The concept is the message
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During Masters training, one of my professors said her experience was that math operations familiarity was as good as memorization; if the student understood the concept, she was unconcerned about memorized basic math facts.
Students struggle with memorizing their facts, without connecting the concepts to the seemingly endless operation tables.
We're reaching for math fluency with the operations tables: a level of understanding similar to reading fluency. Your student know the basics so well they're able to play around with them in multiplication, division and algebra.
So, does your student need to memorize their basic operations tables?
Memorization isn't learning. It's key, though: our brains exist as networks of linked information, and our memories are the net that catches and connects new knowledge. So a student experiences and learns that quantities can be counted by numbers, that a larger quantity has a larger number. They build on the memories of counting when learning the adding algorithm: this group of X items, combined with this group of X items, creates a larger number of items.
Once your student understands that the addition process is manipulating whole numbers or groups of numbers to get a larger total, yes. Work on memorizing the tables.
This requires patience, and time, and possibly bribery. The payoff in their competence and confidence is worth it.
Start on a morning when they're well-rested and you've got manipulatives to hand. Set a purpose with your student: making addition easier is a great one. And then try a few things to figure out the best avenue: songs? Worksheets? Color coding units, tens and hundreds or odd/even numbers? Absolutely start with the manipulatives, go slowly so your student identifies the pattern (the total goes up by one, or two, or three, etc.) and build three facts at a time. One caveat: random flash cards do not build the patterning capacity we're after here.
When you are confident your student knows three facts cold, give them a little low-stakes quiz, one fact at a time. If they answer one incorrectly, ask them to show you how they got their answer with the manipulatives. This process will let you in on how they understand the concept, and help you guide them to both recall the pattern of that table and combine quantities to see the correct answer. Build in a reward: checking the facts off the table, more time online; again, whatever works.
I'll be back next week with a post about flash cards.