Math You Use?

More than 60% of students entering CUNY community colleges place into a remedial mathematics course. For the vast majority, that means they must pass an elementary algebra course and the CUNY Elementary Algebra Final Exam (CEAFE) to exit remediation and to have any chance of every obtaining a degree. Each semester, more than 50% of students in elementary algebra do not pass the course.

But why is algebra so important that we decree every college student must demonstrate current proficiency in a fairly rigid list of topics and skills before being able to graduate regardless of major? One very common answer is the tautology “Because algebra is part of a well-rounded education.” But where are the data and evidence to support this claim? Indeed, most conversations I have about algebra outside of academia tend to include the phrase “What was the point? I’ve never used it in ‘real life’”.

The truth usually lies somewhere in between, and to me, it seems that the answer really depends on what you consider to be algebra. If algebra is the monolithic list of topics that make up most college algebra courses, then I would agree with those asking “what is the point?” But most, if not all, of us use numeracy and mathematical skills in every day life, and so I wanted to know which are the important concepts from typical algebra courses that we use in “real life”?

As someone who teaches developmental and college algebra, researches abstract algebra and most recently helps his daughter with her algebra homework, I am fairly certain I use more algebra on a daily basis than the average person. So I decided to ask friends, family, colleagues in other academic disciplines, and even strangers on Twitter, how they use math and which concepts and skills are important to them in their work and daily life.

Here are some of the things they told me:

“in my day to day work/home, mostly % and unit rates/ratios, descriptive stats.”

“…as an insurance underwriter I spend my day working with percentages”

“Steamfitters use math for calculating piping offsets, structural supports, pipe fabrication, etc…… trig……. Some Calculus when dealing with refrigerants, chemicals, gasses,etc.”

“Interest rates for loans and credit cards. Budgeting for household expenditure.. Being able to understand how badly journalists and politicians use statistics.”

“Supermarket stuff every day : is X a better deal than Y based on volume and cost?”

“Working out how much paint to buy according to size of walls….. square metres!”

“In music, tempo, time signature, note values, etc.”

“Figuring out the damn tip on a restaurant bill. (Or who owes what in large parties). Life budgets. How much IS 20% off of that dress?”

“Algebra for Cooking: Scaling up/down and going from rectilinear to circular pans in recipes. “

“Adapting a knitting pattern to a new size that wasn’t included in the directions”

“We found ourselves delving into trig and Pythagoras recently working out an order for shutters for an eight part bay window.”

“trying to understand the long-term consequences of taking the student loan v. helping [our children] out….”

Summarizing, almost everything fell into these categories:

  1. Percentages – Almost everyone said this
  2. Proportions – this encompasses unit conversion skills related to supplies, materials, costs, nutrition, health, etc
  3. Descriptive Statistics – finding averages, describing distributions as well as being able to understand and interpret data and charts from business, politics, media, etc
  4. Geometry and Trigonometry
  5. Inferential statistics.

And in general, the common theme was in using arithmetic and logical reasoning skills in context rather than abstractly. Certainly, some skills from a standard algebra curriculum are needed for the above. I would say:

  1. Arithmetic, including order of operations – with a calculator!
  2. Simplifying linear expressions.
  3. Solving linear equations.
  4. Solving proportions, including percentage problems.
  5. Geometry including area and volume.
  6. Radicals including Pythagorean theorem.

However, I don’t believe operations on nonlinear polynomials, factoring and solving quadratic equations, simplifying complicated exponent expressions, and solving radical and rational equations are vital in order to master the aforementioned skills people use.

So the question is this: Why should all students be proficient in algebra to graduate, when an overwhelming percentage of successful adults in professional and even academic careers never use much of it? Before I offer my answer, a couple of caveats.

  1. Students on STEM degree paths need algebra.
  2. We should not create a two-tier system, which bars students from algebra. Every student should have the opportunity to take algebra if they wish to, and to be informed of the implications of not taking it and of the alternatives.

But what about the third type of student who is generally capable of the academic work required to obtain a degree in a non-STEM field and be a productive member of society, but is prevented or delayed from doing so because they failed elementary algebra?

In November 2014, The American Mathematical Association of Two-Year Colleges issued a position statement on “The Appropriate Use of Intermediate Algebra as a Prerequisite Course”  that concluded

“NOW, THEREFORE, It is the position of AMATYC that: Prerequisite courses other than intermediate algebra can adequately prepare students for courses of study that do not lead to calculus.”

Some progress has been made, notably through the California Acceleration Project and their pre-Statistics Courses. At CUNY, there are some Community Colleges experimenting with Carnegie’s Statway and Quantway, as well as the very promising experiment mainstreaming remedial students into a Statistics course conducted by former EVC Lexa Logue and Mari Watanabe-Rose (pdf link).

But significant resistance remains, largely in the form of the aforementioned proclamation that “algebra is part of a well-rounded education.” I believe that we must continue to design and implement alternative pathways in mathematics to better serve the students who traditionally get stuck in remediation; Either through alternative remediation, or preferably in mainstreaming those students into an existing credit-bearing Quantitative Reasoning or Statistics course with extra support for their basic skills. These courses should be supported by proven pedagogy and contextualization of the topics.

Furthermore, I believe such decisions and designs must not rest solely with Mathematics departments, which are service departments in Community Colleges, but in communication with faculty in other academic departments who know what mathematical skills are required to be successful in their courses. We should partner with other disciplines, by collaboratively developing learning outcomes and sharing pedagogical techniques, to help them to support our students’ mathematical learning throughout their education. They deserve nothing less.

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MetroCiti: Professional Development Opportunity for Math Faculty

Arts and Sciences faculty may be interested in a professional development opportunity administered through Teachers College called MetroCiti.  Applications from community and senior college faculty are encouraged; this year Kingsborough, Queensborough and Hostos have faculty participating.  Fellows discuss key readings from the learning sciences and sociocultural research that bear on teaching for diverse students’ liberal learning, and develop pedagogical approaches to implement their findings.

Please share widely with colleagues.  The deadline is April 13.

http://metrociti.pressible.org/

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CUNY Math Challenge for students: registration closes tomorrow!

The 2015 CUNY Math Challenge is open to any matriculated undergraduate student; registration is open through February 18, 2015.  Sponsored by the Office of Academic Affairs and the CUNY Institute for Software Design and Development (CISDD) and supported by the Office of the Chancellor, the CUNY Math Challenge seeks to identify and reward CUNY’s best math talent.  Please encourage students to register!  Cash prizes range from $100 to $2,500.

The contest begins online at 9 am on Monday, February 9, 2015 and ends after an in-person exam at 10 am on Sunday, April 26, 2015.   Winners will be recognized at a reception in May.

Register at http://math.cisdd.org

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The Developmental Math Challenge and Statway at LaGuardia – Part I

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Statway: a Gateway to Graduation I have been an assistant Professor at LaGuardia Community College’s department of Mathematics, Engineering, and Computer Science since Fall 2012. My background is both theoretical Physics and Statistics, and I have an extensive teaching and … Continue reading

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Chancellor’s Award for Excellence in Undergraduate Mathematics Instruction

CUNY’s Office of Academic Affairs has released the 2015 Application for the Chancellor’s Award for Excellence in Undergraduate Mathematics Instruction.

Full-time and part-time faculty at CUNY community colleges, comprehensive colleges, and senior colleges are eligible to apply.  Awards in the amount of $5,000 are based on evidence demonstrating that the faculty member’s students improved their skills in math as a result of a particular successful technique or action. Materials submitted by candidates include evidence of excellent instructional methods, as measured by improvements in student learning, within at least the past year. Eligible courses for the award are developmental or credit-bearing mathematics courses up to and including the first year of calculus.

Applications, which are due February 12, 2015, contain detailed information and criteria.  CUNY math faculty are encouraged to apply!  Questions can be emailed to: mathinstructionaward@mail.cuny.edu

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The Climate March Math

climate march by jonathan cornickThis past Sunday, did you see hundreds of photos from the People’s Climate March posted on your friends’ Facebook and kick yourself for having a lazy afternoon on your couch (as I kind of did)?

The New York Times reported that, on September 21, approximately 311,000 people participated in the March in New York City. The article said that the number was “… provided by 35 crowd spotters and analyzed by a mathematician from Carnegie Mellon University…”

There seem to be at least a few different ways of counting crowds, many of which use a basic “area times density” principle. They include the classic technique developed in the 1960s called the Jacobs Method, and updated, more accurate methods such as Yip and Watson’s.

While 311,000 was more than enough to make me wonder why I didn’t join this historic event, the event’s organizer claims that nearly 400,000 marched. There is no way to know whether this discrepancy comes from simple errors, or public relations motives. Or is there?

Professors: Do you think you can use this topic in any of your math classes? If so, in which course and how?

(Photo courtesy of Professor Jonathan Cornick at QCC, who was one of those Facebook friends)

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Evidence-Based Reform of Remedial Mathematics

I am an Associate Professor in the Mathematics and Computer Science Department at Queensborough Community College, and I have spent the last six years working on improving remedial mathematics.

When I started at QCC in 2007, students either placed into a semester long elementary algebra course, or a semester long arithmetic course after which, if they passed, they were required to take the elementary algebra course. The majority of students coming to QCC placed into one of these courses. Success rates were very low – for example only 3% of students placing into arithmetic graduated with an Associates degree within six years, only 10% of them even exited remediation, and in general passing rates in elementary algebra were consistently 35-40%.

I have been involved in several evidence-based reforms to address the low success rates of students who place into remedial mathematics. Each step the changes have been directed by a growing body of peer reviewed research, and by careful analysis of local statistical data.

In 2009 the QCC math department created a compressed 4-week, 20-hour version of the arithmetic course. This course was successful in the sense that students passed at a much higher rate, despite having the same curriculum and exit requirements as the traditional course. However, later analysis revealed that these students weren’t passing elementary algebra at a greater rate than before. The arithmetic course(s) seemed mainly to serve as an obstacle to student success. In Spring 2013 the department voted to eliminate the arithmetic course completely for a variety of reasons.

Together with my colleagues G. Michael Guy and Karan Puri, we studied the effect of the course elimination and found that students who would previously have placed into arithmetic were not adversely affected in the rate at which they passed elementary algebra. This study has been published in MathAMATYC Educator.

Of course, we are under no illusion that we have magically solved the issue of weak arithmetic skills in some of our students, but we believe that an arithmetic course is not the solution to this issue. Students, who learn an arithmetic skill in one course, aren’t likely to remember it 4-6 months later when it’s required in algebra if they weren’t given a context in the first place.

However, whether students take arithmetic or not, exit rates from remedial mathematics at QCC remain disturbingly low in the 35-40% range. In an attempt to address thiswe wrote an elementary algebra book in which we contextualize arithmetic skills and introduce them “just in time”. For example, we start with linear equations, which only require positive integer operations to solve, then review signed numbers, and then move on to linear equations with negative number operations. Initial results have been promising, in a study involving six instructors using this textbook students were nearly twice as likely to pass the course as opposed to a control group taught be instructors using the standard departmental text.

Our emphasis is on rethinking pedagogy and using time more effectively for student centered problem solving rather than shifting the issue to a lower course.

My research, supported this year by a Chancellor’s Research Fellowship for Community Colleges, will focus on these questions:

  1. How do students who would have formerly been placed into arithmetic perform in their credit math course(s)?
  2. How do students who take remedial algebra in classes with our contextualized textbook and student centered problem solving pedagogy perform in subsequent credit math course(s)?
  3. How do various attributes and attitudes influence student success, and what can we do inside and outside the classroom to support those which have a positive effect, and change those which have a negative effect?
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Chancellor’s Research Fellowship

In Spring 2014, Interim Chancellor Kelly awarded 19 “Chancellor’s Research Fellowships” to faculty at CUNY’s community colleges through a highly competitive process.  These fellowships fund research in many disciplines during the 2014-2015 academic year.  Three of the Fellows are mathematicians.  Luis Fernandez from Bronx Community College submitted a proposal regarding the curvature of harmonic surfaces in spheres. Uma Iyer, also from Bronx Community College, will examine representations of algebras of quantum differential operators.  Queensborough Community College’s Jonathan Cornick will engage in a longitudinal study of remedial mathematics reform.  Congratulations to these faculty.

Stay tuned!  Professor Cornick will keep CUNYMath blog readers apprised of his research.

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Calculus Boot Camp

Calculus Boot Camp, an initiative of Interim Chancellor William Kelly, has launched at six CUNY campuses.  In July and August 2014, hundreds of students across Baruch College, Brooklyn College, City College, LaGuardia Community College, Lehman College and NYC College of Technology will participate in free workshops on campus.  Designed to enhance  the skills of students between their spring semester of Pre-Calculus and fall semester of Calculus, Boot Camp aims to give participants an advance look at the material they will cover for credit in a few short weeks. The program is sponsored by the CUNY Central Office of Academic Affairs, and will include an evaluation component to gauge its effects.

Math faculty teaching the workshops also serve as campus coordinators for the program.  Special thanks to Professors Peter Gregory, Jeff Suzuki, Matthew Auth, Mahdi Majidi-Zolbanin, Joseph Fera and Satyanand Singh.  Follow along at #CalculusBootcamp

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Congratulations Janet Liou-Mark, recipient of the MAA Metro NY’s Distinguished Teaching Award

City Tech professor Janet Liou-Mark was presented with the Distinguished Teaching Award by the Mathematical Association of America’s New York Section at their annual meeting on May 3rd.   As her colleague, I can confirm that her creativity, positivity, enduring belief in her students, and indomitable energy are truly astonishing – Janet, we salute you!  Congratulations, and well deserved.

Professor Janet Liou-Mark (right) being presented her award by  New York Section Chair-Elect Elena Goloubeva (left).

Professor Janet Liou-Mark (right) being presented her award by New York Section Chair-Elect Elena Goloubeva (left).

For more details, check out the announcements on the MAA and City Tech sites.  For more on Janet, take a look at this great interview by Mari Watanabe-Rose here on the CUNY Math Blog.

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