Two days ago I had a parent/teacher/counselor/student meeting for one of my Algebra II students. The father wanted to know how come his daughter, a straight A student in Algebra I Honors in middle school, was doing so poorly in her freshman Algebra II course.
We batted it back and forth, but what it came down to was that the student understood all the concepts, was applying them correctly, but in the process of solving the problems she was making mistakes in arithmetic and elementary algebra that were killing her final answers. Things like not distributing correctly a minus sign, or making an error in a simple division (35/7 = 6) – these small mistakes were propagating through her problems and yielding wrong and sometimes nonsensical results.
By the way – this student was not the only one. During class work, I circulate among the students and I look at how they do a problem, where they are stuck, why they don’t get the right answers. Often the problem is the same – small algebra missteps, and poor work with fractions.
These are not low level kids – they are not in Honors Algebra II, but they have had a good Algebra I course which they passed with an A or a B. Their middle school teachers were experienced and demanding. The schools they came from are highly rated by the state.
So where is the disconnect? Why do these good students make elementary or even pre-algebra mistakes? Why do they have so much trouble with fractions?
Talking with some my fellow high school teachers elicited three hypotheses:
(a) Elementary school teachers hated math when they were in school so they are not well prepared in math both analytically and emotionally e.g. they are not well prepared to teach fractions
(b) Middle school teachers teach to the test and because of the number of concepts they have to teach, there is no time for review and cumulative practice and testing.
(c) Middle school teachers think of their students as children and treat them as such, whereas in high school the expectations are significantly higher – suddenly!
Of course these hypotheses are based on anecdotal evidence and they can not be generalized to all the math teachers – especially from what I have seen in the blogosphere.
I do have two additional hypotheses however – hypotheses based not only on what I observed in my years of teaching in the US, but also in what I have seen in Europe and especially Eastern Europe/Russia.
The first hypothesis states that in trying to cover so much ground, so many concepts, we do not allow sufficient time for the kids to internalize and practice the fundamentals and we do not expose them to problems that involve critical thinking.
The second hypothesis is that we have gone way too far in the concept of “all kids must go to college”. Students who do not care about math, who do not see around them that math can be useful, who are not comfortable in an academic environment are shoehorned into a three year math program. We do not offer these students another way of finishing school, such as an apprenticeship and we are disappointed when they do not perform well.
So it seems to me that we have a two part problem here – figuring out why our better students are not doing as well as they ought to and figuring out what to do with the student population that should not be forced to take logs, roots of polynomials, inverse matrices and so on. In the end the question boils down to “what do we teach and who should we teach it to?”