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. 

Friday, September 12, 2014

The Common Core High School Math Standards — a closer look

From Henri Picciotto (26 January 2014):

I have recently retired from teaching high school math in an independent school, and now work largely with public schools, as a freelance math education consultant and curriculum developer. If I were still in the classroom, I could have ignored the Common Core State Standards for Mathematics (CCSSM) for a while, because their impact on private schools would take some time to kick in. However in my new career, the CCSSM affect everything I do, so I decided to take a close look at the standards for grades 9-12.
The views I articulate in this paper are based on my own experience as a teacher (42 years in the classroom, K-12), curriculum developer (author of a dozen books, a dozen articles, and a large math education Web site), and department chair (30 years or so at the Urban School of San Francisco.) I realize that this does not guarantee that I am right about any of the questions I'll be addressing. On the other hand, I am confident that my experience is at least as valid as that of any one of the authors of the CCSSM.

Wednesday, September 10, 2014

NCTM Regional Conferences Dan Meyer Doubleheader

Dan Meyer
No, it was not a web page error as I first thought, but Dan Meyer is indeed giving the keynote presentation at two of the three Regional NCTM meetings this fall: Indianapolis October 29-31 and Richmond November 12-14. Here are the details.

Opening Session
Wednesday, October 29 - Indianapolis
Dan Meyer, Stanford University; Stanford, California
Fake World Math: Why Modeling Goes Wrong (And How to Get It Right) 
Meyer works with thousands of math educators every year and finds more disagreement about the CCSS modeling standard than any other. So he has set out to answer the questions, What is modeling, How do we get our students to do it, and How do we get our students to like it?

Opening Session
Wednesday,  November 12 - Richmond
Dan Meyer, Stanford University; Stanford, California
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.

The reason I'm bringing this up besides the fact that Im thrilled for Dan and the NCTM committees that chose him is that he brings his potent message about how math should be taught to the forefront of the math communities in those cities. In Indianapolis he focuses on modeling as something that the common core folks didn't get right which begs the question for me: what else didn't they get right? Since NCTM is supporting CCSS 100% its good to hear that they allow for some introspection via their keynoters.

For more information about this fall's regional NCTM conference programs see:


Wednesday, August 20, 2014

NCTM Conference in Boston 2015 Announcement

I'll be speaking at the annual NCTM conference in Boston next April. Also as has been my custom for the last 10 years I'm planning to preview all the technology related sessions in Boston. (See last year's tech preview of the New Orleans NCTM conference.)

Here's a description of my session:

Title: Inside a Dynamic Math 2.0 Classroom
Description: The Internet, cloud computing and portable devices are making inroads into the classroom. What does a Web 2.0 based classroom involving dynamic math software that produces active learning look like? Examples of collaborative math 2.0 activities will be shared. (These activities are highlighted in my forthcoming - November, 2014 - book "The Wannado Curriculum: Scenes from a Dynamic Math 2.0 Classroom.")

If you are speaking at the NCTM conference next April on a technology theme, please let me know so I can highlight your talk in my preview listing.

Tuesday, August 19, 2014

NEW! NCTM's Journal Blogs

NCTM has joined the blogosphere with three entries: one corresponding to each journal. Here's how NCTM describes them.
Each of NCTM’s three teacher journal blogs has been developed to expand on a theme or topic:

1. Math Tasks to Talk About in Teaching Children Mathematics
2. Blogarithm: Standards of Mathematical Practice in the Middle Grades in Mathematics Teaching in the Middle School, and
3. Joy and Inspiration in the Mathematics Classroom in Mathematics Teacher  
Blog posts are contributed by guest bloggers from within the mathematics education community, and all three invite comments from the field.  Access your journal blog above and join the conversation now.
These blogs are independent of the actual articles in the Journals. The only way to comment about an article is to send an email to the editorial staff of the Journals ( I had a comment about an article in Mathematics Teaching in the Middle School (MTMS) entitled Tasks to Develop Language for Ratio Relationships. (You have to be a member of NCTM to read it.)

I have a problem with young children focusing on such language distinctions as “the blue ribbon is 5 times longer than the red ribbon” and “the blue ribbon is five times as long as the red ribbon”. The important thing is that students understand multiplicative reasoning using whatever language makes sense to them, rather than confuse with language that I as math educator have trouble making sense of.

Is there a public forum for comments about MTMS articles? If not, there should be.

Thanks in advance for a response.


Ihor Charischak
White Plains, NY

Waiting to hear back.

Monday, July 14, 2014

Diane Briar's Core Truth

Diane Briars
At the last NCTM conference in New Orleans (2014) Diane Briars officially became the 48th president of NCTM. One of her mandates as president is to support the roll out of the CCSSM and look at it as a cup half full rather than half empty. In her first president's message entitled "Core Truths" she does an excellent job of presenting the CCSSM as an opportunity for the math community to build on and create curriculums for their districts that empower students and teacher to learn and teach math. About the backlash to the Standards she writes:
"With respect to the Common Core State Standards for Mathematics (CCSSM), what I find most troubling is that much of the rhetoric is based on false or incomplete knowledge about the standards and their development, or it confuses the standards with implementation activities, issues, and policies, including testing policies. Such arguments have little potential to improve mathematics education. Distinguishing CCSSM facts from fallacy is essential both for implementing the standards effectively and for engaging in thoughtful, reasoned critique of them for future refinements."
This is true. In its purest form who could argue that a coherent set of standards would not benefit math education. However, the opponents have some relevant points to make and these are not addressed in her message. It's also not in her role as president, which is too bad. It would have been nice if she had acknowledged the concerns that more than half of the teachers polled in the study Diane mentions have about the standards and how these concerns can be addressed. My main concern is that the standards will be perceived as merely a list of objectives. Unlike the Standards of 2000 which had some spirit and lots of good examples this latest version is more like a set of to dos which teachers in their busy lives will complete in a more rote manner. The Principles to Actions does a little to help, but the examples in that book are not all that interesting. The chapter on technology is excellent in that it appeals to the power of Web 2.0 to transform math education. None of this powerful trend in technology is mentioned in the standards. I'm sure that Diane is aware of this being a long time supporter of technology in math education, but her main purpose in her Core Truth message is to address the negative spin as indicated in her closing remarks that describe the three pronged approach to support CCSSM which I quote below. (It's times like this that I miss the possibilities that Steve Leinwand might have brought to the table as president.)

Here is Diane's closing comments.
"The Common Core State Standards represent too important an opportunity to squander because of rhetoric based on incorrect and incomplete information and public confusion of the Common Core State Standards themselves with shortcomings in their implementation. NCTM has developed a three-pronged approach to support the CCSSM: 
1. Clearly describe and publicize the practices, policies, programs, and actions required for successful implementation of CCSSM through wide dissemination of Principles to Actions: Ensuring Mathematical Success for All. NCTM cannot do this alone. Our Affiliates and their members are important partners in this effort. 
2. Enhance and expand our professional learning opportunities related to Principles to Actions and implementation of CCSSM at our conferences and institutes and in our journals, and continue to build our collection of relevant professional learning resources. This spring, each NCTM committee developed specific plans for this work. 
3. Actively advocate for the Common Core State Standards for Mathematics, correcting misconceptions, clarifying confusion, and highlighting ways in which CCSSM supports students in learning more and better mathematics. Most important, we need to help parents and the broader public become aware that the conceptual understanding and habits of mind—for example, problem solving, reasoning, and perseverance—that CCSSM calls for are essential for students’ preparation for their futures 
This third prong requires all of us, especially teachers and parents, to personalize CCSSM by describing its benefits for their students and children. I strongly urge you to get involved in the dialogue. Correct misconceptions. Separate standards from implementation issues. And highlight the benefits and opportunities that the Common Core State Standards for Mathematics afford to increase the mathematics learning of all students."
I'm an optimist at heart and I wish Diane a successful term as president.

You will find the Diane's entire message here.

Wednesday, June 25, 2014

When Am I Ever Going to Need This?

Jordan Enberg writes in “How Not To Be Wrong - the Power of Mathematical Thinking”  that the best answer to the age old “When am I ever going to need this” question is: tennis. If you want to play tennis you have to do a lot of boring practice to get good. The implication being that you should practice math because it builds up your thinking muscles. That is probably true. For those that play a lot of tennis and work at the skills needed to get better I assume that they really WANT TO play tennis. Enberg’s analogy to math flops because most students once they reach their teenage years would rather take out the garbage than do math.* The problem with it is that there are other more interesting ways to build the same muscles especially for those students more interested in the softer sciences. Children will build their math power if they see a reason to do it. Just because math is cool to people like Jordan Enberg and many others (including me) who want students to really, really like math, It isn’t going to work unless the students see a need for math. 

My favorite example for this is Green Globs (see my blog about it.)  Green Globs is terrific at motivating students to learn how functions work. But the joys of learning functions is not the main reason they want to learn about them. I always tell my students that the reason they should learn about functions is because in two weeks they will be involved in the Great Green Globs Contest and will need to learn to play Globs well enough to help their team win the contest. Since the math in Globs is intrinsically interesting for most students, they are willing to learn what it takes to do well - just like in tennis. In that blog entry I told you the story of Guillermo the failing math student who managed to get a perfect score of 8191 points by knocking down all thirteen globs with one function. What I didn’t tell you is how many students were inspired by Guillermo to improve their scores because they really wanted to learn the math needed to score higher. Now winning the Green Globs contest is a small incentive compared to how we want math to inspire students to really want to do something significant in the world. What is it that inspires kids to want to learn important math that will help them to achieve their personal goals? By creating real world projects as the central goal of curriculums! The math curriculum that almost everyone uses was set up in 1892 by a group of academics known as the Committee of Ten and hasn’t really changed in over a hundred years. Isn’t it time that something new, that students WANT TO buy into becomes the default curriculum? A curriculum that will encourage areas of study that students are passionate about.

At the college level, Roger Schank has “built story-centered curriculums meant to teach practical business by creating simulated experiences. The idea is to deliver it online around the world, using mentors who speak the students’ language. No classes. no lectures. No tests. Graduates get an MBA degree […] The idea is to help people launch their own business or go to work.” (page 58 - Teaching Minds.)

This doesn’t mean that the conventional curriculum doesn’t work. My Columbia Prep teaching days made me realize that there were plenty of students who wanted to take on the Royal Road to Calculus and I say more power to them! What I’m suggesting is what Ronald Wolk writes about in "Wasting Minds: Our Education System is Failing and What we Can do About It." We should develop an alternative curriculum that empowers students to really take advantage of math in ways that are appropriate for them.

*Karim Ani of said this during his presentation at the NCTM conference in New Orleans last April.

Roger Schank. Teaching Minds: How Cognitive Science can Save our Schools
See also Roger’s blog about how to redesign high schools. 

Friday, May 30, 2014

The Mathman Retires

"How can I motivate my students to get more interested in doing math?" was the question I posed to Don Cohen back in 1972 at a Saturday morning math workshop in NYC.  "The problem is that your kids are not really doing math," Don replied as we strolled down a picturesque Greenwich Village street. "What you need to do is get your students to create their own math. But first the teacher needs to do the same. That's the purpose of the workshop I am leading here." That one comment has stayed with me ever since as I continue my effort to inspire teachers to aim for that vision for themselves and with their students.

After 38 years of math tutoring, Don Cohen will hang up his hat as "The Math Man" at the end of this month. (Read more)

You can hear Don interviewed by Maria Droujkova at a Math 2.0 Webinar back in 2010 where he talks about his experiences with Calculus by and for Young People.

Thursday, May 8, 2014

Accolades to NCTM for Tools and Technology Addition in Final Form

In the original draft of the Principles to Action that was available for review this statement appeared on page 81 of the Tools and Technology section:
"While non-mathematical technologies and tools (e.g., word processing, presentation, and communications software) have a role in the mathematics classroom (Cohen & Hollebrands, 2011), they provide a more supportive role and do not have the direct potential to promote student reasoning, sense making, and mathematical thinking found in mathematical action technologies."
In the final version (now available from NCTM in book & eBook form) which I highly recommend purchasing*, the paragraph above was replaced with the following on page 79-80:
"Non-mathematical technologies and tools (e.g., word processing, presentation software, and communications applications)  can also support interactions in the mathematics classroom (Cohen & Hollebrands, 2011). For example, student responses to an interactive poll can be quickly gathered through the use of either a dedicated clicker system or applications on a range of mobile device platforms, to provide teachers with informative information that may help guide instruction.  Interactive whiteboards, document cameras, and web-based presentation applications can help students communicate their thinking to classmates and receive constructive feedback. Students sharing of work can occur beyond the boundaries of the face-to-face classroom through the use of secure Web-based platforms to post and comment on student-made podcasts, digital images of student work, and student presentation files. Students might use text messaging, cloud-based shared documents, virtual whiteboards, blogs, or wikis to collaborate on mathematical problems within the school or with students in other states or provinces or even countries (Rochelle et al. 2010). By making use of these electronic tools, students have a greater sense of ownership of the mathematics their learning, since the applications promote a sense of shared enterprise in the learning of mathematics. 
Finally, a wide variety of web-based resources support the teaching and learning of mathematics. Teachers are increasingly using personal and shared pages to organize and categorize the resources they find most useful. These lists allow them to quickly locate resources that they have found useful in the past and share these with others through social media. Their capacity to do this represents, in a sense the virtual opening of the classroom door to allow for collaboration among classrooms and teachers. Furthermore teachers can organize shared pages to enhance communication with their students and their students’ parents or caregivers."
Principles to Actions: Ensuring Mathematical Success for All
(2014: National Council of Teachers of Mathematics, Reston, VA. p. 79-80)

Thank you NCTM for making the chapter on Tools and Technology relevant to today's Web 2.0 world!

*the eBook version is available for $4.99 ($3.99 if you are a member).

Wanna do Games, STEM and Mr. K

At this week's Global Math Department session, Tim Kubinak shared something "outrageous" that he does with his students on Fridays. He let's them play games for up to 45 minutes. The actual time depends on how well their group did on their math during the week. What games and why? "Let's face it," Tim said, "We're not good at teaching problem solving. We're good at teaching them to solve problems, but not problem solving. If we want to teach them problem solving, we have to exploit their interests. And that's what games do for kids." For that reason Tim makes available a variety of player games for his students. The main goal is to learn problem solving with a STEM theme. He calls it PYG (Play Your Games) which is a gameplay program designed to exploit the interests of students, within the context of reinforcing STEM methodology and problem solving acuity. Students work in groups of three. The amount of time that students are engaged in these activities is determined by results on these quizzes.

Tim has assembled an ecletic collection of playergames, hand held devices, MaKey MaKey touch pads and BYODs as part of his platform for teaching problem solving. Time frame is usually 8:15-9:00 when groups meet to get their equipment for game play. They check on the chart to see how much time is allotted to their group. They are also responsible for filling out the PYG sheet which has instructions for helping them make their session productive.

Though I do the question the method used to determine time for playing (the high scorers get the most time), Tim treats it as a game and I'm sure the kids are motivated to do better on the next grading period so they get more time the following Friday.

The open time for game playing with appropriate rubrics is an appealing way to engage students.

To learn more about Tim's class listen to his webinar at GMD.

Wednesday, April 30, 2014

Global Math Department Launches

Global Math Department
Are you tired of your math department meetings? Are they prone to put you to sleep? Well, there is a cure in the clouds. Its called the Global Math Department and it is housed conveniently on the Web as part of the community.

GMD’s About page tells you all you need to know about the group:
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!
Reading that intro I bit and attended their weekly meeting last night. Chris Robinson, a middle school math teacher from northeast Pennsylvania, was our host and introduced the evening’s presenter Ilana Horn a researcher at Vanderbilt University.
Her topic was: Findings from Research.  Tonight, she presents five findings from research that have influenced how we think about teaching. Ilana Tweets at @tchmathculture and blogs at

You can experience this lively presentation and chat with a small, but very active group of math educators who attended here.

To become an active member of the Global Math Department go here and sign up and subscribe to their newsletter.

It was fun being a participant and I look forward to future sessions and will comment about them here at CLIME central.

Saturday, April 26, 2014

NCTM 2015 New Members Resolution at Delegate Assembly?

After the panel discussion on Friday at New Orleans Conference a young teacher LeAnn Allen approached me and asked me how she can get more involved in NCTM. I shared with her that membership in NCTM would be a good first step and shared some of the benefits of being a member. I didn't think much more about it until I read her blog post which I share with you here:
NCTM 2014 left me ON FIRE. (Almost literally, it was so hot walking around on Saturday.) But seriously, it left me hungry for more: more PrBL in my classroom, more student conversations, more teacher online collaboration, more ed conversations, more all of it.
One conversation that I am glad to see continuing is the one centered around getting younger teachers in the classroom to participate in NCTM. An NCTM rep said the average member of NCTM is 57. Whether or not that statistic is true, here is what I’m interested in exploring from that conversation. 
A lot of young teachers I personally tried to cajole/blackmail/etc into coming to NCTM wanted to come, but couldn’t find the $$$. So, how can we make that more accessible to them? Give a “new teacher” discount” a la student discount (how do you define/prove “new teacher”)? Give a first-time attender discount? Give scholarships? A quick look at the NCTM page gave this single conference scholarship for first-time attenders as well as a similar one for prospective teachers. There’s also some other grants and scholarships but most of them have a requirement that you have to have been teaching for at least 3 years (which disqualifies me until next year). What if MTBoS banded together to come up with a scholarship or 2? I’d be willing to chip in a few bucks. 
April 14, 2014 at 8:30 pm
As a first time attendee, I was also energized, and frustrated with the lack of younger membership and participation at NCTM when it clearly has so much to offer. That said, I think back to Dan Meyer’s point at the start of his talk (you were there, right?) about whether the conference would exist in a few years as we gain the capability to do that over the internet for next to no cost and with more accessibility. I think that might be the direction I’m heading — GlobalMathDepartment, twitter chats, etc.

This is obviously a major concern of NCTM. I'm wondering if the Affiliate-at-Large groups (hopefully soon to be called Special Interest Groups) could address this issue through a resolution at the next Delegate Assembly meeting in Boston.

Any ideas or thoughts on this?

Ihor Charischak
Council for Technology in Math Education
White Plains, NY

Wednesday, April 23, 2014

Maria Droujkova - Make Math your Own

This morning I listened to a recording of Maria Droujkova giving a keynote address at the Learning Revolution Conference Online. The title of her talk was "From adventurous learning to disruptive innovations: brave design in mathematics education." Here's her description of the talk:
Robert Lang is building a space telescope as long as the island of Manhattan. His out-of-the-box origami play helped to figure out how to fold the telescope into a rocket’s tiny storage box. Vi Hart is a mathemusician. Her whimsical sculptures, videos, and workshops are deeply therapeutic for hundreds of thousands of people suffering from math anxiety. Hans Rosling is a doctor, a statistician, and a data superhero who influences the decision-making of millions with interactive infographics. The issues our society faces require innovative, brave solutions. We already have a lot of creative dreamers and doers: our kids! At Natural Math, we design education that recognizes and supports students as creators of their own math. We grow local and global communities of math learners. We advance the view of the mathematical education as an adventurous journey. We develop tasks that are rich and complex, yet easy. And we introduce advanced math concepts to young children, including calculus for five-year-olds.
Maria really captures what young people should be doing: to make math your own, you need to make your own math. Listen to her presentation and be inspired. I was. Here is the link to her slide presentation.

Wednesday, April 16, 2014

Teachers Leveraging Technology in the Classroom Panel Discussion

Do you think this conversation is happening in Finland,  that the Finnish Council of Teachers of Math is having sessions about leveraging technology in the classroom?
-Karim Ani

At the NCTM conference last week I attended a panel discussion and was struck by Karim's comment. He continued with "sometimes I'm a bit of Luddite because often times we use technology as a thing to pursue in lieu of the thing that we actually want to pursue." [That thing being children learning math.] It reminded me of what Seymour Papert wrote back in 1990.
"Well, how many more [conferences on computers in education] should we have? Isn’t it time for us to grow up? And as we grow up, we should stop seeing ourselves as specialists of computers in education, because that casts us in the role of a kind of service profession. Accepting the role allows that other people are the ones to decide the big goals of education, what the curriculum is, how learning happens, what’s a school. And at our conferences we talk about how their decisions can be served by the computers. Well, fine, up to a point. This certainly allows revolutionary actions as long as we are at the stage of crafting Trojan horses to throw into the system. But at some point we have a responsibility to break out of that marginal role and take on our true vocation, which is not one of service but one of leadership. At some point it will be as ridiculous to have a world conference in computers and education as to have a world conference on pencils and education.Perestroika and Epistemological Politics, Seymour, Papert - Sydney, Australia – July 1990
Has Finland turned the corner and "grown up" focusing on learning and teaching? Just like Karim I'm not sure. But it's clear that we as a nation have not achieved that kind fluency with technology that these young panelists exemplify.

Technology can be a distraction. Because unlike a pencil which can be mastered in minutes, technology takes a bit longer and it's easy to get lost in its intracacies and one can lose sight of the prize we are after. But all the panelists on Leveraging Technology in the Classroom embraced technology as a strategy for winning the hearts and minds of children and teachers in our classrooms.

I think at this session there was an attempt to focus on the prize (students learning math). There weren’t any debates about which software was better (e.g. Sketchpad vs. Geogebra.) Though there was consensus that the Desmos calculator was a productive tool in helping children interact with mathematics in a genuine way.

Each panelist contributed something essential in this endeavor to transcend leveraging technology from a “thing” to a support system for the pedagogical idea that teachers value.

Ashli Black reminded us that teachers interacting face to face is still the ideal mode of the learning process. This NCTM conference provided that for educators. So do regional and local conferences. Maybe we need more conferences she suggested.

Conferences are great, but they are expensive said Karim. He’s right. Unlike 1990 when Papert wrote his article pre-Web 2.0 the online platform for collaboration was not available especially via blogs. It’s still not common mode for communication for most teachers, but it is growing steadily.

What’s NCTM’s role in this? Jon Wray said NCTM's mission simply put is to promote successful teaching and learning of math. One concern is that the average age of an NCTM member is 57.5 years. This has to change. I spoke up at the session and encouraged younger participation in NCTM. But NCTM also has to encourage younger teachers to get involved. The NCTM journals need to become more Web-based and interactive to appeal to a younger audience. Also to encourage math blogging and highlight math bloggers in their e-blast publications which tend to focus on what the President is saying rather than what the young teachers are doing. (Their Illuminations effort is more aligned with this, but needs to be better promoted.)

Blogging clearly needs to be promoted. Kate Nowak shared three components of blogging: (1) it has to be sustained over time (2) directy linked to classroom activity and (3) interaction with colleagues is crucial. Don’t do it alone.

The panel was asked what tools they found useful. The response was the technologies that promote communication, discussions and debates.

Raymond Johnson offered that building simulations that helped textbook problems come to life is important. He mentioned Simcalc and the Freudenthal institute as two groups that are making this kind of software available at a minimal cost.

Technology is not yet seamless in schools, but this panel made me more optimistic that blogging will be a powerful tool in encouraging more powerful conversations for students and teachers. That bodes well for the future.

Panelists and their blogs:
Chris Hunter -
Ashli BlackIllustrative math
Karim Ani –
Dan Meyer –
Kate Nowak –
Raymond Johnson –
Jon Wray - panel moderator

Saturday, March 29, 2014

Noon Day Adventure at Panther Academy

Nestled in a nondescript area of Paterson, NJ surrounded by aging warehouses and auto repair garages lies Panther Academy a high school I visited last Thursday and was fortunate enough to watch a small group of high school students - budding future scientists and engineers -  recreate an experiment that Eratosthenes did 2200 years. Mr. Salama helped his  students use the shadow angles and some trig functions to come up with the central angle of the earth. The class partnered with a school in Kuantan, Malaysia to get their sun angle. By subtracting Paterson's sun angle  from Kuantan's they determined the angular separation at the center of the earth known as the central angle was 37.2 degrees. They also knew that the Malaysian school was 4130 km away by comparing latitudes.  So they were able to figure out that there were 360 / 37.2 = 9.68 "Kuantan to Paterson distances" that circumnavigated the globe. Making that calculation 9.68 * 4130 = 39,937.1 km the students discovered that their measurement was very close to NASA's listing of the circumference as 40,030.2 km.
Mr. Salama helps steady the meter stick as the students
determine the shadow length.
Shafi Ahsanul gave the summary report.

In May, the class will go on the field trip and use Al-Biruni's method for determining the circumference of the earth. I'm looking forward it.
Diagram illustrating a method proposed and used by Al-Biruni
to estimate the radius and circumference of the Earth

Friday, March 28, 2014

Access and Equity in Mathematics Education - Where's the Technology?

This week I received the following email. I want to share it with the CLIME community. Please read and comment. Mine is the first one.
Ihor Charischak

NCTM At-Large Affiliate Presidents:
Over the past two years, NCTM has been working to revise its position statement on equity.  As part of this process, it was suggested that each of you be invited to review and comment on the statement from the perspective of your organization.  The attached statement reflects the work of NCTM Board members and some discussions among the Board.  You are invited to submit your comments for the consideration of the authors and the NCTM Board.  We would appreciate your comments by April 3.

Kind regards,
Ken Krehbiel
Associate Executive Director for Communications
National Council of Teachers of Mathematics

Access and Equity in Mathematics Education
A Position of the National Council of Teachers of Mathematics
(Note: Work in Progress - not final version - for review only)

What does creating, supporting and sustaining a culture of access and equity in the teaching and learning of mathematics require?

NCTM Position
Creating, supporting, and sustaining a culture of access and equity requires being responsive to students’ backgrounds, experiences and knowledge when designing, implementing, and assessing the effectiveness of a mathematics program. Acknowledging and addressing factors that contribute to differential outcomes among groups of students is critical to ensuring that all students routinely have opportunities to experience high-quality mathematics instruction, learn challenging mathematics content, and receive the support necessary to be successful. Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.

The practices of access and equity include, but are not limited to, high expectations, access to high-quality mathematics curriculum and instruction, adequate time for students to learn, appropriate emphasis on differentiated processes that broaden students’ productive engagement with mathematics, and the strategic use of human and material resources. When access and equity have been addressed well, student outcomes—including achievement on a range of mathematics assessments, disposition toward mathematics, and persistence in the mathematics pipeline—cannot be predicted by students’ racial, ethnic, linguistic, gender, and socioeconomic backgrounds.

Achieving equity with respect to student learning outcomes by closing existing learning gaps and increasing opportunities to learn requires that educators at all levels operate with belief that all students can learn, focus on ensuring that all students have access to high-quality instruction, challenging curriculum, exciting extracurricular opportunities and the differentiated supports and enrichment opportunities necessary to support student success at continually increasing levels.

To provide access and equity requires all stakeholders to monitor the extent to which all students have access to challenging mathematics curriculum taught by skilled and effective teachers who differentiate instruction as needed, monitor student progress and make needed accommodations, and offer remediation or additional challenges when appropriate.  To do this effectively, teachers must work collaboratively with others educators, including special education, gifted education, and ELL teachers, to ensure that all students have the support needed to maximize their success in the mathematics classroom. In addition, teachers need to collaborate with colleagues to implement the effective teaching practices to promote a growth mindset in their classrooms and school.

Districts and schools must review policies to ensure that systemic practices are not disadvantaging a particular group of students based on assumed stereotypes. This should include a review of the use and impact of tracking, protocols for student placement in mathematics, regular opportunities for both remediation and enrichment, and student outcomes, including persistence within the PreK-12 mathematics pipeline over time.