fantasy vs reality

Dave over at Joannes posted this example of "creative" teaching:

4th grade classroom, students have demonstrated mastery of basic multiplication facts and some conceptual understanding of multiplication as arrays and repeated addition.On the board, the teacher writes a column of 15’s (there are ten in all)151515…15——She instructs students to find the sum mentally but not to raise their hands with any answers at that moment. After a minute, she directs students to discuss their ideas in small groups of 3-4. She tells them to compare their results, not just the sum but HOW they did this. After 2 minutes, she leads a discussion, inviting students from each group to share their ideas. She comments and adds other ways, insuring that students see at least 4 methods. She asks, “Which method is easiest for you? Why?” etc… This does not take more than 15 minutes in all.”

The way it really works:

4th grade classroom, students have demonstrated mastery of basic multiplication facts and some conceptual understanding of multiplication as arrays and repeated addition. On the board, the teacher writes a column of 15’s (there are ten in all) 151515…15——She instructs students to find the sum mentally but not to raise their hands with any answers at that moment. Most of the students breathe a sigh of relief, because they have no idea of the answer. After a minute, she directs students to discuss their ideas in small groups of 3-4. She tells them to compare their results, not just the sum but HOW they did this. The kids form groups and immediately start goofing around. Luckily most of the groups end up with at least one kid who can figure out the problem because their parents tutor them at home. After 2 minutes, she leads a discussion, inviting students from each group to share their ideas. No one answers at first, but she calls on a kid anyway. He mumbles something about doing it in his head. She comments and adds other ways, insuring that students see at least 4 methods. The students furiously copy what she is doing on the board, but not quite sure what she is talking about. She asks, “Which method is easiest for you? Why?” etc… This does not take more than 15 minutes in all. Most of the kids didn’t quite understand the lesson, but that's OK… they will spiral through the curriculum and hit it up several more times over the next year. Eventually by 8th grade 20% of the kids will master the concept. The majority of them will still be adding up the numbers the long way.

Meanwhile over in Sir Zigs class across town. Zig has demonstrated to his students that that if you have the same list of numbers, you can count up how many numbers there are and its the same as a multiplication problem. The kids quickly calculate 10 x 15. Upon Zigs signal, in unison they shout out the answer. Zig gives them several other similar problems, to test their mastery. After 5 minutes, he is sure that they understand. All the kids seem to get it, and he compliments them on how smart they are. It seems like they can spit out the answer almost as fast as he can write problems. This has not taken more 15 minutes. Now that 100% of the kids have mastered this concept, he can move on to something else. He makes a mental note to revisit this concept tomorrow morning, to reinforce it. Eventually, 90+% of his kids will go on to pass the state proficiency exam.

math for all?

From my blog, Joanne Jacobs:

In response to a Tennessee proposal to requires four years of math for graduation, an algebra teacher writes that not everybody can learn algebra or needs to know.

It was totally crazy to ever require algebra -- let alone the geometry all must now take. When will the out of touch realize that some are left brained and most are right brained?

... Here is an algebra problem that any Algebra I student will be taught. Factor 8Xsquared -95X -96 I will bet that very few of your staff or even the state school board could do it.

I do not know anyone who has ever factored anything outside of a classroom. Have you ever rationalized a denominator?

Why is this man a math teacher?

Colby Cosh links to a discussion on whether math has progressive uses. It starts with this post:

I've come to realize that probably one reason I struggled with algebra, geometry et.al., was that it seemed to me that these were basically reactionary academic disciplines, useful for designing weaponry or potentially repressive computer technology, but not with any obvious humanistic or social positive uses.

If I'm wrong about this, I'd appreciate it if people could show me how this discipline can have progressive uses.

I also feel this could be useful in developing better ways of teaching higher mathematics if such uses could be found.

Read it for the philosophy joke.

the high cost of low teacher quality

Cross posted from Joanne Jacobs:

Education Sector's How Low Teacher Quality Sabotages Advanced High School Math is a must-read. Kevin Carey summarizes:

Students who take advanced math courses in schools that employ the fewest well-qualified teachers are far less likely to be adequately prepared for college, or to succeed in college, than students who take the same courses — or even less advanced courses — at schools with the most well-qualified teachers. Students who fail to take advanced courses do poorly across the board. But it turns out that simply enrolling students in more advanced classes isn't enough — you also need good teachers to teach them.

Illinois makes all 11th graders take the ACT. The llinois Education Research Council combined ACT scores and high school grades to rate each students' college readiness.

To create a Teacher Quality Index (TQI), researchers looked at factors correlated with effectiveness: graduation from a "more competitive" college, less than four years of teaching experience, emergency or provisional teaching credentials, one or more failures on the basic skills test for new teachers, composite ACT score and English ACT score.

Few students who took only algebra and geometry were ready for college regardless of their school's Teacher Quality Index. But TQI correlates with college readiness for students who completed advanced algebra, trigonometry and calculus.

Students who took Calculus in the lowest TQI schools were five times less likely to be well-prepared than students who took Calculus in the highest TQI schools. In fact, students who took Calculus in schools with a TQI below the 10th percentile had a lower preparedness rate (16 percent) than students who only took Algebra II in schools that were above the 25th percentile.

There is a confounding factor: Low-TQI schools tend to be high-poverty schools.

Low-income students, who face some of the greatest barriers to education, are much less likely to be taught by teachers with the best qualifications.

More than 90 percent of well-prepared students and 55 percent of least-prepared students enrolled in college. After three years, 10 percent of the top category and 41 percent of the lowest category had dropped out.

Take a look at the charts: At schools with a TQI in the lowest 11th-25th percentile, less than half of students motivated enough to tackle calculus are prepared to succeed in college. In the bottom 10 percent of TQI, fewer than 20 percent of calculus students are prepared.