“… year after year, HS juniors ALWAYS scored lower than the sophomores on the middle school-level items.”
The math instructors at my technical college generalized that “math skills have a half-life of about two years”, which seems to corroborate that experience.
Our business and industry advisory committees demanded that we refresh pencil-paper computational skills for all the school associate-degree programs. Their experience with applicants was that “back-up” computational methods (as well as “back-of-the-envelope”) were needed in the workplace in timely situations when technology was not available. They also emphasized the importance of “use-it-or-loose-it” continuous refreshment of basic skills. They still wanted pencil-paper computations to be refreshed.
My initial course assessment included a set of “no calculator” computations, as well as typical single-step problems for which calculators were allowed. A formula reference sheet was provided. The assessment was self-scored by the student the next class period, and did not impact their course grade. The final test contained the same skills. Item for item, but with different numbers.
Average score on the initial assessment was consistently about 50%, indicating that many skills had not been refreshed in the junior or senior high school years. We also had an approximate 15% non-traditional population, who had been out of school for several years. We noted that those who had dropped out of high school and obtained GEDs scored much lower.
According to my records, completers of my three-credit semester classes over two decades achieved an average of 82%. This gives evidence that recent, relevant, and required refreshing of math skills should be required of ALL students in the junior year.
While we never formalized or documented any research data on these results, our generalizations appear similar to your conclusions. I would appreciate any specific links to research that maybe useful on this important topic.
In any case, we found that carbon technology (the pencil) shouldn’t be discarded just because we now have silicon (the calculator).