Double Dose of Algebra and some Ramblings

Over at Curriculum Matters, they're asking Does 'Double-Dose' Algebra Work?

Across the country, one of the strategies schools are trying to help struggling students in algebra is essentially doubling the amount of time spent on that course. It's a popular tactic in other areas of math, and in reading, too.

A new study, however, says that double-dose courses produced mixed results in Chicago schools. On the one hand, the 9th graders studied saw their test scores rise. But the policy did not appear to result in fewer students failing the course, as school officials had hoped, the authors report. The grades of some struggling students increased, after the double-dosing, though the weakest students did not see their grades rise.

Ignoring the grammatical and structural problems in those paragraphs, I was struck by the apparent surprise. This result seems very obvious to me. With more time devoted to drilling and practicing for the test, you'd expect the test scores to converge on the mean. Look no further than KIPP.

The grades in the course, on the other hand, are based on different criteria. Teachers routinely count "participation," homework, classwork, and behavior. Extra credit and test corrections and grade-adjustment skew the scores. Parents routinely ask for "make-up work," code for "just give him more points without making him do anything or we'll raise hell."

Should advocates of double-dose math courses be pleased with these results? After all, one could argue that student learning—if test scores accurately reflect that—increased. Or should persistently high failure rates raise red flags?

Sure. But Red flags signifying which issue? That the class is different from the test? DUH. Would you be upset if the class averages were in the 90s and the test scores were dismal? Yes, you should. But you'd be worried about the wrong things. Do class averages measure learning? Does the State test measure learning?

When the State scores are low, the usual response is to bitch about the content of the course or the quality of the teacher. This is occasionally the problem. A few people complain about the motivation of the student, which is a big problem. No one ever talks about the idea that the teacher might be teaching material that the State isn't testing, like the algebra the kids need instead of the geometry that the State assumes they should be ready for at age 15.

When the scores don't correlate, too many people spout off about "test-taking strategies" and "test anxiety" and "some kids don't test well" and "only a snapshot."

What is wrong with a "snapshot," anyway? I can't tell you how many times I've had people tell me that the (3-hr, well-constructed and extensively peer-reviewed before and after the fact) State Tests are bad because they're only one day's measurement and thus should be eliminated. These same folks then turn around and push for a final exam (1.5hr, 'constructed' by the teacher at 12 midnight and never reviewed) to be 20% of the kid's grade.

No one ever complains about the most common problem and the biggest reason why grades and State Scores rarely correlate: the teacher has too much control over the way the course is graded and his tests are scored.

Even the newest, most inexperienced teachers are routinely given control over grading, curriculum and student progress.

I have had brand-new teachers tell me that they are going to teach chapters 1, 6, 8, 7, 2, 4, in that order. Why? They thought it was better that way. Ch3 and ch5 are ignored because why? The answer usually has more to do with the teacher's lack of understanding than the stated reason, "Those chapters on matrices and blahblah are not current and blah blah blah." No account is given for the idea that the book was written and vetted by people far smarter (and with a lot more time to consider these things) to be done in a particular order. No thought is spared for the linearity of the material and the fact that most of the problems in ch4 assume that you've done (or at least understand) ch 1-3. Going out of order confuses even the best students; they are constantly asking "Should I have known that really important fact or idea? Am I stupid or did we just not cover it?"

The standards-based movement exacerbates this problem. Instead of following a curriculum, the teacher is supposed to pick and choose from the Standards and individualize the curriculum for each kid based on test scores. The grades coming out of this train-wreck usually have more to do with some vague idea of "effort" than of any assessment of ability.

Beyond the curriculum matters, the teachers also mess up grading. Do you count homework or grade it? Some have participation and brown-nosing scores as high as 10%. Some have tests, quizzes and homework roughly equal. In my school, we even have control over the relative weight of the terms if you can believe it. Some faculty count the two terms and the final as 40-40-20 while others are 45-45-10. Others don't give a final.

Is it any wonder that grades aren't changing in lockstep with the State scores?

Is it surprising that we don't achieve in the same way as the schools in other countries do? You know, the ones that have a national curriculum that aligns with the TIMMS and PISA tests so that those countries will do well on the TIMSS and PISA tests? That have long (by comparison) teacher mentorships so that the new teachers are in line with the older ones and not spinning off like some subatomic particle in their own personal cloud-chamber? Have we learned nothing from the reality of Stand and Deliver or were we just seduced by the feel-good fiction?

I'm not saying this is the ideal but if we wish to repeat their successes, we'll need to at least partially repeat their processes. We also have to consider that learning might not equal scores or grades.

Curriculum Matters continues with another obvious point:

Chicago is, of course, coping with many of the same challenges in algebra that other districts are. The new study follows another one, released last month, which found that Chicago's failure rates increased when the district mandated that students take algebra in 9th grade.

I nominate Curriculum Matters for Poor Elijah's Emperor Awards 2009 (2008 here) "Archimedes Eureka Honorarium" which spotlights the imaginative world of education research. Congratulations to all.