May 3, 2016

Reading and Repetition

Today I had my algebra support block (we run an alternating day block schedule so I see my algebra class every other day for 90 minutes, but half of my algebra class sees me every day for 90 minutes because they also have this support class) and my contained algebra class (they all see me every day for 90 minutes).

Sometimes during the support block we work out of the EDC's Transition to Algebra, which I love. They do a great job of starting with numeric examples and making the patterns very clear. However, they are filled with language. The page is chock full of information (I understand that they are consumable workbooks so they squished lots of information on the page to reduce cost). The problems and hints are conversational, not to mention the actual student conversations mixed in. Sounds great, right? Here's something you probably don't know about my classes - I have many students with substantial language based learning disabilities and a couple students new to learning English (I like the phrase emerging bilinguals except what if English is the student's third language like it is for one of mine?). So this much language is really challenging. However, especially this semester since I'm working with a co-teacher who was in English classes last year, I've taken on the responsibility of supporting their language acquisition while teaching the math.

Monday in support we began exponents in the TTA book. To start, we assigned parts and read out one of the student conversations. I was so pleased how many students wanted to read! It's a huge testament to how much they trust their classmates when students who struggle with reading are willing to read in front of the class. We read it, talked about it, read it again and then made a connection between the reading and their own work. As we discussed I took notes on the things my students said, but then they asked me where to write it down (no spare space on the page, remember?). But, everything we'd written down was in the conversation! So we pulled out the highlighters and kids read the conversation yet again to highlight the key observation we'd made. It's always surprising to me how challenging this is for them. I was always a strong reader and I just cannot imagine going through high school trying to learn content when it's a challenge to locate a key phrase that we've just discussed. Activities like these remind me to slow down, recognize the difficulty and continue pointing out (not to mention recognizing for myself) strategies as we read.

I don't remember who said it, but it's really stuck with me how in math, conciseness is valued. In an essay you read the main idea in the first paragraph, you read more detail and many repetitions of that main idea in the following paragraphs and a recap of the main idea and details in the conclusion. In math we make a definition as dense as possible and that's it. A problem set may contain many repetitions but the language is brief and requires many read throughs. Since hearing that I realized this is exactly what makes a math text book so hard to read and have focused on convincing students that math requires reading many times.

Today we worked on another page in the TTA book. It was all about powers of two. In one question students figured out that if the exponent decreases by one then the value would be divided by two. In the next question students needed to decide what half of 2^50 would look like. All around the room students wrote 2^25. But children! We just talked about that! And then I realized that 1) it's far from intuitive, that's why they included more questions in the book to solidify this idea and 2) the language changed. I went back and we made the connection that "double" and "multiply by two" are the same thing. So then we figured out that "halve" and "divide by two" are the same thing. Then we tried some simpler cases. Then a couple kids changed their hypothesis but most students were far from convinced. Then I wrote out what 2^50 and 2^49 look like. Then I had some more students explain. Then a student was stuck and I had him "phone a friend" and they were silly about it. One friend wasn't helpful. Another friend said "Call me!" The student put him on "speaker phone" to be able to talk and write at the same time. The friend got annoyed how many times he had to repeat himself and my co-teacher said "Now you know what we feel like!" But it was worth the time - first because it's important to play together, and second because hearing something that many times makes it stick! The next question asked students to find half of 2^100 and I was ready to have a debate on that solution but they all got that it was 2^99 on their own!

It's hard to be patient and say something a million times. I already get it. By the time I get to my contained class where everyone has a math disability in addition to other challenges, I've already spent the last 90 minutes explaining this thing. But students need to hear, see and say things many times for it to stick. I need to get them talking to each other as much as I can because I might pull my hair out if I have to repeat something over and over and over, but no matter how many times I've already explained something, hearing a kid explain it to their partner always results in me directing a genuine beaming smile towards the pair followed up with a hear felt "thank you! well done!" after the conversation ends. I love how I can hear myself in student conversations. Instead of telling an answer or even listing a series of steps, they've picked up the questioning and explaining. It's awesome. Sometimes the end of the year is hard, but the hardest part is giving up my wonderfully trained students who are willing to read to the class and take the time to make sure their partner could do the next problem on their own.


  1. I use the TTA series and love it! I think the ladder arrangement of the powers of 2 was really helpful for my students to see that decreasing the power by one was how halving of the number was completed.

    When I introduced the Exponent unit with my students, I used Dan Meyer's idea "If 'blank' is the headache, then 'blank' is the aspirin". I challenged my students to multiply exponents and divide them using their calculator. I told them I could do it faster than the calculator. It drove them crazy that I would have the answer before they could enter it into the calculator. They thought I was cheating, so they then gave me problems. Each time I would be faster. So if multiplying large numbers is the headache, then exponents is the aspirin. Totally sold!

  2. TTA is really great; I would really like to start using it in my program. What you said about how densely-worded math text is really resonated with me and you just gave me a lightbulb moment that I need to start directly helping my students to realize the necessity of reading it multiple times. Even when I reflect on my own math studies, I often have to read something multiple times, or even come back to it later, to really understand what it's saying! Thanks for the post, that was a good read.

    1. We all need to do more sharing about our own experiences doing math. It's really powerful when kids hear that you need to re-read and take a break. I need to talk about that kind of stuff more often.