Math Literacy … Focused on Students

After one week of our new “Math Lab” sections of Math Literacy (‘without a teacher at the center’), I am pretty darned pleased with the early results.

My institution replaced beginning algebra with Math Literacy this year, so we have dozens of sections for Math Lit.  Four of them are “Math Lab” classes, where students spend class time interacting with the textbook and material under instructor supervision but without any presentations.  I am teaching two of these four ‘Lab’ classes, so that is the basis for my comments.

The course work is highly structured.  The book work has been organized within each section/lesson so that students work a  couple of pages at a time (checking work against the solutions posted with each assignment); we have a video with guidance attached to each assignment.  A section/lesson has 3 or 4 of these assignments, along with a typical set of online practice problems at ‘the end’.

On the first day, I did a course orientation so students could see how this worked.  I strongly encouraged students to work together on that book work.  On the one hand, I am disappointed by the ‘together’ part — only a couple of students are working together in each class.

However, the students are getting in to the course work and the book work.  A high proportion are getting sections done (1 or 2 per day).  In the old algebra course, the progress was much slower … the change is evidence that the content & approach of Math Literacy has a higher innate motivation for our students.  Not only are students working and making progress, they are asking questions already (not all students, but more than the algebra course).  The material so far is basic numeracy (uses of percents, proportional reasoning, basic data summaries, etc) … the course transitions into algebra over the next weeks (though some algebra is present throughout).

The course design includes a Quiz (taking online) after the first 3 lessons.  That quiz is on the schedule for yesterday for one class; in that class, ten of the 14 students got to the quiz on time (with the lowest score being a 88%).  [The other class schedule is half a week behind.]  We’ve done quizzes in our Lab classes before, but I have never had even half the class take a quiz on time.

The early results are promising.  My conjecture is that some of the best learning occurs when we get out of the way, and configure the class so that students spend a lot of time interacting with mathematics.

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Math Literacy without a teacher at the center

We are trying something different this fall.  As we’ve eliminated our basic algebra class in favor of Math Lit, we are adding a student-directed format. I’m doing two of these classes as part of my teaching load this semester, and I hope to post commentary each week.

What’s different?  Well, the big difference is that students in this “Math Lab” (student directed) format work on the material without me standing in front of them.  The online homework system has videos in support of the workbook, which focuses on context and concepts; students will be following these detailed assignments for each section, and they are encouraged to work with other students.  [Of course, the students also face the usual assignment of problems to be done after this studying.]  The instructor is available to help when needed.  The goal is to get every student actively engaged with the mathematics (no sleeping in class 🙂 ).

I am testing a conjecture that students can learn significant mathematics (concepts and reasoning)  mostly ‘on their own’, even at this level.  Sometimes, I think we place too high a value on what we say or do.  In my view, all learning is essentially “on my own”.  Help is often needed, but is not always best prior to the learner recognizing that there is a need.  It’s not that one way is better for all students at all times; it’s that a different approach enables more students to succeed — and that this sometimes leads to students understanding the learning process a little better.

We’ll see how it goes!

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Algebra Lament

Woe, my name is algebra.

I help people communicate about important relationships; people use me to predict future conditions.

Woe, my name is algebra.

I have been shunned and made fun of.  The fault is not mine; no, the fault is almost entirely that of ‘algebra courses’ taught without a focus on understanding, without attention to communication about the world.  The quadratic formula is not my fault!!

Woe, my name is algebra.

People think that I am another name for right answers to meaningless questions, that I am the effort to emulate some perfect series of steps to solve those meaningless questions.  I am not some worthless set of dance steps, steps being marketed in the absence of music or creativity.  Just because I can’t carry a tune doesn’t mean that I lack creativity!

Woe, my name is algebra.

I am the written language to communicate about matters quantitative.  Rejecting me is the rejection of the basic goals of education in the modern era.  For, how can people understand the world when all they can do is vaguely describe the qualitative traits … or calculate values for a few specific cases?  I may have faults, but ‘lack of clarity’ is not one of them!

Woe, my name is algebra.

My properties allow people to transition from a sum to a product, and to discover the almost magical explosion of options for working with expressions.  My properties allow people to express functions of variables in ways which uncover critical features of the relationships.  Instead of this beauty, most people are told that overly complicated trivial work is ‘algebra’.

Woe, my name is algebra.

I live in the core of science and society, despised solely for the company I’ve kept.  Did I have any say in that company?  Is it my fault that school mathematics is often taught in poor ways and with ‘outcomes’ which add no value for the learner?

Woe, my name is algebra.

My reputation has been ruined by others.  I am like a poor citizen who needs to be represented by public defenders who do not see my value.  The public defenders have good intentions about our students, but represent me in such a negative fashion that the majority of students conclude that I am worthless … and that they (the students) can never understand me.  My remote cousin with a similar name, ‘linear algebra’, has much better respect and cred.

Woe, my name is algebra.

I have been placed in two boxes.  One box is labeled “use only enough to get an answer”, perhaps to questions students might care about.  The other box is labeled “recipes for right answers to artificial questions”.  Does anybody put geometry in these boxes?  Does anybody put statistics in these boxes?  I can tell you that I seldom have any company in these boxes, and never for very long.  Let me out of the box!!

Woe, my name is algebra.

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Transitioning Learners to Calculus in Community Colleges (TLC3)

You might have heard of the MAA project “National Study of College Calculus”  (see http://www.maa.org/programs/faculty-and-departments/curriculum-development-resources/national-studies-college-calculus ).  That work was very broad, as it studied calculus in all 3 settings (high school, community colleges, and universities).

A recent effort is focused on community colleges  with the title “Transitioning Learners to Calculus in Community Colleges”   (info at http://occrl.illinois.edu/tlc3  )  Take a look at their web site!

One component of their research is an extensive survey being completed by administrators of mathematics at associate degree granting public community colleges, including the collection of outcomes data.  A focus is on “under represented minorities” (URM), which relates closely to a number of recent posts here (on equity in college mathematics).

I am expecting that the TLC3 data will show that very few community colleges are successful in getting significant numbers of “URM” students through calculus II (the target of this project).  The ‘outliers’, especially community colleges succeeding with numbers proportional to the local population of URM, will provide us with some ideas about what needs to change.

Further, I think the recent emphasis on ‘pathways’ has actually decreased our effectiveness at getting URM students through calculus; the primary assumption behind this (based on available data) is that minorities tend to come from under-performing K-12 systems which then results in larger portions placed in developmental mathematics.  The focus on pathways and ‘completion’ then results in more URM students being tracked into statistics or quantitative reasoning (QR) pathways — which do not prepare them for the calculus path.  [Note that the basic “New Life” curricular vision does not ‘track’ students; Math Literacy is part of the ‘STEM’ path. See https://www.devmathrevival.net/?page_id=8 ]

Some readers will respond with this thought:

Don’t you realize that the vast majority of students never intend to study calculus?

Of course I understand that; something like 80% of our remedial math students never even intend to take pre-calculus.  Nobody seems to worry about the implication of these trends.

Students are choosing (with encouragement from colleges) programs with lower probabilities of upward mobility.

The most common ‘major’ at my college is “general associates” degree.  Some of these students will transfer in order to work on a bachelor degree; most will not.  Most of the other common majors are health careers (a bit better choice) and a mix of business along with human services.  Upward mobility works when students get the education required for occupations with (1) predicted needs and (2) reasonable income levels.  Take a look at lists of jobs (such as the US News list at http://money.usnews.com/careers/best-jobs/rankings/the-100-best-jobs )  I do not expect 100% of our students to select a program requiring calculus, nor even 50%; I think the current rate (<20%) is artificially low … 30% to 40% would better reflect the occupational needs and opportunities.

Our colleges will not be successful in supporting our communities until URM students select programs for these jobs and then complete the programs (where URM students select and complete at the same rates as ‘majority’ students).  Quite a few of these ‘hot jobs’ require some calculus.  [Though I note that many of these programs are oriented towards the biological sciences, not the engineering that often drives the traditional calculus curriculum.]

I hope the TLC3 project produces some useful results; in other words, I hope that we pay attention to their results and take responsibility for correcting the inequities that may be highlighted.  We need to work with our colleges so that all societal groups select and achieve equally lofty academic goals.

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