**Watch this video**. Every time you feel you are confused, just pause and rewind the video and rewatch it. Do this until the video makes sense.

Can't do it can you? It doesn't matter how much you pause and rewind a video, if it doesn't make any sense to you, watching it again isn't going to suddenly change the video so it makes sense.

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The Teaching Channel recently **published four videos** which describe much of the work I do with teams of teachers in a project known as Accessing Algebra Through Inquiry (or a2i for short). One of the primary objects of the a2i project is to build the capacity of school-based teams of teachers working collaboratively to improve their practice and make evidence based choices about their instruction.

Topic:

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PARCC recently released some **sample computer-based test items** for ELA and high school mathematics, so I thought I would check them out since NY state is still officially planning (eventually?) to use the PARCC assessments.

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Words are not ideas, anymore than the picture above is a pipe (it's a picture of a pipe).

When we communicate about ideas we are forced to use words (or gestures or images, which are also not the ideas themselves), and so consequently we are never communicating ideas directly. We communicate about ideas through the medium of language.

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I recorded some **video and the audio from a keynote presentation I gave a couple of weeks ago**. It turns out the video wasn't all that useful, but I did a screencast of my presentation notes, and added the audio from my keynote to it.

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The house my wife and I live in was recently sold, and so we have started looking for another apartment. Our current lease expires in a year and a half, and so we decided that, given how challenging the rental market is in NYC, that we should start looking right away. We also decided, somewhat arbitrarily, that we would attempt to find an apartment in the next six months, if only because we knew we would get sick of looking pretty quickly.

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When I first started tutoring students, I often noticed that they struggled to add fractions. The addition of fractions just did not make sense to them. Part of this is caused by students having a weak understanding of fractions, and part of this is caused by them not understanding why the typical algorithms used to add fractions make sense.

Here is one model that I developed for myself, so that I could understand why addition algorithms for fractions make sense, and then use this model to help students make sense of adding fractions.

**Step 1:**

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The definition of what effective mathematics teaching looks like very much depends on what purpose we assign to teaching mathematics. A classroom where the primary objective is to teach students a specific set of mathematical skills for them to use later will look much different than a classroom where the primary objective is to teach students how to think mathematically, although there is obviously overlap between those two classrooms.

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This diagram represents a problem in education which is, by no means, the ONLY problem in education.

How do we change this paradigm?

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This is part two of a three part series on formative assessment. This post deals with some things you can do between individual lessons based on formative assessment and during a lesson. You can **read part one here**.

**Introduction**

Newsletter:

- A discussion with our Education Minister George Abbott
- Comparison of different learning theories
- Questions about the flipped model of instruction
- Using my iPhone as a wireless microphone for my computer
- Why teach math?
- Testing new Captcha system
- Take nothing for granted
- I tried the Khan Academy
- Do iPads improve mathematics instruction? Maybe
- We are homeschooling our son
- Mathematics and Multimedia blog carnival
- Educational chats on Twitter
- New Math equals trouble, education expert says
- The Death of the Amateur Mathematician
- Profile of a phishing attempt
- Powerful ideas in math
- The Case Against 21st Century Schools
- Why we need to change schools
- Children are not railroad trains
- Tutorial: Converting between different media formats with WinFF
- Definition of Cyber-culture
- Can educational technology save money for schools?
- What is the International Baccalaureate?
- How can Geogebra be used to help students understand and visualize mathematics problems?
- As I was travelling to St. Ives...

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