Paper and Pencil
K-12 education should de-emphasize computers and graphing calculators in all but the highest math classes. Too many students are allowed to use electronics as a crutch and thus never learn to walk on their own. I certainly found this to be true on the topic of logarithms, where entirely too many students struggle to solve a problem like 4^x = 8^(x-1) without a calculator. They become masters at knowing what buttons to push, and even of pushing them correctly, but too often they don’t understand the mathematics itself. (To demonstrate this, I used to offer a “logarithm boot camp” at the end of the school year. After 3 days of instruction with tables my students could create and solve problems of types they couldn’t even imagine beforehand. It’s quite fun to watch the improvement.)
Pencil and paper forces the math education, not the calculator education. And thus, for the 2nd day in a row, I point to a study:
One of the most visible changes in math education over the past 20 years has been the shift towards using computers. Many students in middle schools now see their homework problems on screens via tools like ASSISTments and Khan Academy and submit their solutions through screens, too. This shift towards technology comes with some significant advantages: students can receive immediate feedback on their homework; software can model student progress, presenting students with problems that appropriately challenge them; and teachers can know how well students are doing before they enter class the next day. But this technological shift also comes with disadvantages. Sometimes students don’t benefit from two technological tools used by many generations of mathematicians, engineers, and scientists to work through problems: paper and pencil. With the support of the Reboot Foundation, Bill Hinkley, a veteran math teacher, used the math program ASSISTments to explore how his students use paper and pencil when solving math problems, exploring the value of students showing their work. Using a randomized controlled trial — considered the gold standard in research — Hinkley found intriguing results in student outcomes when students wrote down their math problem using a pencil and paper.
Unfortunately, the sample size was too small for the promising results to be statistically significant.
The report goes on to address metacognition and cognitive overload (working memory), extremely important topics in education in general and math education in particular. My experience comports with the points made.
Where to go from here? Conduct larger trials! But, even if the evidence becomes irrefutable–as with the teaching of phonics in reading instruction–will our schools of education take note?