Emma Gargroetzi posts an astounding rebuttal to Barbara Oakley’s New York Times op-ed encouraging drill-based math instruction. Gargroetzi highlights two valid points from Oakley and then takes a blowtorch to the rest of them.

I haven’t been able to stop thinking about her last sentence since I read it yesterday.

Anyone who teaches children that they need to silently comply through painful experiences before they will be allowed to let their brilliance shine has no intention of ever allowing that brilliance to shine, and will not be able to see it when it does.

I’m perhaps more hesitant than Gagroetzi to judge *intent*. Lots of teachers were, themselves, victimized by drill-based instruction as students and may lack an *imagination* for anything different. But I’m *absolutely* convinced that a) we act ourselves into belief rather than believing our way into acting, and b) actions and beliefs will accumulate over a career like rust and either inhibit or enhance our potential as teachers.

A math program that endorses drills and pain as the *foundational* element of math instruction (rather than a *supporting* element) and as a *prerequisite* for creative mathematical thought (rather than a *co-requisite*) inhibits the student and the teacher *both*, diminishing the student’s interest in *producing* that creativity and the teacher’s ability to *notice* it.

Teachers need to disrupt the harmful messages their students have internalized about mathematics. But we also need to disrupt the harmful messages that *teachers* have internalized as well.

What experiences can disrupt the harmful messages *teachers* have internalized about math instruction? Name some in the comments. I’ll add my own suggestions later tomorrow.

**2018 Aug 25**. I added my own suggestion here.

**Featured Comments**

Faye calls out the process of learning content and pedagogy simultaneously:

Many mathematics teachers do not have the mathematics content knowledge that they need themselves. The Greater Birmingham Mathematics Partnership has found that teaching teachers mathematics using inquiry based instruction results in increased content knowledge for the teachers and a change in their beliefs about how and what all children can learn, i.e., acting themselves into changed beliefs.

Math teachers circles (www.mathteacherscircle.org/). They provide the space for math teachers to be mathematicians (in the same way a lot of the arts teachers I know are still practicing artists).

Another Chris echoes:

It wasnâ€™t until I was asked to think about mathematical tasks and ideas for my own understanding that I could ask the same of my students. And then, it was unavoidableâ€¦there was no going back.

William Thill elaborates:

But when I can tap into the emotional and intellectual highs that emerge from playing with cherished colleagues, I am more likely to â€œset the buffetâ€ for my students with more open-ended exploration times.

… watching yourself teach on video is a great experience to disrupt harmful messages about math instruction, like talking too much as the teacher. I know that many math teachers feel the need to provide the most perfect, refined, rehearsed explanation so that students can

seewhat they are supposed to see in the way they are supposed to see it. I certainly felt (at time still feel?) that way. That practice diminishes the studentsâ€™ roles of sense-making on their own. But watching a video of myself teaching was one of the most humbling things Iâ€™ve done and it changed my practice so much. I also watched them among other trusted teachers from whom I learned so much. Having time to stop a video, talk about, reflect on it, etc is very powerful. Even seemingly simple things like wait time and teacher movement/positioning can look very different than what we imagine we look like.

Alexandra Martinez calls out the limitation of reading narratives and watching videos of innovative teaching:

I think the most powerful way to disrupt teacherâ€™s own experiences and expectations is new creative experiences with their own students. The evidence and reflection can support teachers in seeing what is possible. If we ask teachers to imagine what is possible through narrative, they wonâ€™t always believe it. But when they see their own students speaking and thinking as mathematicians, that evidence disrupts their established belief systems. So Iâ€™d say observations, modeling, Coteaching, pushing in, PLC planning with lesson study can all potentially do this.

Be sure, also, to check into Chris Heddles’ a/k/a Third Chris’s dissent:

Iâ€™m going to go against the grain and admit that I use drill as a prerequisite (or at least an opening activity) with many of my students.