Moving Beyond Brownies and Pizza

"A lack of fractional understanding is a well-documented obstacle to student achievement in upper elementary and middle school math" says the National Center for Educational Statistics. This article begins by pointing out their main focus as being about helping 4th graders to use number lines to develop a rich understanding of comparing fractions. The article then goes on to discuss that there are 3 main goals they are focusing on:

1. Build students' understanding of fractions as numbers with a definite magnitude
2. Increase students' understanding of measuring with fractions
3. Develop fraction number sense by avoiding early introduction of traditional fraction algorithms

Then, as they move onto trying to reach these 3 goals, they tell us that they will be focusing on 6 different types of lessons that identify ways that 2 fractions might be related to one another:

1. Both fractions are one unit fraction more than a half
2. Both fractions are one unit fraction less than a half
3. Both fractions are one unit fraction less than one
4. Both fractions can be used in the context of money
5. More of a bigger unit fraction or less of a smaller unit fraction
6. One fraction can be expressed in terms of another

There was then 2 different examples from students and their thought process about different perspectives of the same number line. Even though both students thought differently about the problem, it was clear that the number line was central to their thinking. The same process was shown for different students a few more times, as well. After the lessons, the teacher was able to see that all of the students in the class had made progress in relation to the original 3 goals. 

I had some extremely good thoughts about this article. I really liked the overall idea of getting the students to build an understanding of fractions as numbers with a definitive magnitude. Also, I think this teacher's example of her plan for the class was very well thought out and put into motion the best way it could have been. It also really got me thinking about the troubles students commonly have when being introduced to fractions. It's hard to realize that once some misconceptions or misunderstandings are made right off the bat, it is difficult to help the students get back on track and fully understand the concept they're working with. And this is common with any mathematical concept. This is the main reason I liked this article and it really brought that idea to life.