David Wees's blog

What do mathematics teachers need to know?

I've been thinking a lot recently about what knowledge is needed by mathematics teachers in order to be excellent teachers. It is clear to me that teachers of mathematics must know the mathematics they are to teach, but what else do they need to know?

Different types of knowledge

I was not born to teach

I was not born a technology person. 

Sharing individualized comments with students with Autocrat

Much of the research on formative assessment suggests that grades are not effective as feedback because they do not provide students with actionable information they can use to move their learning forward. Comments and questions are much more useful to students when grades are not included.

Formative Assessment Responses

Formative assessment means more than just giving a quiz or an exit ticket. An assessment is only formative if the teacher (or her students) respond to the information gathered.

However coming up with an appropriate response is typically hard to do. After all, the most common finding in formative assessment is that a significant, but perhaps minority, group of students still do not understand a concept, after the teacher gave her best shot at helping students understand. No teachers save their best strategy for teaching a topic until later.

Two different approaches to teaching

Here's an approach to teaching about the relationships between the different forms of the equation of a line that is based on constructivism.

Magdalene Lampert on Ambitious Math Teaching

This is a video of Magdalene Lampert taking about Ambitious Math Teaching. I'm sharing it mostly so I don't forget where it is.

This Kind of Teaching

I read an important passage in Elizabeth Green's book "How to Build a Better Teacher" and decided that I had missed something important when reading about Magdalene Lampert's teaching. Below is a summary of some of the important features of her teaching as I see them. The first tweet is the thing that I had misinterpreted as students talking to justify their reasoning, which is similar but not exactly the same as students talking to prove their reasoning is correct.

A catalog of mathematics education resources

I'm tired of having to search all over the place to find the-link-to-that-mathematics-resource-I-really-want-now-and-bookmarked-a-year-ago and so I created a spreadsheet to keep track of the various mathematics resources as I learn about them. Yes, I know I could have done this with Diigo or Delicious, but I prefer the portability and simplicity of a spreadsheet.


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