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 http://triadscaleup.org

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

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

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.

References

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.

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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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 ihor@clime.org or twitter @climeguy.

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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:

• In Search of Math 2.0
• The Dynamic Math Classroom 1.0 (version 2.0 in press)

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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 (ihor@clime.org) 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 (mathalicious.org) - 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

All technology related sessions

Previous blog entry on this topic

A Pi Day Mystery

Click above to watch the simulation

My favorite Pi Day activity is the one where random needles dropped on parallel lines lead to an approximation of Pi. Why Pi? Good question. Pi is usually associated with circles. There don't appear to be any circles here. Right? Hmmm. Ponder that question while you watch the needles pile up and the estimate for Pi gets better. Well, at least in theory.

If you are more amibitious and would like to do it with your class see my lesson plan. Also, catch the video of the way one performer does the experiment with taped lines and baguettes. (The link is at the bottom of the lesson plan.)


Related links
Pi Day resources for March 14, 2014 or any day that feels right!