Coordinating Units, Part 3: Fractions

When looking at coordinating units, it is important to consider concepts other than just multiplying. One of those is fractions.

Fractions would be first among these encountered by a child in school. Mental operations that must develop for a child to understand fractional ideas include partitioning, iterating, and splitting. These developments are not taught, much like a child can’t be taught to be taller. These developments are cognitive growths. It is possible to assess whether the child has grown enough mentally to be able to conceive of fractions with understanding and not just by rote.

Here is a task you might try with a student. This task is appropriate for a second through fourth grade student. As the child is engaged in each task, you should not intervene by trying to help or teach. If he/she wants to try again or start over, that’s ok. But you are not teaching, just observing to ascertain their level of readiness to begin working with fractional concepts.

  • Task : Suppose the bar shown below is a piece of candy. Show how someone could share it equally among 5 friends.gastonchocolate

This may not seem like a difficult problem to an adult. It could be easy, difficult, or even impossible to a child – depending on the level of cognitive growth. In sharing out 15 cookies among 5 friends, the child is working with a discrete set. He or she might count them out one at a time until the cookies are all gone. The piece of candy is continuous. This presents two things for the child to do which are not automatic, knowing how many cuts to make and knowing where to make them.

As I stated earlier, we can’t teach cognitive development. So, it might be too simplistic to assume that a child is not learning his or her assigned lessons because of lack of effort or inattention. You can know that the cognitive development is a natural process that you can’t make happen. However, you can give the child lots of opportunities with tasks like the one above to enhance the learning environment.

As you observed the child, what did you notice?  Please share your observations in a reply below. I will respond to each individually.

(Note: This task can be attributed to Wilkins, Norton, and Boyce, 2013.)


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