Here are two reasons to be encouraged about the work and vision of the National Council of Teachers of Mathematics, followed by my hope for its future.

NCTM is obviously interested in recruiting new members, along with all of their new ideas.

Two years ago there was a panel discussion dedicated to technology in math education which featured a bunch of math Twitter-types. The following year saw an entire strand dedicated to ideas from those math Twitter-types. Then the math Twitter-types occupied the opening keynote at this year’s Nashville regional conference, immediately after which Robert Kaplinsky took my favorite photo from that conference.

These @NCTM confs are about the connections you make. cc: @dbriars @TracyZager @mslailanur @mathycathy @jreulbach pic.twitter.com/JhMaklOdSZ

— Robert Kaplinsky (@robertkaplinsky) November 19, 2015

Mark it, friends, or correct me if I’m wrong: that’s the first appearance of a current NCTM President at what the Twitter-types call a “tweetup.”

Just five years ago, these Twitter-types occupied the fringe. It’s so nice to see everybody making friends and learning from one another. This only bodes well.

NCTM’s new conference website has promise.

The history: Zak Champagne, Mike Flynn, and I ran Shadow Con as an experiment in extending the face-to-face conference experience. We offered speakers a more powerful platform on the web for interacting with attendees (live and virtual) than NCTM’s existing read-only conference program website.

We reported the results of that experiment to NCTM’s executive team and that was the last any of us heard from them until this year’s regional conferences when they tweeted out their new conference website. Look at it!

The featured speakers at the regional conferences each get their own page on a WordPress installation. On first glance those pages look just like a conference website. Title, description, and time. Just the facts. But speakers can add files, videos, and other resources. Then there is a comment box where attendees can get in touch before and after the session.

A colleague of mine remarked: “It’s a mixed bag.” Yeah, but what a mix!

Out of the 28 featured sessions across the three regional conferences, seven presenters don’t seem to have visited their page. That lack of attention has basically zero downside. Their pages look just like they would on any read-only conference program website. Title, description, and time. Just the facts.

And across the other 21 sessions, there is a pile of activity!

• David Wees asks Jon Wray to clarify his session description. Savvy shopping, David! Helpful replying, Jon!
• Christina adds a Yelp-style review to Graham Fletcher’s page telling people they should definitely come to his session. Great social proof, Christina!
• Donna Leak’s page has video of her presentation. Video!
• A presenter had to cancel her session but leaves behind an apology and her slides!
• David Barnes collects tweets from his session and adds them to the comments afterwards. Tweets!
• Math Twitter-types like Annie Fetter, Kate Nowak, and Max Ray trick out their pages with resources and interact with attendees like the web veterans they are!

All of this is possible without NCTM site’s but none of it is easy to do and none of it is easy to find.

So here is my hope for the future of NCTM conferences.

Extend this website to cover all presenters from all NCTM conferences and offer it to affiliate organizations for their conferences as well.

I want to click Annie Fetter’s name on one page and see all the talks she’s ever given, across geography and time, including five years ago at some random state affiliate conference I never knew existed.

I want to search for “Kate Nowak NCTM” in Google and find her past conference pages and also her upcoming talks.

Before I attend a conference, I want to locate presenters whose talks seem to provoke a lot of online discussion afterwards, and then attend those.

If NCTM makes this commitment, they’ll increase their value to current and prospective members several times over.

For current members, they increase the value of conference attendance and decrease the pressure on attendees to attend every session. (Expect the question “Will you be posting your resources to your page?” to float around Twitter in the weeks leading up to every conference.) The conference page will connect attendees and speakers in the twelve months between annual conferences.

Prospective members, the kind who wonder “Why NCTM?”, may start to land on conference pages more often than Pinterest boards when they search for resources. As those prospective members explore the resources on those conference pages, NCTM can recommend journals, articles, books, tasks, and other conference pages that may also be helpful. NCTM can point those visitors to upcoming conferences and sessions on those themes, converting non-members into members and members into stronger teachers.

Until future notice, I am a single-issue voter in all NCTM elections and this is my issue.

We’re continuing to host commenters from across a vast philosophical divide (including the co-authors of The Atlantic article under discussion) commenters who are unlikely to share the same physical space any time soon. People have largely kept it together and you’d have to be a committed ideologue not to walk away with a better understanding of the people who disagree with you.

I haven’t been able to shake one particular exchange, though.

Halfway through the comments, two people who disagree with each other as completely as anyone could each made a precise and articulate case for their diametrically opposite theories of learning.

Ze’ev Wurman, a longtime advocate of traditional math instruction:

I thought the purpose of a problem in a classroom is to check whether a student knows sufficient math to solve it, rather than learn bout the nature of human thinking processes. If it is the latter, Dan is completely right, except it belongs to cognitive science experiment rather than a classroom.

Brett Gilland, an infrequent blog commenter who should comment more frequently:

I can not disagree with this enough. The purpose of a problem in my classroom is almost always to understand the nature of that human’s thinking processes. This allows for amplification, further investigation into how the student is able to navigate similar problems with subtle variations and complications, and attempts to draw student mental models into internal conflict to create pressure for remediation and revision of said mental models.

Ze’ev Wurman:

I suspect that Gilland’s employer, and certainly the parents of his students, would also disagree. Some quite strongly. The primary purpose of school is to educate the kids at hand, not to train the teacher. This doesn’t mean that teachers do not learn from experience, but if gaining experience and insight is the primary reason for what the teacher does, he’d better get approval from an IRB and a waiver from each individual student or parent that attend his class.

Brett Gilland:

Funny thing, that. My employer, my parents, my students, my district, the state evaluator for my school, etc. all support my teaching. Most quite strongly. This might be due to the fact that when most people hear “I work really hard to understand your child’s thought processes so that I can better guide their thinking and draw out subtleties and conflicting mental models,” they don’t think “Oh my God, that man is performing experiments on my child to improve his educational practice.” Instead, they think “Oh my God, that man really cares about what is going on inside my child’s head and is attempting to tailor instruction to what he finds there. Thank goodness he isn’t stuck with a teacher who believes that teaching is just lectures interspersed with quizzes to determine if my child gets it or needs to be droned at more with another utterly useless generic explanation that takes no account of what my particular child is thinking!”

I’m sure that everyone walked away feeling like their side won, but one side is wrong about that.

Featured Comments

Chris H:

“Every school should be organized so that the teachers are just as much learners as the students are.” (Adding It Up, 2001, pg. 13)

jennifer potier:

Alas, I feel that Mathematics is reaching a junction — in which the traditionalists and the progressives must come to a head and work together to forge a stronger future for our young mathematicians! Whilst today’s world demands an ability to think and to use available resources to find new meaning, we must not forget those who generated those resources in the first place. a fine craftsman needs to learn the tools of his trade before he or she can produce the creative thinking in his head. A computer programmer must use efficient logic before we can play those game or use those apps to be progressive learners. To what degree should thinking, reasoning, and problem solving come before skills acquisition , or vice versa? Sound like the chicken and the egg to me.

My biggest fear for us as teachers is that we are robbing our young people of the beauty and passion for maths through repetitive, applied drill, just so that they can demonstrate a high level skill skill that they will never use. or, we are not providing enough technical skills to enough of our students to ensure quality craftsmanship I am saddened every single time that my best mathematics students tell me they want to study medicine or dentistry instead of using their mathematical ability to grow our field.

Let us first and foremost provide our students with mathematical challenge- that requires both the creative solution and advanced skills acquisition. Whether the challenge be abstract or modelling a real situation need not matter. What is important is bringing back the passion for mathematics that we, as mathematics educators share, passion- through intrinsic motivational challenge and drive.

In response to yesterday’s post, Jason Dyer offers us a useful thought experiment:

1. Is there a problem that could be completely explained using symbolic notation alone?
2. Is there a problem that symbolic notation cannot sufficiently explain?

I vote yes for both and have added my examples in the comments.

BTW.

I realized that the headline from the Garelick & Beals article doesn’t match their argument.

The headline: “Explaining Your Math: Unnecessary at Best, Encumbering at Worst”

Their article: “At best, verbal explanations beyond ‘showing the work’ may be superfluous; at worst, they shortchange certain students and encumber the mathematics for everyone.”

I can see why The Atlantic would want to sharpen their writing for the headline. They qualify themselves twice in the article (“at best” and “may be”) barely making a claim.

So if they think symbols are always sufficient explanations, let’s offer questions in the comments for which they aren’t. If they think verbal explanations are sometimes necessary, let’s let them articulate when.

Featured Comment:

Ernest Gunn:

There’s a place in instruction (somewhere between ages 3 and 8) where each of the symbols “3” and “+” and “4” and “=” and “7” each need explanation, which might look like
… + …. = … …. = …….

I am pretty sure that Common Core haters dislike the notion that any of that ought to be explained, that they would prefer that this just be one of the 55 addition facts that ought to be memorized, and let’s move on.

At the same time, requiring 3rd or 4th graders to explain why 3 + 4 = 7 seems ridiculous, EVEN THOUGH SOME 3RD GRADERS HAVEN’T MASTERED ADDITION.

I would ask my 8th graders to explain why 3x + 4 != 7x, but I wouldn’t ask for this in a Calculus class, EVEN THOUGH IT HAS NOT BEEN MASTERED BY ALL.

My point is that we use symbols for efficiency, to avoid explanation. Symbols are NEVER enough explanation at the beginning of instruction.

A student’s presence in a given class presumes a level of previous mastery and efficiency WHICH IS NOT ALWAYS THERE, and instruction examples demonstrate the level of explanation that is expected.

To Chester Draws about the quadratic, I would hope for words like “Quadratic => 0, 1, or 2 solutions” in an explanation.

So a really good question is “what level of explanation should students be expected to demonstrate on a national test? (all right, multi-state, but I am in favor of a national curriculum).