Fractional Dispute Part II

While I agree that long division is possibly focused on too intensely to the point of turning some kids off with the duration of repetition, I whole-hearted disagree with teaching a dependence on the tools of the digital age and his stances on long multiplication and especially fractions. Fractions form a core segment of understanding mathematical concepts and are used in numerous other fields to the point that the delaying of teaching fractions puts an undue burden on other portions of the collective curriculum.

What other curriculum would this be in? Physical education, music, art, social studies, culinary classes, industrial arts, extensive in the sciences, and the majority of the required mathematical classes all use fractions in one form or another. A comprehensive curriculum across the subjects can easily be used to teach and reinforce the usage and concepts of fractions to elementary students. So in the regards of decreasing difficulty or increasing the fun of math, such arguments are weak.

So how are fractions used in those subjects? In physical education, many sports or team based games can easily be turned into lessons on fractions which would be impossible to duplicate to explain decimals. I will include a small lesson in a few days to demonstrate. In music, fractions are an integral part as the beat of the music is in 4/4, ¾, 3/8 rhythmic time with whole, half, quarter, eighth, sixteenth notes all divided up into octaves on the pearly white 88 keys. Art is demonstrated when transferring a picture from a small scale into a larger scale or the ration blends of paints for the desired colors. Culinary and industrial arts are the cooking and carpentry statements which I will delve into in another entry. Sciences all requires the use of fractions as early as 5^th grade when instructions are given for the proper ratios of chemicals to blend for an experiment or other measured results. Come 8^th grade if your skills in fractions are not up to par, the kids are now further behind on comprehending chemistry, physics and biology (anyone remember the Tt and TT gene charts that are in ¼s).

Now how about the actual math itself?

“DeTurck does not want to abolish the teaching of fractions and long division altogether. He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn't need to be taught as intensely.”

There is a major problem in his concept as so described. First, this would shift the burden of teaching fractions to the music, social studies (think demographic pie charts), science, Art, culinary and industrial curriculum. To me, the shifting of the education of core mathematical abilities only serves to undercut the students and the overall quality of a well-rounded education for them.

Can you wait until after calculus for learning fractions? Again, the answer is no. You need a strong foundation in the application of fractions before taking the prerequisite math courses before calculus and calculus itself. First and foremost, story problems and numerous equations are not represented in decimal form. They are represented with variables into which data needs to be inserted for proper calculations.

So what is the list of math concepts impacted by focusing on decimals and not fractions?

Fractions summarize the fundamental mathematical concept of division. They are the most visual and commonly used term for the division of a unit into parts such as cutting a pizza into enough parts for a group of kids. Ratios and proportions are critical in the understanding of today’s world and are squarely dependent on fractions. The rational root theorem in algebra courses on how to find fractional roots of a polynomial is another example. The entire basis for Trigonometry and Geometry which are required prerequisites for Calculus are founded in fractions. Calculus is based on fractions such as the common definition of a derivative being rise over run. That isn’t even touching differential equations, abstract algebra or statistical analysis and other higher level math courses.

Also, carpentry and cooking are not the only fields where fractions are heavily used. There are the silly professions dealing with pharmaceutical medications such as the nurses who do not take calculus but do inject the proper ratios of medication into your body.

So in summary, I can only hope Professor DeTurck is being satirical. But with his position and history as our guide, I dread someone will take this seriously and mandate it on the masses.

What is your opinion on this?