Challenges in Creating a Safe Space. Again.

This weekend I had a little revelation. It came when I was reflecting on a conversation I had had with my colleague, where I felt uncomfortable with my part of the conversation. Here's the basic story.

Last Friday I had brunch and a bike ride with a friend and colleague. Throughout our time together, we did a lot of sharing of our current states, and listening to each other, as friends do. And one of the main themes of my sharing was Imposter Syndrome. I feel like I'm doing a kind of crappy job as a teacher right now, and one feeling that pervades is that I've never been trained to teach effectively. Next weekend I'm going to a photography workshop, where I'll probably be working with other semi-professional photographers, and I feel somewhat unqualified to even attend that workshop. I've been appointed as a surrogate chair to a committee, for which I feel incredibly unqualified.

The Challenges in Generating a Safe Space

I've been struggling a lot lately with cultivating an environment in which mistakes are acceptable. As a teacher, I feel like I wear two masks in this regard. On the one hand, I directly tell my students that mistakes are acceptable, and even expected, phenomena in the process of learning. Sometimes I specifically ask students to share wrong answers so we can all learn from them. Sometimes I specifically thank students for having (intentionally or unintentionally) made a public mistake, because we can all learn from them. I intentionally discuss (sometimes ad nauseam) the many ways that we all think about different problems, so that students see that there is no One Way to complete a process. And yet...

Math Burst

This is a write-up about a classroom activity I did back in February, stolen directly from Avery Pickford (who I believe stole at least part of it from someone else... thanks open-source teaching) at a #MTBoSBA tweetup.

The set-up was that students were separated into groups of 4. Two students in each group were designated as the mathematicians, and the other two students were the recorders. They were given four minutes, during which the two mathematicians were supposed to talk through a problem, and the recorders were supposed to write down everything that the mathematicians said. I made strong suggestions that the mathematicians should say everything that comes to mind, not worrying about whether they said something wrong. And the recorders should not speak during this time. They only write down what the other two are saying. After these four minutes, I would call time, and the mathematicians and recorders switch roles. Now the people who were previously recording become the mathematicians, and they start working on the problem, and the mathematicians have to turn their mouths off and become listeners and recorders for another four-minute round.

Brain Dump: How much does(n't) speed matter?

I've been thinking about speed lately, and particularly the speed with which we ask our students to do math. *ALL of the literature I've read lately says that expecting students to do math quickly has a toxic effect. I agree whole-heartedly with this notion, and I do my very best to incorporate techniques into my teaching that allow students personal space and time to think through things at their own pace, not rushed by me or by their peers. It's tough to manage, which is why I work really hard at it, and I am incredibly mindful of it in my classes.

Well, except, I don't actually agree with it, like whole-heartedly. It's more like, I agree that students should have lots and lots of space, and no time pressure, to be able to learn a concept to a degree to which they are comfortable with it, and fluent. But eventually, with enough practice, they should have enough fluency to be able to work much quicker. Which is to say, an algebra student who is learning about variables for the first time may need to have multiple conversations around how to add like terms, and why it works the way it does. But a calculus student should be able to add those like terms without pause.

I think about this in terms of practicing an instrument. When you first learn a new song, you play it slowly. Sometimes so slowly that you can't even recognize the tune. You pause to repeat certain phrases, to embed the physical movements and the sounds into your brain. You work to understand the music. Then, eventually, with enough practice, you can play through the piece at its intended tempo, which may be 3 or 5 or 20 times as fast as how you started out. The practice induces some fluency.

So, don't we want students to gain that fluency? I think we do, and there's a degree to which fluency can present itself as speed + accuracy. Which, I suspect, is the reasoning behind those dreaded xeroxed 100-problems-in-a-minute tests. To be clear, I would never advocate for those awful tests. I remember the anxiety they gave me in 4th grade, and how close I came to being dropped a level because of them (and I was, by many counts, in particular by my own impeccable memory, Good at Math in the 4th grade). However, I wonder if practicing for speed+accuracy has any place in math education. I think it does, and I am interested in figuring out how in a way that does not compromise the very important notion that the beginning of learning a new concept should not be rushed.

Concept-Based Grading

I'm trying a new (to me) grading scheme in all of my classes this semester. Concept-based grading. The short summary of the scheme is this: traditional grading schemes have grades given per item turned in, and each item may cover 1-to-several concepts. Then the items are categorized, and each category is given some weight. For example, a typical grading breakdown for my courses in the past might look something like

10% Quizzes

10% Homework

60% Exams (4 exams at 15% each)

20% Final Exam

Concept-based grading, on the other hand, has the entire course content broken into individual concepts that need to be mastered. Each concept is tested, frequently, and new scores replace old scores rather than averaging in. Here's Dan Meyer's blog post about it, for more extensive reference.

Brain Plasticity and Mindset in College Math Education

The world of math education is, these days, exciting, vibrant, and varied. I’m constantly finding wonderful new materials to use, new research to share, and new discussions to engage in.

One of my (many) struggles is this: so much of the research, and so many of the materials, are centered around K-12 students. I teach community college. My students are adults, some of them are well beyond their 20’s, and I’m going to go out on a limb and guess that none of them appreciate being treated as if they are 12. However, most of the materials and the research around K-12 math education (including some from middle school, and even elementary school) are relevant to these adult students, so I use them in my classroom. I spend a lot of time re-creating materials, not only to adapt them to my personal styles and curriculum, but often just to remove age branding. This week I’ve been using materials from the youcubed.org Week of iMath, and I didn’t have time to recreate all of the materials, so I used a pencil to scratch out “Grades 5-9” from the logo before making copies.