Thursday, November 14, 2013

Heart Warming Approaches to (Core?) Curriculum Reform

There’s a lot of discussion about the CCSSI (do I really have to write it out?) for math. Mostly its about the Standards and assessments which for me is a checklist for what I should include in a curriculum. But what about the curriculum? What does it look like in most schools? I would guess that the textbook companies are controlling that world and that’s very depressing, because I haven’t seen any textbooks that breaks the mould of what we have encountered before even if its been spruced up by the requirements of the Common Core standards. But if you look past the usual suspects, you will find in the blog world some innovative, heart warming approaches. Case in point, Geoff Krall. In his his initiatives. Geoff (My Common Core Problem Based Curriculum Maps) has crafted a game plan for proceeding with reinventing how math can be taught in schools. He has collected activities and projects from his math blogging colleagues and organized them into a curriculum. When I was still at Stevens/CIESE I did a similar approach with the 6th Everyday Math curriculum since the teachers in the Elizabeth, NJ school district wanted more technology based activities that were not part of EDM. This kind of work requires support from the teachers, pedagogical change coaches (like I was there) and administration support to work. Unfortunately, my effort in Elizabeth has sat dormant since I retired from CIESE in 2007.

What we need is a curriculum (a modern textbook, if you like) that is written from a student's perspective. Most textbooks are written so that adults reviewing the books will find all the required checkboxes checked before they adopt. Why can't textbooks be written as engaging stories that students would buy into? I suspect very few kids would choose the books that are currently coming out of the textbook mills if they had a choice. Engaging stories should drive curriculum. Then students would actually want to do the activities in the book instead of being force fed by the teachers because they are "good for you."

Geoff Krall to his credit has listed links to interesting stories, but they are still on the sidelines in the curriculum game. Some day it will happen. The current technology makes it possible and the math blogging community is putting examples out there every day. However, the devotion to the Royal Road to Calculus continues to interfere with student engagement and genuine learning.

Math Stories - Engaging students in thinking about mathematics

In June 2013 I wrote about the Jinx Puzzle where you pick a number and then do several different calculations to that number and the result is 13 no matter what number you started with. I called it the Jinx puzzle for that reason. Why does it work every time? The secret is in the algebra. See below.

1. Choose a number. Call it X
2. Add 11. Now you have X + 11
3. Multiply by 6. Result is: 6X + 66
4. Subtract 3. The result is:  6X - 63
5. Divide by 3. The result is:  2X + 21
6. Add 5. The result is: 2X + 26
7. Divide by 2. The result is: X + 13
8. Subtract the original number that you chose. The result is: X + 13 - X = 13

You are jinxed. Problem solved. Case closed. But what if we were teaching typical 6th graders then a more interesting twist on this story is to not assume the obvious (that it always works) and see whether these students could find a number that foils the Jinx Puzzle. Since testing numbers manually becomes quickly tedious a spreadsheet calculator can help with testing a wide range of numbers. There’s just one problem. If you use a spreadsheet you can get a result that actually foils the Jinx Puzzle! Try something like 3.0 x 10 to the 16th power as your number.

This is caused by the fact that the spreadsheet will round off numbers after a long string of numbers is entered or will send a bogus number because we have gone passed its capability to stay accurate.

Dan Meyer in a his 101 questions activity shows how Google Calc fails to handle a subtraction problem by printing 0 instead of the correct answer of 1 just because it doesn’t play well with very large numbers.

In an episode of The Simpson's called The Wizard of Evergreen Terrace, Homer appears to write a valid solution to defeat Fermat's Last Theorem which states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two. But given that Fermat's last theorem is proven, is Homer's attempt a real counter example that Fermat and others didn't see? Look at the equation (above) that Homer used using the Desmos calculator to check his work. Looks like the real deal doesn't it?
Simon Singh who writes about this in his latest book "The Simpsons and their Mathematical Secrets" calls Homer’s attempt at a solution a near miss. If you use a calculator that’s good to 10 places like Desmos, it seems to work. But the devil is in longer approximations. It’s close, but no cigar. And we need exactitude to proof the theorem. Andrew Wiles who proved Fermat’s Theorem in 1995 has nothing to worry about from Homer Simpson.

Sunday, October 20, 2013

Game Changers: Rethinking the Way We Teach Math

Headlining the regional NCTM meeting this week in Las Vegas, Nevada are four educators whose work is transforming curriculum design and delivery and changing the way students think about mathematics. Board member Jon Wray, Karim Ani, Dan Meyer and Eric Westendorf. They are going to be answering the question: What should effective and innovative math instruction look like, and how can teachers create ideal learning experiences for all students? 

Wednesday, October 23, 2013: 5:30 PM-7:00 PM
Amazon F (Rio Hotel) - Las Vegas

If that session is the standard for the entire conference, then you're in for a treat if you are attending. Unfortunately, the best I can do is participate virtually via Twitter. Hopefully, there will be lots of blogs generated and videos of presentations.

See a listing of all other technology themed sessions in Las Vegas.

I'll share my take on the conference later this week.

Sunday, October 6, 2013

The Math Blogosphere takes off

In my vision of math 2.0 teachers as bloggers are as commonplace as chalk and blackboard used to be. There is much to learn from the young (and not so young) math warriors who are exploring the new frontier of teachers collaborating on how to make math come alive, personable and of course useful in the lives of their students. Unfortunately, to date, very few math teachers know about how teachers are learning and improving their craft online with other like-minded math educators. Well, a group of these pioneers wanted to do something about it and make it resonate not only in the blogosphere, but everywhere there are communities that help young people learn math.

Though their website comes with a formidable handle mathtwitterblogosphere (MTBoS pronounced mitt-boss) don't let that stop you from joining.

Dan Meyer wrote: "File this [MTBoS] as Reason #437 I'm proud to be a part of this enormous professional community. link

Today (October 6th) begins 8 weeks of "Exploring the Mathtwitterblogosphere." Join up and follow this crash course.

Also on Tuesday nights you can join the Global Math Department for weekly presentations about math for teachers by teachers.

This week (Tuesday, October 8th 9pm) Karim Kai Ani (of fame) will be leading the conversation. You are all invited!

Monday, September 23, 2013

CLIME - A Look Back to the Future

Back in April, 1988 I wrote an article "Teaching Math with Logo" for Teaching PreK-8 that included the following:

"In April, 1986 at the annual meeting of the National Council of Teachers of Mathematics a group of math educators who were interested in Logo, a computer programming language, met informally and decided to start an organization which eventually became known as the Council for Logo in Mathematics Education or CLIME for short. These educators taught math at all levels and were from all parts of the United States and Canada. What had brought them together was a belief that Logo could make a significant difference in the quality of mathematics education.

Now there are many other resources - including Cuisenaire Rods, geoboards, rulers and compasses, to name just a few - that math teachers use to help them teach. But to my knowledge no one has ever started an international organization for the purpose of promoting their use. What, then, makes Logo so special?

One way to answer this question is to say that Logo, unlike other resources, comes with its own philosophy of education. This philosophy was introduced to the world by Seymour Papert in a book called Mindstorms: Children, Computers, and Powerful Ideas (Basic Books, 1980). In it he said that children seem to be innately gifted learners who acquire a vast quantity of knowledge long before they go to school. What blocks them from learning is not the inherent difficulty of the ideas, but the failure of the surrounding culture or environment to provide the resources that would make the ideas simple or concrete. In other worlds, one reason why math is difficult to learn is because the culture outside the classroom does not provide the materials or experiences that would support the students' classroom lessons."

That was 1988. Since then CLIME has evolved from the Council for Logo to the Council for Technology in math education. This change was made to acknowledge the development of exciting new environments (like Geometer's Sketchpad) which made me realize that Logo was not the only game in town, but that there were other software environments that encourage this kind of dynamic learning that Logo made possible. With the advent of the handheld tablets and smart phones powerful new math apps are being developed. (For example see Keith Devlin's latest entry Wuzzit Trouble.)

It's been a tough time to be an educator with all the hoopla about the common core and its subsequent imprisonment of laptops and handhelds for testing which will keep the technology away from creative teachers who could use them in dynamic ways. So its easy to see the technology glass as half empty.

In his book "Logo Theory and Practice" (1989) Dennis Harper quotes me as saying that "a Logo environment is  more of a spirit rather than a thing-something that can only be satisfying if experienced, rather than just languaged." (p.26)

And I still believe that today. I recently wrote to one of CLIME's steering committee/board members Robert Berkman that we need to look at the glass as half full and keep a positive attitude because the Internet does have a long tail (and tales) and there are literally hundreds (thousands?) of places, people and environments where adults are helping our young people "construct modern knowledge" something another one of CLIME's board members Gary Stager promotes in his annual Vermont workshops and in his new book "Invent to Learn."

I've been privileged over the years from the guidance of these and other remarkable people who have been good friends of CLIME and members of the CLIME steering committee over the last 25 years. I want to publicly thank them for their help. (You will be hearing from some of them in future CLIME blog posts.)

See a short summary CLIME's journey since 1986.

Tuesday, September 3, 2013

Common Core Curriculum - An Alternative Path

Whether you like the idea of the Common Core State Standards for math (CCSSM) or not, it is here to stay at least until version 2.0 addresses the eventual problem of the scores not going up. Why am I so sure this will be the case? Because CCSSM doesn't ensure a curriculum that actually helps students understand and learn the topics any better than before. For example, learning fractions. In a recent book Keith Devlin describes how easily it is to get confused when doing fractions. (See my blog.) Schools have to use curriculum that match the standards. That's great. But how can they do it well? Since proportionality is such an important concept and understanding it is so critical a carefully crafted set of activities is needed to prevent misconceptions.

Most school districts will probably choose a textbook program that is correlated with the standards. Problem: Most textbooks do a decent job in correlating, but not in motivating students to learn the math. This summer Dan Meyer had a Makeover Monday blog where teachers submitted typical problems from textbooks and Dan's community offered suggestions as to how to improve them. While reading these blogs I became convinced that we need a makeover of textbooks in general i.e. come up with a more dynamic model for lessons that textbooks could adopt. Currently Dan Meyer and Karim Ani ( are creating and encouraging dynamic learning adventures that are interesting to kids and help with deeper understanding.

The giants of the textbook world (Pearson, McGraw HIll, etc.) are trying to modernize their curriculums but they have too much at stake in maintaining the status quo since most teachers and administrators prefer what they are familiar with and find the so called "alternative" models too risky or controversial for district approval. (Larry Cuban describes this phenomenon as dynamic conservatism). Otherwise districts would reject most if not all the mediocre curriculums that are now being published.)

Should Algebra be optional?
Recent articles in Harpers and the New York Times have argued for making the Algebra 1 and Algebra 2 sequence optional especially for kids who struggle with math.

Michael thayer writes:
In an ideal world, kids would sort themselves in this way based on their interests.
Kids in track #1 ("calculus track"): These are the kids who love math, who love the challenge of it, and who see the abstractions of algebra and analysis as pursuits worthy of study.
Kids in track #2 ("statistics track"): These are the kids who recognize the importance and practicality of math, and who see utility for it in their futures.
Kids in track #3 ("one and done"): These are the kids who have had a good experience with math, who have seen the forest for the trees, but do not wish to go deeper as their interests lie elsewhere.

I would also include in track* 3 those students who didn't have a good experience in math and do not have any interest in continuing in math since they would rather use the time to study something else.

My Thoughts on the Path 3 Course
Offer a one year course for students who definitely don't want to do the formal Algebra 1 or 2 path for whatever reason, but still want to go to a "good" college. Their are over 4,000 accredited 2 and 4 year colleges in the US. Getting into a college is usually not a problem, just paying for it is. (Shame on those colleges that afflict serious debt on our students.)  I'm sure there are plenty of colleges out there that would accept students who have (as Mike pointed out in his blog) excellent work habits, overall knowledge base, and interpersonal and time management skills who didn't take Algebra 1 and 2 but rather this richer one year 9th grade math course; something like "Mathematics a Human Endeavor - A Book for Those Who Think They Don't Like the Subject" by Harold Jacobs.  He wrote his last revision of the book in 1994 and the book is still in demand particularly in homeschooling environments.  Anyone out there want to work on an open source version of the kind of one year alternative curriculum that is in the same spirit as Jacobs had in mind? (Here's something I did with his Chapter 3 - Functions and their Graphs.)

Maybe we can do it collectively as an open source project. I volunteer to be a conduit for creating this course! Are you interested? (If so, you might get familiar with Jacobs book to see what I have in mind.)

*Tracking is not the right word for this, because it implies rigidity. These should be paths that students can opt to start on, but can switch to a different path at any time or chart their own course.

Thursday, August 8, 2013

The Spirit of Math 2.0: Computational Thinking

Michel Paul's <> recent email post to is worth reading. This is Math 2.0 thinking at its best.

Michel Paul writes:
Keith Devlin wrote the following to describe the nature of modern (20th century onward) mathematics to current undergraduates transitioning from high school (19th century and before):

"Prior to the nineteenth century, mathematicians were used to the fact that a formula such as y = x^2 + 3x - 5 specifies a function that produces a new number y from any given number x. Then the revolutionary Dirichlet came along and said to forget the formula and concentrate on what the function does in terms of input-output behavior. A function according to Dirichlet, is any rule that produces new numbers from old. The rule does not have to be specified by an algebraic formula. In fact, there's no reason to restrict your attention to numbers. A function can be any rule that takes objects of one kind and produces new objects from them."

- Keith Devlin

Wow! Please read that carefully. Though he wrote this to help today's students transition from the 19th century to modern mathematical thinking, it also describes the kind of thinking one learns to do in computer science! Functions in computer science operate on objects of various types, not just numbers. 

Traditionalists lost the battle professionally in the mathematical revolution that occurred a century ag0 but won in education. Meanwhile, computer science went ahead and got created from the insights of that revolution and turned into the world we now live in. The result? Most K-12 math students and their teachers, us, are unaware of the nature of the mathematical thinking that went on in the 20th century while the technology that surrounds us was built from it! 

The ultimate irony - we use 21st century technology, made possible by 20th century math and physics, to teach students how to do 19th century mathematics that they will never use!

I think this makes it clear that the study of programming can provide a way for math students to encounter and develop some intuition regarding concepts underlying modern mathematics that the traditional high school curriculum does not provide.


"What I cannot create, I do not understand."

- Richard Feynman
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou

Wednesday, July 31, 2013

Reflections on Social Media at the Affiliate Leaders Conference - July 26-28, 2013

This leadership conference was organized mostly to see how social media can help increase the current NCTM membership and encourage new teachers to join NCTM and affiliate groups. One way to make organizations more responsive to young teachers is to take advantage of open source resources like Facebook and teacher blogs. They are avenues that are freely available. NCTM President, Linda Gojak made reference to research indicating that teachers don’t join organizations until they are in their 30s. Since membership fees seem to be barriers to young teachers, One way to encourage membership is to offer discounted membership to young teachers or have no membership fees at all. One conference participant mentioned to me that ‘free’ would create the perception of lower quality. But this doesn’t have to be the case if conferences and other events that require a fee pay the bills. My sense was that most of the affiliate leaders at this conference were not willing to give up on membership fees but were willing to make a serious effort to help young teachers join. Since many of the young teachers are already knowledgeable of the social media resources, they don’t feel  the need to join a group. The challenge for NCTM and their affiliate groups is to use social media in a compelling way. Membership would not be an obstacle if NCTM & its affiliates offered something that young teachers wanted to buy. Starbucks, for example, doesn't have a young people shortage at their counters. Of course you can't compare a Frappuccino with math support; I’m not suggesting that one should, but what is it about the purpose of buying such an expensive food item? (Clay Christensen writes about how a milk shake is a popular drink for people commuting to work and school because it keeps them occupied longer than other foods.*) Learning about how to become a better teacher can be something that young people would buy if is relevant to their needs. Our organizations need to be better connected to the social media to attract teachers to participate at a level they can afford. Schools need to be better places for teachers to learn about exciting things to do. Bloggers now provide these kind of resources for free. Schools and organizations that support the teaching and learning of math need to learn from these structures how to best to provide staff development. There is a hidden curriculum at work in many schools where the teachers are crafting their professional development through open source venues. Supporting young teachers would be much easier if we help them expand their network of communication. Open source materials and teacher blogs are excellent ways to do that. Schools need to become better integrated learning communities that learn both from and with open source resources. Supporting this need should be an important role for NCTM and its affiliates.

*“Rethinking Student Motivation Why understanding the ‘job’ is crucial for improving education
Clayton M. Christensen,  Michael B. Horn, and Curtis W. Johnson

Sunday, July 14, 2013

Constructing Modern Math Knowledge

Ihor, April, and Jim celebrating April's Average Traveler Award
I spent this past week at Gary Stager's Constructing Modern Knowledge Conference in Manchester, NH. There was quite a turnout. Over 150 educators from all over the world enrolled. The modern knowledge that the folks worked on included some strange sounding tools like Raspberry Pi, Arduino, Scratch, conductive paint pens and plenty more. (See "Oh, The Stuff You Might Learn With at CMK 2013") I shied away from being that modern and decided on a more familiar project.

When I walk into a room full of people, I usually think of the famous birthday problem which predicts that if you have 23 people in a room there is slightly better than a 50% chance that at least 2 people will share a common birthdate (month and day only). If there are 100 people, the percentage jumps to more than 99% certainty that this will happen. With a 150 people attending I thought of a more interesting crowd sourcing activity that determines who the "average traveler" to this conference is. Basically I find out which person traveled the shortest distance from the mean distance of all the travelers. I used Google Docs forms and spreadsheet to get the data and Google Maps to display it. (The original plan was to write a Scratch program to do it and this is currently a work in progress.) The form asked each conference participant to enter their name, home or school address and distance traveled (in miles). The results appeared in the Google Docs spreadsheet. See Table 1.
Table 1 - Top 20 finishers
As you can see from the table, April Gustafson was our average traveler. In addition to entering their mileage, participants also added a marker on a Google Maps page. I made a snapshot of the markers and used Geometer's Sketchpad to draw the circle with a diameter approximately equal to the mean of all the travelers. You can see that April's balloon was closer to the circle than any of the other travelers!

I want to thank Jim Scribner for his assistance and friendship doing this project. We discovered a mutual love of baseball that goes way back. Do you remember the Pirates lineup in the 1979 world series? We did with just a little help from Google.

Tuesday, June 25, 2013

2013 Affiliate Leaders Conference: Leadership in an iPad World

As most of you may know CLIME is an affiliate group of NCTM. Each summer NCTM holds a special conference for affiliate group leaders. I have attended such a conference before so I was not particularly inclined to attend this one until I noticed that the theme for the conference is: "Leadership: Building Responsive Affiliates in an iPad World." Since CLIME has been promoting Math 2.0 in this blog since 2009, I decided I couldn't pass up this opportunity to participate in this conference. Here's the bulleted list of outcomes for this 3 day (2 night) conference in Annapolis, MD:

  • learn and share about effective use of social media and new technology to advance your Affiliate’s goals; 
  • develop strategies for strengthening your Affiliate’s leadership role and advocating for mathematics education; 
  • identify ways of addressing equity in Affiliate activities and organizations; 
  • learn about the NCTM structure, resources, and initiatives and participate in discussions with NCTM President Linda Gojak; 
  • and develop or revisit the strategic plan for your Affiliate by integrating ideas gathered through discussion with other Affiliate leaders. 

Click here for more details.

If anyone is interested in joining me (I'd love it) for this conference and/or is interested in learning more (personally from me) about CLIME and NCTM's affiliate program, please let me know at

Monday, June 17, 2013

Makeover Monday - Making Lemonade out of Lemons

Makeover Monday. What a great idea. Readers of Dan's blog and tweets offer suggestions as to how to improve standard textbook problems. This is online collaboration at its best. Only thing better would be not to have to start with lemons. Maybe someday Dan and company will write better, more creative and dynamic "textbooks." Pearson, McGraw Hill, etc.: Are you listening?

Friday, May 24, 2013

Uri Treisman's Wish

Uri Trieisman gave the Iris Carl equity speech in Denver. Dan Meyer summarized it  in detail and recommended it highly, so I listened to it online. I thought the speech was well delivered and the reviews were mostly positive by those who replied to Dan's blog. 

Uri's main message was that poverty sucks. He shows this powerful image that highlights the correlation between poverty concentration and percentage meeting SAT criterion. Sad message indeed.

The most interesting quote for me was "What is the determinant of whether you have a high skill job in the US? Overwhelmingly it's mathematics. The single biggest factor in upward social and economic mobility. It's our beloved subject. It would be wonderful if it were music instead of math. Think how great the country would be if everyone was striving to learn to play an instrument instead of factor quadratic equations. But the fact is it is our discipline that's the primary determinant."

This begs the question whether Uri would actually promote music education over math education if our discipline was not the primary determinate. I doubt it. The reason math is the main determinate is because math educators like Uri Treisman work very hard at convincing the public that math education is important enough so it should be the determinator. Personally, I think a more user friendly approach to math education is needed. Particularly for Algebra. Students need more choices and Algebra as the main staple needs an overhaul. 

Andrew Hacker's New York Times article "Is Algebra Necessary?" last summer brought this issue to the forefront. I would have preferred a different title: "Should Algebra in its present form be required of all students?" which would have helped to refocus the reactions away from getting rid of algebra altogether which of course is absurd. There were 477 comments mostly by math educators who were outraged at the thought of not requiring Algebra for all as if Algebra was the only elixir for cognitive health. 

Unfortunately Algebra for the most part will be taught in same dull way it always has. Economically advantaged students will get the best teachers and do well and poverty will continue to undermine the learning of this subject that most students and adults find/found to be too difficult and unproductive. That doesn't mean there are not empowered individuals like Dan and Karim Ani ( that are finding ways to make math more palatable for students via teachers which for the most part are not working in high poverty area schools. We need to rethink how algebra is taught to the masses. My recommendation is to teach math from the "outside in;" start with activities (i.e. problems/puzzles/games) that interest the kids and then show how the algebra relates to these activities. Karim and Dan are doing this. But until the textbook publishers stop publishing pablum math, most students won't benefit from what Dan, Karim and other reformers are offering.

cc blog 137

Sunday, April 28, 2013

Doug Clements - Lessons from Research

Doug speaking at NCTM 2013

Another one of my heroes in the field of technology in Math education is Doug Clements. I went to hear him speak early thursday morning. His topic was Math Lessons from Research.

Doug was one of the founders of CLIME in the days when the L in CLIME stood for Logo. His voice was always strong in supporting Logo when the critics were saying Logo does not make a difference. He would articulate the positive research that supported the use of Logo in the face of critics who pooh-poohed the results. He continues to be a leader in mathematics educational research at K-2 level and served on the math panel in 2008 that endorsed Logo and passed mustard with the strict demands of the panel members as a worthwhile tool.

His fundamental lesson from research is that very young children are capable of doing mathematics that is complex and sophisticated. Unfortunately, too many teachers do not have access to the information that would help them to help children in this regard. His intervention focuses on something that he refers to as learning trajectories that have three parts. (1) a goal (2) developmental progression and (3) instructional strategies.
To attain a certain mathematical competence in a given topic (the goal), children learn each successive level of thinking (the developmental progression), aided by tasks (instructional activities) designed to build the mental actions-on-objects that enable thinking at each higher level. (Reference 1)
For details about his current work called Building blocks see

The curriculum is available from McGraw Hill. But Doug did say that he was hoping to have an open source version available as well.

1. D. Clements, J. Sarama. Early Childhood Mathematics Intervention. (Science Magazine, 19 August 2011)

Thursday, April 25, 2013

Empowering the Classroom and Beyond

Below is a piece (edited and somewhat embellished) that I wrote in the "Scenes" newsletter in the Fall of 1989. I follow that with comments about three sessions I attended in Denver.

Fall, 1989
I spent the better part of my summer vacation teaching a computers in education course at a local college. One of the topics I discussed with my students was the influence that three computer educators (who I refered to as gurus) had on how computers are used in schools. Each of them has a unique message about how to teach children with computers. Here's a short summary of their points of view along with what I think is an appropriate rallying slogan.

Tom Snyder - Empower the teacher
Tom Snyder Youtube video
Then there is Tom Snyder of Tom Snyder Productions who is considered by many as the champion of the "one computer classroom." He believes that since the classroom is the domain of the teacher it makes sense to give the computer to the teacher and have her use software that is designed to be used by one teacher working with large group. This point of view has made him very popular with teachers.

Seymour Papert - Empower the student
The "father of Logo" believes that children should program computers rather than the computer program them. If you are a veteran Logo user then you probably have seen this quote before, but just in case you haven't here it is again. 
"In my vision the child programs the computer, in doing so, both acquire a sense of mastery over a piece of the most modern and powerful technology and establish us in intimate contact With some of the deepest ideas from science, from mathematics, and from the art of intellectual model building." (Papert, Mindstorms, p. 5) 
So the key for Papert is to put the student in charge of the computer and presumably a love affair with learning will emerge.

Patrick Suppes - Empower the computer 
Patrick Suppes
Patrick Suppes is a pioneer and leading proponent of using computers for computer-assisted instruction who believes that students can learn best if the computer controls the learning through questions with appropriate feedback and monitors their progress. His work paved the way for the CAI (Computer Assisted Instruction) movement in schools.

In the early days of microcomputers it was fashionable for the Logo supporters to argue that the Snyders and Suppes of the world were not using computers effectively. But times and people have changed.  For example at the NECC conference (Boston, June, 1989) Seymour Papert shared a session with Bob Tinker (a BASIC sympathizer) and there wasn't a hint of disagreement between them. What does this mean? Are the debates over? No, they will still continue, but I think what's happening is that industry is maturing and educators are acknowledging that there is more than one way to educate children. It's not that unusual to find in a typical school district Logo being used on the elementary and junior high school levels side by side with Snyder Productions software and all across the district you will find CAI. So what does this mean for you the teacher should you empower the student, the computer or the teacher? The answer is you empower all three.  So the right slogan would be: empower the classroom with dynamic uses of technology that empower students to want to learn.

That was what I wrote in 1989. A lot has changed since then, but the spirit of the three gurus lives on.

At the conference I thought about these gurus as I listened to younger voices. In particular, Karim Ani and Dan Meyer. Tom Snyder's vision of empowering the teacher came across in both cases. Karim's talk Keeping It Real: Teaching Math through Real-World Topics highlighted the importance of connecting math through real world connections based on questions that would interest students. 

Dan Meyer in his Tools and Technology for Modern Math Teaching presentation challenged the teachers in the audience to come up with a Tech/Ed manifesto that would make their teaching more relevant and perplexing for students. Dan defines the state of perplexity as this awesome confluence of not knowing, wanting to know and having the belief that the solution is graspable. So creating an environment where students eagerly embrace perplexity is an ideal condition for deep learning and self motivation. Definitely an important attribute of the dynamic classroom which Tom Snyder promoted. 
Tom Snyder's vision

The modern version of Suppes that the computer can make a huge difference was echoed by Alex Sarlin and David Dockterman in The Gamification of Math: Research, Gaming Theory, and Math Instruction that I wrote about in my previous blog. Suppes believed that behaviorist CAI type of programs could significantly change learning, but the computer is capable of much more than just delivering drill and practice.  It can create scenarios that engages children to want to learn using for example gamification mechanics. There is much promise here where the computer does the heavy lifting. But will it motivate student's desire to be creative and fall in love with math (as Papert believed was possible) if students are left to their own devices and have the autonomy to construct their own learning by building interesting simulations and gizmos themselves. Programming which requires computational thinking is making a comeback and is becoming an integral part of student construction of personal knowledge. The opportunity to learn (that Uri Treisman referred to in his talk) is greatly enhanced by the emerging technologies and communities that embrace it to empower children to be better learners and teaching becomes more focused on supporting that learning. 

Clay Christensen of (Disrupting Class fame) writes (1) that "…there are two core jobs that most student try to do every day: They want to feel successful and make progress, and they want to have fun with their friends." This is foundational for what I call the "Wannado" curriculum.

Larry Cuban (2) who usually reminds us how tech has flopped in classrooms in the past (For evidence see his slide show - a kind of trail of broken dreams) says the following in his recent book (3) "If there is hope for the future it will happen in places where teachers collaborate and create schools where teaching and learning [are] prized." he writes. "[But] will such a ground level strategy of building structures that enable teachers and administrators to work together in creating cultures of learning in classrooms, schools, and districts lead to good and successful teaching and then successful student learning? I hope so - but in all honesty, I do not know."

I'm optimistic that it will and someday we can all look back and see how these young linchpins like Dan Meyer, Karim Ani and Alex Sarlin contributed to this promised land.

1. C. Christensen, M. Horn, C. Johnson, "Rethinking Student Motivation: Why understudying the 'job' is crucial for improving education." Innosight Institute. p. 7

2. L. Cuban, "Framing the School Technology Dream" (4/21/13)

3. L. Cuban, "Inside the Black Box of Classroom Practice: Change Without Reform in American Education" (Harvard Education Press, Cambridge MA) p. 185.

Tuesday, April 23, 2013

The Gamification of Math: Research, Game Theory and Math Instruction

Math 180 - Student Dashboard
In my last blog entry I said I would be visiting the Scholastic Math 180 booth because I was intrigued with their promotion via snail mail. (See previous blog.) According to their website: "MATH 180 is a revolutionary math intervention program for the Common Core. Designed for struggling students in grades 6 and up, the program builds students’ confidence and competence in mathematics, while providing teachers with comprehensive support to ensure success." After listening to their promo and playing around with the demo on the laptops provided in their spacious (mostly empty) booth I came away wondering where's the revolution? Nothing unique or compelling here. That's what I thought until I attended Alex Sarlin's and David Dockterman's session entitled "The Gamification of Math: Research, Game Theory and Math Instruction." It turns out that both David and Alex work for Scholastic and are the brains behind Math 180. It didn't take me long to realize that the goals of Math180 are more involved than my visit to the booth indicated.
David went first and described a typical student who doesn't consider himself a good math student. The question David raises is what will it take to turn this student's self image around and believe that he can be good at math. At this point David introduces Alex who explained how gamification of math can help a weak math student have a much better experience with mathematics. Gamification is not just about games. Its mechanics can be applied to non-game settings like math classrooms. To help explain these mechanics he uses as an example the very popular download Temple Run 2. "You want the game to be easy to learn, exciting, compelling and which elicits a desire to keep playing by introducing appropriate challenges at appropriate times." he explains.  "You are autonomous in certain ways, using your skills to maneuver past obstacles." Also there is a  narrative similar to Indiana Jones.
Gamification techniques leverage people's natural desires for competition, achievement, status, self-expression, altruism, and closure. - Wikipedia*
So how do you gamify a math classroom? Using a curriculum like Math 180 according to Scholastic. The main problem with traditional math approaches is that students don't see the point of what they are learning. Math 180 provides a roadmap to success by providing a "GPS" so they see the larger picture and know where they are going. 

I was excited about learning more about Math 180 so I went to the booth to see more.

The demo only included a small piece of the curriculum: Block 2 the Distributive Property. It was pretty boring. I tried to find some "Indiana Jones" motivation but didn't see anything like that in the software. I complained to a Scholastic representative about it. Her reply was: "The demos will get better." Sigh.

There was no sign of either Alex or David in the booth or any advertisement for their session. 

I'll try to contact David and/or Alex about my disappointment at the booth. I'll keep you posted.

Anybody else visit the Math 180/Scholastic Booth? Impressions? 

*Here's more from Wikipedia about Gamification:
A core strategy for gamifying is to provide rewards for players for accomplishing desired tasks. Types of rewards include points,[6] achievement badges or levels,[7] the filling of a progress bar,[8] and providing the user with virtual currency.[7]
Competition is another element of games that can be used in gamification. Making the rewards for accomplishing tasks visible to other players or providing leader boards are ways of encouraging players to compete.[9] Another approach to gamification is to make existing tasks feel more like games.[10] Some techniques used in this approach include adding meaningful choice, onboarding with a tutorial, increasing challenge,[11] and adding narrative.[10]
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Friday, April 12, 2013

Exhibitors in Denver

A dynamic invitation
Every year around this time I start receiving (junk...) I mean advertising from companies that are planning to exhibit in Denver during the NCTM conference. The invite on the left was interesting because it popped right out of the envelop. (Click on the link to see what I mean.)

I'm not usually inspired to accept such an invitation because I always assume an inverse relationship between the advertising budget of the company and the quality of the product. But since I'm making a big deal about this, I will hold judgement and see the product in Booth #917 on April 18th at 8:45. After I see it I'll report back here with a review.

Here are some other technology oriented exhibitors I plan to visit during my stay in Denver. A lot of old friends and hopefully I'll make some new ones as well. Key Curriclum Press now has a new home in McGraw Hill country.

AT&LT #637 develops 3D math video games. Their current product is the Lost Function: A Math Adventure game. New to me.
Big Brainz #1516 Timez Attack is their big hit product.
Buzzmath #1140 Their mission is to lead middle school students to proficiency in math through suppported practice.
Math Forum - #741 For more than 20 years providing resources to help teachers improve their mathematics teaching and learning. Long time friends of CLIME.
Carnegie Learning #1820 is a leading publisher of innovative, research-based math curricula for middle school, high school, and postsecondary students. 
Calculus in Motion #1131 - Software. Also CDs with tons of Sketchpad applications.
Conceptua Math #823 - teaching and learning everything about fractions is the goal of their software.
Desmos Inc. #916 - Online calculator company. One of the co-hosts of Dan Meyer's and Karim Ani's happy hour on Thursday.
Dreambox Learning #1222 - Lot's of positive buzz about their products. I need to take a closer look.
GeoGebra #1433 - Sketchpad's competitor. Can't beat the price.
Explore Learning #1823 - Always give them a positive review for their excellent applets (Gizmos) and sometimes even their support material. See their equivalent fraction Gizmo.
How the Market Works #719 - Great way to bring real world math into the classroom.
Hooda Math #1538 - new to me.
Mind Research Institute #331 - Adventures with Jiji.
McGraw-Hill Education #731 - Geometer's Sketchpad and Tinkerplots. Sketchpad Users Group after hours session? Will find out...
Neufeld Learning Systems Inc. #2024 Rudy Neufeld - my friend from the early Logo days
Saltire Software #330 - Some really cool software.

See also CLIME's previous blogs about the conference:
Denver's tech sessions: Do they meet the CLIME Standard? - Link
Annual Meeting in Denver Technology Sessions Update - Link

If you are speaking on a technology themed topic in Denver please check for your listing here. If you would like to add or change anything to your listing please let me know via email at or twitter @climeguy.

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Friday, April 5, 2013

Is a "tipping point" in math learning no longer a dream?

Most of you who follow this blog are probably aware that I believe my vision of math 2.0 is no longer a fantasy, but a reality that is doable through the commitment of inspired educators who with the help of powerful technological applications can hoist a learning revolution never seen before. The first step in such a revolution is having the technological infrastructure so that all students have access to the technology. My friend and colleague Joshua Koen, the technology director at a committed urban school district in Passaic, NJ have taken the first steps in that direction. He calls it a tipping point a phrase coined by Malcolm Gladwell in his book "The Tipping Point" which he describes in this video as: "It's a moment in which something explodes, something changes shape. It's that moment of critical mass where everything changes all at once." With the technology in place (1-1 computing with Chromebooks for grades 7-12) the Passaic Schools now have the opportunity to fully embrace a paradigm that focuses more on learning and where teaching and learning are indistinguishable. 

A recent Edutopia article "How to Make your Classroom a Thinking Space" reminded me of the importance of classroom environment as one of the cornerstones* of my Dynamic Classroom model which is the essence of Math 2.0. 
"Take a moment and imagine a creative work environment. Don't worry about the kind of work going on. Just focus on the space. Close your eyes and picture it. What is that space like? What does it sound like? How are people interacting? Is there movement? Is there evidence of work in progress? Is it tidy, or busy-messy? Can you imagine working there?"
To make your classroom work for you the authors suggest the following:
  • Fine-tune the physical environment for PBL (Project Based Learning)
  • Make a place for independent, partner and small-group work.
  • Reimagine who the stuff belongs to.
  • Make for a conversational classroom.
  • Student presentations should be the norm.
  • Encourage hands-on, minds-on creative thinking by providing tools for tinkering.
  • Skype with other schools on collaborative projects.
  • Create a video booth to capture student reflections.
In closing the authors write:

"What's on Your Wish List?

Teachers model creative thinking when they find workarounds or inexpensive fixes to make their classrooms more conducive to project work. They also model collaboration if they enlist parent volunteers and other community members to help. Put your creativity to work by imagining how you might improve your classroom environment to invite good thinking. What belongs on your PBL wish list? How might you make it happen?"
*The others are curriculum, resources, teaching, learning and assessing. See my blog entries for more about math 2.0 and the dynamic math classroom:
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Thursday, March 21, 2013

Annual Meeting in Denver Technology Sessions Update

I've updated the listing of technology sessions at the Denver Annual NCTM meeting including more details about the sessions from the speakers who have responded to my request. If you are a speaker on a technology theme and your session is not listed please let me know ( and I will include your session. Also if you wish to have more detail than what is listed please send me a photo and additional information about your session. We know that you submitted your proposal to speak last May and you may want your potential attendees to know more about you and your presentation. I'll be continuing to update this listing (here is the link again) right through the conference. So its never to late to do so.

I will be attending the conference though this year CLIME will not be exhibiting so I'll be free to roam around the conference and report back to you about the sessions and exhibits that I found interesting.

I hope to see you there.
Ihor aka @climeguy on Twitter
Here is the list of my "go to" sessions from a previous blog. I hope to attend as many as I can.

1. Dynamic Math software
5 -     Chaos Games and Fractal Images
46 -   Collecting Live Data in Fathom
80 -   The Mathematics of Angry Birds
180 - Getting Serious about Games in Middle Grades Math (Lure of the Labyrinth) - Scott Osterweil
207 - Do the Function Dance with Sketchpad 5 - Scott Stekettee, Dan Scher
283 - The Gamification of Math: Research, Gaming Theory, and Math Instruction
502 - Help Students Dig into Data, Statistics, and Probability with TinkerPlots - Karen Greenhaus
279 - Math and Geography: Using Google Earth to Investigate Mathematics

2. Web 2.0 Tools
157 - Math Journal 2.0: Jump-Start Your Students' Reflections (blogging)
447 - Movie Making in Math
468 - Scan It, Solve It, Show It (QR Codes, BYOD-Bring your own device)
565 - Blogarithms: Converting Number Concepts into Talking Points
586 - Moving Beyond the Right Answer: Developing Students’ Math Communication Skills
707 - Sharing Student Lessons with iBooks Author, iBooks, and an iPad
717 - Effective Use of Virtual Manipulatives: Ready to Create Your Own?
724 - Viral Math Videos: A Hart-to-Hart Conversation

3. Dynamic Learning Communities
143 - PLC: The Practices, the Lessons, the Collaborative
680 - An Invitation to Experience Online Lesson Study Firsthand

4. Math 2.0 Curriculum
141 - Learning Online and Outdoors: Integrating Geocaching into the Mathematics Classroom - Lucy Bush and Jeff Hall - see their article on page 20 of this link
184 - Keeping It Real: Teaching Math through Real-World Topics ( - Karim Ani
402 - Stories and Technology: Providing Mathematics Opportunities for All
560 - Powerful Online Tools Promote Powerful Mathematics (Illuminations) - Patrick Vennebush
684 - Tools and Technology for Modern Math Teaching - Dan Meyer
685 - Computers in Early Childhood: Getting the Best of All Worlds - Doug Clements, Julie Sarama
Previous blog entry on this topic