May 4, 2006

When Math = Not Math

When you live in Maryland.

At one time not too long ago, it was a fairly safe bet that when you sent your kids to school they'd be learning how to read, write, do math, and a few other things. There was never a guarantee that the school would be teaching those subjects well, but you could at least rest assured that those subjects would be taught. This is no longer the case.

If you've ever taken a look at the standards set forth by such influential groups as the National Council of Teachers of Mathematics (NCTM) or the National Council of Teachers of English (NCTE) (edujargon alert: high) you're no doubt aware that both groups are on a crusade to remove math and English from math and English instruction.

They've been wildly successful in this goal despite the fact that neither groups' "standards" have any evidence of success behind them. But why should a little thing like evidence stop our educators from changing what is and the way things are taught and engaging in widespread experimentation on millions of children.

For example, the NCTM are big on statistics and probability. As if it weren't difficult enough teaching plain old math, now educators are being encouraged to add in a probability and statistics strand to math instruction. Something will have to give to accommodate this extra material. There are opportunity costs and trade-offs whenever material is added.

Let's see how one state, Maryland, has handled it.

First let's take a look at Fordham's evaluation of Maryland's state math standards, instead of plowing through the edujargon ourselves.

Statistics and probability are overemphasized throughout the grades, and are sometimes too advanced. For example, in third grade, students are expected to make graphs of data using scaling before the appropriate mathematics (division) has been covered. The emphasis on patterns is excessive ... The pursuit of patterns in these standards is an end in itself with little connection to mathematics.
Ya think Maryland's a little over zealous in the statistics and probability department. Wait until you get a load of their state test: Sample Items: Grade 5 Mathematics. About a third of the sample problems are statistics and probability problems. Of the math problems that remain, the math does not appear to be very difficult or computationally challenging. That's a lot of time learning stuff only tangentially related to elementary math. Come algebra time how much good do you think all that statistics is going to be? And, how much more difficult will algebra be if things like fractions aren't mastered?

Now let's take a look at what the kids in Singapore are learning in fifth grade: fifth grade placement test. Now that's math.

The Singapore kids are well prepared for algebra. The Maryland kids are well prepared for a night at the blackjack table.


Mr. McNamar said...

On question number four, I got it right, but still have no clue why? What does that mean? Oh, yeah, it means I teach English!

KDeRosa said...

Picture a triangle extended from two dimensions to three so that the sides are rectangles or squares.

Question 2 falls into the category of barely useful geometry trivia.

Anonymous said...


As you know, I have been struggling with this for quite some time. It started when I first learned that our affluent town was using MathLand. One parent said that it had to be better than what they were using before. After she explained, I couldn't say I disagreed. My public school taught much more where I grew up. Perhaps not very well, as you say, but there was a chance for a child from a lower income family to get on the high school calculus track without help from his/her parents. I am an example of that. This is very unlikely to happen today, by definition. The lower grades have such a fuzzy idea of math that only the very best (with outside help) can make it into the proper 8th grade algebra course. Our public schools only offer "Algebra Lite" in 8th grade, creating a curriculum gap that kids somehow have to magically make up.

I have noticed a definite anti-knowledge and anti-skills philosophy in K-8 education. My son's first grade teacher commented to my wife and I that (for geography) he had a lot of "superficial knowledge". He was and is a sponge for knowledge and she was dismissing it. I wonder if she caught the episode later in the school year where my son had to show the student teacher where Kuwait was on the map when they had their thematic unit on "Sands from aound the world". They probably read a story about how little Ahmet felt about all of their sand rather than look up the country on the map and learn something about latitude and longitude.

Of course, I find all of this completely incredible - unbelievable, actually. After five years I am still trying to see if there is something I've missed. Many of the teachers I have met are hard working and very earnest. They just have a fuzzier and lower expectation view of education. This clearly stacks the deck against those kids who don't get help at home.

My question to teachers is whether they understand this at all. Do they at least admit that there are very real fundamental differences of opinion over what constitutes a good lower school education. They talk about "best practices" and "authentic education", but they must really know that this is all just fairy dust. Do they think we parents are stupid?

I guess I have come to the conclusion that public schools and teachers just want to do what they want to do and that they have no qualms about doing it. As for math, the best thing I can say is that they are clueless. They utterly do not know what is required to be successful in math. They will find some sort of answer or excuse as to why Singapore Math is not appropriate.

At the very least, they can look at the calculus track in high school and work backwards to see what is required for 8th grade algebra. However, there is a big curriculum (and philosophy) wall between K-8 and high school. The head of the math department at our high school admits that they have no influence over anything the lower schools do. The best they can do is offer a good remedial algebra course in high school. She knows, of course, that remediation is not a real solution.

K-8 education seems to be located in fuzzy La La Land. The self-study our K-8 schools did showed that our kids "held their own" in high school. Who knows whether this was because of or in spite of what the school was doing. Their assessment was used to justify doing nothing about our Algebra Lite in 8th grade. By the way our "hold our own" state education ranking is in the 40's out of 50 states. Our cost per pupil is over $14,000. More money will never change the fact that our K-8 schools just don't teach things - on purpose.


KDeRosa said...

Steve, I couldn't have said it better myself.

Anonymous said...

there was a chance for a child from a lower income family to get on the high school calculus track without help from his/her parents. I am an example of that.

This is my concern.

I'd like to see data on this.

As things stand, I'm continuing to ask any calculus-track student I meet about his/her parents & the amount of help from home.

Anonymous said...

I have come to the conclusion that public schools and teachers just want to do what they want to do and that they have no qualms about doing it.

yes, absolutely

around here, it's almost as if the administrators have hobbies they like to pursue at school (far more true of administrators here than of teachers)

Differentiated Instruction is, IMO, close to being an avocation for our superintendent and for at least one of the principals. They love the idea of Diff-Inst; they think it's sound and right; they want to do it.

The fact that no Irvington parent has ever asked for Differentiated Instruction - just the reverse, in fact - has no bearing on the decision to convert the entire district to Diff Inst.

Anonymous said...

At the moment, it seems to me that the only hurdle for administrators is "selling" the school board.

The president of our school board said admiringly, at the last meeting, that when our superintendent came in for her interview, she "opened up her briefcase and it was filled with papers." (paraphrase)

He was impressed by her research, her documentation, etc.

His reaction, along with the reactions of the rest of the board, is the only reaction that matters in this case.

Ed sent him an email saying that Diff Inst is "technocratic" in nature. What we really need is better subject matter content knowledge for teachers.

The Board president answered that we're doing Diff Inst because everyone else is doing it (this is not how he put it) & asking Ed to direct future questions concerning curriculum and instruction to the Assistant Superintendent.

Anonymous said...

As you may have heard, four schools in Montgomery County piloted Singapore math; but 3 of the 4 schools dropped it. One of the reasons cited was misalignment with the state standards.

The Maryland standards for mathematics were in place before the Singapore Math pilot began. The standards include data analysis, statistics and probability, which Singapore’s texts do not address. In 2001, however (during the second half of the first year of the pilot), Superintendent Jerry Weast commissioned a consulting firm to rewrite the entire K-8 curriculum to align it with the Maryland standards.

Little known fact: By state law, each school district has authority over its own curriculum. Although required to administer the state tests, school districts are not required to align their curriculum with the state standards. So, Montgomery Co could have chosen to stick with their curriculum rather than go with the inferior state standards. They could have chosen to aim for world-class standards, which John Hoven (a parent activist who helped get Singapore piloted) says at one time was one of the goals of the MCPS Long Range Plan. But the Plan was revised to aim at state standards instead—a move, say some, that was a district decision to lower Montgomery County’s standards.

Jerry Dancis, a math professor at University of Maryland was one such person who objected both to Maryland’s state standards and the district curriculum revisions they engendered. He wrote a letter petitioning the State Board of Education to revise the state standards to be world class. The petition stated that a key goal of such a revision would be districts aligning their mathematics curricula with the most rigorous international and state content standards available, such as Singapore’s and California’s. He collected 50 signatures of prominent mathematicians.
Dancis presented the petition at a monthly meeting of the Maryland State of Education in March 2002. Donna Watts, the Maryland State Department of Education leader said of the petition that the signers were college professors who were only interested in future college students majoring in engineering and math, thus effectively shutting off discussion from anyone who might have believed that the goal of education is to provide students with options rather than closing any doors.

MCPS’ revised curriculum was implemented in fall 2001, during the second year of the Singapore pilot. With the introduction of the revised curriculum it became obvious where Singapore was lacking, even though the standards requiring statistics had been in place prior to that. Hoven argues that the statistics component of Maryland’s standards is junk mathematics. “It’s just vocabulary; students learn what range, maximum, minimum, mean, median and mode are, plot graphs, and not much beyond that. It’s easily supplemented.” This is what the pilot schools did and what College Gardens continues to do.

Unknown said...

re: "I guess I have come to the conclusion that public schools and teachers just want to do what they want to do and that they have no qualms about doing it. As for math, the best thing I can say is that they are clueless. They utterly do not know what is required to be successful in math."

I am a public school teacher and am currently feeling frustrated about the same thing, but I think you would do well to specify your comment to ELEMENTARY public school teachers. I teach 7th grade pre-Algebra in Utah and this is my first year. I recently got very frustrated with the level of math understanding my students were not bringing with them to my class so I made a careful analysis of our state core standards for elementary math and I was appalled. The way they try to spiral the curriculum proves to me that they don't understand math, math learning, or math teaching.

Example Case: Students are expected to learn how to measure to the nearest inch in 1st grade, half-inch in 2nd grade, ... 1/16-inch in 6th grade! I believe that any student who understands measuring to the nearest 1/2 inch can measure to the nearest 1/16 inch, given that they know something of fractions.

However, elementary teachers feel more comfortable teaching math this way because they have such a little bit of new information to add each year, it doesn't really matter if they don't feel comfortable with it themselves, or really understand how to teach it.

The way things currently are in math education in our country, I think we'd do better to employ math specialists for grades 5 and 6, much like some places have music or art specialists for the elementary level. Then, the elementary teachers wouldn't have to worry about teaching that "scary math" they never really liked or understood all that much themselves.

BTW - My college roommate was a great friend and was preparing to be an elementary school teacher. Having helped her at length with her Math Teaching Strategies class, I think she would be delighted with this solution, too.