At the end of her Kindergarten year, my daughter’s teacher decided to introduce the concept of dimensions to the students. She explained the difference between the three-dimensional objects, like a piece of fruit, for example, and two-dimensional ones, like a piece of paper.

She told them that the way to distinguish between them is to see that the 3-d ones don’t need to be supported to stand, while the 2-d ones will fall down and lie flat. I had the laugh of my life that evening when my 5-year-old proclaimed that the little babies are two-dimensional because they can’t stand on their own, and become three-dimensional when they grow up a bit and can stand by themselves.

While this example is funny and probably harmless, it illustrates

the importance of choosing the words really carefully when teaching children. Here is a not-so-harmless one. At the end of the first grade now, a different teacher informed my daughter’s class that addition is the same thing as subtraction. What she meant (I hope!), is that from the fact that when you add 2 and 3 you get 5 it follows that when you subtract 3 from 5, you get 2. In elementary schools these days they say that the math sentences 2+3=5, 5-3=2, and 5-2=3 belong to the same “number fact family”. My kid, however, only heard the “addition is the same as subtraction” part. I let it slide the first time she told me that, because it is SORT OF true, addition IS the same thing as subtraction. In a few days, however, there was trouble. My daughter, who, until then, was perfectly capable of solving the addition/subtraction word problems, was stumped by something like this:

* Mary has 6 apples, Jack has 4 apples. How many more apples than Jack does Mary have?*

What are you supposed to do, add or subtract? You were just told that addition is the same thing as subtraction, so why not add?

At this point I realized that I cannot trust my child’s mathematics education to her school. I see way too many college students who just “cannot get” math because of the misconceptions instilled in them when they were in grade school, let alone who don’t know their multiplication tables because of the lack of practice. I don’t want my children to become mathematicians, but I don’t want them to suffer in high school and college the way my students suffer. Way too many of them have to give up on their dreams, which have nothing to do with mathematics, like medical school, nursing degree, pharmacy school, because they can’t get through the required math courses.

But I don’t trust myself with teaching mathematics to elementary school kids either. I cannot project the methods I use with adults onto little ones. There is a reason why the degree in elementary education exists, the elementary school teachers are supposed to know how the little brains work, and teach mathematics appropriately. This brings me to the issue of “Saturday School”, those extra math classes that so many children take these days, at the expense of family time, playground time, etc…, let alone money. Here is my daughter’s take on her extra math class, which follows the Singapore Math curriculum. Her regular school follows Pearson Success enVision Math now, which is much better than Everyday Math that many schools still follow, actually.

*Fourth grade Singapore Math is not really 4th grade.*

*“Grrr!” Go all of my classmates while doing Singapore “Grade 4” math. “This is so easy” all of my classmates say while doing Pearson Success enVision Math. What I mean by this is that 4th grade Singapore Math is not really 4th grade. Let me explain.*

*Ugh, Singapore Math is just so annoying. It is very, very hard. From my perspective, 4th grade Singapore Math is just way too hard for me, as a fourth grader. I have examples. For example, do 4th graders multiply, divide, add and subtract decimals? I don’t think so. But, in Singapore math, that’s just what they do. Also, what 4th grader multiplies and divides units of measurement? I don’t know, yet that’s just what we do in Singapore Math. One example of this is when they ask you to calculate 6 km 250m times 5 and 3 kg 300 g divided by 3. I mean, who does that when they are 9 years old? It doesn’t make any sense to me. Do you see what I mean? I really hope you do.*

*Now let’s turn to the bright side of things. The Pearson Success enVision Math side. As I mentioned before, it is very, very easy. At my school, I finish as one of the fastest finishers in my class and still get the answers all correct. This is the better side of things. We do not do crazy stuff such as the 4 operations of decimals nor do we do multiplying and dividing units of measurement. We do things that are much simpler. For example, we go back to the easy stuff such as adding with base ten blocks. Yes, I know it might sound as if I am in 1st grade but we do it as a review. Don’t you see how much better it is to do easier stuff? It doesn’t make any sense for 4th graders to do work as hard as Singapore Math.*

*In conclusion, I hope that you realized why I think that 4th grade Singapore Math is not really 4th grade. I hope that teachers who teach Singapore Math are going to start explaining it to the kids and telling them that it is hard work to do Singapore Math, as I proved in this essay.*

As you noticed, she learned the fine art of the 4-paragraph compare-and-contrast essay already, but I don’t think I am qualified to comment on English instruction issues, so back to mathematics.

I did a follow-up “interview” with her.

Q: Why do you think it is so easy for you to do the 4th grade Pearson Success enVision Math?

*A: I think it is easy because my teacher explains everything to the kids. She makes sure they understand everything she says.*

Q: How do you know that everybody understands?

*A: I know that everybody understands because my teacher explains it a billion times in a billion different ways*.

Q: But you wrote in your essay that you are usually the fastest. Why do you think that is?

*A: I think it is because the stuff we do is very easy. I know what answer you want. It’s that I finish fast because I go to Singapore Math, but that is very not true, because kids that do not go to places like E-nopi, Kumon, or any other extra math still finish in a snap*.

Q: But there are plenty of kids who get 2’s on their math tests.

*A: I know, that’s because their teachers just tell the stuff and say (without explaining it a billion different times in a billion different ways) go back to your seat and do the following problems.*

Q: How do you know what other teachers do???

*A: I know because I have been in their classrooms and I saw them teaching math. It is not good.*

Q: How do you know about E-nopi and Kumon? You never went to those.

*A: The kids who did go told me about the place and what they learned.*

Q: How many kids in your class go to some extra math class?

*A: 1/8-1/4*

She is a smart kid. She figured out right away what I want her to say, and avoided that with all her might. Unexpectedly, she touched upon the problem of teacher’s quality (and we don’t talk badly about teachers at home, EVER, after all, all women in our immediate family are teachers of some sort), but it’s a different story.

But I know the truth :-). It is not even the quantity of those extra math problems that she has to do. In fact, we switched from one Saturday school to another, Tuesday one, because the former became too “drill-and-kill”. It has more to do with the quality of the problems. In regular school, most of the problems are single-step, with just a few two-step ones.

From Kindergarten to fourth grade, the numbers changed from single-digit to multi-digit, the operations changed from addition to long division, but conceptually the problems didn’t become harder, they are still mostly one-step action. What I like about that Singapore Math curriculum is their focus on the multi-step thinking process. It is a very useful skill, to be able to see through a few steps ahead, like in chess, to see what your immediate action would lead to.

Look at the problems she mentioned. In regular school, they learned that 1 kilometer is a thousand meters, and 1 kilogram is a thousand grams, and THAT’S ALL they learned. They are not supposed do anything with this information. It is no surprise that these facts are not retained, and have to be taught again and again. In Singapore Math, they actually do something at least remotely useful with it.

And it doesn’t hurt that it’s one year ahead of the regular school curriculum.

Now, if only the Singapore Math had just a bit more “drill” in it…

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Looking through the article, do you know of any Saturday/Sunday schools that teach Singapore Math. We did 4th Grade Singapore Math last year at School Plus, but the schedule will not work for us this year. Love Singapore math, and my daughter made such a huge progress with it, trying to find another school. Any information is appreciated, we are in Bayside, NY.

It seems interesting to me that 4th grade seems to be exactly where many of our students become lost. Looking through this list of topics, I am reminded of many problem spots I have encountered in our “college algebra” class at JJ:

http://www.aaamath.com/grade4.html