Skills, Abilities, and Readiness

So, I’ve been thinking about “replacing them all” (a recent post here), and wondering what types of reactions that idea would receive. Do the old courses have something valuable? Would we harm students by getting rid of them? #NewLifeMath #SaveMath

Not all implementations of arithmetic, pre-algebra, beginning algebra and intermediate algebra are equivalent to other implementations of those courses. Certainly, some instructors (and perhaps some institutions) deliver a course that is qualitatively different from the accepted norms for those courses.

However, the norms for those 4 courses essentially define the courses as:

The student will use n procedures to get correct answers in the topics ________.

The courses are designed to maximize the value of n, often while maximizing the list of topics. Our textbooks reflect these priorities; in fact, many of our courses are set up so that there is no textbook — just the class and the online homework.

Part of this set of norms is a fact that the New Life Project has focused on since the beginning.

Most commonly, developmental mathematics is taught by adjunct instructors.

The problem here is not the employment status of adjuncts. The biggest problems deal with support for adjuncts and expectations — adjunct faculty do not receive the same level of support as full-time, and adjuncts are expected (in general) to follow the normal expectations. For us to make any significant improvements, this pattern needs to be broken.

As long as we offer the traditional courses, there will be a very strong trend towards doing exactly what we’ve been doing — focus on skills, measure by correct answers, and avoid reasoning. The traditional dev math courses produce completers who are the same as the starters, except for a finite number of specific skills which tend to be forgotten before they can be used again.

The reform dev math courses (all similar to the New Life courses at this basic level) focus on student abilities (reasoning in particular) along with a focus on strategically chosen skills. The courses are qualitatively different in several ways.

Adjunct faculty can certainly teach Math Literacy and Algebraic Literacy. However, in most cases, this will require an increase in institutional support in professional development. Our hope is that this will become “the new normal”, which will tend to integrate adjunct faculty more completely into the math department.

We’ve approached “readiness” as a check-list of skills … frequently including far too many ‘skill’s … with no emphasis on reasoning abilities. Skills can be quickly reviewed, as needed — IF the student has the reasoning to support it. Reasoning is the ability that can not be ‘reviewed’.

The traditional dev math courses, with their focus on skills, provide such a limited benefit to students that we can safely replace them. This is especially true if their replacements are engineered to develop a healthy combination of reasoning and skills, which the New Life courses do.

This change from ‘old’ to ‘new’ is more of a problem for us, than our students. Are we ready to offer math courses which focus on central ideas and reasoning? Can we give up the ‘easy’ path of doing the same old stuff? This change issue is true for all college mathematics in the first two years; external forces are causing us to start with developmental courses, though pre-calculus and calculus courses will go through similar changes.

We are not changing “for changes sake”. We are changing for the sake of our students … we are are changing to save mathematics.

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Math curriculum in general, Professional Development | Jack Rotman | February 11, 2016 9:55 am

3 Comments

By Peter Brown, February 11, 2016 @ 10:42 am

Good post Jack. I am noticing a ‘gap’ between students coming into QR through Into Algebra, and those entering through Math Literacy (we use Almy). THE biggest problem is reasoning- although perhaps more precisely a lack of a cognitive framework, and no metacognitive skills. Prior knowledge is not the issue.
By schremmer, February 11, 2016 @ 3:14 pm

Re. The student will use n procedures to get correct answers in the topics

Not to be contrarian, but don’t we all use procdedures to get correct answers?

The problem is of course a lot deeper than that. There is what precedes the procedure, namely the analysis of the problem the solution of which the procedure is, so to speak, going to automate. In that sense, the procedure only “streamlines” what reason eventually got us to do. In that sense, then, the procedure is the end result of an inquiry.

But there is also the context in which the problem for which the procedure will provide a solution. There are the various relationships between the issue at hand and other issues. There is the language in which to specify what is given, what is to be inquired into. There is the sense of construction from the simple toward the complex. Etc. In other words, there is a lot more than “literacy”.

And then there is what one might call the metacontext, namely:

the ability to read “pencil in hand”,
the ability to distinguish what is germane to the issue at hand from what is not, and, in particular, the ability to ignore what is irrelevant,
the ability to discern when some idea can be transferred from one situation to another.
Etc.

All these abilities need to be explicitly developed.

For instance, in my books, I used to devote most of the contents to the “discussions” and leave the “streamlining” to the reader. However, I have come to realize that, ab inition, students find it all but impossible to do that final streamlining. And, since, they only have limited time and thus get impatient, they try shortcuts—invariably disastrously. So, since my books are for raw beginners, I am editing a lot of “discussion” out and including “procedures” as conclusions.

For an example of, and to embody the above, see
By schremmer, February 11, 2016 @ 3:25 pm

I still have trouble with the formatting. So, let me try again what I suggested that one see:

Reasonable Algebraic Functions

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