You must be joking!

Large excerpt from interview with on Education Next Stephen Wilson is: "a professor of mathematics at Johns Hopkins University, served on the National Governors Association-Council of Chief State School Officers “feedback group” for the Common Core standards, and was mathematics author of Stars by which to Navigate? Scanning National and International Education Standards in 2009: An Interim Report on Common Core, NAEP, TIMSS, and PISA."

My comment notes follow.

[Education Next]: Will the Common Core put an end to what has sometimes been termed the “math wars”? In your view, do the math standards resemble those recommended by the National Council of Teachers of Mathematics (NCTM), and what do you make of that similarity (or lack thereof)?

[W. Stephen Wilson]: The end of the math wars! You must be joking.

There will always be people who think that calculators work just fine and there is no need to teach much arithmetic, thus making career decisions for 4th graders [1] that the students should make for themselves in college. Downplaying the development of pencil and paper number sense might work for future shoppers, but doesn’t work for students headed for Science, Technology, Engineering, and Mathematics (STEM) fields.

There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem.

There will always be the standard algorithm deniers, the first line of defense for those who are anti-standard algorithms being just deny they exist. Some seem to believe it is easier to teach “high-level critical thinking” than it is to teach the standard algorithms with understanding. The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared.[2] Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.

There will always be people who believe that you do not understand mathematics if you cannot write a coherent essay [3] about how you solved a problem, thus driving future STEM students away from mathematics at an early age. A fairness doctrine would require English language arts (ELA) students to write essays about the standard algorithms, thus also driving students away from ELA at an early age. The ability to communicate is NOT essential to understanding mathematics.

There will always be people who think that you must be able to solve problems in multiple ways. This is probably similar to thinking that it is important to teach creativity in mathematics in elementary school, as if such a thing were possible. Forget creativity; the truly rare student is the one who can solve straightforward problems in a straightforward way.

There will always be people who think that statistics and probability are more important than arithmetic and algebra, despite the fact that you can’t do statistics and probability without arithmetic and algebra and that you will never see a question about statistics or probability on a college placement exam [4], thus making statistics and probability irrelevant for college preparation.

There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics[5] with content.

There will always be people who think that teaching kids about geometric slides, flips, and turns is just as important as teaching them arithmetic. It isn’t. Ask any college math teacher.

The end of the math wars! You must be joking.

[1] " making career decisions for 4th graders "

This is one of the big problems I have with the kids' school. Their curriculum makes it almost impossible to follow a path towards a STEM career. Our school uses the weak "Everyday Mathematics" curriculum, but even does that poorly--every year, they only get through about 2/3rds of the material. Year after year, those 1/3rds left behind add up. The entire 6th grade math curriculum is a review of 1st-5th grades, because the kids are so poorly prepared for pre-algebra. And even there, they are already 60% of the way through their school year (even counting the week-long trip that is coming up in March) and are only through chapter 5 of a 13 chapter text. Chapter 6 is the always-exciting "Using Multiplication"!! This is supposed to be 6th grade, third trimester work, and these kids have no idea how to work with fractions, calculate the area of a circle, or the volume of anything! This is simply not a track that will allow kids to take calculus senior year of high school, which is what many STEM majors in college need.

[2] "The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared."

Try the lattice method with large numbers or decimals! At open house for 4th grade this year, the parents were doing a good job of eating the teacher alive. Sure enough the lattice method came up, and someone asked about doing it with bigger numbers. My sister piped up and asked about doing it with decimals--The teacher didn't know how to do it! Another parent, with an older kid, started to explain, and my sister said--"Yes, we know how to do it; the point is she (the teacher) doesn't know how to do it!" Yet, they still spent several weeks doing it this year, and if you used the standard algorithm on your homework, you were graded down.

I remember when the 3rd grade teacher wanted to show his students how well and quickly the lattice method worked. He had someone come up and do the standard algorithm on the board while he did the lattice method. Lo and behold, the teacher won! Our kid came home defending the lattice as "quick!" I had to point out to him that the teacher had cheated; he had drawn the lattice in advance—the most time-consuming part was thus ignored. I showed our kid how long it actually takes to do the two methods. But it's a strange thing, kids can get very defensive about their teachers, even when the teachers are full of … The kid got mad at me for showing him the teacher was wrong.

[3] " you do not understand mathematics if you cannot write a coherent essay "

This is actually a bigger problem than it seems. There has been a push for many years to drive reading and writing into every class, including math. No similar push has been made to get math into reading and writing classes—leaving less math time for actual math. But that's not even the big problem.

Some kids excel at language, some kids excel at math. Not all the kids who are good at one are also good at the other—though many are. In particular, many boys hate the language parts of school (especially when they are forced to write or read self-reflective pieces about emotions, hopes and dreams—sometimes it's better when they are allowed to blow things up with words and read snot jokes.) For many of the boys who struggle with language (and it can be something as simple as have slower-to-develop fine motor skills which makes writing a (literally) painful chore) math is their salvation. They can be good at math without having to put any of it into words.

At least, they used to be able to. Now half the problems are word problems, and half their answers have to be too. This is one of the reasons boys are having so much trouble in school. For the more math-oriented boy, they no longer can escape their weak language skills.

Also, ask yourself this: which do you think is easier for kids to master, a set of 26 symbols with 42 different sounds, joined together in increasingly complex and confusing ways. Or a set of 10 well defined symbols that always mean the same thing and follow simple and easy to experience rules. "Wind" can be something that blows, or "wind" can be something that rolls up. 10 is always 10, 15 is always 15. There is some evidence that pushing arithmetic at an earlier age and backing off on the language skills could be beneficial for a non-negligible segment of kids. In essence, kids can develop a natural and strong understanding of numbers before they develop a similar understanding of phonics, vocabulary, language and the motor skills needed for reading and writing.

[4] " you will never see a question about statistics or probability on a college placement exam "

I'm not so quick to dismiss statistics. I think it is the most-important worst-taught subject in school. If it is not part of the regular math sequence, I think it should be a separate semester-long class at the high school level. Every single day we are bombarded with statistics, and without learning how they can be manipulated, exaggerated, and misused, we are all apt to fly off the handle when we hear our (completely insignificant) RISK HAS DOUBLED! Or 50% of people polled think you're an IDIOT (when they only asked your best friend and your twerp of a brother.) People need a far better understanding of statistics than they currently have. My high school required a one-semester economics course; they should also have required one semester of statistics.

[5] " You learn Mathematical Practices just like the name implies; you practice mathematics"

Amen. I keep telling the kids this one. You can only get good at math and science by doing as many problems as you can get your hands on. If the teacher assigns the even problems, and the book has the answers for the odd in the back, do the odd too! The more, the better.

This is also the biggest problem with the ALEKS online math program. They give a kid three problems, and if they get them right, that's it. Eventually, the kid will be given a test on whether they've really learned it or not, and often will have to repeat the section, again and again—with a feeling of failure instead of mastery. It would have been better to be given many more examples before letting the student cross that topic of their list. It takes a lot of practice to really learn long division or how to find a least common denominator. Practice makes perfect.

Paying the price

The 9-year-old boy is bored.

This is becoming quite a problem, and he's complaining about it more and more.

First of all he's bored in science class. This particular problem started when I decided to be sneaky. I noticed that "The Magic School Bus" was airing on TV, commercial free in the mornings, so I set our DVR to record it. If you don't know about this show, it is a science-based cartoon where a magical teacher takes her third grade students on science adventures. They might shrink to the size of cells and enter a body to see how the immune system works, or they might go back in time to see the dinosaurs. The episodes are well done and actually informative. If you watch all of them, you really would have a good elementary-school level knowledge of science. When I began recording the show, I didn't tell him to watch it, or even tell him that I was recording it. I thought he might find it on his own on the DVR's menu. He did. It became one of his favorite shows, and he's watched each episode several times.

The problem is, now everything he is supposed to be learning in science class he has already learned from "The Magic School Bus," so he's bored in class. I still think there are valuable things for him to learn in class, and the teacher is one of the best in the school, but most of what he's being taught he already knows. The one good thing on the horizon is the school science fair. In third grade they present an animal (he did Great Horned Owls) and in fourth grade they present either a recent development in science or a major historical invention (his sister did the Mars rovers Spirit and Opportunity). That project should start up in the second semester, and should help alleviate his science boredom.

The second problem is in math class. Because he's been working on Aleks, and has done a sizable chunk of the 4th grade standard curriculum (in 2 months), everything in his math class is going to be review. The other day they started to work with variables in his class; he said he'd done this already, and the teacher asked him to help her present it. That was nice for him, but he's still bored and frustrated that he isn't learning anything new in math class. As far as I can tell, this problem is permanent. I'm going to keep him moving in math at home regardless of what happens in school. (I spent some time this morning creating and finding some supplementary material on multiples, primes, and factoring.) He needs to spend some time outside of Aleks solidifying some skills that only come through practice: standard arithmetic algorithms for addition, subtraction, and multiplication. Lots of practice with long division (which his school's text book literally doesn't believe should be taught at all.) And lots of work with fractions. But I see him getting to the 5th grade curriculum within a month or two.

That's fine by me. The school's curriculum moves too slowly and they allow no opportunity for kids to work ahead. But moving ahead will make all math at school from this point on review and, thus, boring.

I guess the kid will just have to be bored.

Aleks update

It's been about a month since the boy bumped up to the Level 4 course on Aleks. When he started, he knew about 63% of the fourth-grade curriculum, according to the California state standards.

One month later, he has spent about 9 hours working on the program. He is finding fractions very confusing; in part because he is always trying to figure them out pictorially, and he doesn't know how to go about it. Today however, I got him to some level of understanding of the "bowtie" method of adding and subtracting fractions with different denominators.

Bowtie method:

1) Get a common denominator by multiplying the two denominators together.
2) Multiply the left numerator by the right denominator
3) Put in the correct sign
4) Multiply the right numerator by the left denominator.

I also think I drew enough pictures so that he sort-of gets it. He needs more work on fractions in general, though. Especially converting mixed and improper fractions, and reducing fractions.

I have been assigning him some extra work in multiplication, which the program allows me to do. They call it a quiz, but I think of it more as a review worksheet. Sometimes you just have to work dozens of problems before it really sinks in, and Aleks doesn't do that unless you tell it to.

So, after a month, the boy has learned about 20% more of the curriculum, and currently stands at 84% of the CA standards for 4th.

He is doing about 7 topics per hour, and he has about 32 topics left. So another 5 hours or so should get him through. I would love for him to complete level4 before he does standardized testing in mid-November. That should be doable.

Aleks says...

A few days ago, the boy (9) was working on Aleks. He had 3 of 5 pie pieces done, and another one was nearly done. Then, he got a bee in his bonnet and spent over an hour two days straight on the program. It's a really nice problem to have when you think your kid is working too hard and should back off! I didn't want him to burn out.

Still, yesterday, with the promise of getting his very-own real-world pumpkin pie if he finished his virtual math pie, he got through the rest of Level 3. This means in less than a month, he has done 45% of the California state standards for 3rd grade. How well he knows it, I'm not sure. Each topic only needs about 5-6 problems done correctly to pass it. It might be too much of a once-over-lightly approach, but, since math is cumulative, I'm hoping it will stay in his head.

Here are his pies:

Tomorrow, I'll switch his account to Level 4, and he'll take the Level 4 assessment for the first time, and get a brand new pie to work on.

Today, he was very proud of himself, and was shouting: "I won the pie!"

To which I answered; "I two the pie."

"I three the pie," he answered.

"I four the pie."

"I five the pie."

"I six the pie."

"I seven the pie."

"I eight the pie," I said, triumphantly.

"YOU ATE MY PIE!!!" he said as he attacked me.

We laughed and had a good day.

Spending time with Aleks

The 9-year-old boy has now used the Aleks program about 4 times. Some of that time was working with their "Quick Tables," which is a math-fact learning tool.

Quick Tables was a bit frustrating at first, because before they throw one math fact at you, they want you to have the keyboarding skills to be able to type in the answer quickly. After several sessions of simply typing in numbers, I punted. Though he was getting faster, he still wasn't getting to the point of the exercise: math facts. So, I took over the keyboard and now do the typing for him. We've used it twice, going over all 4 types of facts, but focusing more on multiplication. The program works cleverly. You begin with very simple facts like x1 or x2, then move up from there. It knows what you know and works on improving. I like it. I also like that it isn't flashy or time-wasting. Many online math games are more game than math. The kid ends up spending their time shooting asteroids instead of doing math.

The second part of the program is the Pie. The boy has a pie chart with each segment partially shaded. The shaded area shows how much of the pie he has mastered. He gets to choose which pie piece to work on, and which topics to learn. For each topic the program offers a few problems with an explanation there if you need it--you don't have to see it if you don't need it. After you've done a few problems--I think you have to get 3 or 4 in a row correct, the program allows you to move on. I'm happy that the boy realizes that three or four problems are not enough to really get a math concept, and he will often choose the "More Problems" option without any prompting from me. After a couple more problems, the program moves him on and back to his pie to choose another topic. He has already mastered 14 topics of the total 127 in the 3rd grade curriculum. That means he has moved from a 55% to 66%, To put it another way, he's learned 11% of the 3rd grade curriculum in just 4 sessions.

Instead of logging into the program and walking away, I sit with him. I can catch when he is going wrong, prompt him to use the explanations, and explain further if he needs it. The one time I walked away, he found it frustrating. I don't think he wanted to look at the explanations, or he didn't understand them if he did.

I also wonder if the initial assessment wasn't off because we did it near the end of a lazy summer vacation. I think that probably caused him to get a lower score on the basic arithmetic, but while sitting with him, I realized he has some big gaps. He's been doing geometry and was confused about the terms perimeter, parallel, and perpendicular. The perimeter problem surprised me a great deal. He was presented with a grid with a shape shaded in the middle. He easily counted the shaded squares to get the area (or multiplied if he could), but he wanted to count the number of unshaded squares around the outside and call that the perimeter. I think he got straightened out now, but he needs to review that a couple of times to lock it in. He also had no clue about equivalent fractions (x/5 = 12/20, what's x?,) but caught on very quickly. I don't think he's done much in the way of fractions at school other than counting what fraction of a figure is shaded.

I'm going to continue working with him every-other or every day if we can manage it. I don't want to do long sessions and burn him out, but he seems to enjoy it, and would often go on longer. Right now, I have my sites set on his standardized testing for this year. He'll do it in November, and at this rate, he should be done with the 3rd grade content and on into 4th grade math by then.

Update: We finally got past the assessment for multiplication, and I saw a great difference in his interaction with it almost immediately. He was shown the grid of multiplication, shown which he's already mastered and which need work. The program then offered several for him to focus on. We must have had some typing problems because there were several x2's that he certainly knew. With the chart in front of him, he quickly became interested in mastering the unmastered. In addition, he now has access to a couple math games. He also worked on a few new math topics in the main section of Aleks. He's almost up to knowing 70% of the 3rd grade curriculum! Wheee.

Aleks says

In an effort to make sure that the 9 year old boy isn't playing catch-up as much as his sister, I've signed him up for Aleks.com's math program. It is an online math tutoring program that I found mentioned on several home schooling and parent websites. It starts with a 30-question evaluation of what the student knows.

I gave the boy, who is going into 4th grade, the 3rd grade evaluation. I wasn't entirely surprised, but I was entirely disappointed, that he only scored 55% on the test. That means he knows 55% of what he should--and that is comparing his knowledge to the California standards (we live in Los Angeles.) He was okay with the basics, but weak in geometry and fractions. His math program is philosophically opposed to teaching long division, so he will need some work with that, and his sister hasn't really been taught unlike fractions either, or division of fractions. Aleks, I hope, will fill in the blanks.

I gave his sister the 6th grade test (she's going into 6th and has been getting a great deal of tutoring in the last 6 months) and she scored a 71% on it--not bad. She already knows 71% of this year's curriculum and school doesn't start for a few days yet.

So, I will be using Aleks for him and not for her.