Here’s some of the findings presented at a session on U.S. math instruction at the AERA annual meeting on Tuesday, April 30, 2013.

**Another data-driven study shows that the judgment of teachers can often be wrong.**

In a study of middle-school math education in a California school district, standardized test scores and grades were a much better predictor of whether a student would pass eighth-grade algebra than whether his seventh-grade math teacher thought he was ready for it. That’s according to an unpublished paper, The Missing Link in Algebra Policy Analysis: A Case Study of Placement in Eighth-Grade Algebra by Andrew Thomas (Walden University), Michael H. Butler (Public Works, Inc.), Robert Kaplinsky (Downey Unified School District).

The issue of when a student takes his first algebra course is of great interest to academic scholars and policy makers. Some theorize that taking algebra early in eighth grade will lead to more students taking advanced math courses in high school and ultimately going to college. Kids that don’t study algebra in eighth grade are tracked into curricula that effectively shut them off from many educational opportunities. Many districts and states around the nation have been pushing schools to teach algebra earlier. Nationwide, about 6 percent of districts — many of them low-income schools — are now requiring algebra in 8th grade. But there’s also concern that pushing unprepared kids into algebra too soon sets them up for failure. California recently reversed its decision to require algebra in eighth grade.

This particular study found that middle-school math teachers recommended that a little more than half of their students (53%) take the more advanced algebra class in eighth grade. But half of these purportedly “stronger” students ultimately failed to get at least a C grade in the class and score “proficient” on the California state exam. The district was not identified in the study. These same teachers recommended that 38 percent of their students take a more basic arithmetic class, often called “pre-algebra,” postponing algebra until ninth grade. But a big chunk of these supposedly “weaker” students – 209 of them — were nonetheless put into algebra classes and many of them succeeded in passing the course.

This study shows that teachers make two types of judgment errors. They overestimate the abilities of half the students they think are strong. And they underestimate the abilities of a big chunk of students they perceive as weak. In both cases, the mistakes can be heartbreaking for the student.

What’s fascinating is that, if the math teachers just looked at the grades they themselves gave their students in seventh grade, these errors would have mostly vanished. Most students who got at least a B in seventh grade math succeeded in eighth grade algebra. Can you believe that there were teachers who gave a student a B in seventh grade math, but didn’t think the kid was ready for algebra? And they thought many of their C students were ready? Did the teacher think his own grading system was bogus?

(These results make me question the whole validity of teacher recommendations. Why are they so important to college admissions departments?)

An even better predictor than grades was the student’s score on the annual California State assessment test. But the results of that test come out too late for the school to use it for placements.

The school district also developed its own home-made diagnostic test. But it was not a good predictor of whether a student was ready for eighth grade algebra.

**Not all algebra classes are the same**. Another paper, Breaking Down the Achievement Gaps Among High School Graduates: Contributions of Geometry Content Rigor by Kathryn S. Schiller (University at Albany – SUNY), Janis D. Brown (U.S. Department of Education), Robert Colby Perkins (Westat), Stephen E. Roey (Westat), found that there was wide variation in the content of high school math courses with the very same title. Some are rigorous. Some are lame. Even an honors geometry course could be quite watered down and focus more on two-dimensional objects and nearly ignore the important topic of three-dimensional objects that move in space. The weird thing is that there was no correlation between the rigor of the math class a student took and the score he got on the NAEP. Whites and Asians tend to outscore blacks and Hispanics regardless of the rigor of the math class they took.

**Better to go for the easy A or fail a hard class?** That’s the question asked in a working paper, entitled Success and Failure in Eighth-Grade Mathematics: Examining Outcomes Among Middle Schoolers in the HSLS:09 by Keith E. Howard (Chapman University), Marty Romero (University of California – Los Angeles), Derrick Saddler (University of South Florida), Allison Scott (University of California – Berkeley). The researchers found that the California State standardized-test scores were about the same for similar students whose only difference was that one failed algebra in eighth grade while the other passed an easier math class. But there were significant psychological wounds. The ones who failed felt that they weren’t good at math, didn’t like the subject and they didn’t pursue math later in high school. The equally weak students who lived in ignorant bliss liked math more and continued with the subject.