Tuesday, July 17, 2007

Math in Connecticut

Update 7/20/08: For those of you who stumbled across this post in response to the CNN article about the subversive parents teaching their kids 'traditional' math while their schools use concept-based math, read on. The 'math wars' are old news for those of us who have been trying to decipher public school pedagogy.

Another search phrase you can look up is "constructivist math." This is another term for the type of teaching you'll see in schools using bad math curriculums like Everyday Math, Math Trailblazers, and TERC Investigations. Constructivism means that the teachers act more like facilitators in helping your children recreate the greatest math advances human kind has ever made. Let me just state for the record that it took pure genius of the first order for whoever made the first advances in place-value, area and volume calculations, and any other math we may take for granted. The reason it seems so easy to us as adults who understand math is because we were lead through the process appropriately by the teachers who taught it to us. Children may or may not be able to puzzle out every major mathematical discovery, but even if they can it takes a lot of time that could be spent actually learning harder breakthroughs that came later.

For additional information please see NYC Hold and Mathematically Correct. If your school district uses Everyday Math, or any of the others, my God have mercy on your soul and may you have enough money to start using Kumon and Sylvan or enough time to afterschool with Saxon, or Singapore. Read through all the way to the comments where you will see pleas from people stuck with this program and a school board who will stick to their guns (and their bad curriculum) until the children are stuck taking remedial math in college. (end of 7/20/08 update)

Region 15 school system in Connecticut uses the Math Trailblazers curriculum. This curriculum is related to Everyday Math without being quite as bad (though it is abysmal). In one of the local weeklies, a mother wrote a letter to the editor criticizing the curriculum for not teaching her child how to do long division. The letter actually got attention in one of the board meetings.

Approval of minutes out of the way, Joseph Zukoski introduced a Letter to the Editor of Voices newspaper that was highly critical of the Trailblazer math program based on a "progressive concept based" approach to mathematics.

Board members requested Superintendent of Schools Dr. Frank Sippy to look into the allegation that the "holes" in the curriculum are greater than the sum of its parts.

Three weeks later, the superintendent answered the criticism.

On December 14, Dr. Sippy did exactly that. Conceding his own "passion for mathematics" he found that the method provides the basis for a "rich and rewarding" education in "mathematics" as opposed to merely "arithmetic."

He acknowledged that there are differences of opinion in academia about how the subject can best be taught whether by rote, by formula or by applying experience based on real-life situations where first-grade children talk about the same concept from parallel perspectives or fourth graders discuss probability; or growing up to cultivate styles of thinking about problems and situations in real life terms beyond the confines of arithmetic.

Dr. Sippy made clear that the region's administrators and teaching staff are solidly behind applying life problem-solving techniques to the process of learning how to add, subtract, multiply and divide.

Full implementation of concept-based math is in its fourth year at the elementary schools and in its second year at middle school level.

Dr. Sippy told Voices that the full effect of the program cannot be evaluated until these children "funnel" in to the high school three or four years hence. But he believes it will create a cascading effect as the child grows older. [Emphasis added]

Meanwhile, at the December 14 board meeting, Ginny Erickson, who teaches math at Rochambeau Middle School, talked about how problems were solved by sixth graders dealing with the unknowns inherent in math problems by applying everyday life examples and vice versa, understanding that multiplication is repeated addition and division repeated subtraction.

Memorial Middle School Principal John Saylor noted that children entering middle school from the elementary schools were well prepared to deal with the challenges calling for mathematical skills they encounter in the higher grades.

This is precisely the type of thinking that those of us concerned with the state of public education despise. Here is the region 15 superintendent admitting that there is no basis for using this curriculum and whether or not it works cannot even be evaluated until the children have been using the system for eight years. Until then, they will go with gut-feelings and anecdotes. In addition, there is no plan to have a formal evaluation.

If there is any evaluation at all, it will consist of teacher's stories. Even the Connecticut Mastery Test scores will be unreliable without a very large upward change in scores. Trailblazers introduces estimation early in the curriculum. An example cited by Illinois Loop:

Lesson 2: "Is It Reasonable?" 1 hour

The problem for the whole class to discuss is: I used $1 to buy a 29-cent
pretzel, and I got 2 quarters and 1 nickel back. My change should have been
about 70 cents. How do I know they gave me the wrong change?

The teacher can expect strategies (that I have simplified) such as

  1. 29 is almost 30, and 10 — 3 is 7…
  2. 29 is almost 30, and I can count from 30 to 100 on a 200 chart…
  3. 29 is almost 30, and 100 — 30 is 70…
  4. I should have gotten a penny in change.
In a multiple choice test, you may have four or five answers to choose from. The random guessing chance of success is 20% to 25%. Imagine that children do learn the ideas of estimation. This could allow the students to eliminate one, or even two, answers without actually being able to get the right answer. In a test with five possible answers, the children raise their ability to guess correctly (remember that guessing correctly should not be the goal of math) from 20% to 25% or possibly 33%. Using only estimation could increase test scores without actually demonstrating understanding. Of course, the test scores could go down, that would make it easy as long as the tests are not changed over the eight year period.

Many parents are appalled to discover that curricula are not picked based on research and extensive testing. When they then realize that their children are the guinea pigs, the shock deepens. How do schools pick curriculum? That is a really good question.

I attended a homeschool seminar run by a homeschooling mom who had previously taught mathematics in the public school system. I was able to glean some understanding of how 'new math' became popular.

As an introduction, she had all of us homeschooling moms brainstorm about how we use math everyday. A lot of us answered cooking, grocery shopping, balancing the bank account, and tips. Then she had us say whether we estimated, used a calculator, or used mental math. She then used this starting point to talk about how we should teach math to our children.

This exercise was completely invalid--unless you're teaching your children to become homeschoolers. There was no discussion of how physicists, chemists, or astronomers use math everyday. Not all of our children will have the desire or ability to become any of those; however, if we start teaching all children in elementary school for the type of math homeschoolers (or teachers) use everyday--then they can never become physicists, chemists, or astronomers because they will not have the mathematical basis.

Another glaring misconception that I witnessed was the typical establishment contempt for 'algorithms.' Algorithms (if you've not been following the debate closely they are the set of instructions that you and I were taught to follow in order to find the answer to harder problems) are pretty much condemned by 'new math' along with drill and kill. The woman leading this seminar stated that once children learn how to multiple multiple digits or use the long division that we've all learned, they drop the place-value of the number. In other words, you have:
x 24

and you proceed to multiply through 3 x 4, then 1 x 4, and 1 x 4 and locate them properly but do not think '3 x 4, 10 x 4, 100 x 4). For the tens multiplication you use 3 x 2 and don't think 3 x 20. It is a huge mistake to think that this is a failure of the algorithm! It is WHY the algorithm is so much better. It is a higher level abstraction to understand that you can ignore the place value as long you put the product in the proper place value location! If teachers are not explaining and showing HOW the algorithm works (it holds the place for you so you can simplify your work), then the teachers are the problem--not the algorithm.

UPDATE: I am taking dog training classes in Southbury (one of the towns in the region). It turns out that another dog owner is the Pomperaug Elementary School Physical Education teacher. She is on the math curriculum selection team. Perhaps physical education is encompassed in an all-around unspecialized elementary teaching certificate? Perhaps her basic major before educational school was math? I do not understand what the criteria they use for selecting people to be on the MATH curriculum selection team could be. The math curriculum isn't just used in elementary school either. It is for the entire region. Once she heard my opinion of Math Trailblazers, she said the discussion was closed.


Darren said...

Hear hear!

(from a high school math teacher)

carol said...

Well I'm not a math teacher..but what is wrong with learning the algorithm by rote anyway? Plenty of us did that. What changed?

Learning the "concept" or why something works seems like something for later. I think they're straining too hard to make it "relevant" when it's just as interesting as a puzzle. No one cares why Sudoku "works," you just solve the puzzle.

Unless you're a smarty pants.

Kim said...

Hi Carol,

I just spent some time thinking about what I knew about the algorithm when I was using it in school. Not much--just how. I'm pretty sure my teacher showed why it worked, but once I realized that it was valid, just forgot about it completely. It was only when explaining it to my daughter that I "reverse-engineered" the method of how it works.

So I do believe that teachers should show HOW the algorithm works so that students will realize that it is a meaningful and true way to use math. Otherwise they'll just think the teachers taught them a whole bunch of BS based on nothing but their teacher's and other people opinions. Once the validity of the algorithm is shown--then just do it.

So, for me, it comes down to certainty. The students should now the algorithm did not come out of thin air. Other than that--memorize and use!



Dee said...

Kim, Are you still in the district or do you homeschool? I'm in the district and have experienced the following: They are teaching them that if they want, they can subtract left to right (you try this with big numbers and borrowing). They teach the "forgiving" method of division where I-- with a math related college degree-- could not help and the answers to the problems were different than the traditional division. Kids can have their own "stategies" for solving problems which they would not presume to tell them is not the best way. So what this translates to is that if kids want to count on their fingers to add, or add 3+3+3+3+3+3+3 to get 3X7 they will not interfere with the students personal strategy. A sixth grade teacher told me that kids will just naturally fall into doing math problems the right way, without being taught that it is the right way. I could go on and on.

I'm with you on the need to teach why we use the algorithm, but it needs to be the correct algorithm that they'll use for algebra, etc. And not give so much air time to the kids own solutions, which with this program could, for some kids, amount to years of academic math time. No wonder American students are falling behind in math and sciences.

We need people in the district who understand and care about this issue. Are you still in?

Dee said...

P.S. I just looked at the "forgiving" method for one night's homework, after that my son figured it out for himself. So I could be wrong about it being a hard concept.

P.P.S. I actually had one teacher tell me that they "want the kids to know that there isn't just one answer to a math problem." Huh?

Kim said...

Dee, I hope you check this again. After checking out the curriculum and interviewing the principle of Pomperaug Elementary School, I decided to keep my daughter in private school and then homeschool her. Does that sound like a district that is willing to listen to parents? Given the Department of Education's persecution of people trying to withdraw their children from school for homeschooling, I have been keeping my head down in town. I believe, though, that you are correct. Those of us who understand the importance of math in the real world (instead of the school-world) really ought to take a stand. I wonder if they'll be as defensive as Region 14 was about the buses. If you're interested, you can e-mail me at turnermcneill .at. yahoo .dot. com