Clear as Mud, Dept

.Jason Zimba one of the lead writers of the CC math standards, when asked to explain whether there is a distinction between being “fluent” with math and “memorizing” offered some explanations.

First, on the issue of whether CC requires memorization:

“The standards require students to know basic facts. Here is the language for multiplication (page 23): ‘By the end of Grade 3, know from memory all products of two one-digit numbers.’ We can debate the best ways to help students meet this expectation, and we can debate the best ways to assess whether students have met the expectation. Those are good discussions to have. But there is no room to debate the expectation itself. The language in the standards is unambiguous.”

Then he distinguishes between “fluency” and “memorization”

“Fluency pertains to an act of calculation. In particular, to be fluent with these calculations is to be accurate and reasonably fast. However, memory is also fast, so the difference between fluency and memory isn’t a matter of speed. The difference, rather, has to do with the different nature of calculating versus remembering. In an act of calculation, there is some logical sequence of steps. Retrieving a fact from memory, on the other hand, doesn’t involve logic or steps. It’s just remembering; it’s just knowing. The mental actions of calculating and remembering are different. The standards expect students to remember basic facts and to be fluent in calculation. Neither is a substitute for the other.”

So, they don’t mean the same thing, except when they do. Here, read it and tell me what it means. I’m having a beer.

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3 thoughts on “Clear as Mud, Dept

  1. Barry,

    You wrote: “they don’t mean the same thing, except when they do.” But I’ve looked again at the quoted text, and I can’t see where it ever says that the two phrases refer to the same thing. What I see is a consistent attempt to differentiate them. Note the words “…difference…difference…different…on the other hand…different…neither is a substitute for the other.”

    As far as I can see, the only moment where I allow any similarity is when I point out that both remembering and fluent calculating are fast. Writers differentiating two things often note briefly what the things have in common, so that readers will know enough not to be misled by superficial similarities. Admittedly, that makes the paragraph more complex; I apologize if it was poorly written. I trusted that words like “…difference…difference…different…on the other hand…different…neither is a substitute for the other” would guard against misinterpretation.

    The fuller context also helps; this is shown below.

    (Lacking HTML, I have set off a few key phrases using all-caps. Please adjust the volume downward.)

    Amber Northern: “Some folks seem to think that ‘know from memory’ also means ‘being fluent in.’ Can you clarify the difference?”

    Jason Zimba: “THEY AREN’T THE SAME THING, and the language of the standards makes this clear. Let’s look again at the standard on page 23, which reads in full as follows:

    “3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 Ă· 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

    “The first sentence sets an expectation of fluency. The second sentence sets an expectation of knowing from memory. If being fluent were the same thing as knowing from memory, the second sentence would not have been necessary. That the second sentence was included shows that THE TWO THINGS ARE NOT THE SAME.

    “In the context of arithmetic, the word ‘fluently’ is used nine times in the standards; there is also one instance of the phrase ‘demonstrating fluency.’ In every case, fluency pertains to an act of calculation. In particular, to be fluent with these calculations is to be accurate and reasonably fast. However, memory is also fast, so the difference between fluency and memory isn’t a matter of speed. The difference, rather, has to do with the different nature of calculating versus remembering. In an act of calculation, there is some logical sequence of steps. Retrieving a fact from memory, on the other hand, doesn’t involve logic or steps. It’s just remembering; it’s just knowing. THE MENTAL ACTIONS OF CALCULATING AND REMEMBERING ARE DIFFERENT. The standards expect students to remember basic facts and to be fluent in calculation. Neither is a substitute for the other.

    “Researchers in cognitive science could probably find fault with my description of the differences between calculating versus remembering as mental actions. Setting all that aside, it still remains the case that THE STANDARDS AS WRITTEN PLAINLY TREAT FLUENCY AND MEMORY AS TWO DIFFERENT THINGS. According to the text of 3.OA.C.7, you haven’t met the standard unless you know the products from memory—even if you are fluent in calculating products and quotients.

    “You said that some people seem to think that ‘know from memory’ also means ‘being fluent in.’ I suspect that talking this way is something people do when they wish that the standards hadn’t set an expectation of knowing from memory. Rhetorically, they try to write the word ‘memory’ out of the standards.”

    I hope this clarifies the difference between fluency and memory or at least clarifies that my aim was indeed to stress that the two are indeed different.

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  2. Thank you for the clarification. I think my confusion comes from my own use of the term fluency as in “procedural fluency” which can include calculation. It is a matter of both memorization and automaticity, so for me the distinctions get blurred a bit and fluency for me is very close to memorization. But I see the point you’re making. I disagree about it being a complicated thing to assess, however.

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  3. Dear Mr. Zimba,

    I don’t care how the math standards were written. Your re-iteration is useless, because through application it is as ‘clear as mud’.

    I can say this because I’ve spent the last four years RE-TEACHING my child basic K-3 math, including MEMORIZATION of math facts so that they could become FLUENT.

    The multiple strategies imposed by Common Core are flat out ridiculous and require the child have the basics first the vast majority of the time. As a mom of two young children, I can say without reservation that the Common Core standards read like stereo instructions and are just as easy to follow. They look great on paper, but the application in K-5 is age and developmentally inappropriate rubbish.

    Thanks, but no thanks.

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