  • Video Editing --- applications that make video editing quick and easy
If you know of resources that should be added to this list, please feel free to use the Suggest tab at the top of the page to make your recommendation.  Or, leave a comment on this page with your recommendation. 

I'll also keep a list of these sites on this blog, but you'll find more detailed information about the applications and their possible uses on the site.  Here's a list of what's on The Best Technology Tools for Teaching and Learning so far:
  • Glogster --- make interactive posters  
  • Voice Thread --- create conversations around multimedia
  • Spliced --- this site allows you to get clips of YouTube videos
  • Hofli Online Charts Builder --- site for creating different types of graphs
  • Math Dictionary --- this glossary of math terms hosted by Alberta Learning uses visuals and interactive applets to explain/demonstrate math vocabulary 
  • Poll Everywhere --- free student response system...create multiple choice or free response questions for your students and see resultants in real time
This is a new list so it's not very big right now.  I'll continue to add things regularly and it will continue to grow.  

If you use any of these tools, let us know how they work for you. 

You may also want to follow my other topics:
Stay tuned!  I'll be creating and sharing more math related topics soon.

Monday, October 10, 2011

Hands-on Lesson for Area of Circles

This video was created by Karyn Hodgens of Kidnexions.  Karyn gives step by step instructions for having students make targets in order to practice finding area of circles.  I really like the way she incorporates problem solving into the lesson.   She also has some good ideas for demonstrating the concept of subtracting the areas to find the area of the outer rings of the target.

In order to extend this lesson and tie area and circumference into other math standards, you can have students create graphs for the area and circumference of each circle in the target.

Have students: 
  • compare and contrast the 2 graphs
  • describe what types of patterns they see on each graph
  • determine which of the 2 graphs shows a proportional relationship and describe what makes it proportional  (Proportional relationships are linear and they goes through the origin.  They always go through the origin because there is no constant.)
  • use the graphs to make predictions about data points that are not on the graph
  • relate the graphs to the formulas (equations) for area and circumference
  • describe how the equation (formula) and graphs for Circumference are different when you use radius instead of diameter as the independent variable 

If you like this lesson, you might also like Circumference: The Evolution of a Lesson.
What else could you do to extend this lesson for middle school? Leave a comment and share your ideas.

Amazing Illusion! Magnet-Like Slopes

This is a really cool illusion to share with your students.  This was the winner in the 2010 Best Illusion of the Year Competition.  Check out the other finalist here.

It would be interesting to see if any of your students could duplicate this.  Trying to figure out how this was created could lead to some interesting mathematical discussions.

Sunday, October 9, 2011

Posterous Spaces - Excellent Tool for Beginning Bloggers

If you've never blogged or had your students blog, Posterous Spaces is a great beginners tool.  It's the quickest and easiest way to start a blog (that I know of anyway!).  With Posterous Spaces, anyone can easily create an account and write your first blog post in 15 minutes.  It may take a little longer to set up your profile and pages, but even that doesn't take too long with Posterous Spaces.

Posterous Spaces has some features that help to make it a nice blogging tool.  
  • Posterous Spaces formats your posts for you.  Just write the post and attach any videos and images you want to go with the post.  Posterous Spaces does all of the formatting for you.  
  • You can write new posts on the site or in an email.  Not at your computer, but you want to write a blog post.  No problem with Posterous Spaces!  Just compose an email, attach images and/or videos and send to your Posterous Spaces email address.  They will format everything for you.
  • Posterous Spaces has an auto-posting feature.  After you write a post, you can have it automatically auto-posted to Facebook, Twitter, Linkedin, Blogger, any many others.  
  • Posterous Spaces has privacy settings that make it an ideal tool for student bloggs.
Today on Free Technology for Teachers, Richard Byrne, posted the following slide show.  He goes through all of the steps necessary for starting a Posterous blog.

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!

Friday, October 7, 2011

View and Share Websites Without Ads

I send out a periodic newsletter titled Web 2.0 Resources for Teachers.  In a recent edition of this newsletter, I shared information about PageFlip-Flap.  PageFlip-Flap allows you to turn documents, images, and videos into an interactive flipbook.   Soon after the newsletter was sent, a reader emailed and asked me if I knew other applications that did the same thing without ads.  With PageFlip-Flap, your flipbook has ads along the side.   I recommended that he try FlipSnak, a similar application.

Recently, I found out about  This is an application that takes the ads off websites.  You get a link that you can share with others.  With, you can share sites with your students that you may not have used before because of unwanted ads.

You can subscribe to my  Web 2.0 Resources for Teachers Newsletter by clicking on the link.

Thursday, October 6, 2011

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
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?

Wednesday, October 5, 2011

How would our world be different without Steve Jobs?

I was out running errands when I heard on the radio that Steve Jobs has passed away.  I couldn't help but stop and think about how our lives might be different if it weren't for his forward thinking and creativity.  He exemplified the characteristics most of us would like to see in our math students.  He was a problem solver, innovator and creative thinker.

Many middle school students may not know who Steve Jobs is and what he's offered to the world, but they certainly use his products and benefit from his ingenuity.  Yesterday, I wrote a post titled Math Curriculum: How and Why it Needs to Change.  This post is about the role of technology in mathematics curriculum reform.  If it weren't for Steve Jobs and others like him, there may not be a need for this type of discussion.

It may be worth taking a few minutes of valuable class time to discuss his accomplishments and contributions with students.  And, to ponder how our world would be different without his contributions.

You might also want to share Steve Jobs' 2005 Standford Commencement Address with your students.  (via: Richard Byrne)

Tuesday, October 4, 2011

Math Curriculum: How and Why It Needs To Change

It seems that everyone is talking about math reform these days.  But, what does that really mean?  What does it or should it look like?  The truth is there are many facets of what should make up math reform including things like assessment, understanding how students learn, metacognition, technology and math curriculum.  This post will focus on the need to rethink math curriculum and the role of technology in transforming math curriculum.

You've probably noticed that over the last few decades, our world has been changing rapidly.  Technology has changed the way we operate our daily lives.   And, technology has certainly changed the way businesses  and industries operate.  But, surprisingly (or not), technology has not really impacted math curriculum as a whole.  

Traditionally, math curriculum has been all about computation with little, if any, emphasis on understanding or context.  Until the last few decades, math curriculum needed to focus on arithmetic and computation because we didn't have technology that could do the computation for us.  

Today, we don't need as much emphasis on computation and arithmetic because we have technology that can support this.  Let me be clear, I'm not suggesting that we don't need to teach any computation.  I'm saying that computation should not be the primary focus in our math classes.  For students to be successful in our ever changing world, they need to be able to demonstrate mathematical reasoning, think critically, apply math to real situations, interpret and analyze data, and problem solve. The beauty of technology is that it allows us to spend more time focusing on higher order thinking, making real world connections to math and problem solving skills with less time spent on teaching arithmetic.

There are two TED talks that describe what today's math curriculum should look like.  The first one titled Teaching Kids Real Math with Computers is from Conrad Wolfram.  The second one titled Math Class Needs a Makeover is from Dan Meyer.  Both of these TED Talks do a great job describing why we need to rethink math curriculum and how technology can help make math more relevant, interesting, and practical.  They also show how technology allows students to gain deeper mathematical understanding and become better problem solvers.

Some key points form these videos are:
  • Math looks different in the real world than it does in a typical math classroom
  • Math helps everyone make sense of the world
  • Math is NOT computation
  • Math is about posing the right questions 
  • Computation should arise from a need to answer a mathematical question
  • Calculating no longer has to be the limiting step in answering mathematical questions
  • Math in the real world is popular
  • Math is used regularly by many professions
  • Math in the real world is difficult and often doesn't look like a bunch of calculations
  • Sometimes math doesn't look like math
  • Estimation is a necessary and valuable skill
  • Technology allows students to see a need for computation
  • Technology allows for deeper more meaningful mathematical dialogue
  • Technology allows students to experience and understand difficult math concepts like Calculus much earlier

Teaching Kids Real Math With Computers by Conrad Wolfram

Math Class Needs a Makeover by Dan Meyer

If you're interested in more resources from Dan Meyer and Conrad Wolfram, check out these sites.
The purpose of this post is get you thinking about how you approach math instruction.  What changes can you make that will help your students become more equipped to function in today's world and in their world of tomorrow?

Monday, October 3, 2011

Come on Down! Problem Solving on the Price is Right

If you're looking for an interesting activity that requires students to practice problem solving, look to The Price is Right!  Surprising right?!

For the 39th season of the show (aired in 2010), The Price is Right introduced a new game called Pay the Rent.  This game is interesting because, unlike most of the games on the show, it requires the contestant to use some problem solving skills.  I guess that should be expected since it's a $100,000 game!

Using this with Students:  

Begin by showing the following video clip.  This is a clip of the day Pay the Rent was introduced on the show. 

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After showing the video clip, ask students to think about what question comes to mind about the game.  There is an obvious question that most students should be able to figure out.
The Question(s):

Is it possible to win this game?   If so, how?...The answer to this question should lead to another question.

If you can win this game, are there multiple ways to win?

Students might also wonder if this game is fair.  The question of fairness could be a good question for debate after students figure out if it's possible to win the $100,000 prize.

Next Step:

After students come up with the question, have them use the prices from the game to see if they can find a way to win the game.  

Once a student or groups figures out one way to win a new question should arise.  Is this the only way to win the game?  

Have students continue to see if they can find multiple ways to win the game.

Class Discussion:
  • Have students share their answers with the class and discuss the possible ways to win.  
  • Discuss the problem solving methods used by students.  
  • Ask students if answering this question was easier or harder than they thought.  Why?
  • Ask students students if they would go about solving this problem the same way again, or if they think there is an easier way to solve it.
  • Ask students if they would want to play this game if they were on The Price is Right.  Why or why not?  Ask if they think it would be easier now that they know the key to the game.
The Answer:

After students have had time to try to figure out if the game can be won, show the following video clip.

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This clip proves that the game can be won and demonstrates how.  If you want students to continue problem solving, have them use the values in this video clip to see if there were other possible to win.

Possible Extensions on this lesson:
  • Have students journal about the methods they used to solve this problem.
  • Have students create a Glog (interactive poster) that illustrates the question and their solution.
  • Have students create a new Price is Right game that involves problem solving. 

Would you use this activity with students?  How would you extend this activity?  Leave a comment and let us know your thoughts.