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Mathematics Curriculum-It's Time for a Change

In his recent article in the New York Times, entitled “Is Algebra Necessary?”, Andrew Hacker makes a strong and provocative statement:

“There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic”.

In this article I will use the word Algebra to mean the traditional curriculum found in the courses typically called Pre-Algebra, Algebra I, Algebra II, and Pre-Calculus. The name Pre-Calculus can be used as a synonym for Algebra when grouping all these courses together because the primary purpose of these courses is to prepare students for Calculus. Surprisingly, my research indicates that only about 8% of people in the US take and pass Calculus. It seems that we are failing, both literally and figuratively, the vast majority of our students. They sense that the traditional mathematics curriculum is not for them, and they are correct.

When it is proposed that the US mathematics curriculum should be overhauled by eliminating much of the Algebra currently taught, the typical rebuttal is to point out that when students learn Algebra, in addition to being prepared for Calculus, they learn how to think quantitatively. I agree, but suggest it makes more sense for students to become quantitatively literate while studying topics that are relevant to their everyday lives. To get a sense of how irrelevant the current high school math curriculum is, look at the SAT Math Level II questions on http://www.analyzemath.com/practice_tests/sat_subject/level_2_sample_1.html. Most of the problems on the SAT II, Math Level I and Level II are not applicable to real life. There are some potentially useful topics included, namely Statistics, Probability, and Data Analysis, but unfortunately they represent only 10% of these standardized assessments. The College Board, as well as the Common Core Standards, emphasize pure mathematics almost to the exclusion of real-world applications, forcing the math-teaching community to spend the vast majority of class time on traditional, Calculus-driven “skill & drill”, which hasn’t changed much in over a century.

What is particularly bizarre about the preoccupation with the teaching of Algebra/preparation for Calculus is that very few of the 8% who do take and pass Calculus actually use it in their professional lives. Most engineers and doctors, for example, use Statistics on a daily basis, but rarely or never use Calculus.

Unfortunately, colleges view students’ success in arbitrarily chosen Algebra/Pre-Calculus curricula as a proxy for intelligence. It is time that educators, administrators, and policy-makers wake up and smell the Statistics. It is time to turn the tables on the standard math curriculum by spending the vast majority of our time teaching Statistics, Probability, and Data Analysis; these are the topics that help students make sense of what politicians say, decide whether to buy a lottery ticket, and plan for retirement. When that is accomplished, the general population will become quantitatively literate, will see the relevance of math in everyday life, and will enjoy mathematics for a change. To a large extent, the current mathematics curriculum limits students’ access to educational and occupational opportunities. Let’s instead inspire students with intriguing, powerful, and useful mathematics that prepares them for the 21st Century; if we do they might be motivated to continue studying mathematics… including Calculus!

Nils Ahbel is a mathematics teacher at Deerfield Academy in Deerfield, MA. His free, full year high school math course available at https://dalearn.deerfield.edu/login/index.php; click “Login as guest”.
November 27th, 2012 @ 10:48AM | 0 Comments | Post a Comment

Communicating The Way Mathematicians Do

I've been a mathematics educator for over 20 years and have always kept abreast of the latest technology. There are many excellent tools for investigating mathematics, but until recently all the available tools forced users to use the computer or handheld keyboard, which is clearly not the way mathematicians work. Unlike the subjects of English and history in which a QWERTY keyboard is an excellent interface, mathematics and science are at best clumsily communicated via a traditional keyboard. For that reason, we preferred paper and pencil or marker and whiteboard. On the other hand, interactive whiteboards and tablet PCs represent an environment in which mathematicians and scientists can easily share their ideas electronically. Fortunately, software has begun to emerge that recognizes handwriting so the software is simply a natural extension of the stylus or marker.

One such piece of software with which I have been working is FluidMath. This software has improved my teaching experience immensely. In particular, the software lets me write anywhere on the page and will recognize my handwritten math expressions and equations and turn them into graphs and tables quickly without thinking about or navigating the user interface. From my perspective as a math educator, I feel my work has greatly benefited from these capabilities. Everything on the FluidMath page is dynamic so, for example if you change a function, the associated graph, table, and solution change as well. Variables can be associated with sliders, so the environment is incredibly dynamic. Both graphs and sliders are created by a one-stroke gesture.

Click here to see video demonstration 1: http://www.youtube.com/watch?v=vREuu7fGorA

The FluidMath software platform also includes a broad and general-purpose Computer Algebra System (CAS). The Common Core Standards Initiative (1) lists CAS as an appropriate tool when solving a mathematical problem. CAS has been getting more attention in textbooks and will, in my opinion, continue to see increased emphasis. The teacher or student interfaces with its CAS through handwritten input via the screen of the computer in order to do mathematical computation or graphing. With Fluidmath, the tablet PC is not used as a substitute for manipulation skills, but rather as a tool for investigation. This change in perspective is incredibly important – it helps students be mathematicians and not just learn mathematics.

Click here to see video demonstration 2: http://www.youtube.com/watch?v=lOmt2R79sPA

In sum, I see the advantage of this software for 1:1 educators as three fold. First, the handwriting recognition is outstanding. Second, FluidMath uses standard mathematical notation so teachers and students alike need not learn any new syntax as you would with almost any other mathematical software. Third, the dynamic nature of this software means mathematics no longer need be a ‘paper and pencil’ subject but it can now come alive.

Based on my experiences, FluidMath in conjunction with tablet PCs make the learning of mathematics more effective, more engaging, and more enjoyable.

(Note that this software is not yet on the market but is scheduled to be released in the near furture. For more information, visit: www.fluiditysoftware.com )

(1) "Common Core State Standards Initiative | Mathematics | Introduction | Standards for Mathematical Practice." Common Core State Standards Initiative | Home. Web. 04 Feb. 2011. .
March 8th, 2011 @ 3:03PM | 0 Comments | Post a Comment