Here are two seemingly unrelated items that have been recently published and reported in the NYTimes.
How to study
Under the somewhat daunting title, “The Critical Importance of Retrieval for Learning,”
a paper in Science described the results of an interesting experiment done at the Department of Psychological Science of Purdue University.
Students were taught words of a foreign language. They were then divided into 3 groups. One group studied once, and then repeatedly tested. The second group studied and re-studied, but never tested. The third studied once, and never re-studied or tested. Here is how the authors summarize their results:
“Repeated studying after learning had no effect on delayed recall, but repeated testing produced a large positive effect. In addition, students’ predictions of their performance were uncorrelated with actual performance. The results demonstrate the critical role of retrieval practice in consolidating learning and show that even university students seem unaware of this fact.“
In other words: Memorize! Repeat again and again, because that’s how the brain consolidates its information.
How to teach (and study) math
Why are American students always at the bottom of the list in the international rating of math proficiency? The National Mathematics Advisory Panel issued a 120-page report (www.ed.gov/mathpanel) on the importance of preparing students for algebra, normally taught in the eighth and ninth grades, and its role as a gateway course for later success in high school, college, and the workplace.
The panel members had to navigate between two competing ideologies. Parents and teachers have fought passionately in school districts around the country over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to do problems and then drilled on them, versus reform or child-centered instruction, emphasizing student exploration and conceptual understanding. It said both methods had a role.
The report urges educators to keep it simple: Define a few key topics and teach them until students master them. Along the way, it says, students should memorize basic arithmetic facts and spend more time on fractions and their meaning.
“Memorize”—we can now readily accept; the Science paper elegantly proved its importance in learning. But fractions? Why are they that important? Here is the commission chairman’s answer:
“Fractions have been downplayed. There’s been a tendency in recent decades to regard fractions to be operationally less important than numbers because you can express everything in decimals or in spreadsheets. But it’s important to have an instinctual sense of what a third of a pie is, or what 20% of something is, to understand the ratio of numbers involved and what happens as you manipulate it.”
My personal experience
I was educated in the old-fashioned, European-style system of, God forbid, “rote memory”. There is something disparaging about this term; You half expect a smirk to accompany it. Is it because it reminds us of “rot”, as in “rotten”? Is it because we disparage Asian education as “rote memory”?
When I was in fourth grade (not fifth grade, as recommended in the report), I was expected to know the multiplication table so well that I did not have to think about the answer—it became instinctual.
When I was in high school, having to take English as a foreign language (I wasn’t asked whether I wanted it or not), I had to memorize Shakespeare’s soliloquies in Macbeth, Hamlet, and King Lear. How many native-born Americans know what “soliloquy” means?
Did it do me any good? I attribute my understanding of Shakespeare, my love of words and language, my pleasure in reading poetry to the soliloquies and sonnets of The Bard. I hated it when I had to suffer committing them to memory. But I am eternally thankful to my old-fashioned, uncompromising teachers who, despite the stink bombs, the pranks, the schemes, were unrelenting. They gave me a gift that lasted a lifetime.
I remember my son when he was in fifth grade. He had a hard time memorizing anything, but it was no big deal because he was hardly ever expected to know anything by heart. But I drew the line when he struggled with the multiplication table. I still remember the Saturday afternoon when I drilled him until he was on verge of tears, but learn he did. That was unconventional; it was frowned upon, almost child abuse. The idea that just “knowing” it is not good enough, that a child of 11 should also “understand” numbers theory, sounded preposterous to me. Now come the National Mathematics Advisory Panel and the scientists at Purdue to tell us that we were wrong all along. Old-fashioned teaching and testing is the way to learn and retain the knowledge for a lifetime of usefulness and enjoyment.
All I can say is: Amen, and it’s about time!