This approach not only complicates the simplest of math problems; it also leads to delays. Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them "understand" the conceptual underpinnings.Once again, knowledge stored in memory is entirely different from knowledge stored on Google.
Biological memory is a biological process that requires a period of time during which new memories are consolidated:
Memory consolidation refers to the idea that neural processes transpiring after the initial registration of information contribute to the permanent storage of memory.I don't know how much time the brain requires to consolidate memories, but I recall John Medina suggesting that the figure may be as long as 10 years. (That would jibe nicely with the 10-year rule for development of expertise, wouldn't it?)
￼Memory consolidation, retrograde amnesia and the hippocampal complex
Lynn Nadel* and Morris Moscovitcht Cognitive Neuroscience
The "consolidation lag" between first learning a new skill and really knowing that skill explains why "just-in-time" learning is so crazy. There is no such thing as just-in-time learning. The brain doesn't work that way. No matter how smart you are, if you are 17 and you don't know how to do long division, you can't just have your professor show you how and then start doing it. Knowledge has to be consolidated before you can use it well, and consolidation takes time.
Here is James Milgram on his experience teaching Stanford students who had not been taught long division:
What happens when you take long division out of the curriculum? Unfortunately, from personal and recent experience at Stanford, I can tell you exactly what happens. What I'm referring to here is the experience of my students in a differential equations class in the fall of 1998. The students in that course were the last students at Stanford taught using the Harvard calculus. And I had a very difficult time teaching them the usual content of the differential equations course because they could not handle basic polynomial manipulations. Consequently, it was impossible for us to get to the depth needed in both the subjects of Laplace transforms and eigenvalue methods required and expected by the engineering school.There is no just-in-time learning, and you can't catch-up.
But what made things worse was that the students knew full well what had happened to them and why, and in a sense they were desperate. They were off schedule in 4th and 3rd years, taking differential equations because they were having severe difficulties in their engineering courses. It was a disaster. Moreover, it was very difficult for them to fill in the gaps in their knowledge. It seems to take a considerable amount of time for the requisite skills to develop. [emphasis added]
Transcript of R. James Milgram
1999 Conference on Standards-Based K-12 Education
For the sake of argument, say it takes two years to consolidate the skill of adding and subtracting double-digit numbers. (I'm guessing it takes more than two, but I don't know.) If a child learns to add and subtract double-digit numbers in second grade, he or she will be proficient in fourth grade.
Delay teaching the algorithms until fourth grade and now you have a cohort of students who won't be proficient in addition and subtraction until 6th grade.
That's the way it works. Two years is two years.
Eide Neurolearning explains elaborative rehearsal