## Teacher Incompetence Plays a Role

Although I share Joseph Ganem’s concern and experiences [

*APS News*Back Page, October 2009], with both teaching undergraduates and helping my own children with high-school mathematics, his conclusion does not follow from his observations. Yes one must teach age-appropriate concepts, but he offers no evidence to support the popular theory he espouses that the cause of inappropriate teaching is an “adult obsession with testing.”

My own view is that, in mathematics particularly, the main cause of inappropriate teaching is incompetent teachers. It seems hopeless to me to expect students to learn concepts of trigonometry, calculus, or linear algebra from teachers who don’t themselves understand them. What appears to happen (by my observations) is that the teachers don’t teach or explain them. They tell the students to read the textbook and set them exercises. (The interesting personal examples Ganem relates support this view more than his own.) In today’s internet and mass-media culture, this approach is even less likely to succeed than ever.

It has been established by “new math” experiment and study over many years that children in their mid teens are able to master mathematical concepts that to their parents seem very advanced, when properly taught. If the problem really is testing, then one would expect students in countries in Europe, or, for example, China, where testing is even more emphasized than the US, to produce students weak in mathematics. The opposite appears to be true. While I can’t say whether the school mathematics curriculum in Maryland is appropriately sequenced, or should be adjusted, I will say that attacking the idea that mathematical competence can and should be measured hardly seems likely to enhance the understanding and accomplishment of our young people in mathematics.

Cambridge, MA

**Ian Hutchinson**Cambridge, MA

## Joseph Ganem responds:

I would not disagree with the assertion that the quality of math teachers could be improved at the high school level. However, the stories I told about the teachers were not meant to disparage them, or their abilities. My intent was to illustrate that the curriculum had become so advanced that the math problems in it challenged me. I do not expect a high school teacher to have the depth of understanding of math that I have. Maybe a competent high school math teacher should know math at the level of a professional physicist. But, I don’t think my level of understanding is necessary for a high school teacher using an age-appropriate curriculum. Without an age-appropriate curriculum, it is difficult to judge the competence of the teachers.

It was also not my intent to suggest that math achievement not be tested and assessed. I believe that we should test for student math achievement. I am attacking an educational mindset, in which test scores are not measures of learning outcomes; the test scores are the outcomes. While that distinction might be subtle, it has real effects on how classes are taught and in the messages we communicate to students about the goals of an education. Tests are measurement tools; they should not be the reasons that students come to class.

## Bad Schools Lead to Math Paradox

As a member of the physics faculty at UCSD and father of two daughters, I share the experiences that Joseph Ganem describes [Back Page, October

*APS News*]. Nevertheless, I think his extrapolation is incomplete. My daughters are lucky. They have attended some of the best public schools in San Diego county. As a result, they have been exposed to math at every step of the way that was challenging for them, and fun for me.

However, that’s not the education that the vast majority of incoming students have received when they enter UCSD.

A few years back, I volunteered to participate in the interviews for hiring new math and science teachers at a startup Charter School.

This gave me a thoroughly different perspective on the San Diego school district, as I got to interview teachers with shockingly different backgrounds and daily routines. Quite honestly, it scared the living daylights out of me.

Maybe the reason for the math paradox Ganem describes is simply that 49% of the incoming students at colleges in Maryland have not had the privilege of attending decent public schools. Maybe the reason for the problems we see among the incoming classes at our Universities is that there is too little standardization in high school. When I think back to my own high school experience in Germany, there was no need for an SAT, no need for a math entrance exam at Heidelberg University. My peers and I knew where we stood in math. All we needed to look at was our math and physics grades in the high school exit exam.

San Diego, CA

**Frank Wuerthwein**San Diego, CA

## Math Misery Loves Company

Kudos to Joseph Ganem on the wonderful article on the Back Page of the October 2009 APS News. I’m glad to know I’m not the only one having a hard time with math! I got all the way through college algebra in high school and was placed into remedial math in college, only three months after graduating high school! I’ll graduate this year (B.S. Physics) on the five year track, thanks to the first “no math no physics” year of my college career.

**John Metcalf**

Huntsville, UT

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