Throughout my years in the middle school classroom, I could not help but notice a huge discrepancy in my students’ number sense. This impacted their computation skills, their concept of a reasonable answer, but where I noticed it most was in the first unit of the year. Traditionally the first unit of the year is something along the lines of number systems. Fractions. Integers. Decimals. Percents.
It was rough.
I could easily see where they stood and decipher who would need extra support.
Apparently, I was not alone.
“In 2010, the U.S. Department of Education’s Institute of Education Sciences released a report on effective K-8 fractions instruction as part of its What Works Clearinghouse. The report noted that half of 8th graders could not place three fractions in order from least to greatest on the 2004 National Assessment of Educational Progress in math.”
I am not surprised. Are you?
The writers of the Common Core State Standards took note as well. Have you noticed the great weight and priority placed on fractions when looking at the standards?
In a recent edweek article, Approach to Fractions Seen as Key Shift in Common Standards by Liana Heitin, she mentioned the need for students to have an integral understanding of what a fraction is. Deeper than “part of a whole”. This is where the concept of the number system comes into play. Do fractions belong on the number line? Can you have “parts” of a whole? When would you want to work with fractions rather than decimals?
I remember so often having students who would see a fraction and instantly divide to find the decimal equivalent. I would often ask them why. Most of the time they could not explain, just that they had been shown to do that or they liked decimals better. Maybe students have an intuitive understanding of decimals? I believe they divided because they didn’t really understand what seven-ninths looked like. Sure, nine boxes with seven shaded. But what does that mean? Where does it go on the number line?
The article also mentioned a few other big changes.
Not emphasized in standards:
- Lowest common denominators
- Proper and improper fractions
Greater emphasis in standards:
- Fluency with the number line
- Operations on the number line
- Decimal equivalents
“With more traditional methods of instruction, “students end up thinking there are all different types of numbers—fractions, mixed numbers, and decimals—and they’re all different animals,” said Mr. McCallum. But the number-line approach makes it clear that these can all be the same number: “You’re simply writing the number in a different way.”
What if we showed students how numbers are all related? What if we emphasized their equivalency?
My philosophy was always to combat this from the very beginning. We would attack number sense, we would learn how to work with different forms of numbers, we would learn when one form was more useful than another, we would practice this over and over and over. I may or may not have worn them out.
However, I got a lot of bang for my buck.
Proportions, simple. Unit rate, check. Measurement concepts, so much easier. Reasonableness, hallelujah.
And of all my students, my ones who struggled, who came to me behind, they were the ones who benefited the most.
Tomorrow, I will share 3 great ideas for emphasizing equivalent forms of numbers (with a freebie) and how to implement them in your classroom.
Happy Teaching!
