Saturday, February 4, 2017

Curriculum Reform Done Right

I recently reread Rick Hess’s book The Same Thing Over and Over: How School Reformers Get Stuck in Yesterday’s Ideas. In it Hess argues that “most of today’s reforms thought to be cutting-edge – merit pay, charter schools, extended school days and years, Teach For America – aren’t really cutting-edge at all. And in the long haul, most aren’t likely to result in significant change.” Also he says that “…most of our current strategies to get better teachers into classrooms, including alternative certification, are essentially just “throwing thimbles of water into a river” – which is a slightly more polite way of saying they’re totally inconsequential.”

Why? Because, Hess says, we aren’t willing to start from scratch in our thinking about what it means to be a teacher in the twenty-first century.

Of course in “starting from scratch in our thinking” is something that is tried frequently but always fails because the obstacles to real change (or common sense change in contrast to status quo change as Hess puts it) are so difficult, if not impossible. On my wish list of difficult/impossible, but transformative reforms is something that at its core makes sense to everyone involved that's interested in math education reform. 

My version of common sense reform is much “simpler” than what Rick writes about. It’s about dramatically improving curriculum materials for students. Isn’t it possible to create programs of study that students would actually enjoy reading? My current list of math books that I’m enjoying reading (and some re-reading) are:

Why do I reread them? Because like cinema and theater I love math when it is couched in a fascinating context. In other words because it is intrinsically interesting, engaging and challenging.

Why can’t student materials be written in this spirit? Hess says because status quo reformers just want to tinker around the edges of current textbooks which doesn’t stop alienating most students in their study of math. A colleague of mine Gary Stager (who is definitely a true common sense reformer) calls “curriculum” a dangerous idea. That’s because math curriculum in the form of textbooks are such an abysmal read for most students. And even the students that do well and like math usually are mostly influenced by good teaching that makes the drab material come to life. I’m really tired of the fact that Dan Myer has to make “fun” of actual activities in math books in his blog. (See

We have the talent to do better, but unfortunately not the will.

If you agree let me know and maybe we can start a movement protesting text book companies for their poor approach to writing textbooks. Instead of resigning to choose the best text out of all the bad choices offered, we force them (are you listening Pearson & McGraw Hill?) to start from scratch and come up with well written books/media that would inspire both teacher and student to read. 

Is this possible or am I just dreaming? I’d like to hear from you.

Hess, Frederick M. The Same Thing Over and Over: How School Reformers Get Stuck in Yesterday’s Ideas. Harvard University Press, November 2010. 

Monday, November 14, 2016

Innov8 starts this Wednesday

This fall (in two days!) NCTM will host its new professional development conference in St. Louis, Mo. Innov8 is not a traditional professional development experience, this innovative and team-based opportunity is centered around acquiring the necessary skills to provide high-quality mathematics education for learners of all abilities. So bring your team and engage in a hands-on and interactive learning experience for math education.

If you are going to this conference I would love to hear about your experiences. I’ll be following on Twitter.

Friday, October 21, 2016

NCTM Phoenix Regional 2016 Technology Sessions

If you are going to Phoenix for the regional conference and are interested in attending some sessions focused on technology, you might be disappointed by the availability if you use the search by topic in the Conference Planner link. Why? Because there are only 19 sessions highlighted there.  I found that there are actually 48 sessions that highlight some form of technology in their descriptions. I list them here. The keyword breakdown is a as follows.

Also the deadline for voting for the Board of Directors starting in 2017 is October 31. Check out @Samjshah post describing the candidates. 

You need to be a member of NCTM to vote. This is an excellent reason to join. NCTM’s voting website is here.

Tuesday, September 20, 2016

NCTM Events Fall, 2016

If you are looking for some informal professional development, get inspired about your work or just get away for 3 days, then the upcoming regional conferences will be well worth your while. First there are 2 regional conferences one in Philadelphia, PA and the other in Phoenix, AZ.

Highlights in Phoenix

The keynote will be an IGNITE session with seven past presidents of NCTM participating. Should be fun. Too bad it can’t be a debate.

Though technology is not a strand some of the highlighted speakers will no doubt share their expertise with technology in the classroom. The highlighters I’m familiar with are: Karim Ani (, Robert Kaplinsky (, James Tanton ( and Patrick Vennebush (

Highlights in Philadelphia

The opening sessions is once again an IGNITE session. This time it’s not the presidents though Matt Larson is one of the presenters. Each igniter gets 8 minutes and will preview some aspect of the conference. By now I’m all ignited out, but if you are a fan or new to this format, I’m sure you will enjoy it.

Tools and technology IS a strand so there will probably be more technology sessions than is usual. I can’t tell you how many because the full list of speakers is not out yet. 

The highlighted speakers that I would go hear or recommend: Karim Ani (, Dan Meyer (, Sarah Bush (, and Tom Reardon (

Innov8: A New Conference Experience from NCTM

Also this year NCTM is rolling out a brand new and exciting conference called Innov8 which focuses on engaging the struggling learner.

November 16-18 in St. Louis, MO 


Use #NCTMinnov8 to get the latest updates and engage with others about NCTM's new learning experience on social media. A clarion call. I look forward to the twitter blogosphere continuing to become a growing trend as we go further into the 2016-2017 school year.

The new Innov8 conference experience is designed to support mathematics teachers and teams in identifying, analyzing, and planning for instruction and intervention around a self-identified problem of practice related to learners who struggle in mathematics. (more)

Annual Meeting in San Antonio
April 5-8 2017

It’s too late to be a speaker, but not too late to participate. See my blog entry about the conference.  It should be great.

Tuesday, August 30, 2016

What is a coherent pedagogical framework?

In a recent blog, Henri Picciotto (following a successful workshop series that he led) shared a participant’s comment. Henri writes:

“One of the participants in my Making Sense in Algebra 2 workshop had an interesting criticism. That anonymous participant pointed out that I presented no coherent pedagogical framework for the activities I shared. Good point! I did not present a coherent [pedagogical] framework because, well, I do not have one to present.”

I was puzzled. Which coherent pedagogical frameworks was the participant referring to? Webster states that a framework is a basic structure underlying a system, concept, or text. For math education that structure is a curriculum. Pedagogical refers to the myriad of approaches that a teacher can take in presenting a curriculum to students. And a coherent pedagogical framework would be a pedagogical framework that made sense. So conjuring up the meaning of those three words together Henri continues with why he doesn’t have one to present.

“During my four-plus decades in the classroom, I've seen many math edu-fads come and go: new math, individualization, manipulatives, problem-solving, group work, constructivism, constructionism (yes, that's a thing), portfolios, complex instruction, differentiation, interdisciplinary-ism, backward design, coding, rubrics, problem-based instruction, technology, Khan Academy, standards-based grading, making, three acts, flipping, inquiry learning, notice-wonder, growth mindset... not to mention various generations of standards.”

So instead of following some fad-like frameworks, Henri says:

“We need to be eclectic, and select "what appears to be best in various doctrines, methods, or styles." Instead of rejecting the fads wholesale, we need to consider each one as it comes along, as all (or almost all) have some validity. Instead of shutting our classroom door and continuing business as usual, we should keep it wide open.  Without becoming a dogmatic across-the-board adopter of each pedagogical scheme, we need to learn what we can from it, and incorporate that bit into our repertoire. This is how we get the sort of flexibility that makes for good teaching. If we do that, our lessons will not fit a standard mold. Quite the opposite: they will depend on the myriad variables that make teaching such a complex endeavor.”

Like Henri I too have spent more than 4 decades working in math education. I’ve also worked with many of the edu-fads he mentions. In my private school teaching days I eclectically developed my own curriculum which included lessons borrowed liberally from Harold Jacobs’ “Mathematics: A Human Endeavor.” In fact, Harold’s work helped me to develop a coherent pedagogical framework - a classroom strategy model - that served me well in my modeling of how to teach coherent lessons to the teachers I worked with. My model went something like this.

Each lesson (approximately 45 minutes) had three parts.

The first part I called: Set the Stage. This part would motivate the activity that followed. (I never wrote objectives on the board.)

The second part was: Do the activity. Students would usually work in groups. They would discuss and record their findings on a handout I would give them. (See 5th grade example.)

Finally (and maybe most importantly) was Debrief. What did we learn today? This is where the objective is revealed or left open for further noticing, wondering and even debating.

This was the model I used with teachers who were teaching math in conventional ways. For teachers who were interested in exploring more innovatively, I modeled a collaborative project approach - usually referred to as Project Based Learning (PBL) which was an edu-fad back in the 1920s, but recently is undergoing a revival according to the Buck Institute. What I like about PBL is that it takes into consideration student interest. My example of PBL is the Noon Day Project which is a recreation of the measurement of the earth done by Eratosthenes in 200 BC. See my blog entry about it here.

Monday, July 25, 2016

Mathematics & Technology - Perfect together in La Crosse, WI

I was in La Crosse, WI earlier this month to give a keynote talk at the University of Wisconsin Teaching Mathematics with Technology conference. The night before a group of the conference attendees were treated to a cruise on the the La Crosse Queen which is a replica of the old riverboats which used to ply the Mississippi River in the 1800s. Our host was Josh Hertel (the tall guy in the photo) who organized the conference.

A unique feature of the conference was that all the attendees including the speakers were in the same room and got to see all the presentations. It made for a more intimate experience.  Unlike most conferences my keynote was the last scheduled talk so I had the full flavor of the conference before I spoke.

I focused on the 3 big technological ideas that are driving math education today.
  1. Dynamic Math Software
  2. Web 2.0/Social Media
  3. Technology-based learning Communities
When these 3 dynamic forces come together a synergy of innovative curriculum development follows (think Dan Meyer) which engages students in activities that are highly motivational as well as mathematically rich.

I shared several activities that did just that.
  • The Famous Jinx Puzzle
  • Fermat's Last Theorem... Debunked? (By Homer Simpson no less.)
  • Average Traveler Activity
  • The Weird Number Video and the Irrational Invasion
  • The Librarian who Measured the Earth 220 BC
  • The Green Globs Challenge
For more details see

Handouts of other presenters are available at:

Here are some additional ideas shared by David Wees that I should have referenced in my talk.

Friday, June 3, 2016

Response to Questions about Tech Use at NCTM Conferences - A Collective Answer

Response to David Barnes' (Associate Executive Director for Research, Learning, and Development at NCTM) question about technology use at NCTM conferences.

David's question: "So the question for you and your crew is what makes a quality technology session? What does it need to do, include, address, etc?"
  • Tech sessions should focus on larger themes that transcend tech brands or even technology itself. A quality technology session will integrate the tools with the content, demonstrating how the power of visualization enables students to generalize properties and consequently understand concepts more quickly and effectively. Technology is a means, not an end.  It needs to be pedagogically sound.
  • As a participant, I want to know what the big pedagogical ideas before the presenter shows me how a particular tool can realize them.

  • Sessions should generate ideas that make math more interesting to my students and will help me become a better teacher. I will use any tool at my disposal to make the subject more palatable (and fun) for my students, pique their interest, and make the math come alive. 
  • Examples of how to interpret the output of technology to demonstrate understanding and computational fluency should be included. After all, the goal of teaching with technology is to help students learn what tool is appropriate to make mathematics meaningful no matter whether it is a calculator, computer, or pencil.

  • Learning the tools is also very important. The vendors can contribute during their exhibitor sessions and do demonstrations at their booth in the exhibit area. Participants should have the opportunity to USE the technology during the session.
  • An area in the exhibit hall should be devoted to helping teachers get hands-on experience with various effective software programs and apps. That’s something the Math Forum could do in their booth.
  • Encourage the use of social media that helps promote the communication standard both with students and teachers through the use of Twitter and blogging. Members of the MathTwitterBlogosphere could help with recruiting & supporting new members at their booth.
Thanks to Ray Klein, David Wees, Henri Picciotto, Tom Beatini and Dan Meyer for their comments.