Before this week’s tutoring session, I received the announcement that in several weeks my assigned student, Zoey, a fifth grader, will have end-of-year proficiency tests in reading and math. I’m not certain, but I suspect these tests mainly benefit the tutoring organization, which annually must justify its existence to expand its reach as a tutoring program.
When I began as a volunteer tutor this past September, I agreed to teach reading. Through no fault of their own, my initial assigned students were washouts. Suddenly, they simply stopped coming to our weekly Zoom sessions. I do not know their exact fate, whether they voluntarily dropped out or else were dismissed by the program for failure to attend.
You see, every pupil who is enrolled in the program has been identified by his or her school as a person who could benefit from tutoring. Some kids appear to have significant family issues; most are poor. Regardless of their circumstances, these kids still deserve to take advantage of an opportunity to improve their odds of achieving success in life. It saddened me to deal with such self-centered or detached adults, parents who were uncommitted to their own child’s educational success.
Fortunately, Zoey was a reliable and enthusiastic student, whose own father is a willing supporter and a positive influence when it comes to her education. It helps, of course, that Zoey herself is a consistently polite and pleasant young lady. For these reasons, after just two sessions together, I agreed to be her tutor, despite the fact Zoey was enrolled in a broad-based program, which includes mathematics in addition to reading. For reasons I can’t explain, Zoey didn’t have a volunteer tutor before we met.
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This past Tuesday evening, we were reviewing some sample math problems like those likely to appear on the fifth-grade proficiency exam. When Zoey gave a correct answer to a multiple-choice question involving subtraction with large numbers, I asked her to explain her methodology for finding the right answer. Her reply mystified me.
Zoey explained that she had used addition to solve the subtraction problem. Naturally, I had to “correct” her, so I took some time to show her precisely how I would have solved the problem to arrive at the identical correct answer.
Next, there was a multiplication problem involving an operation referred to as the “partial product method.” The term seemed unfamiliar to me. I searched my memory, straining without success to recall it based on my own experience as a fifth grader, but, after all, that was more than sixty years ago. As Zoey and I concluded our Zoom session, I made a mental note to research this matter the next morning.
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People of a certain age might recall the “New Math,” which the 1960s constituted a major change in the way mathematics was being taught to American grade schoolers. Parents and teachers who opposed this new math model complained that the new curriculum was far removed from students’ ordinary experience, that it took time away from traditional topics, such as basic arithmetic operations, and that it put demands on both teachers and parents, who did not fully understand the material they were supposed to be helping their kids to understand and use. The truth is that New Math was as much about the pedagogy of mathematics as it was about mathematics itself.
Widely criticized, even at the time, see e.g., Why Johnny Can’t Add: The Failure of the New Math by Morris Kline (1973), New Math quickly fell out of favor. Indeed, the phrase “new math” is used now to describe any such short-lived, discredited fad. “New Math” even made Time’s ignominious list of the one hundred worst ideas of the 20th century.
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What did my research reveal? Well, among other things, it suggests the more things change, the more things stay the same.
For example, I discovered that in 2010 various politicians and “blue ribbon” panels across the United States led an initiative to develop standards for English and math. Known as the Common Core State Standards, these new standards were implemented to, “provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them.” See http://www.corestandards.org/. To date, the standards have been adopted by at least forty-one states, including our state.
I was surprised to learn that when it comes to math, these Common Core standards mark a return of some New Math principles, including teaching students to use addition to solve subtraction problems! Zoey had gotten it right after all, but I had been ignorant to recognize it. Looking back on our most recent session, I seem to recall her puzzled look as I attempted to “correct” her flawed methodology. I must apologize when we meet next week.
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Now, I see how my well intended efforts to help Zoey might have been confusing to her, even detrimental. Like the New Math before it, Common Core mathematics imposes numerous steps and additional operations that I viewed to be superfluous, while the actual goal is to impart a deeper understanding of the underlying mathematics to the student. I realize now that I am not qualified to teach Common Core mathematics.
Next year I might simply hold my ground and decline to tutor a subject other than English or reading. Or perhaps, before the start of a new school year, I will bone up on the current math, an old dog trying to learn new tricks.
