Before school let our for the Christmas break I was at my wits end with trying to teach equivalent fractions and simplifying fractions to students who were deficient in their understanding of the “true” meaning of multiplication and division. I know that there are so many different skills that students need to have mastered before they can simplify fractions. I had to face the fact that the students who were sitting in my classroom did not have the prerequisite skills to understand how to simplify fractions. Believe me it showed! Every time I tried to show them a different way of how to simplify fractions the students would mentally check out.
So out of frustration I did the unimaginable, I divided my classroom of 28 students in half. I began teaching the students how use the tape diagram as a model to add fractions with like denominators. After adding the fractions I asked the students was the answer in simplest form. I then proceeded to demonstrate how simplify the fraction and as soon as I finished one of my students raised his hand and said, “I don’t understand that GCF stuff.”
I took a deep breath and looked at the problem and began to write 9/12 in dot form. I then took the GCF which was 3 and divided the numerator into groups of 3 and the denominator into groups of 3 to show 3/4. After I did this there was a collective….”Ohhhhhhhhhh, I get it!”
As a 5th grade math teacher as you can imagine, I felt like I had sank to my lowest point because I had to resort to dots. I begin to ask myself how the heck am I suppose to teach these students how to distinguish between multiplicative patterns and additive patterns when their understanding of multiplication and division is weak. Like most teachers who feel defeated I needed someone to talk to about this. I went home to vent to my fellow math educators in my Mathematics Education Research Facebook group. After posting my picture and making my frustration known the teachers jumped on the bandwagon one comment at a time. Their comments made me feel so much better!
As I read through the comments one of the teachers mentioned Hung-Hsi Wu a math professor at the University of California who had written articles about how fractions were the gateway to algebra. When I visited his page I found the article The Mathematics Early Grade Teachers Need to Know- What it Means to Know It. Mr. Wu said in the article that a teacher who knows mathematics does not impose rules without reason. So the more a teacher knows about what she teaches, the more options she has on how to teach it, and the more she can convince students that mathematics is worth learning. Reading this made me feel like I was on the right track. Even though I had done my color tile lesson with the students there were those students who are not strong with their 3rd grade math skills that needed a way to connect what little bit that they understood about division to simplifying fractions. Since I know mathematics I could give them another option which was showing the students that division is division no matter what by using the dots to simplify. Wow!! I felt like I deserved a gold star!
As I prepare to return to school on Monday,I feel more confident about teaching the remainder of the fraction curriculum to my students. I know that I have the math content knowledge to teach that helps me to present the math in multiple ways.