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**

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Part of my current role is to help teachers use formative assessment in their teaching. This has turned out to have some interesting challenges, and has helped me grow tremendously as a teacher.

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Here are seven questions my son asked today.

- Who invented buildings?
- Why don't we slip on salt?
- When you hold your eyes closed does more water get on the eyeballs than just blinking?
- Why do hummingbirds move so fast?
- Why are butterflies so pretty?
- How did we get the name "people"?
- Why do bees hum?

Kids are scientists. My job with my son is to teach how to answer his own questions.

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A few days ago, my wife told my son that he should do some mathematics from a 2nd grade workbook we had, and told him he could choose what he worked on. My son opened up the book to near the end of the workbook and decided to try some 2 digit subtraction exercises.

Here is an example of his work.

Topic:

Newsletter:

- Creating a WiiMote interactive white board at my school for under $50.
- 20 reasons not to use a one to one laptop program in your school (and some solutions)
- For whom are Interactive White boards Interactive?
- What is Edcamp?
- Mathematics education blogs
- Forget the future: Here's the textbook I want now
- Eight Videos to Help Teachers Get Started Using Twitter
- Why educators should blog: A helpful flowchart
- There are no aha moments
- Paper use in schools
- 15 things kids can do instead of homework
- Online Geogebra training
- The difference between instrumental and relational understanding
- What is The Effect of Technology Training for Teachers on Student Achievement?
- Why teach math?
- Using Google forms for a "Choose your own adventure" style story
- Ways to use technology in math class
- A Fundamental Flaw in Math Education
- We are homeschooling our son
- A Restitution Guide to Classroom Management
- The Death of the Amateur Mathematician
- 25 Myths About Homework
- Migrating away from Google Reader
- Free tools for math education
- The Role of Immediacy of Feedback in Student Learning

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