I’m in the middle of teaching my girls how to conceptualize proportions. They can solve them with no problem, but they don’t really understand what they mean…and that all lies in their (in)ability to truly understand fractions.
Typically, fractions literacy begins in grade 3 ( according to the online version of NCTM’s Principles and Standards ) and continues to develop until grade 6. However, as any middle grades ( or high school or college ) math teacher can tell you, students never fully grasp the concept of fractions as comparing a part of something to a whole ( or in the case of rates/ratios comparing a part to a part, part to a whole, etc ).
I discovered just how bad off my students were in this regard when I tried ( unsuccessfully ) to show them the visual representation of proportional relationships.
I was using an activity involving scaling down recipes to illustrate the physical aspects of proportional reasoning….and fractions. The activity required us to take 3 cups of flour (required for the original recipe) and divide them each in half, thus leaving us with 6 piles of flour, each measuring a half of a cup. The questions that followed included:
How many 1/2 cup piles have you created ? ( 6 )
How many of the 1/2 cup piles are need for the scaled down recipe? (3)
How many scaled down versions of the original recipe can you make? (2)
I thought the process would be much smoother than it actually was, but the students had trouble understanding the visual representation of each pile being divided in half. Even more difficult, was understanding that the concept of half is relative to what is considered a whole. Essentially, we couldn’t get though the discussion of dividing the piles of flour into 6 halves and that the 6 half cup piles are equivalent to the 3 whole cup piles….or that the 3 half cup piles of flour is the same as 1 and 1/2 cups of flour.
But…they could do all of the above with numbers…and I was stumped, frustrated, and slightly annoyed.
How do you teach students who have internalized a process to understand a concept rooted in physical reality ?
Tags: 1 Comment







