I have a bone to pick with the mathematics education community. I suppose my opinion is unfair, and it neglects all sorts of history and context about how discussions of mathematics education have played out in the United States. But I am still a little bit angry, and I still hope to make those who study the teaching and learning of mathematics feel a little bit guilty so that the situation might change.

Here is some basic context. I am a mathematician by training, but an educator by employment. I work in a blended math/math ed/stats department where we all get along well–even the math ed people say so. About five years ago I started experimenting with the Moore Method in my classrooms, and I am now a dedicated practitioner of Inquiry Based Learning. I care about being a competent professional in the classroom, and I know I have a lot to learn. Lately, I have been following Raymond Johnson around the internet, and I appreciate his efforts to share what the mathematics education community has learned. In the last week or so, we have also learned about Jo Boaler’s troubles. And Tim Gowers manages to sound innovative while saying something math ed researchers have known about for a long time. (I don’t mean for that to sound dismissive. Gowers obviously cares, but I find it discouraging that his anecdote and gut feeling is replacing the work of systemic studies conducted by mathematics education researchers.)

## Why didn’t you tell me?

It seems that the mathematics education community has learned some Really Big Things about effective instruction. But as a practicing educator, I have to go find those things out for myself, and chasing them down is not easy. In fact, as college professor, I could have a long career blissfully ignorant of any of these things and no one would say anything about it.

**Why do I stumble on these things only to find that they have been understood for decades? Why didn’t someone knock on my door and tell me I was doing it wrong?**

My basic point is this: If you do research on teaching and learning, you owe it to society to share what you know. Scholarly publication doesn’t count. The mathematics education community talking to itself is a necessary condition for sorting out the truth of things, but it is insufficient for educating the public and for changing practice on a large scale.

If you know that the standard lecture-homework-exam format is much less effective generally than an active, student-centered classroom, then how do you not shout from every rooftop that things have to change?

## A Hallway Conversation

I was talking with a good friend and colleague about this issue earlier in the week. I picked her because she is a mathematics education researcher, and because she has heard me swear enough times to not be bothered by it anymore. Our conversation had the additional context of discussing instruction at the college level.

Her first responses were these:

- Mathematicians don’t want to hear it.
- The big power differential between math and mathed faculty gets in the way.

I countered with some more swearing. Suitably cleaned up, I think I said this:

- What matters more, “want to” or “need to”? Are you really going to let systemic bad practice go on? At best this sounds timid and an worst it sounds lazy.
- I understand that in a university setting many mathematicians are arrogant and dismissive of education research. But you won’t change any minds unless you challenge this. Certainly mathematicians hold more institutional power. But are you just going to cede the ground? Power unchallenged only becomes more entrenched.

It seems that one way to change some minds might be to very loudly engage in public debate.

## What I Would Like to See

Let’s have a real large-scale conversation. Let’s get education researchers out into the public spotlight to share what they know about effective instruction. Let’s start to inform the wider public.

Perhaps, the mathematics education community could write more surveys of its generally accepted findings and broadcast this information as a guide to instructional practice. Maybe another approach would be more effective.

#### Let My Re-education Begin

This is the third version of this post. I still don’t like it, but it at least starts a conversation I wish to have. So, feel free to correct me in the comments.

I welcome your ideas and opinions.

As a high school teacher who believes that student engagement is at least as important as

content, I have three thoughts on your post.The first is

entrenchment. A cliche in teaching is that we teach as we were taught, and most current teachers were taught under the model of teacher as deliverer of content and student as recipient of content. It worked for us, so why should we change?That brings us to

evidence. What evidence is there really that lecture-based instruction is “much less effective generally than an active, student-centered classroom”? What would this evidence even look like? Keep in mind, I believe this is true, but how do we really know? And how do we really convince those whodon’tbelieve it already?And this brings us to accountability. My friend ran the physics department at my school, and wanted to transition the department from chalk-and-talk to modeling. He believed in engagement, and even had a few studies he could point to as evidence. But the reaction of teachers in his department was predictable: we’ve been using chalk-and-talk for years, and

we get results. By results, they meant that their students scored well state exams. And if you’re not aware, student test scores have quickly become a mandatory factor in evaluating teacher quality. The more test scores become the goal, the harder it will be to change practice.I see each of the issues that Patrick Honner raises. Since I teach at a University, the accountability issue affects me differently. Of course, I teach at a *public* university, so I bet that things will change some…

Entrenchment is exactly the problem I want to rail against. The majority of my students are pre-service teachers. I have to take as granted that I am a role model, positive or negative. Part of what I do is help my students expand their abilities as mathematicians, but the other part is to give them a sense of how a student-centered classroom feels. They can judge for themselves if it is worth the extra effort.

As for evidence, my math ed colleagues tell me that what I am trying to do lines up with what they believe is best practice. At least, we use a lot of the same language, and we seem to share a common set of goals. I have not pressed them for papers describing the studies. The work I know about best is that done by Sandra Laursen and her group in Colorado. http://www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf

I wish I could tell you the actual timestamp for the information, but if you listen to this (rather excellent) conversation about education in general, at some point the discussion the panelists are asked whether there is any evidence that project-based learning (which I gather from the context is something similar to what you’re talking about) is actually more effective than traditional models. I seem to remember them citing from research, and also claiming that project-based learners actually to *better* on standardized tests, even though they’re not force-fed the necessary facts.

http://www.commonwealthclub.org/events/archive/podcast/education-beyond-talk-amazing-impact-learning-doing-101712

I am highly skeptical of “Evidence” related to education. At best it is usually an opinion which references the opinions of several other researchers. The actual studies, when they are done, are almost always poorly designed. The few that have taken reasonable steps to eliminate bias, as determined by the US Dept. of Ed. for example, typically contain no conclusive results.

You can’t imagine how much nonsense has been presented to teachers as “Evidence” to support the beliefs of educations gurus/professors, administrators, politicians, math reform supporters, “traditional” math supporters, charter school advocates, Ed Reformers, etc. Boeler’s main critics come off as cranky and narrow minded to me, but I would not be at all surprised if their was quite a bit of unintentional or intentional bias affecting her findings and the way in which they were presented.

The notion that researchers know what works and they just need to get the word out… I don’t think so. Most of their ideas have been around in the US for at least a hundred years. The interaction of teaching and culture is complicated.

Thanks for the link. Your statement is exactly the kind of information I hear. More active classrooms don’t hurt standardized test performance, and they might help. What they really do well is to leave students with a positive disposition towards the subject—something mathematics could use dearly.

Education research is a branch of social science research: it is difficult and messy. This is no reason to give up. And though I welcome skepticism, let us not write off the work of hundreds of thoughtful and hardworking people.

I am an adult, and I can try to put what others say in context. But the silence is deafening! I want them to share with all of us what they have learned. I doubt that it is nothing.

While there are a lot of things in learning science research which have scant or poor or too-complicated-to-clearly-evaluate evidence, there are a few which have high levels of evidence. Meaning study after study shows the same result. The IES practice guides are good collections of such findings: http://ies.ed.gov/ncee/wwc/Publications_Reviews.aspx?f=All%20Publication%20and%20Review%20Types,3;#pubsearch

I think it would be great if there was a more accessible introduction to education research results and advice out there, and I think everything you’re asking for would be excellent (I’m a physicist who teaches math and physics, and in PER, we do have something like that getting started — perusersguide.org ), but I would flip your guilt trip around — why doesn’t every mathematician or physicist who teaches seek out educational research on their own? Why should education researchers have to make an easily digested version of their work, just to get mathematicians to pay attention? Do you really think they haven’t been trying? How come it’s not obvious to _professional teachers_ that they should seek evidence to support their classroom practices? Why would a Fields medalist need to be told something like that?

Obviously all those things are true — most mathematicians and physicists do need to be told and do need to have it digested appropriately first, and ed researchers will have to do their best to make it happen. But if anyone’s guilty here, I don’t think it’s the education researchers.

I don’t think this is the way things should be, but a lot of mathematicians are content. Presenting clear lectures is not that hard a skill to master, and when it doesn’t work you can blame the abilities of the students. Students are used to this crappy lecture mode, and they have internalized the idea that they are probably not smart enough to continue with mathematics after a certain point. And the current set up is adequate to the task of identifying and training a bunch of people to be the next generation of mathematicians.

The reversal of guilt trips is readily accepted. I feel guilty for those students I “taught” before I became mindful of what I was doing. I feel guilty about those students who suffer through my inadequacies as I try to reinvent myself and learn my profession.

I feel terror over the large number of mathematicians who have not ever been told that they are really doing it wrong.

Somehow, I feel betrayed in that I was allowed to teach so poorly without intervention for so long.

I remember reading about Oncologists and how quickly research spreads in their field. Supposedly, if one researcher finds a technique which is even a small percentage more effective than another, the technique quickly spreads through the entire field. If educators weren’t so tied to their methods, and if educator researchers could share their research more effectively, maybe we could see the same thing happen in education.

Maybe teaching is more difficult than oncology, but I doubt it.

The thing is, the guilt trip doesn’t really work on a lot of people — it just makes them double down on what they were doing already, hence the soft sell from ed and ed policy people. I think the single thing that has helped the most in physics is Eric Mazur’s conversion experience — it’s hard to impeach a Nobel laureate who had already been known as an excellent lecturer, who writes as compellingly as he does about how he was finally convinced that his students weren’t learning anything from those lectures. It shouldn’t _have_ to be Nixon that goes to China, but apparently it helps.

David Wees: I think teaching _is_ more difficult than oncology, but the useful thing to take from that anecdote is that doctors actually work _with_ each other, and they watch each other work. Teachers are totally alone once they go in the classroom, and they seldom get (or take) opportunities to witness other teachers at work. And of course the effects of a different teaching method are often harder to prove than the effects of a different surgical technique.

One reason I have hope that things might eventually change is that at least one major professional society for mathematicians does seriously promote alternatives to lecture. The Mathematical Association of America is important to me in many ways, but this is a big one. It seems that a few people in the American Mathematical Society (which is much more research and researcher focused) also seem to be leaning this way at the moment. Timothy Gowers is a Fields Medalist, so he has stature much like Mazur, but I don’t think he has quite undergone the full conversion, at least in public. There are other figures: David Bressoud, Keith Devlin to name two. Bressoud in particular is taking a very data-driven approach, specifically aimed at the standard calculus sequence. This seems like the obvious first target: If thousands of failing calculus students doesn’t get your attention, then nothing will.

As Mark said, doctors work with each other and watch each other work. I would really like to see collections of videos of actual units in actual classrooms being presented in a variety of teaching styles. Researchers are often ignored by teachers because they don’t seem to have relevant examples for what they are advocating. Teachers tend to be very practical – if you can SHOW them that something really does work, you will win them over.

I don’t want to write off the work of hundreds of hardworking and thoughtful people (the researchers), but I also don’t want to write off the opinions of hundreds of thousands of hardworking and thoughful people (the teachers). With good reason, there is a great deal of skepticism about the findings of education researchers.

The data driven approach to showing effectivness has not been successful with math programs and techniques. Ryan give the link to the “what works clearinghouse” that collects well designed studies. Some call it the “nothing works clearinghouse” because the studies are so rarely conclusive.

Finally, I am never quite sure what people mean when they say lecture. It seems to me that the pure lecture is getting to be a pretty unusual method pre-college. It is entirely possible to have an engaging lesson that is teacher directed – see just about any Japanese lesson for example.

at the college level, lecture is still the default mode. I know of those who believe a more student centered environment is “lazy,” presumably because the instructor isn’t burning calories lecturing, writing on the board and vigorously erasing.

Since it has come up, there is a set of videos about an implementation of a variant of inquiry based learning in a college setting. I have not watched these, yet. Maybe when the semester ends.

Yes to having a large scale conversation! All of us who teach math need to be learning from each other. And we have to do that by active discussion because even when there are specific pieces of information we can learn from education research, we have to make sense of them for ourselves and figure out what it means for our practice. It’s like learning math — you can’t just expect to read it or hear it and get it — you have to get in there and work on it for it to really make sense. And this is why I think we need the Mathematics Teaching Community https://mathematicsteachingcommunity.math.uga.edu

I like the idea of your site. I spotted it through the magic of twitter a few weeks ago, and I already have signed up.

As a former student of David Bressoud’s (he was my undergraduate advisor), I can say he’s doing something very right in his approach. Almost all of the classes I took with him, including ones with supposedly math-hating students, were discussion-centric. He has a talent for wiping away the residue of poor mathematics teaching and not only giving students confidence but also getting them interested in the subject. Part of his approach, at least back in the mid-90s, was to flip test anxiety inside-out. In Combinatorics, for example, we took two tests. The first was an in-class written exam of the basic concepts. The second was a much more complex take-home exam that we had 3 days to work on. We were not allowed to seek help from people or books for either of these; however, once the tests were returned we were allowed to do them over again and seek any help we liked. It was clear from the beginning that what he cared about was that we learned the concepts, and, crucially, had an understanding of what we *didn’t* know or understand. I think he’s devoted a good deal of his career to improving the teaching of mathematics at all levels. My memory is a bit vague, but I seem to remember that he left a tenured position at Penn State to work at Macalester College because their commitment to quality teaching was higher.

Bressoud is certainly a leader as far as college math teaching. He used his time as the President of the MAA to focus some attention on teaching issues–but that crowd doesn’t need the call to action quite as much.

And I had an interview with Macalester once upon a time. It was just a preliminary screening interview… but I will always regret how poorly prepared I was for that.

Replying to mr. bombastic among others — Education research is very complicated, and the evidence may never be “conclusive”. I think if we wait around for “conclusive evidence” then we will never get anywhere. I think we have to stop pretending that education research ought to be rigorous on the order of laboratory physics or FDA trials and just accept it as a flawed system — and listen to the results of what people do with a view towards improving student learning.

I think a large number of people fail to adopt research-based teaching strategies due to paralysis by analysis. An even larger number have no intention of changing away from the traditional lecture format and use the design flaws of education research as a straw man. Meanwhile such people make zero effort to look for evidence that supports *their* teaching methods — anecdotes are enough. But that’s another rant.

Charles Henderson et al. have done a lot of work on why faculty adopt research-based teaching methods and others don’t (and why some adopt and then drop them). I did a blog post on that yesterday (http://chronicle.com/blognetwork/castingoutnines/2012/11/07/adopting-new-instructional-strategies-going-with-the-gut/) and I have another, in response to this post by Theron, tomorrow, if you want to extend the conversation here.

The problem we have in teaching, I think, is that we don’t currently have a system in which we compete for peer admiration. We will never get improvements just by having knowledge about how to improve be available out there somewhere. We will also not get lasting, strong improvements by imposing external criteria or mandates or by focussing on improving test scores. The only way to have teaching be a strong profession is for us to become a vigorous community in which we share what we know and in which we develop standing in the community in the process. This is the way it is in research communities and it leads to stunning productivity. In case anybody is interested, see more about this at these (sorry if too long!):

Beckmann, S. (2010/2011). From the Common Core to a Community of all Mathematics Teachers. The Mathematics Educator, volume 20, number 2, pages 3 – 9:

http://math.coe.uga.edu/tme/Issues/v20n2/v20n2.html

http://math.coe.uga.edu/tme/Issues/v20n2/v20n2_Beckmann.pdf

Beckmann, S. (2011). The Community of Math Teachers from Elementary School to Graduate School. Notices of the American Mathematical Society, 2011, Volume 58, Issue 3:

http://www.ams.org/notices/201103/index.html

http://www.ams.org/notices/201103/rtx110300368p.pdf

Commentary–Community of all mathematics teachers:

https://mathematicsteachingcommunity.math.uga.edu/index.php/25/commentary-community-of-all-mathematics-teachers

How to fix our math education: make math teaching a vibrant profession:

https://mathematicsteachingcommunity.math.uga.edu/index.php/66/how-our-math-education-make-math-teaching-vibrant-profession

What’s a math educator to do? Response to Garfunkel in the Notices of the AMS:

https://mathematicsteachingcommunity.math.uga.edu/index.php/182/whats-math-educator-response-garfunkel-the-notices-the-ams

Why we need a mathematics teaching community across all levels of math

https://mathematicsteachingcommunity.math.uga.edu/index.php/234/why-need-mathematics-teaching-community-across-levels-math

So, given that I don’t have time to read all of those exactly this instant … (but I do appreciate the links! I will get there some time.), I want to ask for advice on how to foster such a community.

I want something I can do locally to help change the culture at my institution. Maybe I will write a careful question and put it in the next post. It will be more visible that way. It really is a new phase of the conversation, anyway.

One thing which I observe as a university lecturer in a South African university, with increasingly large classes (200 in my junior year continuum mechanics class), and shortage of skilled lecturers is that it’s not always clear whether teaching practices which are effective with small groups and skilled teachers will still be an improvement on traditional lectures when the lecturer is unskilled and the circumstances are worse. At least with a bad lecture reading from the textbook, the students have access to some resources. With a bad lecturer or badly structured class in an inquiry-based model, the students can be really left in the lurch. South Africa’s experiment with Outcomes Based Education at primary and high school has largely failed because the students and teachers were not well-enough resourced to create their own knowledge. This article from the Atlantic has a similar observation from an American school

http://www.theatlantic.com/magazine/archive/2012/10/the-writing-revolution/309090/?single_page=true

I’ve been trying to use pre-class reading assignments, with quizzes online, to move my class towards Just in time teaching, and I observed a greater number of students who disengage from the whole class because they don’t have reliable internet access. Should I continue to do online quizzes because it is clearly a better teaching method, and I will then be teaching half my class well, or should I be more traditional, and teach all of my class less well?

I don’t have answers to these questions, but I think any research on education which assumes that 15 – 30 students are learning in a well-resourced classroom/university/school with a skilled teacher fails to address the whole question. I’m really interested to hear comments.

Helen, I agree. Circumstances bear heavily on what will work.

Understanding the boundaries between the situations and what resources are required to make a particular set of practices work are important considerations for educators making design conditions, but should also inform policy decisions.