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?

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**I was not born a technology person. **

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**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.

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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.

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

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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.

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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.

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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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