That’s exactly what no one at the national level really understands, and if they do, it’s discouraged.

I’m struck by how at odds her thought process is (a process I’ve gone through myself many times) with the national discourse on teaching math. Which textbook? How much technology?

Rarely do you see a discussion of the typical life of a teacher in an at-risk community, where we struggle to teach content at something approximating the course title while moving the needle for the many kids who don’t have the skills for the course title.

They talk about technology engaging students, or whether or not discovery curriculum will help students more than a more “traditional” textbook, or whether we need teachers with more skills or more diversity. Reality is about teaching rational expressions when a lot of your students add one half and one fifth to get two sevenths, or, happier story, can do fractions so long as there aren’t any of those pesky letters. Or teaching exponential functions when none of your students understand percentages. I recently wrote about a little discovery activity I did (https://educationrealist.wordpress.com/2017/11/23/teaching-with-indirection/) and why it wouldn’t have helped to have more technology and certainly wouldn’t have been possible with a textbook. I was trying to help my students become aware of the unpredictability of exploration by (paradoxically) giving them seemingly random instructions that seemed pretty logical. I had to plan the activity carefully because I had both very high achieving and motivated as well as extremely low-motivated, relatively low ability students. How do I keep the timing and discussion reasoanable for the range?

This is very much related to your last post. That is, we are dealing with seniors in high school, in pre-calc, who aren’t comfortable with fractions. Then they are going off to college, where they originally were put in remedial math. Now some state university systems are declaring sure, put kids who don’t know fractions into precalc, so we can admit them, but we’ll be unsurprised when they can’t do fractions and put them in middle school math. For credit.

And so then I wonder: we don’t see teachers discussing these challenge in stats. Does that mean stats is easier, or that teachers haven’t even begun to struggle with teaching unprepared students stats? I am really skeptical that they don’t exist. Make stats universal and see what happens.

“you get when you spend thousands of hours in math classes, reflect on those observations, write about them, talk with other people about them, and then use them to inform what you do in another math class.”

This is why I mentor, both officially and unofficially.

Good post on her part, good catch on yours.

https://www.suny.edu/masterteacher/about/domains/

Here are some pipe dream methods for developing teachers’ capacity in these areas:

1. Spend lots of time teaching in a wide variety of grade levels. This variety will not only expose you to content as it develops over the years, but also to the different needs of students of different age levels.

2. Spend lots of time writing your own learning materials from scratch. The process of crafting a learning experience from the ground up forces you to consider elements from all three of the domains in excruciating detail.

3. Spend lots of time teaching with a wide variety of other teachers. Watching other teachers teach is extremely informative. Picking up on and mimicking things you actually watch another teacher do well live and in-person is a fast track toward improvement.

The above experiences are not always easy to have, especially in large amounts, given teachers’ schedules and job requirements. But the more the better. Keep looking for opportunities.