(NOTE: If you arrived here via Facebook, welcome. You may also be interested in the perspective of a middle school teacher, Mr. Aion. Click on through for more.)
You are browsing Facebook on a Sunday evening. Someone has shared a baffling piece of math homework that was sent home with their child. Accompanying commentary bemoans the current state and future trajectory of mathematics teaching and learning, and lays blame for this at the feet of the Common Core State Standards.
You are baffled by the worksheet too. You are about to click the Share button.
But here are five reasons that’s a bad idea.
1. Credentials are not a trump card.
Almost invariably, the parent who shares the worksheet cites a degree as a credential for the critique. “I have a Bachelor of Science in electronics engineering,” wrote the parent in the recent “Letter to Jack”.
The math you need to know to be an electronics engineer is different from the math you need to know to be a math teacher. I am quite certain that electronics engineers use math that I have not studied, and similarly I use mathematical ideas that they have not studied.
When my teacher friends watch the following video of my son Griffin, they tend to see that a number line would be the right thing to draw to capture his thinking, and they tend to know what is coming when he goes to solve the problem on paper. They tend to describe my son’s work as demonstrating competence or proficiency with subtraction, but suffering mechanical errors when solving with paper and pencil.
Non-teachers who view this video are less likely to see a connection to the number line, and they tend to consider Griffin’s knowledge of subtraction to be weak.
The difference is that teachers have a different kind of mathematical knowledge from electrical engineers. Not necessarily more or less knowledge—different knowledge. This is because different mathematical knowledge is required to do their job.
Deborah Ball refers to this different knowledge as mathematical knowledge for teaching. It is what mathematics teachers know who are more successful in their work. This knowledge includes common errors with standard algorithms, as well as their sources [start at about 2:30 in this video]. It includes common correct, alternative ways of performing and showing computations.
Moral of the story: You may not want to look to an electrical engineer as your primary resource for the current state of math teaching.
2. It is probably misinterpreted.
Homework time can be stressful. This is not new to Common Core.
Parents are trying simultaneously to be helpers and enforcers. When a child does not understand what appears to be something simple, tempers can flare.
We parents are not at our most rational at these times, and this may prevent us from fully understanding the goal of the task.
When Frustrated Parent wrote to Jack, he committed two important errors of misinterpretation: (1) He assumed that Jack’s method was being taught as a preferred algorithm for subtraction, and (2) He assumed that something unfamiliar to him must be complicated.
These are totally understandable. I do not hold Frustrated Parent in contempt for his frustration.
I am simply asking the rest of us to resist sharing without asking critical questions.
The strategy shown on this particular worksheet is counting back.
This is how many people count change: You gave me $20.00 for a $3.18 item, so you get $17 minus $0.18 in change…that’s $16.90 minus $0.08…$16.82.
The number line Jack drew captures this thinking.
The number line could have been improved by (1) arrows on the arches, and (2) smaller jumps to suggest that Jack is counting by a small number (as it is, the relative sizes of the pictured jumps on the number line suggest Jack is counting by 10s or 20s to the left of 127—as Frustrated Parent notes in a later Facebook post).
This worksheet was not about getting students to use the number line as an algorithm. It was about having students try to understand the thinking of someone else.
This may have been a bad worksheet—but not for the reasons cited when people share it on Facebook.
[For the record, in this case Jack’s error was forgetting to subtract the 10 in 316. He counted back three hundred, then six ones. The result is that his answer (indicated on the left-hand end of the number line) is too big by 10. He gets 121. The correct answer is 111.]
3. It is probably not “Common Core”.
There is nothing in the Common Core State Standards that requires students to use number lines to perform multi-digit subtraction. In fact, standard 4.NBT.B.4 requires students to “Fluently add and subtract multi-digit whole numbers using the standard algorithm”.
The standard algorithm, of course, is what the frustrated parent suggests that Jack use.
4. Anecdotal evidence is not research data.
While parents who share these worksheets in frustration will make claims such as the old way worked for me, the research evidence is quite strong that the old ways did not work.
Changes being made to American mathematics teaching are (1) very slow to take root, and (2) based on years of American and international research on student learning.
5. Teachers need our support, not our scorn.
The frustration and anger of a parent who is struggling to help their struggling child is completely understandable. Any parent who claims they have never been frustrated at homework time is living in (a) a fantasy world, (b) denial, or (c) both.
But when we widely share the product of others’ frustration online, we amplify the anger. Ultimately, classroom teachers are the targets of this anger, as they are the public face of the education system. As a group, teachers work very hard with limited resources. They are called upon to equalize the inequities our society creates, and to offer not just equal educational opportunities, but equal educational outcomes to all children.
Now—more than ever—teachers need our support, not our scorn.
What to do instead
If you are Frustrated Parent, you can write a level-headed note to the teacher. It might look something like this:
Dear Ms. Crabapple,
I worked with my child on this problem tonight. Neither of us could figure out what is going on with the number line. You can see the work we did together, but we did not know how to write an explanation to Jack. We are confused. Please help.
If you run across the work of another Frustrated Parent online, please consider asking someone about it before sharing it as evidence of the decline of American mathematics education. Some possibilities:
Ask a teacher friend. You probably have at least one on Facebook.
Ask on Twitter. There are many eager-to-help math teachers who follow the hashtags #mtbos and #mathchat—sincere questions asked on those hashtags will get sincere answers and offers of help.
Ask on a website. The Mathematics Educators stack exchange is a new resource for people to ask and answer questions related to teaching and learning mathematics. Anyone is welcome to ask a question, anyone can answer, and everyone votes on the quality of the answers so that you can easily find the best ones.
The New York Times published a piece on “Common Core homework” in July. I wrote a response to it that clarifies a critique in the article about dots. I invite you to read there for more information.
Note: Things got far beyond my ability to curate in the comments, so I needed to turn comments off. I would be more than happy to take up the dialogue on Twitter or through a pingback to your blog. You can also contact me if you wish to discuss further—Hit the About/Contact link at the top of the page.
Second note: I will curate and organize the major threads of the comment discussion in the coming days. In the meantime, I have sequestered the existing comments as the discussion threatened to overwhelm the point of the initial post. I have not deleted them.