Another high school math debate

In a follow-up to the last post, I came across an article in the Salt Lake Tribune (math education in Utah is a particularly fascinating topic). It seems that a district superintendent sparked a debate with the state superintendent when he sent a tweet that called the state’s position on high school math standards, “curious.”

The disagreement comes not from whether students should take more math in high school, but rather from what math they should take. The state superintendent believes that all students should take math through Algebra 2, and then have options for further study. His critic believes that all students should take calculus.

I agree with the first idea, for a few reasons. Calculus has been inappropriately crowned the king of math. Calculus is merely a doorway to further studies in math or a related field. Students considering a career that is rich in mathematics (pure math, math education, engineering, physics, etc.) should plan to take calculus, preferably in high school.

Many college-bound students will benefit more from a statistics course (required if they choose to attend graduate school) than a calculus course. Most students, regardless of their career plans, would benefit from a course in discrete math, although most schools and districts are slow to consider this path.

The danger of the argument is that these options are being labeled “tracks,” a negative term that implies that students that take statistics are not as smart or capable as students that take calculus. The responsibility lies with the schools and teachers to ensure that this ability grouping doesn’t happen, and that students are given every opportunity to follow the path of their choosing beyond Algebra 2.

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…And the Counterpoint

A few days ago, I posted a link and some commentary about reform math in Washington. Today, I came across this post, which is specific to Everyday Math.

The author notes that, “Reform math has dominated our schools for more than 15 years. Over this period, our international ranking has plummeted.” It seems that the article in the Seattle paper directly refuted this claim. At any rate…

The author basically degrades Everyday Math, citing several states that have banned or failed to adopt the program for various reasons. Here’s what might be my favorite paragraph:

Everyday Math has been described as a “mile wide and an inch deep.” U.S. Secretary of Education Arne Duncan is calling for “more depth and less breadth” in education. States like Connecticut are heavily invested in reform programs like Everyday Math. The Hartford Courant newspaper recently reported that 40 percent of incoming college freshmen require non-credit “remedial” mathematics.

Mile Wide, Inch Deep: Show me a core basal program that isn’t. It’s a symptom of over 50 different sets of standards and a long-running debate over what students really need to know.

More Depth, Less Breadth: This should be the goal of every teacher. Figure out what your students know, what the “kinda” know, and what they don’t know, and then adjust your teaching to fit. I’m a big fan of Texas Instruments and what they are dong for education, but stories like the one I received in a TI email today send shivers up my spine: “Imagine having your whole year planned out before stepping foot in your classroom.”

Remedial Math: Only 40 percent? Seems low. Again, this is a symptom of more than the program. It’s about outdated standards, outdated teaching, and a refusal to move away from the teacher’s comfort zone.

So we’re back to the same place: It’s about instruction.

(Note that nashworld does a great job of highlighting the need for quality instruction-through his own experience-in a recent post.)

Related:
How many times do I have to tell you…

What did you expect?

Wait. I Can MAKE Kids Learn?

I came across something interesting today. I ventured (for the first time) onto Google Books to see what they had to offer. I made my way to K-12 Mathematics – no big surprise there. And I came across this:

The Equation for Excellence: How to Make Your Child Excel at Math by Arvin Vohra.

Perhaps I’m naive, but I’m not familiar with Arvin or this book. I’m not going to talk about the author – I’ll let you form your own opinions based on his website.

I looked at the table of contents, and Chapter 11: The Calculator Fallacy caught my eye. So I started reading. I will admit that some of the points are valid and made me stop to think, but there is a general theme of “calculators make students lazy” and “teachers are misinformed.”

Then we get to this: “A student solving a complicated problem spends very little time doing actual calculations. Most of the time is spent examining relationships and determining what concepts apply.”

Wait. Didn’t he just make the case for calculators? I used graphing calculators to help students examine relationships and link concepts. If they used the calculator to multiply six and four, so be it.

The author then supports his statement: “The student who does math by hand has these concepts ingrained in his mind, and is adept at using them.”

Again, wait. Did he just tell us how students gain conceptual knowledge? Wow. We’ve been trying to figure that out for a while, and here was the answer all along. Make them do the work by hand. (Nobody’s ever tried that one before.)

Doing math by hand does not build a solid conceptual foundation for learning. Models help students build this foundation. Rich activities that apply learning help build this foundation. Regurgitating facts and working everything out by hand do not build conceptual understanding.

Finally, this assumption: “Thus, he rapidly sees relationships between various formulas and concepts, and can quickly figure out how to do the problem.”

I can count on one hand the number of students who made connections between formulas and concepts by simply doing problems by hand. I agree with the idea that a calculator in the hands of a less effective teacher is a dangerous thing. But the author discounts the role that a calculator can play in discovering patterns and understanding relationships, and the role of an effective teacher in promoting this kind of calculator use.

Washington’s Miniature War

If you follow the ongoing saga of the “math wars” at all, you are likely familiar with the long-running debate in the state of Washington. Many school districts in Washington were early adopters of NSF-funded “reform” mathematics curricula, and much of the debate surrounding these programs has come out of Washington. (If you don’t believe me, do a search on YouTube for math.)

Even given this background, I was a bit surprised to see this guest editorial in the Seattle Times regarding discovery-based math. Of particular interest to me were the comments.

I think we’d like to believe the math wars are over. This article, and the related comments, bring us back into reality. It begs the question, “Will the math wars ever end?”

Why do I care?

You might ask, “Why does he care about math education so much?”

And then I come across something like this:

If you see what’s wrong with this, you get my point.  If you don’t see what’s wrong with this, you’ve made my point.

If you need a hint, let me know.  I’m still a teacher at heart.

(Image from eggindustry.com)

Talking the Talk

We had an opportunity to welcome Dr. Kevin Feldman to our school district last week. He presented a day-long session on “Narrowing the Lexical Divide: The Critical Role of Vocabulary & Academic Language in Improving Secondary Literacy Across the Curriculum.” His focus on academic vocabulary was of great benefit to the teachers in attendance.

One thing that really caught my attention in his presentation was the discussion about where we find Academic English – that Hayes and Ahrens (1988 ) used a measure of “rare words per 1,000” to evaluate the frequency of word use. They found that the everyday adult speech of college graduates is at approximately the same level as preschool books, and that most informational texts are at a level comparable to newspapers and magazines.

This reinforced my belief that we have to talk about math before we write about it, and also supports the notion of developing formal spoken language as one path to formal written language (see Pimm (1991)). It also made me wonder about the level of spoken English in math classrooms, both by teachers and by students. Then Dr. Feldman showed us this website, which will analyze passages to determine rare words per 1,000.

Those who know me will likely guess what I’m thinking: research. This should be fun!