The Warping of Simplicity and Eloquence
The video above is a must watch for all parents of young children, who have been questioning what in the world is going on with their children’s math work. It is the articulate testimony given by the Chair of the Math Department, Mr. Layton Elliott, at Brebeuf Jesuit High School in Indianapolis, before the Indiana General Assembly Legislative Study Committee on September 10, 2013.
Parents who watch will be relieved to know that they are in good company, in struggling to successfully explain some of the “fuzzy” methods being used in Common Core math programs. Mr. Elliott begins his testimony by describing his experience accompanying high school students on a service project, during which they tutored struggling second graders in math. With over ten years of teaching middle schoolers and high schoolers, Mr. Elliott assumed he would have a successful experience working with the child assigned to him. Mr. Elliott says that upon looking at the child’s work sheet “[he] was immediately confused…” Since the adults monitoring the tutoring impressed upon Mr. Elliott that he was not to use the standard algorithm when showing the student how to add two, two digit numbers, he toiled with the preferred method in vain. He said that when the two hour period was over and the student still had not mastered two digit addition, he “was stunned!” He felt that he had failed the student, whom he was confident would likely have been able to master the standard algorithm had he been allowed to show it to him. Perhaps the most poignant portion of Mr. Elliott’s testimony was when he stated the following in relation to his tutoring experience: “Math’s beauty is in its simplicity and elegance. What is simple and elegant had been horribly warped into something that was needlessly complex.”
Every teacher of young children would do well to listen to Mr. Elliott’s testimony and then ask themselves if their students are enjoying the elegance and simplicity of math. If the answer is no, perhaps they should reconsider just how much they wish to follow along with the Common Core textbook they are most likely required to use. At a minimum, they should consider supplementing their material with worksheets of arithmetic problems to provide the much needed practice so frequently absent in most Common Core programs. Finally, they should take a look at child psychologist Dr. Megan Koschnick’s recent speech at Notre Dame and consider if Mr. Elliott’s unsuccessful experience had more to do with the developmental inappropriateness of the method he was required to use, than it did with his ability to teach or the student’s ability to learn.
While Dr. Koschnick’s speech is primarily about the developmentally inappropriateness of some of the K-1 Common Core standards, there is something to be gleaned for math teachers of students in grades 2-5, as well. Dr. Koschnick explains that students in these grades are in what is called the “concrete operational” period of brain development. According to Koschnick, this is the period in which memorizing and performing “concrete operations” is most in sync with what is occurring developmentally in their brains. As she puts it, these types of rote learning exercises are “fabulous” and “right up the alley” of students this age.
In contrast, while some children in this age group are beginning to be able to think more abstractly, others are not. Therefore, spending precious class time trying to teach ALL children to demonstrate mastery of understanding an abstract concepts on the front end, before ever using it, can be extremely time-consuming. Our hardworking teachers have only so much time in the day. If they are being forced to try and put a square peg through a round hole in some cases, even if they eventually accomplish it, we have to ask at what “cost” does this come. The answer is two fold: it comes at the “cost” of far slower pacing of normal skills progression and often in the form of less overall time spent practicing performing the given operation. This is not to say that teachers shouldn’t begin a new lesson with a brief explanation of the concept, but rather that they should consider putting the “horse back before the cart.” When students are given ample practice, frequently their understanding of the related abstract concept comes naturally, over time, and may not need to be formally “taught” at all.
This is in fact the approach taken by high-perfroming Asian countries, such as Singapore, Japan, and Finland, who outperform the U.S. on tests such as the Trends in International Mathematics and Science Study (TIMSS). Research comparing the math content standards of these three countries against the Common Core’s, shows that the biggest difference is that approximately 75% of theirs involves “perform procedures,” whereas only 38% of the Common Core’s do. The incredibly slow pacing of skills progression under Common Core math standards is one of the reason Stanford Mathematician, and Common Core Validation Committee member, James Milgram testified that Common Core will place American students two years behind their counterparts in high performing countries, by the end of 8th grade. Can or should we really slow students’ mathematic progression down in order to train them to “regurgitate” explanations of abstract concepts? Or, is it leaving them standing in place, under the guise of “deeper learning,” rather than allowing them to move on and learn the next logical mathematical operation? I maintain that for some students it is needlessly confusing and frustrating, for others it simply a waste of time, and for all it retards their potential progress. All teachers, principals, and administrators should rethink this lopsided bargain!
