Ah, the true joy of waiting a few days for thoughts to congeal (where the thoughtfulness of studying pays off) – literally and figuratively. I read Geek Dad regularly as he makes outstanding observations and always seems to be following thoughtful ideas – whether one is a parent or not. In this instance I ‘knew’ the blog was point on and needed to find a way to support what he was explaining. I racked my brain for a non-teacher, non- ivory tower example and then, out of the blue the answer arrived. Thank you to my ‘since’ undergrad years, artistic friend in Brooklyn for pointing out a great video on Japanese style multiplication.
Memorizing the multiplication of one digit numbers is great until you get past 3×3 or 2×4. Once you leave that realm, one needs to understand the concept of ones and then tens or the power of 10. While it is easy enough to memorize number rules/algorithms (traditional multiplication table), it is difficult to understand if what you are thinking in your head or running on a calculator is reasonable without the knowledge of actually knowing the concept. Without helping our students grasp the concept of multiplication being ‘shorthand’ for addition and division being ‘shorthand’ for subtraction, we do them a dis-service.
Of course, understanding the power of 10, addition (carrying), subtraction (borrowing) is complex. It requires practice, or as Geek Dad states, LEARNING. Learning is a PROCESS of understanding. After the concept is learned, one needs to step back from it and then go back in a few days and STUDY. Then the student needs to go back in another few days and study. There is this loop of learning and studying going on until the ‘aha’ moment. Until ‘aha’, you keep at it. After ‘aha’, you may need to review, but like riding a two-wheeler, your mind recalls the process. People such as Mitch Weathers, of Organized Binder fame, have reinvigorated the process of learning. Unfortunately, many new teachers are not familiar with the concept of mindfulness of learning/studying cycles since they attended college under the NCLB propaganda push.
In America we want efficiencies, we love the test scores. We do not stop to study; We move forward to supposedly learn (as in how teachers need to be on the same concept at the same time and be ready to test at the same time in the school year – spring testing). Learning is not actually efficient because each brain is unique and each child’s experience is unique so the cycling of learning and studying needs to be ongoing. Since learning is not efficient, we try to shorten the pathway with new and advanced ways of learning, when in reality, just doing it the old-fashioned way is actually time and cost efficient.
Having taught and tutored for a number of years (too many to post without giving away my age), what I found was most students were brilliant but were being ‘rushed’ at school. When I broke things back down, did cycles of learn and study for them to do between sessions, everything was solved, as if I performed magic. Parents were thrilled, students gained self-confidence. Dreaded weekly multiplication test scores improved. Whatever we worked on, 50 minutes at school was not enough. I spent part of my tutoring session reviewing how to study.
Clearly the video above is based on knowledge of the powers of 10 (ones, tens, hundreds….), it is artistic/beautiful, it requires more thinking and requires time. If a child truly understands what happens when one multiplies 100 x 10 (you get thousands), then the Japanese style of multiplication on paper would make sense and be predictive of what a reasonable answer should be, even if an exact answer could not be contrived in their head.
Since the advent of NCLB (and even before) learning was something which occurred on a very rigid timeline. Sadly, studying was not taught and it was expected everyone knew how. It has taken a long time for the public (alas, teachers completely understand the concept of studying) to grasp on to the learning cycle. Maybe the folks at UCLA Learning and Forgetting can help us understand what has to occur for true learning (not a test score data point) to take place – before it is too late. In the meanwhile, ask your child’s teacher to look at The Organized Binder.