Monthly Archives: August 2012

Hard Enough Problems

If you don’t make mistakes, you aren’t working on hard enough problems. — Frank Wiczek

Found at Hard Enough Problems

Blogger Initiation Week 2: Working with Scribd

One of our assignments is to upload a document to Scribd and embed it on our blog.  So here we go…

One year I had each class (they are grouped into Houses) create their own review sheets for quizzes, tests, etc.  I created a google doc that anyone could edit.  I sent them the link and they produced:

I don’t know if it helped anyone’s grade, but I think it helped build community within each class.

Update: Embedding Scribd documents is pretty cool.  And pay no attention to errors on the summary.

Rare Political Post: Smog, Math, and Regulations

Los Angeles has a smog problem. In L.A. we love our cars. Gasoline and air go in one end and several different gases (and other stuff) come out the other.  There are the innocuous products of H2O and CO2. (More on my thoughts on CO2 in a future post.) Then there are the immediately harmful products: CO, NOx, VOCs, particulates, hydrocarbons and others.

Volatile Organic Compounds (VOCs) react with nitrous oxides (NOx) to form ozone which leads to smog. We’ve been measuring the smog since at least 1976. The following graph (from the Air Quality Management District) shows two variables over time.

The bar graph shows how many days we exceeded Federal Health Standard levels. In other words, how many days the 8 hour average was greater than 75 ppb (parts per billion). This is the least interesting variable. A day with 76 ppb is counted the same as a day with 300 ppb. So two similar bars could have huge differences in the actual amount of smog.

The connected dots show an average maximum over 8 hours. This seems much more informative. It goes from a high of 321 ppb in 1978 to a low of 123 ppb in 2010 a decrease of 62%. This is a pretty dramatic decline especially considering the vehicle miles traveled (nationwide) increased by 171% between 1970 and 2004. (See long boring pdf.)

So what is my point?

On Topic Rant

The original article I read said:

Peak levels of ozone were 143 parts per billion in 2010, only marginally down from 710 ppb in 1966.

Going from 710 ppb to 143 ppb is NOT a marginal decrease. It is a decrease of 80%! And considering there are almost 3 times the miles being driven, this is an amazing accomplishment. I was really surprised to see this statement in the New Scientist.

This is another reason why students and citizens need to understand math and algebra: So they can apply critical thinking to news reports and not just accept what someone, who may have an agenda, says. (One of the sources for this article was the Air Quality Management District. The AQMD might have an incentive to emphasize that smog is still a problem, which it is. It is just a smaller problem.)

Off Topic Rant

Right now there is a feeling among many voters that “government programs are evil and must be abolished.” Some government programs probably are. But they need to be evaluated independently, instead of voting no, no, no on every proposal that comes along. We should look at some objective, measurable criteria and ask, is this good for society.

It is a pain in the @** to get a smog check. It is even worse when I have to get repairs. But the laws and the bureaucracies (the AQMD and DMV) that enforce them have reduced smog by 80% in 44 years. This has saved lives and improved the health and quality of life for millions of people.

Rant over… I really should be getting ready for school.


Several veteran bloggers from the math twitter-blogosphere are running a Math Blogger Initiation.  They want to help new bloggers get started by writing posts, getting to know other bloggers, etc.  I thought I would sign up to give myself some incentive to keep blogging.  Each week they send out weekly assignments.

The first assignment is due at 11:59 pm on Tuesday August 21…

Holy crap, that’s today!  I managed to procrastinate my very first assignment which is due in 3 hours and 40 minutes!

I should probably read the assignment.

[time passes]

I’m going to respond to the question:

Talk about one or two specific things you plan on doing differently this year… and how specifically you are going to implement them/get the buy-in. Why do you want to do these things?  (If you are a new teacher, what are two specific things you plan on doing this year?)


I mostly want to implement Dan Meyer’s idea of 3 Act Math.  The main idea is to present math as a story.  You ask a question based on some interesting video, image, sound, etc.  You ask students to make high and low guesses.  This is Act 1.

In Act 2 students solve the problem and answer the question.  Instead of showing how to do the problem, you let them struggle.  I try to answer questions with questions.

In Act 3, the finale, you show the results of the problem.  You can even have sequels which extend the idea to other situations.

I think the idea is brilliant.  It helps students see the connections between everyday questions and the math they can use to answer them.  Students get frustrated because most of the everyday questions they encounter don’t require math to answer.  3 Act Math helps them see that some of the questions they encounter can be answered with mathematical reasoning.  I think getting student buy in will be the easy part.  The hard part will be resisting the urge to help them solve the problem.

BTW Dan has helpfully created a list of 3 Act Math lessons which includes all relevant videos, questions, etc.


The other big thing I plan on doing is SBG or standards based grading which I am also stealing from Dan Meyer and others.  (I promise I’ll post something original, eventually.)

I think the buy-in for SBG will also be easy but the execution will be more difficult.  I have to narrow down the Algebra 2 standards and then find good problems for each standard.

I should probably start….

Yeah, but I have 2 weeks before school starts!  🙂

Procrastination Poster is only $15.95 at

Testing x62

I’ve been trying to get embedded GeoGebra graphs to work. I don’t know if I actually tried 62 different things but it felt like it. And it almost works…

I got it to work on blogger.  But I don’t really like blogger so I haven’t given up on wordpress.  There is one more thing to try: use the internet at school which isn’t as slow as mine…

So next week will continue with test #63.

(I wanted to explain in case anyone has noticed my content-less posts.)

When will we ever use this?

Student:  When am I ever going to use this?
Hedman: [mentions a gazillion real life uses]
Student:  But those don’t apply to me!
Hedman: [bangs head against the wall]