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# Subtraction Algorithms

Let’s have a good old fashioned brawl: is there a mistake here or not?

This submission comes from Chris Hunter, who blogs at Reflections in the Why.

## 11 replies on “Subtraction Algorithms”

John Achesonsays:

What is the world is wrong with these problems? I do not follow the thinking on the grading.

mpershansays:

The teacher agrees with you, John. The teacher graded all of these questions to be correct.

@hamann11says:

Is this a standards based grading? Check marks mean the student understands the concept, maybe a minus sign would indicate they do not understand. How many checks until the student has shown mastery? Curious as to the grade level of this assignment and it’s purpose

Perhaps “mistakes” is the wrong word. This is a good example of how ‘correct’ answers don’t always indicate understanding. Does this student understand subtracting two-digit numbers? Perhaps only minimally, and it wouldn’t make a difference if the sheet kept going on for 100 more questions with 100 more checkmarks. The 15-13 answer says a lot – this student is methodically subtracting digits in each column, and not really thinking about place value or the sense of the numbers involved. So in that sense, I’d say that there is a ‘mistake’ with all of them. Even if the “02” answer were written as 2, I wouldn’t know whether the student has understanding. I’d learn so much more from asking only three subtraction questions with an expectation of explaining the reasoning using numbers, pictures, and/or words.

cb1601ejsays:

That’s why you need some non-standard (crisis) tasks in sequences.

I love all the TouchMath dots on all the subtrahends. /sarcasm

From the way you categorized this post, this is from a second grade classroom? Is it from a state that is using the Common Core standards? If so, this teacher does not get them at all. In grades 2 and 3 students should be working with models and a variety of strategies to solve addition and subtraction problems. They are not expected to learn the standard algorithm until the 4th grade.

Ah, I can just make out in the bottom left corner that this is in fact a TouchMath worksheet. Their website claims that their materials are built on Common Core, but that’s either not true or this teacher is still using old materials.

Procedure, procedure, procedure. Isn’t that what math is all about/

Jim Dohertysays:

Is it completely intentional that there is no question where the student needs to think about ‘borrowing’ in the units column? My 3rd grade son was certainly wrestling with this already last year.

Having taught 2nd grade, my guess is that this is a worksheet introducing the subtraction algorithm WITHOUT regrouping. There is likely a series of worksheets coming up that teach and practice the regrouping steps.

@bstockus The issue here isn’t TouchMath (although I don’t disagree with you). And you’re right– Grade 2.

@diaryofapiman nailed it with “This is a good example of how ‘correct’ answers don’t always indicate understanding.” When asked to explain why 35 take away 23 was (is?) 12, the student was confused. She believed she was calculating the answer to two separate questions– 3 take away 2 and 5 take away 3 that just happened to be written close together. That is, she thought she had answered 32, not 16, questions correctly.

Thanks, Michael, for posting this. I wanted to bring attention to the idea that just as we can learn a great deal about a student’s conceptual understanding by looking at his/her mistakes, we can also be greatly misled about his/her understanding where there are no mistakes.

Having taught second grade 35 million years ago (in the cretaceous period – I think) I am pretty darn sure this is an introduction to subtraction without regrouping. I think the mistake is in the way the concept is being taught. First, bstockus has it right that this is not a standard in the second grade common core. Even more than that, it is completely lacking in the INTENTION of the common core. There is no understanding here. A student should NOT be doing 32 iterations of the same procedure at this grade level, nor at any other. Secondly, the touch points tell the student that these problems should be solving in that one way. I can hear the teacher saying “No, boys and girls, use the touchpoints if you have to, but remember they are there so you don’t get stuck.” Thirdly, the arrows above the ones place tell the student “START HERE, BEEP, BEEP, BEEP”. That takes away any possibility that the student may choose to start in the tens place which is totally appropriate even when using the standard algorithm. Fourth, I shudder at the “naked numbers” I see. Okay, so a little practice is okay, but where is the context? Where is the excitement? The only thing worse would be if this is a timed test.