Author Archives: Brook Lewis
Currently, I am in the midst of raising a 16-year-old who has been learning to drive. Recently, I was reminded of what it feels like to do something new while I was doing a math demo lesson in a classroom and how circumstances can bring us back to those early behaviors.
Here in the central valley of California, the fog can get really bad. It can make even seasoned drivers mimic the nervousness I saw in my daughter when she first began to get behind the wheel. All of a sudden instead of driving on autopilot, fog can make you slow to a crawl, hands tightly on the wheel, unsure of your surroundings, behaving like a beginner.
So how does math relate to driving in the fog?
I was reminded of a common phenomenon we have seen as we have been researching how children learn math. When we present a situation to a student that is just outside of what they have already learned, they will often resort to less sophisticated behaviors to tackle the unfamiliar problem.
Let me give you an example.
A particular student I was working with was demonstrating that her way to add two numbers was to count on from the first addend. All of the problems I presented to her so far had contained a second addend within 10 (therefore she could use one set of hands to track her second addend as she counted on). Next, I presented her with a problem where the second addend was 11. She immediately said she didn’t have enough fingers. I worked with her to count 11 fingers, and she began to pull her fingers back after she had counted 10 and then reuse them. So she worked out a finger pattern for 11 that could be useful as she tried to solve this unfamiliar problem. Her next move was to use her new finger pattern for 11 as she counted on, or so I thought. But what she did was start counting all (started counting from one until she reached the first addend and then began to use her fingers to track 11 more counts). Something about the newness of this situation may have put her in a fog so to speak. She needed to revert to counting all to achieve her goal. She demonstrated less sophisticated behavior, while she tried something new.
What is even more interesting is that after counting all for a few problems where the second addend was beyond ten, she began to count on even with the larger second addend. I wonder if she would have made this growth if I had interrupted her counting all method, and expected her to count on? I may have done that in the past, believing that she had the ability to count on, so why shouldn’t I expect it of her? But I think differently now. Now I think of how I revert to beginner behavior when it gets a little foggy, and that enables me to drive in the fog.
Maybe for students, it is similar as they approach new math territory. Do you ever see your students go back to less sophisticated behaviors as they work through a new and unfamiliar problem? Please share.
This blog is the fifth part of a multi-part series titled “Creating Centers in the Classroom.” If you’ve missed the previous installments, you can read part 1 HERE, part 2 HERE, part 3 HERE, and part 4 HERE. Through our experiences with children here at the AIMS Center, based on the research of Dr. Les… Continue Reading
As we (AIMS Research Associates) have been working in classrooms, we have worked with centers of four to six students per group. In classes of 25 to 35 students, this has allowed us to become familiar with the mathematics of our students by seeing behavior up close as we present math tasks. I thought I… Continue Reading
It should be no surprise that, after working at AIMS for nearly two years, my co-workers still have the ability to inspire deeper learning in me. One of the things that the research and working with children have taught me is that their counting is very ordinal rather than cardinal at the beginning of their… Continue Reading
I want to tell you about a boy that we call Greg. If you’re a teacher, you’ve likely had a Greg in your class before. He’s the one that fascinates you because he thinks so deeply, is so curious, and seems to already know everything you’re trying to “teach” him. He’s also the one that… Continue Reading
If you read the previous posts from the Coordinating Units team here at AIMS, you likely know that we are studying how children learn about fractions. Earlier this week I realized that I almost missed something amazing and encouraging about how much our students are actually learning. The tasks we are using with them are… Continue Reading
The team I work with at AIMS has begun working with students on fractional understanding and it has been an interesting couple of weeks. We are seeing the students have opportunities to learn things we never intended but still fit right in with expectations in elementary classrooms. Personally, I have discovered that when we develop… Continue Reading
Every once in a while, something will happen at work that makes me miss the classroom and the kids that I taught. It’s like a craving at times, but today I feel more like the athlete on the bench that wants a shot at winning the game. Here I am on the sidelines, wanting to… Continue Reading
As the Fall semester comes to a close, we are preparing for Spring at our school sites. Next on the list for our team is fractions. I am so excited to begin working with students to understand how they think about fractions and what we as teachers can do to give them opportunities to increase… Continue Reading
***This is the final installment of a series. Click the links to go back and read part 1, part 2, part 3, part 4, part 5, and part 6*** For the final blog post in this series, I wanted to address one of the questions that was asked at the October colloquium regarding ways to… Continue Reading