## Is Remedial Elementary Algebra Harder Than College-Level Introductory Statistics?

My coathors (Dr. Mari Watanabe-Rose and Dr. Daniel Douglas) and I have learned that our article on a college-level statistics course alternative to math remediation, published in *Educational Evaluation and Policy Analysis *(*EEPA*), was the most read article in EEPA for 2016. *EEPA* is an AERA (American Educational Research Association) journal.

Our research shows that when nonSTEM majors, assessed as needing math remediation (elementary algebra), are randomly assigned to college-level statistics (with extra support) they are more likely to pass and to continue to accumulate more college-level credits afterwards than similar students randomly assigned to traditional remedial elementary algebra. However, adoption of this alternative to math remediation has been slow at The City University of New York, where the research was conducted.

A few CUNY math faculty have questioned our results, saying that the higher pass rate in statistics was due to statistics being easier to learn than is elementary algebra. Or that the higher statistics pass rate was due to statistics requiring only a 60% score to pass, whereas elementary algebra requires 74%.

Let us leave aside for the moment the fact that, in our experiment, students randomly assigned to statistics with extra support accumulated more credits in college afterwards than did students randomly assigned to elementary algebra, indicating that elementary algebra was not as necessary a prerequisite for students to satisfy their college-level course requirements as some have claimed.

For now, let us just consider the validity of the statement that statistics is easier to learn than elementary algebra, or the logic of comparing the percentage needed to pass statistics vs. elementary algebra.

First consider that, in grading any course, the percentage of correct answers that any student gets is completely arbitrary, because the percentage of correct answers is a function of the difficulty of the quizzes, exams, homework assignments, etc. A faculty member can make those tasks really hard, so that even good students get few questions correct, or really easy, so that most students get everything correct. With elementary algebra, there are CUNY-wide standards and tests, so you can be pretty sure that, if 20% of students consistently pass in one faculty member’s class and 60% in another, the latter faculty member is actually teaching better than the former, at least if the students in the two faculty members’ courses are similar at the beginning of the semester. But if there isn’t a CUNY-wide syllabus, final exam, and grading rubric (and, in fact, none of these exist for Statistics), you can’t tell which faculty member is teaching the material better without obtaining much more information.

Now consider the fact that statistics and elementary algebra are qualitatively different courses, which means that, by definition, they can’t ever have the same syllabus, final exam, and grading rubric. Which means that the percentage passing, or the percentage you define as passing, simply can’t be directly compared across algebra and statistics. Which means that there is no way to say that one is easier than the other.

Suppose, in any sample of 100 students who took both statistics and elementary algebra, 60 scored at least 80% correct in statistics and 40 scored at least 80% correct in elementary algebra. Does that mean that the statistics course is easier for the students than the elementary algebra course? Perhaps in the simple sense of the students getting better grades in statistics. But inherently easier? No. The faculty teaching statistics could simply make their exams much harder, and the number of students obtaining 80% correct in statisticss would plummet, and then an observer might say that the statistics course is the harder one.

A more useful question for our research was whether the faculty in our experiment graded statistics according to the standards by which they usually graded statisticss. In our published paper we list nine pieces of evidence that are consistent with the hypothesis that the faculty in our experiment graded statisticss as it is usually graded. We can therefore reasonably conclude that many students, though assessed as needing remedial elementary algebra, can nevertheless pass college-level statistics, taught as it usually is except with some extra support (a weekly 2-hr workshop), as well as passing other subsequent college-level courses. Students are more likely to pass college-level statistics (taught as usual except with extra support) than remedial elementary algebra (taught as usual).

Of course, just because a student can pass college-level courses without having first passed elementary algebra doesn’t mean that no student should have to take elementary algebra, or higher-level algebra courses. A college or university could decide that it is important for every graduate of that college to demonstrate knowledge of at least elementary algebra, or that students majoring in certain disciplines need to do so. But such statements are different than saying that every college student needs elementary algebra in order to be able to pass required college-level courses, a statement that our research does not support.

At CUNY there are some faculty who believe that every CUNY graduate should demonstrate knowledge of algebra, at least elementary algebra. However, the CUNY-wide general education requirements do not currently require that every student know algebra. Passing college algebra is sufficient for passing the mathematical and quantitative reasoning general education requirement, but it is not necessary. Passing statistics can also satisfy this requirement, as can passing a quantitative reasoning course. And given that we now know that passing elementary algebra isn’t necessary in order to pass statistics (taught with extra support), it follows that there is no current requirement for all CUNY students to demonstrate knowledge of algebra.

Assuming that CUNY’s general education requirements do not change, all CUNY students who do not require algebra for their majors, and who have been assessed as needing math remediation, should have the opportunity to take statistics, or another quantitative alternative course, with extra support, instead of traditional elementary algebra.