Saturday, January 10, 2015

Pushing the Technology Envelop 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?"

Thursday, December 11, 2014

NCTM Annual meeting in Boston Technology highlights

Now that Black Friday is history, it's time to think about the upcoming annual conference in Boston next April. I realize it’s a bit early, but since NCTM has already posted a description of the 733 sessions, I went shopping for technology sessions that would reflect the vision of the Technology Principle which is now "Tools and Technology" as described on page 5 of Principles to Actions:
"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."
I also looked for sessions that promoted Math 2.0, which is my vision of how powerful math-based software combined with the use of collaborative Web 2.0 tools in a dynamic classroom can produce engaging learning experiences for both teachers and students.

Here’s what I found out.
  • There were 97 very interesting sessions (out of 733) that highlighted technology in some form. That was 13.2% which is low compared to previous annual meetings.  Last year in New Orleans 21% of the sessions were technology oriented. In 2013 in Denver 28% of the sessions had a technology theme. Philadelphia set the record in 2012 with 38% tech sessions.
  • 32 of the sessions mentioned technology either in the title of the talk or in the description. 
  • Next most frequent mention is handhelds (TI-Nspire, Graphing Calculator, calculators, CAS) which totaled 15 sessions.
  • Other key words and their frequency (shown below.)
Overall, I'm disappointed that there are only 97 sessions devoted to technology, but also that there are so few sessions devoted to Math 2.0. But overall there were a lot of interesting sounding sessions. Here's my list of "go to" sessions:

#20 - Blended Learning, Blended Pedagogies, Blended Content. Speaker: David Docterman
#59 Integrating Project-Based Learning: Teaching Mathematics across the Curriculum Speaker: Anthony Matthew Rodriguez
#149 Online Teaching and Learning Communities
Elena Kaczorowski & Elaine Siga
#170 B.L.A.S.T. into Online Professional Development Speakers: Donna D. Williams & Erin M. Nguyen
#187 Motivating Our Students with Real World Problem-Based Lessons Speaker: Robert B. Kaplinsky (Great website)
#194 Powerful, Playful Learning 
Speakers: Susannah Gordon-Messer & Louisa Rosenheck & Carole Urban
#250 Tired of Plain Old Tests and Bell Ringers? Introducing Alternative Assessments Speaker: Niccole Taylor
#260 Imagine, Innovate, and Inquire with Tools and Technology Speakers:
Angela M. Waltrup & Christopher R. Horne
#302 Authentic Learning through Computer Coding: Turning Consumers into Creators Speaker: Dawn DuPriest
#416 Developing Your Classroom beyond the Walls Speakers: Dvora Geller & Scott Bruss
#423 Spreadsheet Math: A Powerful Tool for the Practice of Mathematics Speakers: Art Bardige & Peter Mili
#465 Enhancing Social Presence in Online Math Methods Courses Speakers: Heidi J. Higgins & Tracy Y. Hargrove
#520 Future of Learning: The National Science Foundation's Focus on Mathematics Speakers: Joan Ferrini-Mundy & Karen King
#611 Hour of Code: Inspiring Students to Learn Math through Technology Speakers: Karl Henry Romain & Elizabeth Clifford
#656 Teaching with Technology: Tips for Success Speaker: Nancy J. Sattler
#666 The Algebra Artist: Drawing with Desmos Speaker: Darin E. Beigie

Look here for more details on these sessions. Here is the list of all 733 sessions.

More about the Boston conference as we get closer to the event.

Thursday, December 4, 2014

Personalized Instruction Revisted

Math 2.0: It takes a village
 In a recent book by Rick Hess “Breakthrough Leadership in the Digital Age: Using Learning Science to Reboot Schooling" he writes “The question that motivates this book is ‘Given what we know about learning, how can new technological tools help promote great teaching and learning?’ The good news and bad news about technology and learning are one and the same. Schools have not yet begun to systematically tap learning science through technology to deepen, accelerate, and nurture learning. The “bad” here is obvious. So what’s the “good” news? It’s that, since we mostly haven’t figured out the right way to put things together, we’re in a position to make enormous progress by tapping emerging tools and technologies the right way.”

In a recent report on personalized instruction written by UCLA professor Noel Enyedy revealingly entitled “New Interest, Old Rhetoric, Limited Results and the Need for a New Direction for Computer-Mediated Learning”, the author writes:
It seems that the pace of technological advancement, combined with the clear success stories of how technology has improved productivity in other sectors, is leading policymakers and educators alike to take another look at computers in the classroom, and even at computers instead of classrooms. In particular, advances in computational power, memory storage, and artificial intelligence are breathing new life into the promise that instruction can be tailored to the needs of each individual student, much like a one-on-one tutor. The term most often used by advocates for this approach is “Personalized Instruction.”  
However, despite the advances in both hardware and software, recent studies show little evidence for the effectiveness of this form of Personalized Instruction. This is due in large part to the incredible diversity of systems that are lumped together under the label of Personalized Instruction. Combining such disparate systems into one group has made it nearly impossible to make reasonable claims one way or the other. To further cloud the issue, there are several ways that these systems can be implemented in the classroom. We are just beginning to experiment with and evaluate different implementation models—and the data show that implementation models matter. How a system is integrated into classroom routines and structures strongly mediates the outcomes for students. In light of recent findings, it may be that we need to turn to new ways of conceptualizing the role of technology in the classroom—conceptualizations that do not assume the computer will provide direct instruction to students, but instead will serve to create new opportunities for both learning and teaching.”* 
It will be fun to watch this opportunity manifest itself in the math arena in the coming months and years. I call my vision of this Math 2.0 and I'll be writing about it in future blogs.

*The full report is at

Sunday, November 9, 2014

Technology Highlights at the Richmond NCTM Regional

Click above for more information
If you're going to Richmond, VA for the NCTM regional conference you will have some interesting sessions involving technology to choose from. Leading off on Wednesday night is Dan Meyer's keynote session.

Beyond Relevance & Real World: Stronger Strategies for Student Engagement
Highlighting relevance and real-world connections are often seen as the most effective strategies for engaging students in difficult mathematics, but both strategies are limited and can fail in crucial ways. We'll add strategies to our repertoire, looking at research-based methods for creating need and developing questions instead.

You'll notice a new look to the conference sessions website. Larger font size and links to all the relevant social media sites (Facebook, Twitter, etc.)

As far as technology sessions go there will be less than usual in Richmond. I counted only 36 sessions out of 291 (12%) that focused on the role of technology in teaching math. (See my list.)

Of the 36 I list these are the ones I would definitely attend if I was going (which I'm not.)

Cure for the Common Core (Love the title) Speakers: Patrick Callahan and Kate Nowak
Common Core and Web 2.0 Speaker: Nicole Shobert

Related previous blog entry

Wednesday, October 29, 2014

Scaling the Algebra Wall

Two of the barriers that students must overcome in the course of their math studies are fractions and algebra. Recently Heinemann published a textbook that makes it a lot easier for students to scale the algebra wall. The title is Transition to Algebra. It starts off in lesson 1 with exploring number tricks the kinds that I first learned about when I read W.W. Sawyer's Mathematician's Delight in 1972. A simple example is shown here in this video produced by Heinemann.

I highly recommend this EDC developed curriculum to any school that's interested in getting all their students to appreciate algebra for the first time ever and scale the algebra barrier. Other algebra texts make learning it insurmountable and the best they can hope for is a fragile understanding. Transition to Algebra makes learning algebra an intuitive and engaging endeavor!

Friday, October 3, 2014

NCTM's Grand Challenge

This post was written by Raymond Johnson, a graduate student in mathematics education at the University of Colorado Boulder. His interests include the relationship between education research and teaching practice and he works with teachers to help them evaluate curriculum quality and student growth. You can find Raymond on the web at

A few months ago the NCTM Research Committee asked people to submit ideas for "grand challenges" in mathematics education. I've commented on some of these challenges at (post one, post two), but here I want to talk about what I see as a grand challenge not for math education, but for NCTM itself.

The Old and the New

NCTM has a generation gap problem.
What Dan was noticing at the 2013 NCTM Annual Meeting may not have been just about age, but age is a big part of it. During a session at the 2014 NCTM Annual Meeting, Jon Wray reported that the median age of an NCTM member is 57.5 years. 57.5 years! I personally have a fondness for NCTM veterans and enjoy the history of mathematics education, but a median of 57.5 is big when compared to the current distribution of teacher ages, where we see a median age closer to 40-42 and a modal age of about 30:

Teacher Age
(Source: Ingersoll, Merrill, & Stuckey, 2014)

This age difference is noteworthy for NCTM because older generations, like those in the upper half of NCTM's membership, tend to be relatively loyal to their institutions. But that's not the case for younger generations that now comprise the bulk of new teachers. Millennials often fail to find relevance in institutions, or they share in Generation X's tendencies towards institutional mistrust. Claims like these are symptomatic of NCTM's challenge:

It's not that Millennials don't value the power of being organized — they just tend to use the internet and social media to organize rather than rely on help from established organizations. An increasing number of math teachers are using Twitter and other social networks to organize themselves in both less- and more-formal ways. There might be no better example of self-organization than "Twitter Math Camp," an institution-free math conference where attendees tend to be young, connected, and not members of NCTM. (Attendees also tended to be very white and male, even more so than for the profession as a whole. That's a challenge for TMC and our social networks.)

The degree to which NCTM understands the changing needs of its membership is not entirely clear. On the one hand, NCTM does have an organizational social media presence (Twitter, Facebook, and LinkedIn) as well as blogs and social media accounts for their teacher journals (TCM, MTMS, and MT). Yet, not so long ago, members of NCTM's Research Committee appeared unaware that such tools could be used for connecting with teachers. In a 2012 report, the committee's recommended strategies for reporting research to teachers focused on journal-based publications and conferences. There were zero mentions of the internet, the WWW, blogs, social media, virtual teacher communities, or anything that would have distinguished their recommendations from plans NCTM might have formulated in the 1980s or before. While the committee's recommendations for how research gets reported in their journals and at their conferences might be sound, an assumption that math teachers will be loyal journal-reading, conference-attending members is not. NCTM's grand challenge is not to refine how well it preaches to its choir.

Thankfully, NCTM is not monolithic and some clearly understand the challenge NCTM faces in being relevant to the various needs of young math teachers. Peg Cagle is one of the better-connected members of NCTM's Board of Directors (Jon Wray is another), and if you click through to see the replies to Peg's question, you'll see a lot about what teachers want and what they feel NCTM is currently providing.

Beyond Content 

In 2010 Google's Eric Schmidt famously claimed that every two days we create as much information as we did from the rise of civilization through 2003. While the accuracy of such a statement is difficult to establish, there's no doubt that we are awash with content.

Included in all this content are materials for math teachers, such as curriculum materials, lesson plan sites, instructional videos, test generators, and other teachers' reflections on their practice. What's more, this content is cheaper, more abundant, and more accessible than ever before. When math teachers perceive NCTM mostly as a provider of journals and conferences, NCTM risks becoming just another (and more expensive) content source in a vast sea of content sources. The quality of NCTM's resources certainly helps their cause, but we shouldn't ignore the possibility that people sometimes settle for good enough when they can get something easily at low or no cost. For all its journals and all its conferences, NCTM's game can't be to out-content the rest of the internet.

The internet has spawned many disruptive innovations and NCTM is one of many institutions facing challenges in this content-rich era. Traditional news media is similarly challenged to attract younger subscribers/readers/viewers who are accustomed to using the internet as an abundant source of news coverage, much of which is localized, specialized, and free. We've seen traditional news organizations experiment with variations of familiar revenue strategies, such as targeted advertising and freemium subscription models, but some think it's time for a more fundamental shift in how news media serves the public.

One of my favorite thinkers on the future of news is Jeff Jarvis, a journalism professor, blogger, and podcaster. Recently, Jeff has been working to answer the question, "Now that the internet has ruined news, what now?" Jeff has partly given his answer to this question in a five-part series (1, 2, 3, 4, 5) on Medium as he writes his way towards a new book due out in November. At the core of Jeff's vision is a service-oriented journalism based on relationships, where content is just a means to that end, not the end itself. Journalists would position themselves to work closely with communities, privileging community knowledge instead of acting as the content authority and gatekeeper. Social media would be a key tool for building and maintaining these relationships, as Jeff describes in this selection from Part 2 of his essay:
Now we have more tools at hand that enable communities to communicate directly. So perhaps our first task in expanding journalism’s service should be to offer platforms that enable individuals and communities to seek, reveal, gather, share, organize, analyze, understand, and use their own information — or to use the platforms that already exist to enable that. The internet has proven to be good at helping communities inform themselves, sharing what’s happening via Twitter, what’s known via Wikipedia, and what matters to people through conversational tools — comments, blog posts, and tweets that, never mind their frequent banality and repetition and sometimes incivility, do nevertheless tap the cultural consciousness.
To be clear, Jeff isn't saying journalists should just be replaced by the public sharing of information. Journalists can add value to the community's knowledge by raising new questions, adding context, bringing experts into the conversation, fact-checking, and performing other duties long-associated with quality journalism. What's different, says Jeff, is that "simply distributing information is no longer our monopoly as gatekeepers and no longer a proper use of our scarce resources." Content doesn't go away, but it takes on a supporting role for journalists focused on maintaining personal relationships with their community and its members.

I may be overestimating the similarities between challenges faced by news organizations and by a professional teaching association. But where visions for the future are concerned, I think Jeff Jarvis's service-oriented, relationship-based model for journalism may also be a promising model for NCTM. When I re-read Jeff's essays and mentally substitute "NCTM" for "journalism" or "news," I start to imagine a different kind of NCTM focused on privileging and coordinating the knowledge and relationships of a community of math teachers, one in which journals and conferences are merely seen by members as means, not the ends.

What Now for NCTM

I may be guilty of armchair quarterbacking. I also may be guilty of underestimating how much NCTM members already feel part of a strong professional community built on relationships. During the same panel at which Jon Wray mentioned NCTM's median age was 57.5, he also proudly expressed that he thought of NCTM as a collection of members he could refer to as "we" or "us." That's great for Jon and like-minded members, but that's not where NCTM's grand challenge lies. The challenge is with those who see NCTM as an "it" or a "they," likely young teachers who only associate NCTM with conferences they might not attend and publications they might not read.
I do not profess to be an expert in relationship-building, nor do I believe there to be easy answers. That's part of what makes this a grand challenge. That said, here are a few ideas for moving forward:
  • Don't be faceless. NCTM's blogs and social media accounts are a good start, but to build strong relationships we need to associate with each other as individuals, not as product titles. For example, instead of a @MT_at_NCTM Twitter presence to represent the journal, NCTM needs the editors and authors of Mathematics Teacher to represent themselves online as individuals. The same goes for board members, NCTM staff, and anyone else who identifies with the organization. It's easier to build trust with a person than a brand, and in my two years of helping teachers develop criteria to identify quality resources, I still don't think any indicator of resource quality matters more to a teacher than to have a recommendation from an individual they trust.
  • Find teachers where they are. Perhaps a time existed when it would have made sense for NCTM to build its own social networking site, but that time has passed. We should leverage the networks that already exist and find the teachers there. Some math teachers already use social media for professional reasons and would be easily engaged by NCTM. Other teachers of mathematics, who may only use social media for personal reasons, number in the tens and potentially hundreds of thousands. They may or may not be NCTM members, or regularly interact with other teachers online, but they exist. NCTM needs to organize its membership so that we seek these teachers out, show them that we care, and offer our support.
  • Don't just push, listen. The most common behavior I currently see in NCTM's social media streams is pushing content. To again use @MT_at_NCTM as an example, instead of just pushing out a daily link to an article or calendar problem, show that you're listening to the community. Talk to teachers about what they need and want. Use the journal to respond to these needs and show the community that you're listening. When there's a new article to share, arrange for the authors to engage in discussions and Q&As around what they've written. Again, engage as individuals, and use the @MT_at_NCTM account (and likewise, the other journal social media accounts, blogs, etc.) to highlight and point people to these community interactions.
  • Build a thank you economy and know your members. NCTM should take a few pages from Gary Vaynerchuck's playbook and establish a "thank you economy" with its members. Gary's current business is helping brands with their marketing, focusing more on listening and thanking than with pushing and closing deals. The language Gary uses in his keynotes is NSFW and his message is bold. Here's a 10 minute version and hour-long version of Gary's talks. (Note that these are 3-4 years old but still sound cutting edge. On Gary's clock, that means the next big thing is probably already here.) Gary is a big believer in knowing your customers and using that knowledge to show how much you care. Imagine an NCTM that used social media to know more about you as a teacher — the subjects you were teaching, the textbooks you have, the length of your class period, nuances in your state and local standards, etc., and used that information to help you in ways very specific to your needs. That kind of listening and caring about teachers as individuals builds loyalty.
  • Play matchmaker. At both the AERA and NCTM Annual Meetings this year I heard someone say something like, "We need a for connecting teachers who want to work together" or "We need a website that connects teachers who want to work with researchers." Along with knowing teachers well enough to match them with relevant content and material resources, NCTM should know enough about its membership to connect members with each other.
  • Guide teachers towards mastery. In a 2001 article in Teachers College Record, Sharon Feiman-Nemser discusses what a continuum of teacher education might look like if it began with preservice teachers and continued through the early years of teaching. This continuum would need mentorship and induction programs better than what we have now and, most importantly, someone to coordinate teacher learning across university and school boundaries. For math teachers, NCTM might be the organization that could make this happen. If NCTM knew the strengths and weaknesses of teacher preparation programs, and of individual graduates, and knew more about those individual teachers' needs and experiences, they could position themselves as the facilitator/provider of high-quality, ongoing professional development for teachers. Examples: Maybe I'm a new teacher hired to teach 7th grade, but I student taught with 11th graders — NCTM could build my 1st-year PD around video cases with 7th graders. Maybe my teacher education program was strong in its approach to formative assessment — NCTM could provide support in furthering my practice instead of starting back at the basics. Maybe I switched states for my new teaching position — NCTM could help me better understand how teaching math is different in my new place, and what's worked well for other teachers making a similar move. Yes, this is that big data stuff that scares some people, but I'm not sure the size of the data matters much when it leads to something genuinely helpful.

These are just some ideas. Others will have different perspectives on NCTM's challenges and possible ways to meet them, but I hope this either starts or adds to conversations about math teaching as a profession and we should value in our professional organizations. While I understand why some teachers aren't members of NCTM, I think math teaching is a stronger profession with a strong NCTM. It's a better "we" than a "they." This stronger NCTM lies in a new generation of math teachers, ones who I believe are willing to connect and collaborate as part of an organization committed to forming relationships with them and amongst them, not just providing content to them.

Wednesday, October 1, 2014

The Math Blogger Sphere Goes Viral (or so we hope with the growth of MTBoS)

As I mentioned in a previous blog entry NCTM has joined the blogosphere with three entries: one corresponding to each journal. I want to highlight one post corresponding to the middle school journal (Mathematics Teaching in the Middle School) written by John Golden* where he extolls the virtues of the Twitter Math Camp that occurred last summer. Here is a piece of John's blogpost:
A lot of my personal professional development experiences now come from interacting online—mostly through Twitter and blogs—with an amazing group of teachers from around the world. These teachers have become the self-declared Math-Twitter-Blog-o-Sphere (MTBoS). Members of the MTBoS are deluged by interesting reads and intriguing conversations, including accounts of classroom practice, assessment dissection and analysis, activity development, and even discussion of research. Three years ago, a small group decided to meet in real life in the summer, and Twitter Math Camp was born. Last year, the group met at Drexel University in Philadelphia, home of the Math Forum. This year, 150 of us met at a high school with a stunning STEM facility in Jenks, Oklahoma (pronounced “jinx”) for three days. more
One of the proud members of this group is Dan Meyer who wrote this about that. 

In the next CLIME Connections a guest blogger will share his take on the relationship between NCTM and the rise of these independent teacher bloggers. Stay tuned.

*John Golden, @mathhombre, is a member of the department of mathematics at Grand Valley State University in Michigan. He teaches math and elementary and secondary teacher preparation courses. At, he blogs about math games, geometry and GeoGebra, lesson ideas, and teacher prep.