I recently read the Common Core standards for Math for grade 6, which is where the concept of variable appears to be introduced. The standard in question reads: Write, read, and evaluate expressions in which letters stand for numbers. I tweeted this out, and one person responded with this observation: @davidwees in d/dx[f(x)]=mx+b …d, f, […]

## Monthly Archives: October 2013

### Getting started with programming JavaScript

JavaScript is one of the primary web programming languages. It is the language used in Google Apps Scripting, and in HTML5 interactive documents. Chances are pretty good that most of the interactive features that you see in websites were coded in JavaScript. Much of the power of JavaScript comes from its power to manipulate and […]

### So you want to learn to program…

When I was 8, my father gave me my first computer. There were two things I could do on this computer; program or write. I found programming to be much more interesting! So with a little bit of support from my father, and a copy of the Wang BASIC reference manual, I began the long […]

### We are homeschooling our son

My wife and I decided a couple of weeks ago to withdraw our son from our local community school and homeschool him. We realized that the constraints on the school, and the choices made at the school were going to prevent him from getting the exercise, play, and intellectual stimulation he needs to remain healthy […]

### Using technology to facilitate noticing and wondering

Today I observed a teacher using **this tool **built by **Jennifer Silver** to engage her students in mathematical reasoning. It was a powerful reminder to me of the intersection between effective uses of technology to provoke thinking in students, and the pedagogy used to support that student reasoning.

First, the teacher brought up the interactive diagram up on her Smartboard, and then she asked a student to come up to change the slider values. She repeatedly asked students to say what they noticed each time the slider was changed. She took the time to have multiple students clarify what they said, to have their peers restate and respond to each other’s reasoning, and to have students take the time to make mathematical observations. **She engaged students in collaborative mathematical thinking for 30 minutes. **At the end of the class, at least 10 students came up en masse to play with the interactive diagram themselves and continued to ask her questions and make observations. She had to promise them she would email them the link to the diagram so that they could continue to play with it themselves.

The point here is that the technology made the conversation easier. Instead of creating 20 different examples of graphs and seeing what happens as each variable is changed, students were able to visualize the changes, both in the graph representation, and in the formula representation. When asked if they noticed anything after the “Point on the line” slider was changed, one student said they noticed the Intercept-slope form of the equation did not change. Another student responded to him with “that form of the line doesn’t depend on which points you use.”

It was fantastic.

### What does your online assessment actually measure?

What exactly does our assessment measure? I watched my 7 year old son complete an online assessment of his fluency with addition facts last week, and I noticed a few things the assessment measured unintentionally, at least to some degree. It measured his ability to decode the symbols presented (eg. 2 + 10 = __). […]

### Benny’s Conception of Rules and Answers in IPI Mathematics

My colleagues and I have formed a journal study group where we intend to share pieces of research which are interesting, and have some compelling story to tell about understanding research. I’ve chosen Benny’s Conception of Rules and Answers in IPI Mathematics by Stanley Erlwanger. In order to support our discussion of the research, I’ve […]

### Ten rules for living

Life isn’t fair. Do something about it. The world may not care about your self-esteem, but having a healthy self-image is more likely to lead to positive relationships with the people to whom you are close and having healthy relationships is the key to having a happy life. Don’t focus on the money. […]

### Hacking the webinar format

I’ve recently been tinkering with the format of an online webinar in an effort to make what happens in a webinar more engaging and "minds-on" for teachers. The problem, as I see it, for most webinars is that the presenter spends 99% of the time talking during the webinar, while the participants, if they are […]

### Explaining subtracting negative numbers to my wife

Tonight my wife asked me why 4 – (-3) = 7. Apparently my son had "explained" it to her earlier tonight, but she hadn’t really understood his explanation. So I gave it a shot. First I tried the same explanation that seemed to work for my son when he asked me what 4 – (-3) […]