Tuesday, November 17, 2015

Reinventing Mathematics Education - A bold new conference

It's Time for Action
Math Education: Problems & Opportunities
by Gary Stager

There has never been greater interest in mathematics education, yet there is little consensus on how best to prepare children to face an increasingly complex future. We live at a time when politicians call for an emphasis on S.T.E.M. while students dislike math, teachers lack confidence in their mathematical ability, achievement is static and inequitable, computational thinking is required for navigating a successful life, and your phone can solve every problem in the existing math curriculum - simultaneously. Reinventing Mathematics Education is a unique symposium addressing challenges in teaching mathematics and exploring opportunities you may never have considered. The day features a balance between a theoretical understanding of how children learn to think mathematically and the implications of a technologically sophisticated society on the future of schooling. Our keynote speakers are among the best thinkers, scholars, and practitioners in the world.

For details about this exciting conference visit this website: http://reinventingmath.com

Thursday, September 3, 2015

Out-of-the-Box Baseball Gets an Upgrade and Inspires My First Project-Based Math Experience

 Replica of Musial’s disk created in Geometer’s Sketchpad
In his 8/4/15 blog Dan Meyer summarizes everything he has learned about modeling. Here's a paragraph from that blog:

"Modeling asks students a) to take the world and turn it into mathematical structures, then b) to operate on those mathematical structures, and then c) to take the results of those operations and turn them back into the world. That entire cycle is some of the most challenging, exhilarating, democratic work your students will ever do in mathematics, requiring the best from all of your students, even the ones who dislike mathematics. If traditional textbooks have failed modeling in any one way, it’s that they perform the first and last acts for students, leaving only the most mathematical, most abstract act behind."

When I was 13 I learned about using mathematics to model something I was very interested in. I was making a disk to represent the production in a typical game of my favorite baseball player Stan Musial. Missing from the image is the spinner that would determine the outcome of an at-bat. Notice that the K slice is bigger than the HR slice. That's because Musial - a Hall of Famer - struck out more often than he hit home runs. Also his 1B is huge because he had a career (22 years) batting average of .331.

I think you can see that having a collection of these disks unique for each player allows you to play a relatively realistic game of baseball. This was the essence of the board game All-Star Baseball which was very popular in pre-computer days. I wrote about my math experience with these disks in Chapter 1 of my book The Wannado Curriculum. (Link)

Tuesday, July 28, 2015

Twitter Math Camp (#TMC15)

Twitter Math Camp 2015 ended last Friday. Mary Bourassa is one of the organizers and is not afraid that calling this conference a Twitter event will scare away most "reasonable" thinking math educators. Why? Because this may be the best math event anywhere. Just ask any MTBoS member who attended the conference!

Here's one. Christopher Danielson was a participant, speaker and early blogger of his experience there.

And another. Meg Craig. Important things you need to know (about TMC15)

More experience sharing via blogs is coming. Just follow the hastag #TMC15 and keep up with the commentary.

VIP Matt Larson (president-elect of NCTM) is now on Twitter! He also attended TMC 15. Things they are a changin'.

Hot off the press: Math Forum Joins NCTM!

Thursday, July 2, 2015

Logo Under Fire - a little history

I got some email about my previous blog (A Conference Experience Like No Other) asking me why Logo faded from the limelight after much hype about its potential to transform education.

When Logo first came on the scene after Mindstorms was published (1980) enthusiasm about its potential for educational reform grew. Not only was Logo the first significant piece of educational software that included programming, but was also a catalyst for much discussion in schools about its potential for effective teaching and learning. Other educational software began to emerge from publishers like MECC and Sunburst but it was mostly of the CAI and drill & practice variety. Computer Literacy emerged as an important competency and learning how to program was a big part of it. By 1983 already there was grumbling about programming. Fred Hechinger in a New York Times article (July 26, 1983) wrote that the school's approach to computers was wrong in focusing on programming and drill and practice. He quoted Marc Tucker (prominent at the DOE at the time) as saying that teaching BASIC to kids makes them think crooked, if at all. Teachers were also not happy with having to learn to program in BASIC or Logo for that matter because it was time consuming. But still there were plenty of Logo enthusiasts who saw Papert and Logo create a new culture in the classroom that was student centered and teachers were "guides on the side." Critics began to surface and Papert had to come to the defense by explaining Logo's role as a microworld for learning which can be used ineffectively without proper understanding of how Logo should be used. There was one significant study that was done by Roy Pea and D. Midian Kurland of the the Bank Street College Center for Children and Technology that probably did the most damage.
"Among other things, Pea and Kurland tested children who had been exposed to Logo in specially set classroom situations. Since they wanted the study to mimic the effects of discovery learning. Pea and Kurland gave the teachers stringent guidelines to curtail their learning. At the end of one year, student who had worked with Logo were tested to see how their planning skills had been affected. Students in the control group which did not have Logo were given the same tests. The results showed no differences between the two groups leading the authors of the study to conclude that Logo does not help teach planning. Further the results caused them to question whether Logo supports other kinds of cognitive development, as its promoters claimed." (Note 1)
As you might expect this study made Papert furious mostly because he thought the students in the Logo experience group learned a little Logo and not much else so the results were not surprising. Pea fired back defending the experience by claiming that Bank Street was well versed in guiding students so that they have the Logo experience. There were other studies that showed positive results of the Logo experience, but the damage was done. Papert and MIT hosted several Logo conferences (Logo 84, 85 and 86) that I participated in that were intended to counteract the negative press. At the final session of Logo 86, Brian Harvey author of several Logo texts, held a session entitled "Whatever happened to the Revolution?" referring to Logo, of course. Geraldine Kozberg, director of staff development in the St. Paul, MN school district, who kept the Logo spirit alive in her district for the next 10 years spoke about Brian's talk at Logosium 96 conference in St. Paul. She had the same title as Brian's: What ever happened to the Revolution?" You can read her transcript here. Well worth it.

CLIME also had a transformation of sorts around the same time as Gerry's speech. In 1994 CLIME changed its name to Council for Logo and Technology in Mathematics Education to reflect new constructivist sofware developments in math especially Geometer's Sketchpad. The name of our acronym however remained the same (L is not changed to T) in honor of the Logo movement and Seymour Papert that inspired so many of us. Also the lack of technology sessions at annual NCTM conferences led to the reframing of CLIME's mission statement. (Note 2)

1. A Conversation with Seymour Papert: Logo Under Fire (Classroom Computer Learning, January, 1985)
2. In 1997 of CLIME does one more name change. It becomes the Council for Technology in Mathematics Education. Though Logo is dropped from the name, its spirit lives on. It just means that Logo has a lot of good company on the software shelf these days.


Thursday, June 18, 2015

A Conference Experience Like No Other


"At the National Council of Teachers of Mathematics (NCTM) conference this past April, educators Dan Meyer, Zachary Champagne and Mike Flynn devised Shadow Con, an effort to change the way in which attendees, non-attendees and presenters interact before, during and after a conference. Between three hosts, six presenters, over 425 physical attendees and thousands of others online, it was a conference experience unlike any other." Kristin Gray

Two unique features of each talk was first that the speaker had a fellow tweeter share via #shadowcon15 highlights of their approximately 10 minute talk. Secondly, at the end of the talk the speakers had to come up with a "call to action" which would motivate listeners both live and online to share their experiences of the conference and inspire these educators to follow through on the message of the talk.

Last night I listened to what amounted to a debriefing of this "conference within a conference" by the speakers and organizers themselves. After it was over, I got the feeling there was a movement afoot. Next week the organizers are meeting with the current president and president-elect of NCTM to share their excitement about what occurred at this conference. I'm very interested in what develops.

You see, this has a special meaning for me because 29 years ago at an NCTM meeting in Washington, DC (1986) approximately 125 educators - incuding me - responded to a call by John Van de Walle to come to an "after hours" meeting for folks interested in Logo, a programming language for kids developed by Seymour Papert , an MIT mathematician. Out of that exciting meeting a group was formed later to be named "The Council for Logo in Math Education" which a year later became an affiliate group of NCTM. I became its first president. We had our annual meetings during the NCTM annual conferences in a room provided to us at no cost by NCTM. Also CLIME got an invite to do a presentation at the conferences from 1988 through 2007! Here is a brouchure for our 1995 meeting in Boston.

Clime meeting - Boston, 1995
We also had a newsletter. The first one was sent out in March of 1987 and included a two sided Call to Action which we called CLIMEaction. In it I wrote:

In order for CLIME to grow and flourish, many people need to work together and separately, taking small steps that collectively impact math education. CLIMEaction is an attempt to rally you to take concrete steps to help our organization pursue its vision of what math education can be like.
Each of you is doing something of interest with Logo. If we can  get everyone to share, then you can gain from the collective wisdom of the group. I know this is summer and some of you will find this June issue buried under piles of unread mail, we would appreciate it if you can give some thought to what your contribution can be. Some of you expressed interest in helping but were not sure how. On the other side are some suggestions and some questions regarding this issue of the CLIME newsletter. Please take the time now to respond. We need your input and your help! -Ihor Charischak

That was 1987. And for the next decade we had an energetic group of math teaching Logo users collaborating and sharing which was a joy for me to experience. But the number of CLIME members never exceeded 300. Snail mail and a lack of easy communication made it difficult for the organization to grow. And then Logo lost its allure especially when other software like Geometer's Sketchpad took center stage and pushed Logo onto the back burner. Logo in its many forms still has a strong niche following, but nothing like in its hayday of the 80s and early 90s. 

Now its 2015 and the tools for communication are here. And a new group of enthusiastic math teachers are anxious to share with other math teachers via social media. And once again, NCTM has taken notice. The organizers of Shadowcon 2015 are meeting with the president and president-elect of NCTM next week and I expect some exciting collaborative outcomes. Stay tuned.

Tuesday, May 19, 2015

A Paradigm Shift at NCTM

As I was preparing for a talk on Math Future about my recent book, I was struck by the interesting, but contrasting parallels between the impact that Seymour Papert's Logo movement and the emergence of Dan Meyer and his 37,000 followers on Twitter made on NCTM.

In 1986 at the annual meeting of NCTM in Washington DC, John Van de Walle organized an after hours meeting for attendees who were interested in Logo. According to my count there were about 125 educators in attendance. As a result an organization called the Council for Logo in Math Education (CLIME) was formed which eventually (in 1988) became an affiliate group of NCTM. Our hope was that Logo would enter the mainstream of math education and be promoted by NCTM. And, especially, NCTM would invite Seymour Papert to be a keynote speaker at an NCTM conference. The movement was a disappointment and Papert never spoke at an NCTM conference. There were many reasons but generally I would say that NCTM was not ready to support this disruptive innovation at that time that was focused mostly on computer use and was considered inappropriately technocentric.

A more recent “disruptive” activity is what Dan Meyer has brought to NCTM. Using the power of blogging Dan has become the pied piper of mathematics education reform. In Boston his sessions were filled to capacity and NCTM supported his after hours Shadowcon event. This is all good stuff. I’m all for it. I’m just disappointed that Logo didn’t get its due way back when.

Monday, May 11, 2015

Geometer's Sketchpad User News

As you may know Key Curriculum was folded into McGraw Hill last year so now it's more difficult to find out what's going on in the Geometer's Sketchpad community. Fortunately, Dan Scher and Scott Steketee keep the spirit of this great piece of software alive with their blog where they present excellent ideas for teaching math with Sketchpad.  The one pictured on the left is named Around and Around: Investigating Multiples. Click here for more details. If you are so inclined comment on their website and thank them for their efforts!

Monday, April 27, 2015

Boston Math Conference - Friday Morning

On Friday morning I was following a trail of people leading me towards the 9:30 session lead by Dan Meyer. I walked into the ballroom and it was completed packed. So I checked in next door (Ballroom A) which also had hundreds of seats, but were mostly empty. The title (Stop answering questions - countering the Google Generation) intrigued me so I sat in but still thinking I would eventually go next door (Ballroom B) for Dan’s inservice-like session about building better lessons involving modeling. But I wound up staying to hear a most interesting session not so much about stopping answering student questions but rather leading discussions with questions that the teacher poses that keep students from asking questions that lead to dead ends. The model for the teaching was the answer to Jon Ail's question. (See image.) It struck home because teaching with questions was my main method of modeling an effective way to generate a discussion with students. This means that you avoid answering questions of students that would take them of the hook for productive thinking. For example, giving answers to problems that students might have come up with on their own. Caveat: thinking for students can be painful if the context is not within their zone of proximal development said Jon Ail one of the session leaders. So the questions teachers ask must be carefully, contexually crafted.

I'm sure Dan's session was very enjoyable session for his participants, but he probably had a lot of answers to offer. I was more intrigued with how questions can deliver productive discussion and resolution. Actually this is also Dan's message which he posts on his website: Dan Meyer - less helpful.

See Jon Ail's and Tifiny Howard's slides here. Thanks, Dan for making the slides easily available.

Tuesday, April 21, 2015

MTBoS and other NCTM Boston conference adventures

"We are math teachers who share what we've learned, cause we don't want our classes to suck the energy from students. Professional development among friends, not just colleagues. Fun! Immediately useful! Interesting!" So starts the description of MTBoS a 
The chart
refreshing new movement in the NCTM world. Armed with a table in the exhibit hall at the annual NCTM meeting in Boston this fledgling group of young social network activist teachers are slowly yet exponentially changing the face of math education. At least that's how it appeared to me every time I passed the booth and could barely squeeze in to say hello to the latest facilitator (of which there were many) at the booth. Led by Tina Cardone's enthusiasm the MTBoS booth was the best place to visit. What did they have to offer? Lot's of free stuff that members created and shared passionately with visitors. "Do you tweet? Do you blog?" If no was the answer then newbie visitors were given a 5 minute overview of the advantages of these socially viable venues. I'm sure many "joined" the movement and signed their names on the chart with their new twitter handles.
At the MTBoS booth

Tonight MTBoS will be doing a webinar having participants share their experiences at the conference. Click here for details.

I hope to "see" you there!

More NCTM conference adventures in my next blog entry.

Wednesday, March 25, 2015

Goodbye, math and history: Finland wants to abandon teaching subjects at school

Jerry Becker sent me this.
Goodbye, math and history: Finland wants to abandon teaching subjects at school

By Kabir Chibber
Finland already has one of the best school education systems. It always ranks near the top in mathematics, reading, and science in the prestigious PISA rankings (the 2012 list, pdf) by the Organisation for Economic Co-operation and Development. Teachers in other countries flock to its schools to learn from a country that is routinely praised as just a really, really wonderful place to live.

But the country is not resting on its laurels. Finland is considering its most radical overhaul of basic education yet-abandoning teaching by subject for teaching by phenomenon. Traditional lessons such as English Literature and Physics are already being phased out among 16-year-olds in schools in Helsinki.
Instead, the Finns are teaching phenomena-such as the European Union, which encompasses learning languages, history, politics, and geography. No more of an hour of history followed by an hour of chemistry. The idea aims to eliminate one of the biggest gripes of students everywhere: "What is the point of learning this?" Now, each subject is anchored to the reason for learning it.

Pasi Silander, Helsinki's development manager, says the world has changed with the spread of technology and many of the old ways of teaching have no practical purpose. "Young people use quite advanced computers," he told the Independent. "In the past the banks had lots of  bank clerks totting up figures but now that has totally changed."

Many teachers in Finland, many of whom have been teaching single subjects their whole careers, oppose the changes. It is not hard to see why. The new system is much more collaborative, forcing teachers from different areas to come up with the curriculum together.  Marjo Kyllonen, Helsinki's education manager and the person responsible for reforming the system in the capital, calls this "co-teaching" and teachers who agree to it get a small bonus on top of their salaries.

Kyllonen told the Independent: "There are schools that are teaching in the old fashioned way which was of benefit in the beginnings of the 1900s-but the needs are not the same and we need something fit for the 21st century."
Later this month, she is proposing that the new system is rolled out across the whole country by 2020. Will the rest of the world follow the Finns' lead?


Wednesday, March 18, 2015

A Goal for Math Education: A Wannado Curriculum

In a post last July Raymond Johnson includes 11 major problems in math education that Hans Freudenthal outlined in an ICME talk in 1980. One of them struck a chord with me. Here’s Raymond’s take on that problem:
How do we create contexts for mathematizing? I think there's been a wealth of work in this area, from work based in Realistic Mathematics Education, work on word problems like that from Verschaffel, Greer, and de Corte, and, most recently, Dan Meyer's work. I could go on, as there are many more examples, and perhaps future work will give us a clearer picture about which contexts work best and why.
For me the answer lies in effective curriculum that students actually want to do. I take as a model children’s books that make math come alive for children. The Librarian who Measured the Earth by Kathryn Lasky comes to mind. This could be the nucleus of a chapter in the curriculum unit about how Eratosthenes in 220 BCE measured the circumference using only sticks, shadows and brains. Students can recreate this measurement by participating in the Noon Day project sponsored by CIESE/Stevens every March and September and can learn a lot of important math in the process.

Harold Jacobs wrote a wonderful textbook back in 1970 called Mathematics: A Human Endeavor* which was described as a textbook for students who didn’t like the subject. The book went through 3 editions. Subsequently he wrote a high school level algebra and geometry book that were in same spirit.

Curricular student engagement is the key. Unfortunately all the good stuff that’s out there is considered side dishes or dessert to the main course which is usually boring to the population of students who need more support and encouragement in doing math.

Textbook companies who produce the main courses are not helping in this regard. We need a new paradigm of textbooks that children actually look forward to reading. Wouldn’t that be a refreshing change from the textbooks that continue to be as much fun for children as taking out the garbage?

* (A 4-star review on Amazon:) I'm a 36-year old homeschooling mother who had done calculus in high school and college, and mechanically got some right answers, but never knew why. I hadn't bothered to slow down and notice the beauty and power of the language of mathematics. In his textbook, Mathematics: A Human Endeavor, Harold Jacobs smashed my lack of confidence into a million pieces. He showers the student with so much real-life relevance and humor, that even a slight amount of curiosity about the subject bears delicous fruit. Working through this book will convince any human being, of almost any age, that he or she is a born mathematician.

Thursday, March 5, 2015

Blended Learning - the new technology revolution in math education(?)

I’ve been reading Michael Horn’s new book Blended - Using Disruptive Innovation to Improve Schools and realize that we now have new buzz words for what used to be called "Integrating technology into the classroom" (ITC). Now there is a nomenclature for ITC which include sustaining models such as station rotation, lab rotation, and flipped classroom which adhere to traditional educational goals and disruptive models such as individual rotation, A La Carte and enriched virtual which offer students alternative paths to learning 21st century skills in a more open ended, student driven way.

There's a lot to digest here and I'll have more to say about this in future blogs. For a comprehensive overview of the various models of using technology in the classroom I recommend reading Classifying K-12 Blended Learning by the same authors.

Saturday, January 10, 2015

Pushing the Technology Envelope in Math Education

Keith Devlin author of "Mathematics for a New Era: Video Games as a Medium for Learning" has thrown down the gauntlet in a recent article for NCTM to become more proactive about the use of technology in math education. In  his Huffington Post article "Edtech Investment Is at Record Levels -- Where Is All the Money Going?" he says that though there is $1.36 billion headed towards Ed tech very little of that money reaches down to K-12 education. Most of it winds up in Higher Education leaving a mere $642 million for K-12 where most of that money goes to few entrenched incumbants like Pearson. Dr. Devlin writes: "The situation may be starting to change a bit. In 2014, a few of Silicon Valley's top-tier venture investors dipped their financial toes into the K-12 market for the first time in over a decade, putting funds into companies such as Remind, Edmodo, BrightBytes, and Clever." So there is evidence that teachers are starting to use more technology in the teaching of math. But it needs encouragement.  NCTM is trying, but there is a rub. Dr. Devlin continues:
"The National Council of Teachers of Mathematics (NCTM), the dominant US professional organization for math teachers, has the use of technology in classrooms as a main pathway to improving learning. The NCTM's Principles to Actions says, on page 5: 'An excellent mathematics program integrates the use of mathematical tools and technology as essential resources to help students learn and make sense of mathematical ideas, reason mathematically, and communicate their mathematical thinking.'
So one way to find out what the vanguard of K-12 mathematics teachers are doing in their classrooms -- and are planning to do -- is to look at the list of presentations given at the huge annual NCTM meeting. How many of those presentations are about, or at least make reference to, technology?  
Ihor Charischak, president of the NCTM-affiliated Council for Technology in Math Education, has done just that. He released his findings in a recent blogpost.
According to Charischak, at the NCTM Annual Meeting to be held in Boston, MA, next April, there will be 733 sessions. He combed through them and identified just 97 that highlight technology in some form. At 13.2 percent, not only is that low, it indicates a continuing drop in interest in educational technology. At last year's NCTM Meeting in New Orleans, 21 percent of the sessions were technology-oriented, a year earlier, in 2013 in Denver, 28 percent of the sessions had a technology theme, and the year before, in Philadelphia, there were 38 percent tech sessions, an all-time record.  
Not only is there relatively little evidence of teacher interest in incorporating any kind of technology in the classroom, but the trend is clearly down. Moreover, what technology interest Charischak could identify was hardly in new technologies: It was predominantly the use of handheld calculators and Computer Algebra Systems (like Mathematica), which where highlighted in the title or abstract of just 15 sessions.  
What these data show is that, to date, practically all that much-hyped edtech funding has had virtually no direct impact on what goes on in the K-12 math classroom. Overall, K-12 math teachers are not incorporating new technology in their teaching."
Dr. Devlin finishes with this:
"Genuinely revolutionizing K-12 education within a decade requires a transformative, national, public-private initiative, perhaps reminiscent of, but much less expensive than, the NASA Apollo Project to put a man on the Moon.  
How badly do we want 21st-century-relevant, first-class education for the nation's children?"