Sunday, April 24, 2016

The wrong way to teach math

We're teaching the wrong math Montclair used to have the Interactive Math Program, also known as Chicago Math. It was great. I sat in on a bunch of classes and it was discovery math. It introduced a new concept with an idea rather than a skill. It would give problems that required skills the kids didn't have. They tried to solve it without the skill, then learned the skill. It was math that stuck because it was MEANINGFUL. Think back to everything you learned in school. What did you remember? The answer is easy: that which was meaningful to you, that had some context, connection, some meaning to you attached to your present world. But they dropped it. Why? Because these kids were not as good on the SAT's. They were better math students, though. They might do better on the PARCC, I don't know, but, in theory, that would be so. I am someone who found math pretty easy, but who began to really hate it when teachers would try to teach method instead of meaning. I had an AP BC Calc teacher who would put proof after proof on the board because of the elegance, but Calculus was designed as a tool to solve physics problems so that was how it should have been taught. So we shove Geometry and Algebra II and on and on down kids' throats, most of whom will never need it, never use it, never remember it and never appreciate it. Math for much of us should be about taking information and analyzing it. There was an irony when we had that course. The principal at the time said it was great because 100% of the kids passed the HSPA. No control, no comparison, not a mathematically sound statement. Maybe they all would have passed in a regular math class! We keep on designing solutions, like particular tests (SAT, PARCC) looking for a problem, without questioning core assumptions. For most kids, there is a math that will be useful in their lives, and it is not this. I get preparing kids to be scientists and engineers, but the cost of preparing every kid to be a potential engineer is years of useless skills that are no more educational than learning chess and a lot less fun. Read Andrew Hacker, a math professor, who is much more articulate than me.

Sunday, April 03, 2016

The Law of Unintended Consequences

Much has been written about the inability of some to be able to foresee the potential downsides of a decision.  Psychology and business publications abound with examples of cognitive dissonance preventing us from truly looking at all possible implications of a decision.  What I am exploring is somewhat more specific to decisions made in education.  More specifically, it is about how a decision affects those who are NOT the target of the particular decision.

There are a couple of decisions in schools I worked in that illustrate this.  At my former school, half the students were white and the other half African American.  There was consternation that there were very few students of color in the National Honor Society.  The cutoff of 3.9 (out of a maximum 4.7) covered about a quarter of the student body.  The decision was made to drop the maximum to 3.6 to allow more students of color to apply for NHS. 

On the surface, the decision was quite successful in meeting its aim.   The number of students of color increased from a handful to around 30 students.  The percentage of minority students in NHS more than doubled.  So what could be wrong with this?  The problem is with viewing the problem and the solution solely from the viewpoint of the membership of NHS.  The consequence of lowering the GPA threshold not only brought in about 25 new students of color into NHS, but it also brought in about 100 new white students.  Now, almost half the students in the school were eligible for NHS. 

The greatest impact of this decision was not in the composition of NHS; it was in the composition of the non-NHS pool.  With the 3.9 GPA cutoff, the non-NHS group was pretty evenly mixed between white students and students of color.  With the 3.6 cutoff, the non-NHS group became mostly students of color.  With all good intentions, this decision created a virtual caste system in the school.  Students who were not eligible or accepted into NHS were relegated to a pool of students who were predominantly black and of a lower socio-economic status.

At my present school, there is another decision what equally pernicious in its effect.  We got a new superintendent who was stressing “ascendency”.  Teachers, supervisors, counselors and parents were asked to be on board with getting more students to go into honors and AP classes.  Teachers were told that supervisors would be looking at their course recommendations for their students to make sure they were recommending students for a higher level.  Counselors were given incentives based on the number of students they were able to get to ascend. 

It worked marvelously.  In some subjects, the number of students entering honors and AP courses doubled.  And not only that, like NHS in the example above, the number of and percentage of black and Hispanic students increased significantly.  Unfortunately, the A level classes (non-honor) became predominantly populated by students of color, students in need of remediation and special education students.  Prior to this, the A level classes were an acceptable alternative for a wide variety of students.  The classes were highly mixed by income, race and ability.   Now, with the much academically weaker population of students in these classes, as well as their lack of diversity, we again have created a caste system where one did not exist before.

In education this seems to be the norm.  Well meaning educators created select charter schools or small learning communities in schools that leave the non-participants behind.  In cities with a large number of charter schools, many doing wonderful things, the remaining students in public schools are disproportionately students who are in special education, who have behavioral difficulties or who are English Language Learners.

Almost all new principals and superintendents see themselves as agents of change.  Whether that is productive is open to debate.  But what is certain is that looking at a change only in respect to the desired outcome on the goal of the change, ignoring the impact on those not the target of the change may make the school, the students and the institution worse off in the end.