If you are visiting Boston this week for the American Mathematical Association of Two Year Colleges (AMATYC) Annual Meeting, stop by Booth 336 to meet the Mathcad Education Team and to learn more about Mathcad 15.0 and its role in PTC’s STEM Education Programs. Ned Daniels and I have been working hard to prepare for the conference. We both have a strong interest in supporting the hard work of teaching mathematics to the next generations of American workers. We know that AMATYC’s membership shares our passion for this mission. We look forward to many engaging conversations at AMATYC Boston!
Whether you are attending the conference or not, I hope that you will take a few minutes to read my most recent thinking about the challenges that we face in mathematics education in the United States at the close of the first decade of the 21st Century.
Community Colleges are the new Firewall for Math Education in the US
In mathematics education the first two years of college at four-year institutions and at two-year colleges is becoming the critical junction in the American educational system. Perhaps this was an inevitable result of the way that we, in the United States, approached reform in mathematics education. As our current reform era has marched forward the K-12 educational system has become increasingly effective at promoting students within a standards-based assessment regime. In doing so, the K-12 system is passing on the problems of deep, generative learning outcomes to higher education. As a consequence the largest growing sector of mathematics education at the college level is developmental mathematics.
At PTC we are deeply concerned about this trend. If US Schools do not prepare students for high technology jobs in the product development industry, it will be difficult for the US Manufacturing Sector to recover. For a company that develops innovative software solutions for the product development industry, a vital and growing manufacturing sector is good business for PTC. Beyond this bottom line issue, the challenge of improving mathematics education is one that sparks our intrinsic interest. We are a company of tinkerers, designers, and creative problem solvers with a passion for learning and problem solving – we love to help our customers solve the complex design and engineering problems that they face when they compete in a global economy. It concerns us that K-12 schools and community colleges continue to lack the necessary resources to offer all students a high quality mathematics education. It worries us that so many students are arriving at college with inert knowledge of key mathematical concepts and poor number sense. As a result PTC is committing more and more resources to support the improvement of STEM Education in the United States.
PTC is a major sponsor of a number of outstanding education programs in K-12 and higher education. One of our biggest corporate initiatives is our sponsorship of the FIRST Robotics Competition. More recently, PTC has increased its sponsorship of the Formula SAE Collegiate Race Series and it has joined the AMATYC Student Math League Competition as the Official Moderator Sponsor. In sponsoring teams in each of these programs PTC is committing time and resources to supporting the preparation of the next generation of STEM workers.
At PTC, I work within the Mathcad Unit in support of our partnerships and programs in STEM Education. If you are unfamiliar with Mathcad, I would introduce it to you as a powerful communication tool for use in science, mathematics, and engineering applications. Mathcad’s user base is diverse, stretching from economics and finance to chemistry and physics to all branches of engineering. Thus, there is no shortage of opportunities to promote Mathcad in K-12 and/or higher education. My biggest challenge, then, as Mathcad’s Education Program Manager is to build a program for Mathcad on sound principles for best practice in STEM Education. In pursuing this goal, I have spoken to many professors around the country about the hurdles that they face in teaching mathematics, and concepts built upon a foundation of mathematics, to the students entering college today. I also read the research literature in order to find the empirical evidence necessary to support the development of our educational program.
Recently, I came across the following quote from a report on the current state of developmental mathematics education at community colleges:
… there are long-term, negative consequences of an almost exclusive focus on teaching mathematics as a large number of procedures that must be remembered, step-by-step, over time. As the number of procedures to be remembered grows – as it does through the K-12 curriculum – it becomes harder and harder for most students to remember them. Perhaps most disturbing is that the students in community college developmental mathematics courses did, for the most part, pass high school algebra. They were able, at one point, to remember enough to pass the tests they were given in high school. But as they moved into community college, many of the procedures were forgotten, or partly forgotten, and the fragile nature of their knowledge is revealed. Because the procedures were never connected with conceptual understanding of the fundamental mathematics concepts, they have little to fall back on when the procedures fade (Stigler, Givvin, and Thompson, MathAMATYC Educator, May 2010, p. 15).
This quote interests me greatly because Stigler and colleagues posit that many developmental mathematics students have acquired a spaghetti knot of mathematical procedures in high school, but their knowledge of these procedures congeals into a blob of unrecognizable goop at some point before entering college. As a result, when they are put in a position to apply their skills, their reservoir of mathematical procedures is a stagnant and unusable.
Turning the Spaghetti Knot into Scaffolding
Mathcad 15.0 is a general productivity tool with many features that can be leveraged to build scaffolding for the application of mathematical procedures, rather than a spaghetti knot of tangled algorithms. For example, Mathcad can be used as a dynamic notebook for class notes, labs, and problem sets. In Mathcad’s whiteboard interface text, live mathematics, graphics, and images are integrated in a single document format. In math class students can record notes and problem solutions, revise their work or add annotations, and produce textbook quality presentations of concepts, investigations, and solutions. Unlike a traditional pencil-and-paper notebook, students can go back and interact with their notes by changing parameters, cutting and pasting formulas into new documents, and inserting notes.
Another important feature of Mathcad 15.0 is its use of standard mathematics notation. Unlike other CAS systems, students are not required to learn a programming language in order to use Mathcad. Instead, they can use Mathcad’s tool palettes and keyboard shortcuts to construct their solutions more or less exactly as they would be presented in a notebook or on a blackboard. At the same time, Mathcad has a powerful set of integrated mathematical functions – more than enough to take students a long way down the road to learning how to use computational thinking to construct models and solve problems.
Because it is unit aware, Mathcad also adds precision and confidence to students’ work in mathematics, science and engineering. Mathcad has outstanding unit capabilities enabling students to perform calculations on equations and expressions with quantities that are labeled with appropriate units. Moreover, Mathcad combines and simplifies units automatically, performing all necessary calculations and informing the user that there is a mistake when units are not consistent. Teachers and professors with experience teaching with Mathcad swear that this capability makes students more thoughtful and careful with unit calculations because there is more to be gained in terms of accuracy, than lost in terms of time, by using units in all scientific and engineering calculations. (See also http://blogs.ptc.com/bid/30820/Why-is-Mathcad-so-Keen-on-Units by Mike Baldani).
As a former middle and high school mathematics teacher, I believe that Mathcad 15.0 offers a unique set of capabilities that can enrich any learner’s mathematics education. I also see Mathcad as a platform upon which to build the scaffolding to support a more integrated STEM education program where students acquire confidence and skill in science, technology, and engineering through the skillful and confident application of their knowledge of mathematical procedures. Over the coming months and years I look forward to the opportunities ahead of me as I partner with schools, teachers, and professors to implement this vision in the American Educational system.