First, the fact that infant learning initially occurs accidentally then intentionally through trial and error drew a connection to a colleague's 14 month old daughter, Jayden. The first time Jayden came to school, she was immediately attracted to the magnets on my filing cabinet. She took them off, one by one, then took great delight in putting them back on the filing cabinet, and watching them stick. She tried sticking the magnets on my desk, and discovered they didn't work quite the same, then went back to the filing cabinet. On each subsequent visit to the school, Jayden never fails to come to my filing cabinet and is able to remember where the magnets stick.
The opening vignette in this chapter is one in which a teacher gave her 3rd grade science class a problem to solve through trial and error. In the vignette, the students were unable to think logically about the problem they were posed because there were too many variables. Reading this made me think of a question on a science quiz that we recently gave our 5th graders:
A teacher carefully pops the balloon with a pin. The students pick up the pieces of the balloon and compare them. Which of the following properties of the pieces should be most similar?
A. color
B. shape
C. size
D. weight
In our weekly science team meeting, we analyzed data from the quiz, and found almost 80% of students answered this question incorrectly. Based on this percentage alone, we decided we needed to model this event (the balloon being popped) and allow the students to make actual observations and test their theories about which properties stayed the same before putting a question like this on a quiz. But, in reading this chapter, my ah-ha moment is to question whether or not this problem was developmentally appropriate for 5th grade students. Our students are currently in Piaget's concrete operational stage of development, where they are improving in their ability think logically, but unable to think abstractly. This makes me wonder whether our assessment was designed appropriately, and guarantees that we will keep the stages of cognitive development in mind when developing our next assessment.
Thinking about reversibility in the preoperational stage of development made me question why I have observed 5th graders struggle with this principle, particularly when doing inverse math equations (-/+, x/÷). For example, most of our 5th graders are able to tell you that if 3 + 5 = 8, then the opposite is: 8 - 5 = 3 by simply reversing the equation and using the inverse operation. But, when given the same equation 3 + 5 = 8 and this inverse: ___ - 3 = 5, our students struggle to fill in the missing digit of the equation. I wonder why having the same numbers but merely switching the order makes this problem more difficult to solve.
While reading about the concrete operational stage and the skill of transitivity, I immediately thought of the problem of the week we will introduce on Monday in math class:
PROBLEM OF THE WEEK: #4
Jocelyn, Henry, and Matty are folding origami paper
cranes. Henry folded 7 paper
cranes. Jocelyn folded 8 times as many
cranes than Henry. Matty folded 4 times
as many cranes and Jocelyn. How many
cranes were folded all together?
In order to be able to solve this problem, students will need to first figure out how many paper cranes Henry folded, then multiply this number by 8 to find out how many paper cranes Joclyn folded, then multiply that total by 4 to find the number Matty folded. Finally, students will need to add the three totals together to arrive at the final answer. 5th grade students should have the cognitive ability to solve this problem, and I will watch this week to see what students struggle with finding the relationships between the three people in this problem and the number of cranes each one folds.
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