Author Archives: Brook Lewis
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 tasks designed to engage the students with mathematics rather than telling them about mathematics, they learn so much more than we intended.
The task we have been working with uses strips of paper that we pretend are candy bars to be shared among a certain number of people. The students are asked to find the size of one person’s share. This will then lead to counting using fractional language and begin developing the concept of parts out of a whole. Sharing tasks help students begin thinking about fractional meaning because they are familiar with sharing in their day-to-day activities. When they are asked to share, it initiates a need for the pieces to be equal. The next step is to use up the whole candy bar with the pieces. We didn’t anticipate this would be a struggle for children, but the students in the initial stage of this development did struggle to think about same size pieces while also trying to “exhaust the whole” candy bar. I will be writing more in future blog posts about the task, and what we are doing in particular, as well as what the students end up learning regarding fractions. For now, though, I want to talk about what they are learning that we didn’t intend.
The first struggle I had with this task as a teacher was the terminology. Phrases like too big, too small, or just right. The students would make a guess at the correct size of one person’s piece and then have to prove if it was the right size or not. They would get three tries in all, which required them to think about whether the guesses in their first and second try were too small or too big. Another challenge involved thinking about what to do with the next piece if they had made their piece too small initially. After only two visits with the students, they are now able to think about the relationships between the pieces, the results, and next steps with relative ease. We didn’t intend for this to be an area of growth with the task but the students struggled their way to understanding these things as they approached the task.
The students also were highly engaged in attending to the precision of their pieces and proving their piece was appropriate. This allowed them to learn about estimation and measurement, as well as Common Core Mathematical Practices. What started as a fraction task turned into a rich experience from which the students were able to develop multiple new understandings.
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
***This is part 3 of a series. Click the links to go back and read part 1 and part 2.*** In last week’s post, David Pearce described a modification of the Towers Task in which the students are asked to build two sets of towers and combine them. For example, the student may be asked… Continue Reading
I wrote a blog post at the beginning of the school year talking about our plans for research this semester. I’ve been reflecting on our project and the progress we have made so far, and I thought I would share a few of those reflections with you. As I mentioned previously, we have been working… Continue Reading
As an instructional coach, I would travel from school to school working with different teachers every week. While I would visit the same sites repeatedly, I would use my navigation system to find them initially. After a couple of months though, I noticed that I still needed directions to get to some of the same… Continue Reading
ZAC or Zone of Actual Construction: what the student will be able to accomplish or solve unassisted. ZPC or Zone of Potential Construction: the range determined by the modifications of a concept a student might make in, or as a result of, interactive communication in a mathematical environment. This year we are excited to be… Continue Reading
Now that the school year has ended, our research team has been gathering our data from time spent working with students and analyzing it to answer the question: “what have you learned this year?” More importantly, I wanted to figure out what I have learned that will actually enable us to help kids. After completing… Continue Reading
Two experiences this month have opened my eyes to the value of the research we are learning about at the AIMS Center. One involves my 5th grade daughter Neva, and the other was a conversation with a second grade student I have been working with. Neva says she doesn’t like math, but she has been… Continue Reading