Common Core Math Myths
[dropcap]T[/dropcap]he tide of Common Core criticism is growing – some of it deserved, but much of it not. I have noticed a rash of attacks lately that really have nothing to do with the Common Core standards. Some of those attacks involve beloved math strategies that I have taught and used with students for over three decades. How they can be maligned is one thing, but then to attribute them to the “failed” Common Core goes over the top. In this article I will describe three math techniques that are currently under attack.
The first math strategy I call the Number Shift. This has been around forever, but recently it has been labeled an awful “Common Core” technique. 10s, 100s, 1000s are very easy round numbers to work with. With this effective technique, students are taught to shift numbers around to make an even 10, 100 or 1000 and then add or subtract from there. For example, let’s take 8 + 5. Sure we can memorize that the sum is 13 or we can simply add 5 onto 8, but for some students teaching them to take 2 from the 5 and sticking it on the 8 to make an even 10 is a better strategy. That leaves 3 on the other side to add onto 10. Many students can learn to “number shift” so quickly to make even 10s, 100s, 1000s that they often add or subtract much more quickly than other students calculating using the traditional method.
Another effective technique is called “Compensation.” Let’s say you had the mental math problem of 98 + 47. The traditional method requires the following process: 8 + 7 = 15. Put down the 5 ones and regroup the 1 ten. Then add the tens column of 1 + 9 + 4 which is 14 tens. Connect that to the 5 ones and you end up with 145. Many children have difficulty going through that process in their heads. So, instead, we can teach the strategy of compensation. Let’s pretend 98 is 100 and then add on 47. That’s easy, 147. Then take off those 2 we used to round up to 100 and we end up with 145. Most kids can pick up on this technique very quickly and use it effectively. This technique is also maligned as a “bad” Common Core failure. Not only is this technique excellent, but it’s been around forever and has nothing to do with the Common Core.
The last strategy discussed in this article has also been posted all over the internet as an awful “Common Core” math failure. I call it the “counting up” strategy. I taught this technique to third graders as far back as the mid 1980s. Let’s say we are in a department store and intend to purchase an item that costs $2.73 and we want to figure the exact change we should be getting back from a $5 bill. The “traditional” method of subtracting $2.73 from $5.00 is as follows. 0 minus 3 ones needs regrouping, so we take one from the ten’s place. However, there are no tens, so more regrouping is needed. Take one from the hundred’s place leaving 4. Trade in the hundred for 10 tens. Ones are still needed, so we trade in a ten leaving 9 and now we have 10 ones. Regrouping is completed. We now subtract 3 ones from 10 which leaves 7 ones. Move to the ten’s column and subtract 7 tens from 9 leaving 2 tens. Move to the hundred’s (dollars) column and subtract 2 dollars from 4 which is 2. The result is $2.27. This traditional method using mental math is extremely difficult for most students (even most adults). So, using a “counting up” technique is much easier. With this technique we find the difference between $5.00 and $2.73 by counting up to $5.00 from $2.73. $2.73 to $2.75 is 2 cents. $2.75 to $3.00 is a quarter. $3.00 to $5.00 is $2. The result is $2.27. I can personally attest that students using the “counting up” method in this type of mental math scenario will be much more accurate and quick than struggling through the traditional method.
All three of the examples above have been labeled bad Common Core practices. However, not only are they VERY good and effective practices, but they have little association with the Common Core. Certainly they can be used under a Common Core math activity, but they were not designed or invented through the Common Core. I find it personally troubling that these excellent techniques that I have used for over 30 years are being taken out of context and maligned as awful techniques. Even politicians and leaders have jumped on this bandwagon – likely without even thinking it through. We need to get away from playing these political games that malign the Common Core and good educational techniques.