Mathematics and Multimedia Blog Carnival 18

Welcome to Mathematics and Multimedia Blog Carnival 18!

Before jumping into the blog posts, here are some Fun Facts about the number 18:

• the only positive number that is double the sum of its digits
• the third heptagonal number
• a semiperfect number because 3 of its factors (3, 6, and 9) add up to 18...All multiples of semiperfect numbers are also semiperfect numbers.
• the atomic number of Argon
• the legal age for voting for most countries
• Bobby Labonte's car number in the NASCAR Winston Cup Series when he won the 2000 Championship.
• the number of chapters Ulysses, James Joyce's epic novel, was divided
• 18:00 corresponds with 6:00 pm in military time

Now that we've enjoyed some trivia about the number 18, let's move on to some excellent blog posts related to mathematics teaching and learning.

Just for Fun:

Guillermo Bautista (founder of Mathematics and Multimedia Blog Carnival) recently wrote a fun post titled 25 Signs You are a Future Mathematician.  You can check out more of Guillermo's posts at Mathematics and Multimedia.

15 Items or Less, an image posted by Dave Gale, is sure to get a laugh.  Dave's blog is Reflective Maths Teacher on Posterous.

Wild About Math sometimes reviews math related books.  Review: Magical Mathematics was a recent post featuring the book Magical Mathematics.

Articles Related to Teaching Mathematics:

In his post, Calculus and Kobe Bryant, Dave Martin uses a video clip with Kobe Bryant to engage students in problem solving.  Dave blog is Real Teaching Means Real Learning.

Back to Back Shape Describing Game, another post from Dave Gale at Reflective Maths Teacher, requires students to know and use math vocabulary in order to draw geometric figures.

Patrick Honner presents A Quadrilateral Challenge at Mr.Honner Math Appreciation.  He recently posted a creative solution to his original challenge.

What's your problem Part III, is the 3rd in a series of posts by David Coffey.  In this series, David explores assessment and evaluation.  David's blog is Delta Scape.

In Mixed Up Mixture Problems, David Cox uses Geogebra  created graphics to demonstrate how proportional reasoning can be used to solve these traditional algebra problems.  You can find more of David's posts at Questions? Trying to Make it Matter.


Technology Integration:

Colleen Young shares some of her favorite online resources for teaching mathematics in Top 100 Tools for Learning 2011.  You can find more resources from Colleen at Mathematics, Learning and Web 2.0.

Using Popplet in the Math Classroom is one of the most popular posts from this blog.

For Students:

Colleen Young recently started the blog, Mathematics/Learning Mathematics - Resources for Students.  A Variety of Online Resources is one of her latest posts in which she shares some useful applications for students.

Sanjay Gulati shares many ready to use Geogebra applets at Mathematics Academy. His latest applet demonstrates Adjacent Complementary Angles.

6 Supurb Universities Around the World to Study Math was recently posted on the Tripbaseblog. 

Well, that's it for Mathematics and Multimedia Blog Carnival 18.  I hope you enjoy these articles as much as I enjoyed putting this Carnival together! 

Zootool: A Visual Social Bookmarking Tool

Oct. 23 was a sad day for me because my favorite bookmarking tool, SimplyBox, closed to the public.  I liked SimplyBox because of it's ease of use, organization and functionality.  But, most of all, I liked that it was visual.  You could collect screen shots of the sites you wanted to bookmark.  So instead of just seeing the name of the site, you would also see the screenshot.  SimplyBox was such a excellent tool, that I wasn't surprised with their decision to focus on Enterprise and close to the public.

So, that sent me on my quest to find another visual bookmarking tool that also had the ease of use, organization and functionality that I wanted.  I came across several candidates in my search, but Zootool was by far the best for meeting my criteria.  When you save a bookmark in Zootool, it takes a screenshot of the website.  You can organize your bookmarks into categories, which Zootool refers to as Packs.  You can also organize your bookmarks with tags.  The only real drawback I've found with Zootool is that the application doesn't allow you share an entire Pack.  You can only share a single bookmark or Profile Page link, which gives someone access to your entire collection of bookmarks. 

You can share your bookmarks and follow other users with Zootool .  If you find a Zootool user you want to follow, you can follow them through the application and/or through RSS.  The RSS option for following a user is located at the bottom of the users Profile Page.  You can find my Zootool Profile Page here if you'd like to follow my bookmarks.  You can follow and add your comments to my bookmarks.

Zootool also offers an iPhone app.  I put the app on my iPad too!  There was a small fee for the iPhone app, but it's well worth it! The Zootool app ranks very high among my favorite apps.

Another feature of Note is that you can place bookmarks into multiple Packs.  The iPad app allows you to select multiple Packs at the time of bookmarking.  If you're bookmarking on a desktop or laptop, you can select one Pack at the time of bookmarking.  Once the site is bookmarked, you can simply drag it into as many Packs as you want.

Calling All Math Bloggers Round 2

I'm pleased to announce that the Mathematics and Multimedia Blog Carnival is on its eighteenth edition and will be hosted here.  This is the second time I've had the privilege of hosting the Mathematics and Multimedia Blog Carnival, and I'm looking forward to making it one to remember!  The Carnival will be posted on Monday, December 19, 2011.  The deadline of submission is Wednesday, December 14, 2011. You may submit your articles here.

To increase the chance of your article of being published, read the Mathematics and Multimedia Carnival’s Criteria for Selection of Articles. To view the list of previous carnivals click here.

Note:  As of now the Blog Carnival Submission System is down.  In the meantime, you may submit your articles directly to me at kristi.grande@gmail.com.  

I look forward to receiving your submissions!

If haven't seen it yet, the Math and Multimedia Carnival 17  is now live at Mathematics for Teaching. 

Fun Math Trick Video: I Can Guess Your Phone Number

Here's a fun math trick video that your students might enjoy.  It's a trick where the calculations will result in your phone number, excluding the area code.  Students may find it interesting that you have to enter your entire phone number as part of the trick, but a series of calculations are performed with the digits.
 

I'm sharing this just as a fun thing to use with students.  It would be perfect for a time when students need a short "brain break".  You'll probably have at least one or two students who are interested in trying to figure out how the trick works.

 

Viewing Tip:  You can use SafeShare.TV to safely share YouTube videos with students.  SafeShare.TV takes all of the ads and comments off the videos.  I've already uploaded this video.  You can view it in SafeShare.TV by following this link.

Inspiration Can Come From the Strangest Places!

Gotta love it when great math content just comes to your inbox!  The image below was part of a GoDaddy.com ad I received recently.  When I saw the ad, I was immediately inspired to write this post.   Guess you never know where you might get inspiration for math content or teaching strategies!!! 

The subject line of the email was "Choose your savings, all the way up to 30%".  Here's a screenshot of the GoDaddy.com ad:
 

Why I like this graphic:

Often times in math, we concentrate our efforts on the topic we're teaching to the exclusion of other questions or topics that could arise from the same problem or situation. By doing this we unwittingly lead our students to become locked in to one way of thinking about the situation. This causes problems for students when they later (usually on standardized tests) experience problems/situations that are a variation of or the counter to the problems they're used to solving.  Or, if the question that accompanies a familiar picture is different than the typical question.  For example, when students see a picture of an aquarium, they automatically think that they're going find the volume.  But, the question could ask how much sand is needed to cover the bottom of the aquarium.  If students have only found volume when given pictures of rectangular prisms, they won't even consider that the question could be asking for the area of the base.  If we don't give students experience in generating questions from given situations, they'll continue to jump to the wrong conclusions even if they do read the problem!  That's the big problem with formulaic teaching rather than teaching students to think and problem solve.

The graphic above is a prime example of this type of formulaic teaching.  Most students would look at the graphic and automatically think they need to find 10% of 50, 20% of 100, and/or 30% of 130 in order to answer the question.  Did you notice that there really isn't a question?...At least not one posed by a math teacher!  "How much do you want to save?" was part of the graphic in the email, so I'm not counting that as the question right now.  But, students may think this is the question.  If so, they'd probably still jump right to the calculations mentioned above.

The beauty of this graphic is that there are many questions that can asked about this sale offer. And, some of them lead to some interesting mathematics and considerations.

Generate Possible Questions:

Have students brainstorm questions that could be asked about this image.  There are many possible questions.  It will be interesting to see what students come up with.  You may learn a bit about what student's know, or don't know, about percents and interpreting information by the questions they generate.  You might want to check out the first post of my Brainstorming series to see some benefits of brainstorming.  Here are a few possible questions that came to mind:

• How much will you save if you choose the 30% option and only spend $130?
• How much more will someone save if they choose the 20% option over the 10% option?
• Why would Go Daddy make this offer?  What's in it for them?  Which offer do you think Go Daddy wants people to choose?  Why?
• What's the most I can save if I choose the 20% option?  What's the least I can save if I choose the 20% option? 
• Which one is the best deal? 
• Are the offers proportional?  Why would this matter?
• If I choose the 30% option, am I saving 3 times what I would if I choose the 10% option? 
• If I'm planning to spend $115, should I just go ahead and spend $130 to get the 30% discount?...At what $ amount, would it make sense for someone jump to the next level of savings?

Some of the questions above have a correct answer and some are great for discussion because they don't have one correct answer.  

Added Benefits:

There are also some added benefits of having students generate multiple questions for a given situation.  These are a just a few of extra benefits:

• Natural Differentiation --- As you can see from the questions listed above, there are questions at various levels.  Once you've created the list, you can assign students questions based on their level of readiness.  
• Built-in Choices --- This is a great way to provide students with choices.  Students can choose which question or questions they find most interesting and really want to answer.  Providing choices is a key component in effective teaching because it gives students a sense of control.   It's also a way to differentiate by interest.
• Teachers Gain Insight About Students Level of Understanding --- When you have students generate questions, you get see where they are with their understanding of concepts and problem solving skills.  In the beginning, some students will only be able to come up with surface level questions.  As they gain more experience with problem solving and generating their own questions, you'll be able see and document their growth. 
• Student Attitudes Improve --- When students become more involved in their learning experience, their attitudes generally improve.  If you combine this with differentiation and giving choices, you're likely to see an even greater impact on student attitudes about math and learning.
• Opportunities For Problem Solving Arise --- From the questions above, you can see that some of them would involve problem solving as opposed to rote computation.  And, I would venture to say that many students would much rather answer some of these problem solving questions than the more basic questions.  The best part is that the skill practice we want students to have is automatically built-in to the problem solving experience!

Whether or not you use this particular scenario with your students, you may want to begin having students generate their own questions with other content.  Give it a try and you might just see some unexpected growth in your students. 

Hopefully, you've found this post useful.  If so, please pass it on to someone else who may find it helpful.

If you enjoyed this post, you might also like:

Five Benefits of Brainstorming in the Math Classroom 
Questions That Cultivate Mathematical Thinking
Seven Ways to Go from On-task to Engaged 
Come On Down! Problem Solving on The Price is Right
Looking Beyond the Obvious to Deepen Understanding

Questions That Cultivate Mathematical Thinking

I just had the privilege of presenting at two of the 2011 NCTM Regional Conferences.  While attending both conferences, I noticed that a common theme in many presentations related to creating/developing mathematical thinkers.  This got me thinking about how the questions we ask, or more importantly, don't ask students on a daily basis can cultivate, hinder, or even prevent mathematical thinking. So, I've started a list of questions/question prompts that can/should be used regularly to help cultivate mathematical thinking and reasoning.
 
 Questions That Cultivate Mathematical Thinking  (this list in no particular order):

• Why?...Why did you do that?...Why do you think...?...Explain your thinking. --- In my opinion, asking "why" is one of the most overlooked, undervalued, and important questions a math teacher can ask.  This question helps teachers by giving them a better understanding of where the student is coming from and how much they really do understand about a given topic, concept, or problem solving situation.  Asking "why?" requires students to think about and verbalize their thought processes.  When you ask students "why?", you gather information to help you ask other questions that address misconceptions and further mathematical thinking. 

• What if...? ---- "What if" questions allow teachers to change constraints on problems/situations.  This furthers mathematical thinking by having students see patterns and relationships beyond the initial problem.  "What if" questions also help students to see that their initial thoughts about the answer to the question or their problem solving strategy may no longer apply to the new situation.  This understanding helps students learn to focus on the context of a problem rather than what they perceive as "set guidelines" for solving a particular type of problem.

Example of "What if" questioning:  The two tables below represent the sales from Fu Do Chinese restaurant in Anchorage, Alaska.  The premise of the problem is that Fu Do, a family owned and operated restaurant, had to close four days during the week of 10/9 - 10/15 due to a death in the family.

The questions: 

First Question:  Which measure of center (mean, median, or mode) best represents the sales of Fu Do on Oct. 2 - 8 (a typical week)? 

"What if"Question:  What if Fu Do had to close 4 days for a funeral?  Which measure of center best represents the sales from the week of Oct. 9 - 15?

In Table 2, the constraints of the problem were changed resulting in the possibility of a different answer to the question.  This type of problem and questioning provides a basis for rich, interesting discussions about which measure of center is the best representation and what factors impact this decision (range, the context of the situation, etc.).  Students begin to see that they need to consider many factors when answering a question like this.

This problem/discussion/question can be taken even further by asking another "What if" question that again changes the constraints of the problem.  

Another "What if" Question:  What if Fu Do only had to close 3 days during the week of Oct. 9 - 15?  Which measure of center would best represent the sales from Oct. 9 - 15?

Now the mathematical thinking and discussion can really get interesting!  By changing this one constraint on the problem (only 3 days closed), you've opened up new questions and factors that need to be considered when answering the question.  You can cultivate mathematical thinking even more by opening up the discussion to include comparisons between the 3 different scenarios. This may lead to asking other questions like "Under what conditions would mean be the best representation?...median?...mode?"

• What patterns or relationships do you notice?...How can you use this pattern to solve the problem?...How do these patterns/relationships help us to think about the problem? --- Mathematics is all about recognizing and using patterns to answer questions and/or learn more about a situation.  As students get better at recognizing and understanding patterns they begin to develop number sense, see connections between mathematical concepts, and become better problem solvers.

• Is this the most efficient way to solve this problem?...What's the most efficient way to solve this problem? --- It's important to have students explore various ways for solving a problem.  But then it becomes important to have students evaluate strategies for efficiency.  Some methods will always be inefficient and should be discarded as such. With other methods, efficiency may depend on the individual.  The method that's most efficient for you may not be the method I find most efficient for solving the same problem.  The key to this questioning is to get students to recognize that there are various methods for solving problems, that it's important to consider efficiency when choosing a strategy, that some methods are valid but inefficient, and that efficiency can depend on individual understandings and preferences.  

In an effort to keep this post from getting too long, I'll stop elaborating on each question.  Below are a few more questions/question prompts that help cultivate mathematical thinkers.

Questions that Cultivate Mathematical Thinking Continued:

• What other ways can this problem be solved?
• How could you represent this visually?...differently?  In what other ways can this problem be represented? (tables, graphs, equations, pictures, etc.)
• Compare and contrast these two problems...How are these two problems different?...How do these differences affect how you would solve each problem?
• How could you define or explain this without using numbers?
• Based on ________, how would you approach this problem differently now? 
• How has your thinking about this problem changed? 

 Tip:  If you're just beginning to incorporate these types of questions into your daily practice, write some of the question prompts on posters and place around the room.  They'll serve as a reminder if you draw a blank.  And, students will think you posted the questions to prompt their thinking.

By no means is this an exhaustive list!  It's just a work in progress.  Let's continue to build this list together.  Leave a comment with your favorite questions that help cultivate mathematical thinking.  

No Clickers, No Problem! Try Poll Everywhere

Want to create class surveys and get instant student feedback about math problems, but you don't have access to clickers?  No clickers, no problem!  Poll Everywhere allows you to create multiple choice and free response questions for your students.  You'll get instant results that can be shared with the class. 

Poll Everywhere is committed to education and has many features that make it ideal for classroom use.  Below is a list of some of these features:

• Create as many surveys as you want with a Free teacher account...With a free K-12 account, you can have up to 40 students respond to each poll.  Just create a new poll or If you have a single class with more than 40 students, you can email them and they will adjust your plan.
• Polls are quick and easy to create...You literally could have a poll created and ready to use in a couple of minutes.
• Multiple ways for students to vote...Students can text their responses in or they can vote online if they have access to an iPad or computer.  
• As responses come in, they automatically appear on the results chart...You don't have to refresh in order to see newest results.
• Results charts can be embedded into blogs, websites, Power Points, etc...This is a nice feature which would allow for comments about the poll or survey.  You could also use this as means to address student misconceptions if they were responding to a math problem.
• No spam or advertisements!

The features listed above are all available with the Free teacher account.  If you'd like to be able to get reports, moderate responses, and create response segmentation for contests or comparisons, you can get an individual teacher plan for $50 per year.  School and district plans also make these extra features available.

In a future post, I'll give some specific suggestions/ideas for using Poll Everywhere in the math classroom.

I've added Poll Everywhere to The Best Technology Tools for Teaching Math list.

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. 

 

I'm adding this Math Glossary to The Best Technology Tools for Teaching Math  list.

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 Scoop.it.  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 Scoop.it 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 Scoop.it topics:

• IGNITE Student Engagement in Math!
• Powerful Technology Tools for Teaching and Learning

Stay tuned!  I'll be creating and sharing more math related Scoop.it topics soon.

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.
 

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!

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 AdOut.org.  This is an application that takes the ads off websites.  You get a link that you can share with others.  With AdOut.org, 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.

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?

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)

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.

• Less Helpful - Dan Meyer's blog...It's full of math curriculum based on interesting real world questions. 
• Conrad Wolfram and Math Does Not Equal Calculating and  - Conrad Wolfram's websites  

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?

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.