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]
Last week I attended a workshop on the Common Core State Standards. Some of the good things about the workshop:
Designed specifically for math teachers
I don’t know how many workshops I’ve attended which were taught by, and designed for, History/English teachers. They always say, “And this concept also applies to math teachers.” The concept might but the examples usually don’t. The attendees were also math teachers. It was good to discuss real life classroom issues with real life math teachers.
Demonstrated some great math tasks
Common core has a big emphasis on problem solving. The idea is to give students open ended problems which have more than one solution pathway. They showed us a variety of these math tasks and modeled how to use them in the classroom. (It was interesting to watch math teachers pounce on these type of problems. We also seem to have a competitive streak. Everyone wanted to finish first and, of course, get the right answer.)
Some great online resources
We also got a list of some great online resources including professional development modules. (I will eventually post the best links. The list is rather long.)
The workshop was also frustrating in some ways. (Note: none of these are the fault of the presenters. They did a great job.)
There are still a lot of things we don’t know. What will the CA state frameworks look like? What will the courses and textbooks look like? Will we still have the CA High School Exit Exam? How will the textbooks be paid for? How will the required computers be paid for? etc. The answers to these questions depend on the CA State Legislature, the CA Department of Education, the UC Regents, and our local districts.
The websites I mentioned above have a lot of resources, but they are scattered all over the internet. (There are a number of math teachers starting to organize them so this is probably a temporary problem.) They also had a list of about 50 different websites without much information about why I should visit them. One example is Utah Resources. I’m sure it has some great stuff but why should I visit it. No one has time to visit all 50 pages.
Too many standards
I was going to write a whole blog post on this problem but I’ll let the following slideshow speak for itself. (Each one of these lists was mentioned at the workshop. How many different ways can we say the same thing? Give me a list of less than 6 process standards and then let me do my job.)
Last spring I attended my first common core workshop and wrote the following:
Common Core Curriculum
People don’t like change. There seems to be a lot of angst among teachers about the implementation of the Common Core Standards.
Some see it as a continued move towards useless high-stakes testing. Others see it as another annoying thing teachers have to deal with.
This year I went to an seminar thingy where we learned more about the standards. Teachers came from all over LA county. Some of the details contribute to the overall angst. The standards will be tested during the 2014-15 school year. Textbooks and other materials will be available in 2016. No I’m not kidding.
(According to the presenters. I’m not sure how accurate that is since I’ve already found quite a few materials online. Besides by 2016 textbooks will be obsolete. Whether we still use them is a different matter….)
A lot of questions went unanswered: Will we still have the STAR tests? What about the High School Exit Exam? The answers depend on legislation which hasn’t been passed by our not-at-all-disfunctional California legislature.
I’m actually looking forward to the changes.
1. Process Standards: The math standards are more aligned with the NCTM standards and include 8 process standards which emphasize a problem based approach. These standards emphasize the process of problem solving not just learning content. I admit students may not ever need to understand hyperbolas. But the process of learning about hyperbolas has always been valuable. And now it will be emphasized.
2. Computer Adaptive Testing: The inevitable tests will be done on the computer. As students get questions correct the questions get harder. When they miss questions they get easier. The advantage is fewer questions are needed to figure out what the student knows. Another advantage is that it identifies what the student knows, not just what they don’t know.
3. In high school, only juniors have to take the state mandated tests. This should reduce the angst among 9th and 10th grade teachers. There will be tests available for these grades. But it looks like the data will be mostly used to help teachers.
4. All juniors will take the same test. This really helps at our school…
(Thoughts on this years workshop coming soon.)
I first saw this a few years ago at Shodor Interactivate. I think it is a good way to start thinking about functions. My favorite part is having students make up stories for each graph.
This is the first time I’ve put it into a Google Doc presentation. Feel free to copy and improve. (Right now it is just an introduction. When I have more time I’ll actually put in the brief notes on functions.)
See update below…
I’m not sure if you can make a copy from the embedded version but you should be able to make a copy from this.
I should probably elaborate on how I use this. I show the class a graph and ask 3 questions:
1) Is the graph possible or not?
2) If it is not possible, how could you change it to make it possible?
3) Make up a story that goes with the graph.
I give students time to discuss the questions with their partner and then I call on random students to answer each question. Since some graphs have multiple interpretations, I can ask different students the same questions.
It leads to some interesting discussions. The first graph seems to imply time travel. And I can ask how fast the person in going back in time. Is it a jump back or is it just moving back at the same rate we’re moving forward? Another graph seems to show teleportation.
At the end I show all of the graphs, I remind students which ones were possible and I ask them to come up with 3 things that all of the possible graphs have in common. This, sometimes, leads into the idea that a single x can’t have more than one y. If it doesn’t come up I remind them of the “vertical line test” and we talk about functions.
I do point out that “Is it possible?” and “Is it a function?” are NOT the same question. After all not all functions are possible. And impossible graphs still might be functions. (Is that saying the same thing?)
Anyway, my favorite part is when students make up stories to go with each graph. This year the stories seemed to mostly involve the death of a character… or food…
Thanks for the mention Dan.
When Dan Bowdoin updates his list of assignments, it automatically updates the embedded file on his class blog.
So lets see if I can embed on wordpress. (It looks like it uses iframes and I’m not sure if wordpress allows that….)
Off to create some class blogs!
I didn’t mean to post our actual assignments. So I’ve replaced the original with a generic template.
Also, if you want to make it wider you can adjust the code where it says width = “500” Just experiment with different numbers…
If you don’t make mistakes, you aren’t working on hard enough problems. — Frank Wiczek
Found at Hard Enough Problems
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.
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.
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 despair.com
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.)
Student: When am I ever going to use this?