Common core math primary grades (college, private school, mathematics, techniques)
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Hello. I am hoping to get some insights on how other schools get their primary students to memorize math facts. Here is the question: Do you end up taking the driver's seat on teaching a primary student how to do mental math or does your school do a good job on this?
This is my observation. In Florida, where the Go Math series is used, "fact" lessons are taught as a new concept for just one day and then a new concept is taught the next day. For example, there was a lesson on fact families, but what my daughter learned from that was simply to find the missing number. She didn't actually memorize the facts or apply it.
She recently was taught how to break apart a 2 digit number in order to subtract it from another 2 digit number. For example, 86-18 would be 86 - (10-6-2). What I noticed was that she did not break apart but went back to counting in her head or fingers. So when I required her to redo her homework, I realized she did not use place value to her advantage. So I taught her how to subtract 10 from any number. 86-10.
Then I had to teach her that if the ones are the same, you will end up with zero. For example, 86-6=80. Finally, I had to make sure she memorized the addends of 10 so that she could get the final answer without using fingers. 80-2 = 78. I did this all in one afternoon and let me tell you, my daughter was angry. However, after practicing this for several days, she now enjoys adding and subtracting mentally.
When I asked the teacher about this, her answer was, don't worry, there will be a lesson on how we traditionally add and subtract.
I will admit that I dropped the ball for not recognizing that her finger counting had gone on too long. The thing is she does it so quickly that it was difficult for me to determine if she was doing it or simply taking her time to recall the fact. Thank goodness I caught now.
What about you all? Do you end up teaching your kids how to do math mentally (memorizing as well) or does your school do a good job of it?
I didn't have to teach my kids basic mental math, but where we struggled and I did have to teach them was how to solve problems in a logical way. That is how to write things down in a structured manner so it was easy to see where you were and error check later and how to work through the problem one step at a time. The methods they were being taught skipped steps and were often incomplete. The methods taught in elementary school worked OK on the simple arithmetic problems of elementary school but did not provide the proper fundamentals for high school and college when the problems got much harder and more complex. And those fundamentals are needed to keep from falling behind as the math gets harder.
And yes, my daughter was very angry. In elementary school. In college she gave me a very public thank you because she used those fundamentals daily.
I didn't have to teach my kids basic mental math, but where we struggled and I did have to teach them was how to solve problems in a logical way. That is how to write things down in a structured manner so it was easy to see where you were and error check later and how to work through the problem one step at a time. The methods they were being taught skipped steps and were often incomplete. The methods taught in elementary school worked OK on the simple arithmetic problems of elementary school but did not provide the proper fundamentals for high school and college when the problems got much harder and more complex. And those fundamentals are needed to keep from falling behind as the math gets harder.
And yes, my daughter was very angry. In elementary school. In college she gave me a very public thank you because she used those fundamentals daily.
Thank you for replying. I think we share a common experience, that at school, steps are skipped so that students cannot do more complex math. For example, Go Math assumes that because you learned about fact families one day, that knowledge would later be used to break apart.
My daughter hasn't thanked me yet but told me she now doesn't like being required to show her work. Haha!
I teach the facts concepts to my 2nd grade special ed students. I spent 2 lessons teaching addition facts that equal 10. Now every day we do a warm-up with a large foam die where they roll it and then have to state the number needed to make 10. Then we all recite the fact and the turn-around fact. Then we go round robin where I say a number (including 7,8,9 since those aren't on the die) and they have to quickly state the other number to equal 10. We have also been practicing the 10+_ =_ facts. My students don't see the patterns and I have to review this every day.
Those steps were essential to what we are doing now which is adding digits like 8+7. They have to choose the greater digit and make it a 10 by stealing from the 7 which becomes an easy 10+5. This takes ongoing practice, otherwise my students revert back to finger counting and counting mistakes. I have them use connecting unifix cubes (10 of each in 2 colors) to show the problem and move the blocks from one stack to the other. Later on they will be able to do this in their heads.
The lesson in the book has me moving on to subtraction the very next day, but I teach to mastery and give my students time. While the pace is slower, they end up being pretty good at adding and subtracting using mental math.
If you wish Common Core math do its magic, your kid will be doom. American kids are significantly behind Singapore kids by the end of primary school. Use our PSLE as a yardstick, see if your kid can measure up.
Do your kids a favor and teach them to memorize addition and subtraction fact families as well as multiplication and division fact families. Common core is a total disaster and makes simple arithmetic overly complex.
I send my kids to the best private school in our state. The school still sucks at math IMO. So I buy the math curriculum books from Singapore (Primary Mathematics) and teach my kids math after school. Including the mental math strategies you have really nicely outlined in your OP. At first I tried to talk to the teacher about math, now I have given up. Even the most well-meaning teacher at the best private school doesn't have the time to really focus on these sorts of details (like if they are still counting in their heads rather than using place value tricks in their heads) for every single child in their classroom. At least not with an American style spiral curriculum.
Primary Mathematics does have an edition that's aligned to Common Core, although good solid mental math strategies are taught in all three of their editions made for the US (the US edition, the Standards edition, and the Common Core edition). Another really good resource I've found for teaching mental math strategies is Dreambox on the iPad and computer.
Don't have them memorize facts until they are solid on how to derive the answers first. A kid needs to fully understand why 8x8=64 before memorizing it. But once you get to the point where they need to memorize them, there is another computer / iPad program that my children's school uses that's very good for memorizing addition/subtraction/multiplication/division facts called Reflex Math. They also teach the facts with a heavy emphasis on fact families.
Why was your daughter angry? Was this the first time you ever tried to teach her math? Or was she angry she didn't know how to do it already? I started teaching my kids math in preschool, and they both love it. Maybe if you did it regularly, she won't be angry?
Do your kids a favor and teach them to memorize addition and subtraction fact families as well as multiplication and division fact families. Common core is a total disaster and makes simple arithmetic overly complex.
Kids do need to memorize fact families, but not until they understand how to derive them. "Common core" is a total disaster, but not because it makes simple arithmetic overly complex. It's because American teachers got little to no training on what they were supposed to be doing, and they have horribly written spiral curriculums that confuse them even more. The "overly complex arithmetic" is actually really useful mental math techniques that develop a great number sense, if you teach them as mental math techniques instead of written math techniques, and if you impart an understanding of why they work, and how they continue to work with more complicated problems.
And like Lobo said, you have to practice new mental math techniques. You cannot spiral them. Spiral is best for review, not new instruction.
Do your kids a favor and teach them to memorize addition and subtraction fact families as well as multiplication and division fact families. Common core is a total disaster and makes simple arithmetic overly complex.
Rote memorization doesn't really teach anyone anything. Plus its just a few months' of activity maximum. You going to carry on "teaching" that for how many years? All you need is a book of tables, a "teacher" for that is entirely optional.
My son, now 9, can do mental arithmetic very quickly with fairly complex and large numbers already because of the concepts he learned. I've got a PhD and a JD and there is no way I was at his level of understanding of math when I was 9. It comes down to how our state implemented common core.
The only disaster is the facile notions and misunderstandings associated with it. No doubt it will be dismantled, I'm happy my son got to leap ahead because of it though.
Rote memorization doesn't really teach anyone anything. Plus its just a few months' of activity maximum. You going to carry on "teaching" that for how many years? All you need is a book of tables, a "teacher" for that is entirely optional.
My son, now 9, can do mental arithmetic very quickly with fairly complex and large numbers already because of the concepts he learned. I've got a PhD and a JD and there is no way I was at his level of understanding of math when I was 9. It comes down to how our state implemented common core.
The only disaster is the facile notions and misunderstandings associated with it. No doubt it will be dismantled, I'm happy my son got to leap ahead because of it though.
As someone who took quite a bit of advanced math in my lifetime I have to say that having the arithmetic facts memorized makes all the advanced stuff much easier. I agree with the poster above who said that kids need to learn how to derive the arithmetic fact families. Then they should memorize them.
After they memorize the fact families all the manipulation that common core teaches can be useful.
I doubt your 9 year old is working with Complex numbers.
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