Dealing with abstract thinking
St. Joseph's School | 5th Grade | Math, Science | Present: 24
students, teacher and myself | 1.5 hours field experience including
reflection time for each of Math and Science
Math
This week the class is working on fractions, the concept of equivalency of fractions and simplest form.
The biggest lesson I took away is that fractions are a hard, hard concept. To begin with, there is the idea of parts, which is easy to grasp but then there is this funky symbolic notation to deal with that makes little sense when just thrown at you. And, then there is the idea that multiplying a fraction makes it smaller. This is boggling. One insight I had was that fractions are all expressions in relation to the whole — 1/1 but that we don't emphasize this idea when dealing with pairs of fractions that are not the whole. I am not yet able to completely grasp the idea of what it might even mean to do this.
I was kicking myself for not being there when the teacher introduced the concept of fractions. How might one even begin to talk about fractions? What makes fractions meaningful to the life of a student? We all get the "when you want to share something with your friend" story but it is a story and just that. Really when you want to share, you kind of split something but you don't feel a need or care to compute for it. I am still struggling with this idea.
The students worked with Fraction bars which I found meaningful having once created fraction bars myself in an attempt to explain fractions to a student.
The class is split in its level of understanding of fractions. Some students have grasped the concept at its abstract level and can work with fractions. Others are still struggling with the concept and need manipulatives to work on fractions. The teacher handled this split skillfully. She talked to the students about all learning to walk at different times and feeling readiness for various things at different times. So too with fractions. With the stage set, she had the two groups work on slightly different problem sets with different instructional methodologies in use.
The group that is struggling with fractions worked as partners on a worksheet using fraction bars. Those that got fractions worked on a different problem sheet and did not use fraction bars. I was the lifeline for both groups, helping out as needed.
One student approached me saying, "I did all these but I don't know how". I love this! This child is able to work on fractions but cannot explain the concept. This either means he understands it so deeply, he doesn't know how he does. Or that he gets the mechanics but doesn't get the concept. In working with him, it became clear that he just gets fractions — he can see them and gets them but cannot explain how he does. I helped him think about how he might be thinking about it by offering examples of how I think about fractions. In hindsight, I should have asked him self-reflective questions that would help him uncover his thinking, not in relation to my ways of thinking. This is hard to do. I need to work on this.
Science
After working on Math, the group turned to work on Science. They are learning about water and the water cycle. They have studied the cycle and the teacher has tried to teach them the harder concepts (like condensation) through a variety of hands-on experiments. On this day, they were writing their story of a water molecule. They had worked on the story at home making sure to cover all the steps of the water cycle in their stories. Now it was time to put their stories on a storyboard. That is what they worked on.
The teacher spoke to me about the condensation experiments. She told me about how right in the middle of fifth grade most students start grappling with more abstract thinking while others are still in the phase of being literal. Right around Spring when she does the water cycle she has a group of students that just cannot believe that water exists in our air. They just don't want to believe condensation. So, she illustrates it to them in a variety of different ways — letting a glass of colored cold water sit until water droplets collect on the outside, creating rain and so on. She says, she still doesn't get all the students on board. I am intrigued by this.
Closing remark
I closed the day wondering about the introduction of abstract concepts in a child's world. Children can be quite literal and then as they come around to being in fifth grade or so, they start dealing with more abstract concepts. In my observations on this day, I noticed that the students were constantly being presented with counter-intuitive ideas, which are a form of abstraction. Two examples I encountered were — multiplying a fraction makes it smaller in value and that when water freezes, its molecules are closer but it occupies more volume. I wonder if it would be meaningful to speak about this idea of counter-intuitiveness more openly so it is something that might go towards developing abstract thinking.
I think our work as educators is to be researchers of our students and identify how they learn, the very basic processes that guide their learning and to address these ways of learning in meaningful ways.
Posted