Because I am a tiny bit obsessed, I commandeered my colleague’s computer and 2nd grade daughter, E, and let her play DreamBox for about 45 minutes.
Once again, I am very impressed by the depth and breadth of the activities available. For example, there are quick image activities just like for Pre-K, but instead of five circles, there are multiples of ten beads shown on a 100-bead rekenrek. E wanted to count by fives, but kept running out of time. After a couple of missed questions she switched to a count-by-tens strategy and blew through the lesson. It was really fun to watch a kid come up with a more efficient strategy, simply based on a well-designed activity.
I had shown my colleague, Meredith, the videos of J, so she asked me to start filming E. I got a fantastic 90 second clip of her next activity.
The goal of this game is to make the same number a different way. In this case you were supposed to use the entire top row and as many additional beads from the bottom row. E has been getting through the lesson pretty easily when this happens:
Ok, so first she shows her awesome strategy for adding 8, which is to add 10 and count back by 2. You can hear her say “two less than 18” before she counts down to 16.
E used this strategy whenever the second addend was 7, 8, or 9. I have no idea what the standards look like for addition strategies, so I don’t know if this is explicitly taught, or something E came up with on her own. Either way, I loved the strategy.
So she uses it correctly on this problem, but when she goes to build her answer, that 17 that she said out loud gets stuck in her head and she builds the wrong answer. At this point, Meredith starts waving at me to stop recording and I swat her hand away because I AM CAPTURING AWESOMENESS.
DreamBox says “Something is not quite right” but doesn’t specify the exact problem. E has to look back at her work and find her error, which she does. No adult needed to intervene in order for E to catch her error.
Let’s be clear: E knows how to count to 16 and build it in a different way. But she isn’t fluent yet. This is the sort of mistake that happens a lot when a child is becoming fluent with math. And it’s a vital part of the process. Notice how much more quickly she added 8+8 the second time. She is deepening these grooves in her mind as she practices problems that are within her comfort zone but not easy for her.
Then comes the second bit of awesomeness: Open number sentences! She has to represent what she did in an equation. I love this equation because it has a full expression on either side of the equals sign. So already, in second grade, E is learning that the equals sign represents equivalence, not “where the answer goes.” DreamBox even gives her the option of placing 16 in her answer, but she knows by this point in the game that the first number needs to represent the top row and the second number needs to represent the bottom row. Beautiful.
So E does some more activities, like one where she has to add two numbers, except one is expressed as a numeral and the other as a series of dots. Cool stuff.
Then we get to this activity, where I captured yet another AWESOME bit of student thinking.
E has to build her 100-bead rekenrek to match the one in the top left corner. She then has to find the numeral that matches the two-digit number she built.
E starts by counting rows, but she uses her count-by-fives strategy that I saw her use in an earlier activity. Except now she’s counting entire rows by fives. She realizes her mistake partway through and corrects herself, going back to count by tens.
Then she makes that exact same mistake five more times in a row. On every subsequent problem, she counts rows by fives before switching to counting by tens. On the fourth problem, she only catches her mistake when she sees that 25 isn’t available to click. Her mom, Meredith, is losing her mind in the background but doesn’t say anything because she knows that if you want your kid to learn sometimes you just have to shut up and let them make mistakes.
I thought, at the time, that she got the strategy right on the last problem, but watching the video I see that she never fully corrected this mistake. But if I were E’s dad or teacher, I wouldn’t mind one bit.
As I mentioned at the top, E just started using counting-by-tens as a strategy on a previous activity. It’s a new strategy, and one she’s less comfortable with than her count-by-fives strategy. So she’s trying to become fluent with her new idea but her old one keeps getting in the way. She’s regressing a bit in her counting as she tries to upgrade her strategy. Which is exactly what she should be doing.
Every time I try something new in my classroom, I become a somewhat worse teacher in the short term. When a golfer tries to fix her swing, she gets worse at golf while she acclimates to the new motion. I have no doubt that E will become fluent at counting by tens. But she’s probably going to keep making mistakes for a while. And that’s fine.
I am so glad I caught that moment because it’s a great reminder to me as a teacher that students don’t automatically incorporate new information or correct their own misconceptions. Even if they can catch themselves, they are still prone to error as they build fluency. But as long as I can give them the time and space needed to become fluent. they will be fine.
After this afternoon of watching E play, I am even more convinced than I was last weekend of the value of this program. E is talking the way I want my students to talk and thinking the way I want my students to think. Not only that, after 45 minutes she turned to her mom and said "Can we play this some more when we get home?"
When my trial runs out, I am signing our family up.