My 5 Reasons Not to Share post has gained new life in the last week. It is evidently being shared widely on Facebook.
One consequence of this is that I am getting daily emails from people who read the piece and feel moved to comment. I do believe the Internet ought to facilitate dialogue. So I have been replying to these emails.
Sometimes, people leave a wrong email address in the contact form and they bounce back. So, in a show of good faith, I share with you a recent email and my reply. Perhaps Gavin will come back to the blog and read my reply. Perhaps he will not.
Anyway, here goes.
Gavin writes:
I do not know if you failed to do your research, but the number line is clearly part of Common Core, for instance:
“CCSS.Math.Content.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.”I am not sure how to comment on the article because you have banned commenting on them. I do not have a twitter and therefore cannot join the disucssion there. I hope that you’re not intentionally trying to cast a positive light on Common Core but are instead trying to give an unbiased account of it.
I reply:
Thank you for taking the time to read, and to write.
I just want to clarify that my claim was not that number lines do not appear in the Common Core. They do appear there, as you point out with your citation. You are completely correct.
But if I remember correctly, the worksheet in question was a second grade worksheet. My claim was this: “There is nothing in the Common Core State Standards that requires students to use number lines to perform multi-digit subtraction.”
I stand by that claim. Even the number line standard you cite in sixth grade doesn’t reference the number line as a way to understand multi-digit subtraction. Instead the spirit of that standard is to use the number line as a way to represent negative numbers (such as -9 or -1/2), and then to understand the coordinate plane. Simply put, if students are going to graph functions in algebra, they will need to work with number lines in earlier grades.
As for the comments thing…I was saddened to have to turn them off for that 5 reasons post. But I am committed to maintaining a reasoned and productive tone on this blog. The comments (both pro- and con- on the Common Core) were spiraling out of control and I simply did not have the time to manage them. It seems clear to me that people are able to comment on the piece as it gets shared on Facebook, but I don’t have access to the comments on other people’s shares so I cannot speak to their quality, and I am not responsible for them in the way I am when they are on my blog.
Finally, you can search my blog for “Common Core” and find that I have made some rather pointed critiques of some specific standards in the Common Core—including engaging and arguing with Bill McCallum (a Common Core author) on matters involving rates, ratios and unit rates. All on the record, and you would be welcome to join the conversation in comments on those posts. I have no interest in promoting CCSS. I do have an interest in making sure that critiques are honest and fair.
Best wishes and thanks again for writing.
Christopher
Overthinking my teaching 
You said many people count change this way and gave an example. I count change on a daily basis as do my employees. We never count change the way you presented which is ludicrous. I have a degree in political science, sociology, and work in the financial sector. Therefore, I am pretty clear what is trying to be accomplished here. It is much deeper than basic math.
James – you missed his original comments, I suppose. He did not say that cashier’s or people dealing in money count change this way, he said that many people do. Instead of saying “Well, *I* don’t” or relying on your N=50 sample set of people you know, why not consider that there are lots of customers themselves who do it this way, or who count up, etc – perhaps people you don’t encounter in your day-to-day work. I am not a teacher, I am a highly educated numerical modeller in the water resource engineering field – but I think his point, to teach how OTHERS may do things is an important one. I moved from North American to Germany 10 years ago, and now my children are in German school – I am amazed at how well they teach them the different approaches to simple every day math and how efficient the German kids become at it – like it’s second nature. And so easy to adapt to an abstract or foreign way of approaching problems. Many of their exercises reflect some of these CC worksheets that Americans are complaining about, like the line example. I just discovered this blog today and find it very reassuring that North American math education is improving and their’s potential to catch up to the countries that are doing well. Keep up the good work Christopher – teachers like you will make the difference.
first if all tessernet, the plural,of cashier is “cashiers,” not cashier’s. That’s the possessive, not the plural. Secondly, I know NO ONE who counts change the way it was described (very few who even know how in the first place), but the convoluted way described here is insane. Now, I will admit, I’ve seen a lot of people do math a thousand times better then most American high school graduates. But I blame the entire U.S. Educational system, not that the way of doing it is so wrong and needs to be replaced with this complicated crap. Make the teachers more accountable for the students’ success and less accountable to the unions, and maybe you’ll see better graduates.