Author Archives: Brook Lewis
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 their conceptual understanding in this area.
As a highschool teacher, I experienced firsthand the phobia fractions would cause students. They would be able to work problems without a second thought, but throw in a fraction and it became a whole new level of complication. I am sure if you are a teacher reading this, you have experienced the disconnect that is presumed between fractions and whole numbers. It would sometimes feel as though the students didn’t really think fractions were numbers at all. Dr. Les Steffe has proposed that this is due to the way we present fractions to students (Steffe, 2010).
Dr. Steffe calls this his Reorganization Hypothesis. He claims that students can “reorganize” their whole number concepts in order to use them in continuous scenarios. A continuous scenario would be something like a string. It is countable if you choose a unit by which to measure, such as an inch. Then you can begin to overlay your number sequence onto the string and count. This can then turn into fractional understanding when the children also begin to partition items. For instance, sharing a candy bar among five people is a task that allows students to use their number concepts to fit within a whole. They have to use the whole candy bar to make five equal pieces. Steffe’s understanding is that students use their whole number concepts to do this, and that by separating fractional understanding from whole number understanding, we have created problems for students.
So this is what the Coordinating Units team will be exploring this Spring, and I have been reading for over a year now to prepare. If fractions are of interest to you in your classroom, then keep reading this blog, and feel free to write questions and comments. I will be sharing what we learn as we go.
***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
A few posts ago (December 13, 2016 and February 21, 2017), I discussed the importance of skip counting with meaning. If you are teaching particular grade levels, you may have students who skip count to solve problems already. So, how can we tell if skip counting is meaningful to them? Often times, a student will… Continue Reading
In my previous blog, I talked about a composite unit, what it is and how it plays an important role in many different aspects of students’ construction of mathematics. One of these areas is fractions. So how does the student’s ability to take a number as something that is countable affect their understanding of fractions?… Continue Reading