James Shuls, a former elementary teacher working on a doctorate, and his wife, a Spanish teacher in the local school district, wanted their first-grade son to learn standard math algorithms, he writes on *Education News*. The teacher said the math program focused on “deep understanding.” When they asked for a meeting, the teacher called in the principal, which felt like “being sent to the principal’s office” for challenging the teacher.

The principal offered the chance to observe math classes in three grades.

The (first-grade) teacher was enthusiastic and had a great command of the classroom. I could tell she had experience and connected well with her students. To start the lesson, she read the word problem aloud with the students. It was a multiplication problem in which a boy had five bags and 12 cars in each bag. The teacher wanted to know the total number of cars. Students were reminded to use their strategies to solve the problem, but were not given any specific strategies. What struck me most was the labor-intensive nature of this form of instruction.

. . . even this good teacher could not get around to every student and take the time to help them understand the nuances of every problem-solving strategy that they had developed. As a result, some students were copying, some students had no one-on-one instruction, and other students looked just plain lost. In the entire hour-long lesson, the students worked on only this problem, and by the end, several students appeared no closer to an answer than when they began. Three students were invited to share their strategies at the end of the class, but after they shared their strategies, the lesson was over. The teacher never explained how to solve the problem.

My experiences in the second- and third-grade classes mirrored the first observation. Some students developed strategies, some did not. Never once did a teacher directly teach students how to solve a math problem. At the end of my three hours of observing, I realized that this instructional method encouraged even those students with deeper understanding to work extremely slowly and absolutely left behind all other students.

All the local public schools use the same math program and there are no elementary charter schools in the area. At significant financial sacrifice, they moved their children to private school. We need school choice, concludes Shuls.

In the comments, a parent says “deeper understanding” is code for low expectations.

Also: Why Johnny can’t subtract.

I call BS on this. This tripe not only wastes lots of time but fails to teach kids valuable and necessary skills. The result is incompetence. There is no deeper understanding, there is no conceptual understanding, no number sense and no ability to solve real-world problems (cue my recent account of bakery employees trying-unsuccessfully-to calculate sales tax with a calculator).

BTW, my oldest grandkids are first-gradersin a public school that switched to Singapore Math a couple of years ago. By the end of the year, they are expected to know all their addition and subtraction facts and be able to add and subtract double digits, at least, USING THE STANDARD ALGORITHMS. They will do some work on multiplication, as part of teaching addition.

In elementary school math, manipulatives are used to scaffold the standard algorithms — to give students a concrete sense of what the operation is meant to show you. It’s a principle of good education that you don’t use more scaffolding than the students need. Variant strategies for finding answers are not rejected, but they are used as illustrations of how numerical values can be manipulated correctly using more than one path — not as equally valuable ways to use going forward.

The example given at the top of the post are not bad ways of illustrating the use of manipulaties (in this case, visual ones), but forbidding the standard algorithm is a really stupid way to guide parents. If the kid is ready, s/he is ready. The description of the 3 classes is just horrifying.

The 3 strategies used are superior to the stack um and add um way. The problem seems to be that the teacher didn’t first identify one strategy, logically expain that strategy, and then practice it with them using several different problems. Working their way through all 3 strategies explaining and practicing as they go would probably led to a better understanding of addition. This would be time consuming, though. Singapore math uses exactly this kind of explanation with practice. An average level of their text covers fewer topics with more depth.

Stacy, I disagree. The 3 strategies are only superior to “stack ’em and add ’em” if the students need a visual representation or picture in order to do the problem. The minute they don’t need that, it’s a waste of time to insist on it.

No. It’s not about a visual representation. To understand two digit additon you must first understand place value and the power of 10. The strategies are better because they illustratate both of those. Stacking numbers CAN lead to memorizing the procedure with no understand of why it works. Folks who are quick and automatic at mental math understand number relationships (like the power of 10) better than those who use procedures only.

The problem with the lesson described above it that the teacher didn’t first choose the most efficient strategy, teach it directly and clearly, and then practice it several times with her students.

I assumed that the students had already been shown how place value works. I certainly was, in second grade, as a part of learning the standard algorithm. I agree if students are not shown how place value works first, the standard algorithm would seem arbitrary.

“Deeper understanding” is a way to complicate what’s essentially simple thus justifying ever-increasing budgets, personnel levels and pay.

“Deep understanding” of arithmetic is no more necessary, when all you’re doing is arithmetic, then is a deep understanding of the principles of an automatic transmission when all you’re doing is buzzing down to the grocery store for a loaf of bread.

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“Deeper understanding” should wait for college. The vast majority of students will never need “deeper understanding”. What all the students need is “basic competence”. They only need to know that 15 + 5 = 20, not why it does.

Time to call the local Kumon instructor, because the kids won’t be learning any math in this class.

The article that reported Scarsdale, NY’s adoption of Singapore Math also quoted the local Kumon director as saying he would have to change his marketing strategies. Everyday Math drove lots of kids right into his site.

If the goal of teaching arithmetic is deeper understanding, shouldn’t they be teaching Peano’s Axioms? Yes, turn our 6 year olds into metamathematicians! They still might not be able to do arithmetic.

Students should be able to demonstrate multiple ways of solving problems. If my student used the standard algorithm, I’d accept it, of course, but would also challenge him/her to show me another way of solving it like one of the 10 + 5 + 5 ways shown.

The irony is the “deep understanding” isn’t actually mathematical understanding. Math is a language, with significant parts of it happening to map well to activities in the physical world. Showing clever counting techniques is helpful for some sorts of intuition, but is the opposite of “deep understanding”. Ironically, teaching math as a language, with emphasis on “vocabulary” (including memorizing addition and multiplication tables, and formulas) and “grammar” (the rules of arithmetic and algebra) is more helpful.

Also, by teaching that easy math problems require complex “strategies”, the message being reinforced is that “math is hard”.

God help the elementary teacher that tries to pull this crap with my kids when they go to school – I’m a teacher and a near-obsessive (well, not “near”) pain-in-the-arse when I get annoyed.

Has anyone else noticed that #’s 2 and 3 are absurd, and #3 is also wrong?

In #3, the “ten” box is roughly four times the size of each “five” box. That may seem nitpicky, but any six year old can tell you that those two fives aren’t as big as the ten. If the goal is to improve understanding, the information given can’t be contradictory.

The bigger problem, though, is in the assumptions made to get to those strategies. #2 requires the knowledge that 15=5×3, and #3 requires that you know that 15=10+5. The problem solving strategies are considerably more complex then the problem. You can’t teach addition by assuming students already have a complete mastery of addition.

I hope this type of circular reasoning isn’t typical of current teaching methods. If it is, the only possible expanation is some kind of massive conspiracy to make people stupid. I’d rather not believe that, so I beg anyone to explain to me how it’s rational to teach addition based on a functional understanding of multiplication and division. You’d have to believe it is, to claim that this method is reallyabout teaching math.

You can’t test for deeper understanding, since it’s too fuzzy. Bingo. No way to evaluate. Nice

However, if you want to see if it actually worked, you run the kids through the kind of arithmetic education everybody got–and I mean “got”–for the last hundred years, and don’t tell anybody. Then you test for “deeper understanding” by seeing if they can answer the problems.

Momof4,

My niece who is in 1st grade can already handle addition and subtraction of 2 digit numbers (she was able to handle single digit addition and subtraction before first grade), and knows how to multiply and divide also.

Of course, the dreaded word problem has been a bane to math students ever since the dawn of time (IMO). If you teach the student how to break down the word problem to numeric values, it becomes quite easy to solve 🙂

Assuming this is a for-real thing, it reminds me of my fourth grade year. The previous summer, my mother taught me long division the “old fashioned” way – the way I daresay most people do it, if they have to use a pencil and paper. But no. Even though I could get the right answer and explain what I was doing, that wasn’t good enough, in fourth grade that year we were supposed to use a “grouping” method, “thinking about” 1s and 10s and 100s…..it took much longer to come to an answer and I resisted it.

I wound up staying in at recess a couple days for “remedial” work (read: punishing me for wanting to do it a different way, even though that way worked).

The next year, the math teacher I got said, “I’m close to retirement and they can’t do anything to me. I’m going to teach you the REAL way to do long division” which turned out to be the way my mother had taught me. I liked that teacher much better….