Ed Begle:

1. The validity of an idea about mathematics education and the plausibility of that idea are uncorrelated.
2. Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.

Begle coined those two laws in the latter half of the School Mathematics Study Group, a multi-decade project to figure this mathematics education thing out. I’ve heard those laws before but I hadn’t tracked down the original source until today. He seems weary in the speech. His list of tried-and-failed innovations is lengthy and disturbingly current.

Over forty years after Begle’s work with SMSG ended, those laws still offer us lots of comfort and at least a little humility. Math education is hard. My gut is probably wrong. Anybody who says differently is selling something.

Reference

Begle, E.G. Research and evaluation in mathematics education. In School Mathematics Study Group, Report on a conference on responsibilities for school mathematics in the 70’s. Stanford, CA: SMSG, 1971.

2016 Feb 26. Bowen Kerins’ links to a better copy of the entire proceedings. That site also contains links to some of the SMSG “New Math” curriculum, which I’m excited to investigate.

2016 Feb 28. Raymond Johnson cautions us not to read Begle too pessimistically:

I really do love the history of my subject and posts like Dan’s send me into hours of searching through old papers and citations. But, I must be mindful of our tendency to underestimate change when we read from our wisest predecessors. It’s too easy for us to throw our hands up and say things like, “Dewey knew it all along!” or “We’re stuck in the same damned place we were 25/50/100 years ago.” Is Begle’s 2nd law (“Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected”) still true? I would agree it is. But, as a field, we’ve made enormous progress since Begle gave this talk in 1971. The danger, as individuals, is to not learn from this progress. To avoid reaching the same conclusions as Begle, we need to avoid starting in the same place as Begle. When I browse the pages of Begle’s final book, Critical Variables in Mathematics Education: Findings From a Survey of the Empirical Literature, I’m struck by the sheer number of things Begle and the field knew little or nothing about compared to what we know now. Don’t we owe it to ourselves, as individuals and as a field, to push past prior conclusions by starting farther ahead and taking more seriously work already done?

I don’t have any answers here. I can only do my best to articulate the question.

The collection of tweeting and blogging math teachers we call the Math Twitter Blogosphere confuses me.

Look at this place.

• It has a welcoming committee that organizes challenges to help new members find their feet. It also pairs volunteer newcomers with volunteer mentors. (Shout out to my mentee Lisa Garcia.)
• It comprises thousands of blogs and Twitter accounts. Two weekly gazettes exist just to summarize the activity. (That first link is, without exception, the most valuable post of whatever week it’s published.)
• It organizes weekly webinars with speakers and topics running across every spectrum.
• It organizes an annual in-person conference, which sold out in two weeks last year and in eight hours this year.
• 2016 Feb 12. It has maintained a physical booth presence at three of the last four National Council of Teachers of Mathematics’ conferences, staffed round-the-clock by volunteers.

It bears saying again: these are all volunteer efforts and self-organized.

Someone has to help me. Does the same organization and activity exist in other content areas?

It's long been my hunch that math educators have captured the best of social media and connecting. Good stuff here. https://t.co/GJ6OWdE61C

— Jenn Borgioli Binis (@JennBinis) December 2, 2015

If not, then why not? Each of the efforts above boasts some talented contributors — shout outs to Lisa Henry, Julie Reulbach, Sam Shah, Raymond Johnson, Tina Cardone, and the communities they lead — but I find it hard to believe similarly talented people don’t exist in other content areas. If you had to go back in time and bet that one group of teacher bloggers would break out in these amazing spasms of collaboration, admit that math teachers wouldn’t have been your first or second guess.

So how did this happen?

I don’t get it. I love it but I don’t get it.

2016 Feb 11. Helpful data? Googling “[x] teaching blog,” I find in millions of results:

• Math: 33.9.
• English: 115
• Science: 129
• History: 73.1
• Art: 88.9
• Language: 91.3
• Social Studies: 53.8

Quality, not quantity.

Featured Tweets

@ddmeyer That's quite an undertaking. No other subject area has conquered the internet like math teachers have.

— Jennifer Orr (@jenorr) February 12, 2016

@ddmeyer My theory is, the average math teacher teaches very few multi-day projects. So each day is a new lesson, compared to SS or English+

— Kent Haines (@KentHaines) February 15, 2016

Featured Comments

Claire:

I think of all the disciplines, math teachers are frustrated most with status quo. Personally, I want to change my practice, but on my own have struggled figuring out how to teach differently than I was taught. I don’t have a blog of my own (yet) but have grown so much by blogs I’ve found via Pinterest, Twitter, and google searches.

Brett Parker:

I think that curriculum is a huge part. Almost all secondary math curricula include the same topics. There is much greater variation in what states and districts require for social studies or even science. Different required texts for English classes.

Nathan Kraft:

In my own district, I found it hard to find anyone with much of a passion for trying new things…those who truly wish to invest the time for self-improvement. I sometimes wonder if some of my math colleagues even really like math. I certainly don’t get that vibe from the science teachers or the English teachers. Perhaps that is why I was drawn to this community. It is out of necessity in order to find those who are equally passionate.

Henri Picciotto:

But after a very few years, the group collapsed. Traffic stopped in the edWeb community, and the in-person meeting which had peaked at about 20+ people gradually shrank.

I think the fact that edWeb was a closed community, with formal membership was a fatal mistake. MTBoS is totally open.

Click through to read John Mason response to the age-old question.

I have used this response, or ones like it, for many years with teachers when studying mathematics courses at the Open University, and I have noticed that it is only when I feel I am lost, when I lose confidence, when I feel as though I have reached my limits, that I find myself asking “why am I doing this?”

Co-signed.

They don’t actually want to know. They’re tired of feeling stupid and small.

Featured Comments

Mr. C:

Why do we need to know this? 2 words: Robot Apocalypse!

Who will reprogram the machines? Whose calculations would you trust your life with? I was sent her from the future… to be your math teacher!

Matt E:

I still love Sam Otten’s exploration of this family of questions:

https://www.msu.edu/~ottensam/Otten_2011MT_reprint.pdf

Featured Tweets

Easier said than done:

@ddmeyer "because we care about butterflies and dolphins, that is why". Ask them what else they care about, and connect that to math.

— MatScience21 (@Matscience21) February 8, 2016

I asked my Twitter team to come up with an application of imaginary numbers to dolphins. My Twitter team did not disappoint:

@ddmeyer My submission: pic.twitter.com/TFQr1ov93e

— josh g. (@joshgiesbrecht) February 9, 2016

I spent an hour on The Kathleen Dunn Show on Wisconsin Public Radio earlier this week. I was disappointed we didn’t get around to my thoughts on #PackerNation and Steve Avery, but I enjoyed our conversation about math, education, and technology just the same. Even though Dunn admitted she’s uncomfortable with math, she was gracious enough to let me assign her a math problem. It was also my first time on a call-in show, and the callers did not disappoint. [Show link.]

2016 Jan 27. As long as I’m wearing my public relations fedora, EdSurge just posted my interview with Blake Montgomery.

Geoff Krall:

The crux of Problem-Based Learning is to elicit the right question from students that you, the teacher, are equipped to answer. This requires the teacher posing just the right problem to elicit just the right question that points to the right standard.

Our existing knowledge and schema determine what we wonder so kids wonder kid questions and math teachers wonder math teacher questions. Sometimes those sets of questions intersect, but they’re often dramatically disjoint.

Which makes Geoff’s “crux” a form of mind control, or maybe inception, which is impossible. Kids wonder so many wonderful and weird things. And even if that practice were possible, I don’t think it’s desirable, since it seems to deny student agency while pretending to grant it. And even if it were desirable, I wouldn’t have the first idea how to help myself or other teachers replicate it.

If PBL is to survive, it needs a different crux. Here are two possibilities, one bloggy and one researchy.

First, Brett Gilland:

[The point of math class is to] generate critical thought and discussion about mathematical schema that exist in the students minds. Draw out the contradictions, draw attention to the gaps in the structures, and you will help students to build sturdier, creatively connected, anti-fragile conceptual schema.

Second, Schwartz & Martin:

Production seems to help people let go of old interpretations and see new structures. We believe this early appreciation of new structure helps set the stage for understanding the explanations of experts and teachers — explanations that often presuppose the learner will transfer in the right interpretations to make sense of what they have to say. Of course, not just any productive experience will achieve this goal. It is important to shape children’s activities to help them discern the relevant mathematical features and to attempt to account these features (2004, p. 134).

Notice all the teacher moves in those last two quotes. They’re possible, desirable, and, importantly, replicable.

2016 Jan 12. Logan Mannix asks if I’m contradicting myself:

As a science teacher follower of your blog, I’m not sure I follow. Isn’t that what you are trying to do with many of your 3 act problems? Get a kid to ask questions like “is there an easier way to do this” or “what information do I need to know to solve this”?

I am interested in question-rich material that elicits lots of unstructured, informal mathematics that I can help students structure and formalize. But I never go into a classroom hoping that students will ask a certain question. I often ask them for their questions and at the end of lesson we’ll try to answer them, but there will come a moment when I pose a productive question.

The possibility of student learning needs to rely on something sturdier than “hope,” is what I’m saying.

2016 Jan 13. Geoff Krall writes a post in response, throwing my beloved Harel back at me. (My Kryptonite!) It’s helpful.