### Choosing Textbooks in West Virginia

Math problem number one: How much is 45 divided by 3? Math problem number one, again: Three children have a jar of 45 marbles. If shared equally, how many marbles will each child get?"Instead of giving children 45 divided by 3, you give them a situational task," said Olivia Teel, math curriculum specialist for Kanawha County. "They learn the concept of putting the marbles into sets. That is how it could be done differently as opposed to 45 divided by 3."This is the old false dichotomy we hear about so often--one side decries rote memorization, calling it "kill and drill." The other side says reform methods (like problem-solving, group projects, etc.) leave too little time for actual mastery of skills. These are two sides of a coin, two approaches that should be used together in an appropriate way. You start with a situation to motivate a mathematical concept (how many marbles will each student get?), then you master the skill by practice (45 divided by 3), then you come back around to the situation--now you understand that you can quickly find out how many marbles each student gets by dividing 45 by 3. If you read the math textbooks from circa 1900 they did both kinds. What people in those days knew intuitively was necessary, we now have cognitive psychologists to tell us it is still necessary. It's not us against them, folks. It's what WE need to do to fulfill two complementary aspects of the learning process. Every good teacher knows this (intuitively).

I wouldn't even mention this except that this false dichotomy keeps coming up in one article after another. I haven't looked at the books, and it's probably true that some of them don't balance these things the way they should.

And by the way, the teacher above is misusing mathematical language. She should not be talking about putting marbles into sets. That is an inappropriate use of a mathematical term. Things like that worry me. Does it indicate a level of mathematical ignorance unacceptable for someone choosing a textbook? She may not be ignorant, merely careless in this particular instance. But if she is a math curriculum specialist, the burden upon her to be accurate is particularly great. She needs to be able to spot errors like this in the textbooks she evaluates.

Educators are trying to choose textbooks for students in kindergarten through fifth grade with math that offers the best of both worlds - a book that includes the basics as well as situational tasks. While that might sound simple, consider the fact that the number of possible books to choose from is mind-boggling. The county's textbook adoption committee managed to subtract a bunch and narrow it down to 10 different publishing companies with materials to review for grades kindergarten through five. New math books are to be adopted for schools throughout the county in May at a cost of $ 4.9 million.I didn't know there were so many choices. I thought there were only 3 or 4 textbook publishers left after all of the mergers! Ah, but I'm not accounting for the startups, grass roots efforts, and the experimental curricula. Singapore Math (I like), Everyday Math (I hear good things but suspect short on drill), Saxon Math (highly criticized for too much drill but very successful) are some examples of those. Most likely when you have a 4.9 million dollar budget to spend, publishers come out of the woodwork. Things like that don't happen in my neighborhood.

Teel ... said children need a balance of basics, situational tasks, justifying answers and investigation ... the textbook adoption committee actually considered adopting two books for elementary students to get all of that included.Good! (Well, not the part about needing two books.)

The ultimate goal is to boost test scores, said Teel, the math curriculum specialist, who said the current way of teaching math has become stagnant. Instead of the bulk of emphasis being placed on memorization, practice and drills, students need a better understanding of how math relates to situations, she said.I just can't help thinking: What is making it stagnant? Are the teachers really placing "the bulk of emphasis on memorization, practice and drills?" If so, why? Better yet, what exactly do we mean by this? Practice is a major portion of the necessary learning process in math. Failure in math is largely due to lack of practice. Somewhere around 3/4 of the time should probably be spent practicing. That's not a bad thing. Maybe there's a problem with the kind of practice? Maybe we are practicing too much on topics that we already know? I don't know. It would take a detailed analysis of classroom time usage to understand this. The goal should be to build understanding of mathematical concepts and enthusiasm for the subject, not "The ultimate goal is to boost test scores." Well, that's not MY ultimate goal. I want to boost test scores too, but only because higher test scores are a measure of how much we have achieved in meeting our REAL goals, i.e., students who are GOOD at math and LIKE it. See, we should not base instruction on secondary goals. If you strive for the right goals, the test scores will come along automatically.

According to an article in Phi Delta Kappan, a national educational magazine, math education in the United States has received "blow after blow from recently released studies." Among the issues educators are weighing: too much or not enough arithmetic, calculators or no calculators, problem-solving or calculation.Indeed.