Math Literacy: Placement, Prereqs, and Access

In response to a recent post on placement tests, a colleague made this comment:

In my experience, many of the people who struggle with arithmetic really aren’t ready for Math Literacy. [S. Jones]

This colleague teaches at one of the premier colleges in the “Math Literacy Movement”, with experience and wisdom. I think this is one of the most important issues we face in community colleges.

The intended curriculum in a Math Literacy course has very limited prerequisites. Among these are basic number sense (place value and order), and some understanding of basic operations within contextual situations.

If a student struggles with these items, yes … they are likely to be ‘not ready’ for Math Literacy:

Add 24.1 + 1.3 [know place value ‘across’ the decimal]
Which of these is smallest? 0.23, 0.201, or 0.1065? [order of numbers]
A set of bleachers has 6 rows, and 10 people can sit in each row. How many people can sit on the bleachers? [operations in context]
A recipe calls for 24 ounces of diced dried fruit. The packages I’m buying contains 3.5 ounces; how many packages will I need for that recipe? [operations in context]

On the other hand, struggles with these items are far less related to readiness for Math Literacy:

Add 3/4 + 5/6 and write as a mixed number if necessary
Which of these is smallest: 3/13, 5/14, or 2/7?
Divide (without a calculator): 19.3 ÷ 2.56
If the area of a rectangle is 56 square feet, find the width if the length is 6 feet.

To understand what the prerequisites are for a course like Math Literacy, we need to think about the end point of that course. The goal of Math Literacy is to build readiness for the next math course (quantitative reasoning, statistics, or Algebraic Literacy). This goal drives the content of Math Literacy, which is outlined in four areas in the document mlcs-goals-and-outcomes-oct2013-cross-referenced

This goal, as operationalized in the content, seeks to have students meet the necessary and sufficient conditions for readiness in the next math course … any of those next math courses. None of these courses are arithmetic in nature, though all of them depend upon numeracy skills to some extent.

The problem with our conceptualization of arithmetic in a college setting is that we attribute “here is what we would like students to know” to that content. Of course, we’d like people to be able to perform fraction operations and decimal operations without depending upon a calculator. Of course we would like students to know some basic geometric relationships. In fact, most implementations of Math Literacy will assist students in those areas, but not as a core goal of the course nor as a prerequisite.

The truth is … that arithmetic was never a prerequisite for algebra, based on content structure. Sure, some parts of arithmetic had a role. In fact, we might call those parts ‘numeracy’ just like we do in the conversations about Math Literacy. However, competency in arithmetic procedures is (and has been) unrelated to readiness for a subsequent math course.

Too often, we create artificial barriers to students reaching their goals. One of the largest barriers in a college environment is the “arithmetic placement test”. We have a situation where:

A content analysis does not support the treatment of arithmetic as a prerequisite to a math course. AND
No data exists to suggest that there is any practical connection between competence in general arithmetic and readiness for a math course.

My college is currently using an arithmetic placement test merely for the purpose of sorting students relative to our two Math Literacy courses … the Math Literacy with Review course has a lower cutoff than the Math Literacy without review. We no longer offer any math course ‘before’ Math Literacy. Eventually, we might be able to make the determination about which Math Literacy course from other measures.

Think about this aspect of the situation: Most of the students who might take an arithmetic test have experienced 12 years of mathematics with over half of this time focused on arithmetic. Do we expect to ‘fix’ most of their problems in arithmetic within a few months? Also, what do the students look like who get lower scores on placement tests (especially arithmetic)? The polite phrase is “this group is very diverse”. The fact is that tests on arithmetic impact certain minority groups (race, poverty) more than others. Unless we can show a very strong connection between ‘arithmetic’ and success (in a specific math course, or in general), we have a moral obligation to NOT impose an arithmetic barrier.

Using an arithmetic placement test to identify students required to take an additional math course is a fundamental access issue. Such courses are obsolete relics of a different era, and lack connections to both school mathematics in this century and to other math courses in colleges. We can help thousands of students by following one simple plan.

Just stop it!!

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Mathematical Literacy Course | Jack Rotman | February 20, 2017 10:42 am

4 Comments

By schremmer, February 20, 2017 @ 1:23 pm

Re. “Using an arithmetic placement test to identify students required to take an additional math course is a fundamental access issue.”
Moreover, such testing is totally beside the point.

And here is another issue. A couple of weeks ago, as I was trying to let students see why – times – should be equal to + (To put it briefly by pointing out that nobody objected to losing bad apples.) a student protested vigorously that this was a waste of time, that her Arithmetic teacher had said that “minus a minus was a plus” and that, inasmuch as that had allowed her to get into Basic Algebra, that was all that she needed.

As I once pointed out, How Content Matters, a placement test should be able to ascertain, instead of the students’ “level of preparation”, which is demonstrably meaningless in any case, their likely degree of commitment. More precisely, factors in any kind of screening should be a minimally open mind and being able to accept that some case always has to be made before anything can be accepted as true.
By Jack Rotman, February 20, 2017 @ 6:21 pm

The placement tests, well really ‘singular’ placement test, is/are shifting to more of “measuring the understanding necessary” rather than preparation as in skills. [This is the Accuplacer “Next Generation” system.]
Of course, I’d like “minimally open mind” to be present; in a way, the ideal Math Literacy course works on developing an open mind as part of our work on preparing students for college work.
I don’t see how we could implement a screening based on ‘open mind’, both because an objective instrument would be difficult (near impossible) to develop AND because there is an inherent cultural bias in what it means to have an ‘open mind’. I personally accept as an article of faith that all human beings can develop and re-develop an open mind with critical thinking about the world around us. Therefore, such screening is unnecessary.
By schremmer, February 25, 2017 @ 8:03 pm

Re. “all human beings can develop and re-develop an open mind with critical thinking about the world around us.” I agree of course. But how do you do that in 15 weeks right after at least one course has convinced people that they better “acquiesce”?

Two points:

One is that students like the one I mentioned above, has a very chilling effect on even the students with an open mind. So, if only for that, a screening would seem to be necessary. Then there are the students who may have an open mind but, with two jobs and/or children, just have zero time to spend on the least pondering.

The other is that screening need not be within the third decimal. The student who refuses at interview time to stop and consider for even a couple of minutes, the student who cannot possibly have the time at home should be directed to those sections where no thinking is allowed. And there are plenty of those.
By schremmer, February 25, 2017 @ 8:05 pm

I should have said: By “open mind” I meant just a willingness to stop and think and maybe, just maybe, listen to what the other side has to say.

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