My Try at Differentiation

A few weeks ago, I had something haven’t had all year: extra time! We had finished up our unit on the Pythagorean theorem and had 3 days before the end of the quarter. Instead of starting something new, I thought I would try to extend our learning with those 3 days when a student in class made this observation: “The Pythagorean theorem only works though if you know two of the sides. What happens if you only know one?” I answered him by saying, “Look at your calculator. You see the buttons ‘sin, cos, tan?’ If I give you one side and an angle,  you can find everything else you want to know about the triangle.” It was this conversation that persuaded me to teach trig with the 3 extra days I had.

I started the first day using Geometer’s Sketchpad to show students that the ratios of the sides of a 30-60-90 will always be the same, no matter how I dilate or translate the triangle. I showed them what each of these ratios were called and then we took off. Some students were confused at first and I assigned them the role of finding my third side with Pythagorean theorem,  once someone in their group had two sides of the triangle. We did this for two days and then used inverse trig functions to find angles on the third day.

Once fourth quarter started, we began a new unit over volume of prisms and didn’t use trig at all that week. We took an interim assessment after a week on volume and I wanted to see how many students actually learned trig. But, since trigonometry isn’t one of the 8th grade CCSS, I didn’t want it to adversely affect the grades of those who didn’t understand it. So I made it an extra credit question on our quiz, asking students to find two sides of a right triangle, given an angle and a side. I ended up with 26 out of 96 students getting the question correct after a week of not doing anything with trig. I was pretty happy with this and thought that, even though 70 out of the 96 didn’t know how to do it, but about 28% of my students were allowed to learn and master a concept beyond what was expected of them. I would love to have extra time to do this every unit and maybe will next year, once I’m more familiar with Common Core. Overall, I was very happy with everyone’s participation during class, even if they didn’t understand the trig. I challenge you to try doing something that you feel is too difficult for your class as well, the results may surprise you.


Two New Ways I’m Using GAFE in Class

A few years ago, I started posting my notes from SMART Notebook on a WordPress blog for students to read if they needed them. I would export them to a PDF and then upload them. Some students would read them, but it always seemed like I was going through the work of putting them up there for about 5 students all year long. This year, my district switched to Google Apps for Education (GAFE), so I started using Blogger. I have a few students in class that have bookmarked the page so they can get to the notes for class very quickly. However, I still felt like I was doing it for just a few students. Different students told me they tried to get to my blog, but were having problems finding everything. So I decided to change things a little bit to make it easier for me and them both.

Google Calendar Instead of a Blog

By using Blogger, I already had to upload my notes to drive in order to link to them in Blogger. So I thought more students would see them if I just added them as an attachment in Google Calendar. I’m also able to attach anything students may need for an assignment in class. For example, I can attach graph paper, or a picture students may need, or a screen capture of the exit ticket. It seems as if more students are using the calendar because they can see what we are doing throughout the week. I also share the link to the calendar with parents so they can see what we are doing or get notes if their child was sick. I also keep my Blogger site going and just embed the calendar at the top of the page. In this way, students who bookmark the page to get the notes can still get them and others can take advantage of the calendar. Here is the link to my Eighth Grade Math page to see what it looks like with the calendar embedded.

Weekly Autocrat Newsletter

During the last two units I have taught, I haven’t given any homework. I’ve used an exit ticket every day as a formative assessment. There are days were students don’t finish the problem or don’t do it correctly. I want them to show me before we take an assessment that they can do it correctly, but I don’t want to have to print out a picture of the triangle for Pythagorean theorem or solid for finding volume. Instead, I started using the mail-merge script, Autocrat, in order to send out a weekly newsletter with a link to all of the week’s exit tickets. Here is a video of how to set it up. Here is a copy of the newsletter I sent out last week to each student. It is a personal letter for each student with links to each exit ticket. They can then email me their answers once they have it completed. Students have preferred this because missing assignments don’t pile up on them and they can usually get me the answers right away.

If you send out a weekly newsletter to parents or students, I would suggest using Autocrat in order to save paper. My own children get all types of paper copies of letters and schedules. We use Skyward in my district so it is very easy to get parent emails. The more paper we save, the more we can help the budget. Also, if you are a parent like me, I prefer electronic copy over hard copy. Overall, I encourage you to try using something new with GAFE. It was easy to do the calendar and Autocrat both. I have also used Doctopus and Goobric this year as well. These two things allow you to assign and collect a document for each student through Doctopus and grade it using Goobric, all without using any paper. My district doesn’t have all of the new add-ons for Sheets or Docs yet, but once they do, I’ll post some more things I’m doing with those.

Why Some People May Not Like Math

When I taught stats, the first day I would ask students which was most likely to kill you in the US: a poisonous snake, a vending machine, or falling out of bed?  Students mostly chose the poisonous snake. Others figured it wouldn’t be the obvious choice of the snake, but they couldn’t decided which of the other two would be more dangerous. It turns out that 7 people die a year from snake bites in the US, vending machines kill 13 people each year and falling out of bed kills 450 people annually. Students couldn’t believe it and some even accused me of lying. I then asked which was more likely to a child: a gun in the house or a swimming pool in the backyard? Again, they were shocked to find that children are 100 times more likely to die from drowning in their pool than be shot by the gun in their house. I use this to introduce the class because I told students how important the study of statistics is because we need mathematics to make sense of everything around us because we usually do a very poor job as humans. As I taught this past week, I started to see this at work in my class and thought about how it’s possible some people may not like mathematics because it defies their logic.

At the beginning of the week, students were asking me all about the probability of a choosing a perfect bracket to win the $1 billion from Warren Buffett and Quicken Loans. I showed them how there are 9,223,372,036,854,775,808 possible brackets. We then did the math to find, if every person in the world could fill out a bracket every 3 minutes, it would take about 7,291 years to complete all the possible brackets. Business Insider then posted an article saying that, if you used some knowledge about the tournament, there were more like 128,000,000,000 possible brackets. At this rate, each person in the world would only have to fill out 17 brackets to cover the more likely possibilities. You are 730 times more likely to win the Powerball jackpot. Some students in class then claimed I was wrong. This couldn’t be. There was no way it was that difficult to have a perfect bracket. The math defied their logic.

As long as we’re talking about Powerball, I’d like to bring up something I heard months ago when the jackpot was over $400 million. While buying a ticket, I heard another person say, “I won’t play now, too many people are playing. I’ll wait until it goes down and not as many people are playing. Then, I’ll have a better chance of winning.” That isn’t true. If they chose the winner by putting every ticket-buyer’s name in a hat and drawing one out, then that man would be correct. I didn’t bother explaining this to him though, it would have defied his logic.

Currently in class we are studying volume and I showed students this video made by Dan Meyer. In the video, he takes two normal 8.5″ x 11″ sheets of  paper and rolls each one into a cylinder. One he rolls vertically, the other horizontally. He then pours popcorn into each one to see which would hold more. When students were asked which held more or if they held the same, almost all students said they would hold the same. Their explanation was that it was the same sheet of paper, which would then result in the same volume. Some even talked about how height and radius would change, depending on which way you rolled it, so the volume wouldn’t change, just the dimensions. We then found the volume of each and students claimed that somehow I was lying to them or had tricked them. One student even said I switched out one of the pieces when they were finding the volume of the other. Even after we did the math, they couldn’t believe that the two had different volumes. The math defied their logic.

My wife and I recently watched “White House Down” and I probably felt the same way students do in my class as I watched it. There are so many things in the movie that defied my logic. In fact, my wife says its hard to watch movies with me because I point out all of the unrealistic flaws in any movie. But, it’s possible that I’m the one that wrong and the movie is logical. I mean, I did just see a book on Bigfoot in my school’s “non-fiction” section.

What Am I Really Doing?

As I gave ISAT tests this week, I had a lot of free time to reflect on conversations I have had during the week. I was fortunate enough to have a great conversation with my principal, Bob Beem, after school Tuesday. My wife has also been having conversations with people about Common Core on Facebook. With all of this going on, one main idea kept coming up: What is the real purpose of my teaching? What am I really doing when I am teaching these different concepts and different strategies? What is the reason parents send their kids to my class?

It seemed to all start earlier this week when my wife was having a conversation with someone she went to school with about Common Core. This parent was upset about the new ways that students are being taught different concepts like multiplication. I can understand this parent’s frustration, especially if they have not been informed about the changes or if the teacher teaching these things really doesn’t have any faith in the new ways. While talking to my wife about this, I asked her the question “Why do our kids go to math class?” I think if you asked parents this, they would say that they want their children to be able to “do” all of the mathematics they should be doing at that grade level. However, I have never been at the store, looked on the shelf and seen a box with “2.99x + y = 20.” But, I do see that milk is on sale for $2.99, I have $20, and I need to decide how many I can buy, including tax. There are many different ways I can get this answer, the important thing in life is getting the answer and feeling confident in it. Although some people may not like the new way multiplication is being done, some students may finally understand it and be able to use it in their lives. At the end of the day, I think all of us can agree that our goal is for students to be able to successfully use mathematics, not just do it.

I believe being able to do mathematics involves recognizing how things are related in the real world and then making a decision and planning how I am going to get to an answer. In real life, the use of mathematics isn’t always posed as a question. We see things in life and then ask ourselves those questions. If we have the ability, we can then use mathematics to come up with the answer to our own questions. For example, one day in class I showed this video.  The video is from 101 questions and was uploaded by the highly talented Andrew Stadel. (He’s a great follow on Twitter, if you are looking for some great math educators.) The video doesn’t ask a question. It shows the blue cups being taller when the stacks are 1 cup tall and the styrofoam cups being taller when the stacks are 20 stacks tall. The video then cuts out and shows the two stacks at the same height. In every class I showed this, kids asked right away, “When are they the same height?” That’s mathematics to me. I gave them the dimensions of the cups and they did the rest. After it was all finished, I then showed them this video, which shows them how many cups are in the stacks when they are the same height. Most student got it correct and were very excited with their success.

These two things brought me back to thinking about standards-based grading again. If I believe that students should be in a math class in order to learn how to use mathematics, what does 83% mean? Does it mean that they can use mathematics correctly 83% of the time? Not usually. What that grade reflects is a student’s ability to answer questions correctly, possibly save their notes, sometimes get their rules sheet signed, and even at times bring in the correct amount of Kleenex boxes. Almost none of these show the ability to use mathematics. Maybe someday we’ll have a better way of evaluating and grading our students than letter grades. I’m thinking it might be sooner, rather than later.

When all is said and done, maybe nothing will change. Maybe everyone else is right and I’m completely wrong. However, I think that students benefit any time their teachers reflect on their teaching and discuss it with other educators. Any time teachers think of what they could do better, students win.