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 Mathalicious.com fame) will be leading the conversation. You are all invited!

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.

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 (Mathalicious.org) 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:
 and
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.

The Spirit of Math 2.0: Computational Thinking

Michel Paul's <pythonic.math@gmail.com> recent email post to mathfuture@googlegroups.com 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

Introduction to Mathematical Thinking

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.

-- 

Michel

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

- Richard Feynman

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"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
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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

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.

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 ihor@clime.org.