For a fun and mathematical card game online, visit my Calculation page. Solitaire with strategy.
This is an open letter to the Troy school district, Troy MI, regarding Chicago Math, which was recently introduced into the curriculum.
Dear Faculty and Staff:
I am writing to express my concern about Chicago Math, which is currently being taught in the Troy elementary school system. This program has failed my two daughters, and is not the best choice for our students.
First, allow me to introduce myself. My name is Karl Dahlke, and I have always loved mathematics. When I was in elementary school I quickly learned the basics of arithmetic, using the "traditional" method. By traditional, I mean the method most adults use to multiply and divide large numbers. Something like this:
4218 × 39 ------- 37962 12654 ------- 164502
I pursued advanced mathematics in high school, and then in college, obtaining a degree from Michigan State University, and another degree from the University of California Berkeley. The latter is (in my opinion) one of the top 20 graduate math programs in the country. Today I maintain a web site of mathematics at the undergraduate and post graduate level. You can visit it at MathReference.com.
Before I attended Berkeley, I interviewed at the University of Chicago. I had a chance to talk to their staff, and I realized that this too was one of the finest math programs in the country. The professors at the University of Chicago tackle some of the most difficult math questions facing us today. I'm not sure why I didn't go there, since I already lived in Illinois. Maybe it was the Chicago winters. :-) In any case, I was a bit surprised to learn that these august professors had developed a math curriculum for elementary students. This is like asking Einstein to write a physics primer for young children. The resulting program is probably perfect for the gifted few who will go on to study math and physics in later life, while it confuses the hell out of the rest of us. Indeed, I believe this is the case with Chicago Math.
(I have since learned that "Chicago Math" was not developed by the math department, but rather, the department of education at that university, which is now closed. Some of the math professors would like to distance themselves from "Chicago Math", but at this point it is easier said than done. Anyways, back to the subject at hand.)
Consider multiplication and division. The program asks the student to draw various grids and maintain a catalog of intermediate results, with all the zeros in place. This is suppose to teach you, indirectly, that the integers form a ring, and that the traditional method works because of the distributive property of multiplication over addition, the commutative property of addition, and so on. I see where they are going with this program, but nobody else does, least of all the students.
I have three children in the Troy school system, which is, by the way, one of the finest school districts in the country, with the best teachers I have ever seen. I am proud to have my children attend these schools. Our students are learning math and getting high scores on standardized tests, primarily because of these teachers, and in spite of Chicago Math.
Let me illustrate with my two daughters. (My son is in special education, and is exempt from Chicago Math. He is learning math the traditional way. With all his disabilities, I am glad he does not have to slog through Chicago Math as well. That would simply be too much.)
My first daughter, whom I will call Jane, is extremely bright. She is in the program for gifted children, and does well in all her subjects. Nothing slows her down, except Chicago Math. On rare occasions she has come to me in tears, asking for help. I show her what they are asking for, and she understands the process, but still seems confused. She applies it faithfully on the test and gets an A, but doesn't see the point of it all. Despite her keen intellect, she does not grasp the deeper meaning, the "why it all works". And if she doesn't get it, nobody does! And if nobody's getting it, then we may as well teach the traditional way and be done with it.
My other daughter, Mary, has an average intelligence and a reading disability. Chicago Math has failed her completely, primarily because it entails a great deal of writing and copying. Intermediate results are scattered all over the page, and you have to be an accountant to keep track of everything. For a girl who is borderline dyslexic, every scratch of the pen is an opportunity for error. She needs to multiply and divide using a process that conserves ink as though it were liquid gold. Intermediate results should be kept to a minimum, and the answer should come together just below (multiplication) or above (division) the problem. In other words, she needs traditional math!
I have seen Mary struggle mightily, as Chicago Math presented four awkward algorithms for division. (Yes, they use the word "algorithm". If you don't know what that means, where does that leave our kids?) Perhaps the creators of Chicago Math wanted these four methods to be optional, i.e. select the one that works best and use it to solve the problem, but that is not how Chicago Math is taught in our district. The student is expected to master each method, and is tested on each in turn. By the time the third method fights for territory in my daughter's brain, she is hopelessly confused. Furthermore, none of these methods are traditional, which is exactly what my daughter needs.
After a year of confusion and frustration I taught my daughter how to multiply and divide using the traditional method. The problem is solved in a couple lines, rather than a page of scattered intermediate results that must be assembled correctly at the end like a jigsaw puzzle. I was able to teach her these concepts in one evening. She quickly learned how to multiply our phone number by a two digit number, and then we divided our phone number by a two digit number. The entire problem remained within her visual and mental focus at all times.
At this point I would like to make a distinction between the kid-friendly story problems, and the confusing algorithms and procedures, introduced by Chicago Math. I like some of the story problems, dividing 47 pieces of candy among three friends, for instance, and I don't want to throw out the baby with the bath water. We should continue to incorporate these types of real-world problems in our curriculum. However, there is no point in presenting the above story problem until the student can divide 3 into 47, almost without thinking. The process should be automatic, like driving a car. Unfortunately the (otherwise helpful) story problems are brought in far too early in Chicago Math. Having seen several confusing division algorithms, Mary still had no idea how to divide 3 into 47 when the story problems came rolling in. While she was busy looking for "friendly pairs of numbers", (division algorithm number 3), she forgot the story completely. When she finally had an answer, and the book asked what to do with the remainder, Mary had no clue. It took her so long to do the math, she forgot all about the candy and the three friends. The benefits of the story problem were lost, because the confusing algorithms got in the way.
As an analogy, you don't teach someone how to read a map and find their way around an unfamiliar city (the story problem) until they are completely comfortable driving the car. The young driver is so busy concentrating on the details of steering and braking, he hasn't got time to read directional signs or consult the map. In fact, the two tasks work against each other, making it impossible to learn either one.
Adding insult to injury, Chicago Math teaches you to drive the car by opening up the hood, taking the engine apart, and putting it back together. You are suppose to understand everything from the thermodynamics of internal combustion to the hydraulics of the steering and brakes. When you want to turn right, you are suppose to manipulate all four steering rods with your hands and feet, while keeping your eyes on the road. For a girl who is borderline dyslexic and partly ADD, this is simply impossible. She just wants to drive the car! She doesn't need to know why it works; that comes later. So I showed her how to drive the car in the simplest terms, and she understands. She can now multiply 4218 by 39, as shown above. I just wish we could have skipped the years of confusion and frustration.
In summary, I believe the awkward algorithms promoted by Chicago Math are inappropriate for most of our students. A small percentage of gifted children may grasp the deeper meaning, the detailed construction of the car's engine, but most will not. Many children are left behind, and cannot perform the simplest arithmetic operations that we take for granted. This is especially true for the kids who are already struggling.
When I was a teen-ager I watched my younger siblings trying to learn the "New Math" that emerged in the late 60's and early 70's. I just shook my head in disbelief. I couldn't see the point of it. Why not teach them the same way I was taught? As Tom Lehrer quipped in his famous parody, "The important thing is to understand what you are doing, rather than to get the right answer." In the 80's New Math faded away, and I heaved a sigh of relief. Now we have Chicago Math, and that's even worse! I guess what goes around comes around.
I encourage our school district to return to traditional mathematics, and I hope other districts will follow suit. At the same time, I hope we can retain the valuable aspects of Chicago Math. The alternate algorithms should be made available for the few who do not grasp traditional math, and each child should be allowed to use his favorite method, any method, to solve the problem, as long as he gets the right answer. But traditional math must be taught first, and most students won't need anything beyond that.
When arithmetic can be performed automatically, using one method or another, bring in familiar story problems, and the child will put it all together. These are helpful indeed, provided the child has already mastered the basics. But please remember, traditional math, as a mechanical process, must come first. We've been teaching it for centuries, and despite a few fads in the 1970's and 1990's, there is still no better way.
Read a math teacher's perspective. This is more analytic, and more precise, than my rambling letter as a parent.
Professional reviews of Chicago Math, and other programs.
Read what other parents and students are saying. I'm not being selective here; 99% of the letters I receive express dissatisfaction and frustration with Chicago Math. That's not a typoe or an exaggeration - 99%. Here are some examples.
on this article, or visit my home page.