2013 IEEE Integrated STEM Education Conference (ISEC), 9 March 2013 doi:10.1109/ISECon.2013.6525194
An Interdisciplinary Approach to STEM Education Through Reconsideration of A Classic on Education Robert Christie and Wieslaw Marszalek DeVry University, rchristie,
[email protected] Abstract - Our paper addresses the issue of STEM education within the larger context of interdisciplinary education. We ask: Is an interdisciplinary approach to education, in particular to engineering education, superior, in some sense, to one that is narrower but deeper in content, a specialized education wherein a person learns about and studies the cutting edge recent discoveries or theories that are understood by only a handful of people in this world? Our thesis is that such an interdisciplinary approach can indeed be superior to, and enhance, a field-specific education. We pose several major questions in regard to STEM education, and then suggest an approach to address these issues from the perspective of a major classic in the field of education. We apply the insights of that classic to these questions, concluding with references to parallel insights from others who have engaged these same issues both in education as well as in the application of our suggested approach in the realm of scientific research. Index Terms – Arts, development of mind, mathematics, interdisciplinary education. INTRODUCTION By way of overview and introduction, we begin by posing four specific questions that we consider basic to STEM education. Next, we raise the issue of the nature or content of such education: is there value to a broader interdisciplinary context within which STEM education should take place? Can such a case be substantiated? How would this improve STEM education? Providing examples from the fields of music and programming, and visualization and the arts, we set the stage for our thesis: a reconsideration of a classic on education for its value in our time: the treatise on university education, An Idea of a University, by John Henry Newman, the 19th century English scholar. After a review of Newman’s principal ideas, we conclude with supporting examples of such an approach in our time, which support our thesis. BASIC QUESTIONS When it comes to the question of educating people in STEM and using the ever expanding technology we ask: (1) What should our priorities be in shaping our students’ minds, intellect and skills?
(2) How deep should we teach the various science, math and engineering subjects and what subjects should be expanded at the expense of others? (3) Should we really care to spend countless hours on emphasizing one particular subject (e.g. mathematics) and cover other subjects only superficially, and (4) What is the proper approach to provide a balance to those we educate to help them to become whole persons? When teaching applied mathematics to engineering students we always face the above questions, analyze them, and try to extract as broad conclusions as possible. In other words, is an interdisciplinary approach to education, in particular engineering education, superior, in some sense, to one that is narrower but deeper in substance, a specialized education wherein a person learns about and studies the cutting edge recent discoveries or theories that are understood by only a handful of people in this world? MUSIC AND PROGRAMMING EXAMPLES To put our deliberations at an appropriate level of a science, engineering and mathematics university education, let us consider a specific example from an upper level undergraduate mathematics course: analyzing a wave equation u xx c u tt f ( x , t ) , which is one of the 2
fundamental equations in many related areas in electrical engineering, semiconductor electronics, acoustic, mechanics, signal processing, filter design and others. Should a whole person studying electrical engineering know all of those applications? If so, to what extend and how deep should, for example, the mathematical analysis of all the possible boundary-initial cases associated with the above equation be presented? What about a numerical treatment of such and similar equations? Should a whole person know computer programming to be able to tackle all the above topics by using a computer and specialized software? What if we just spend our time presenting such a topic as a specific use of the equation in one particular area, but present it with an oceanic depth? What about taking a more interdisciplinary approach and give students just the basics of the LC power line that is described by the wave equation and then advance our presentation further and talk about the same equation in connection to the basic sine or cosine functions A sin( 2 ft ) [1], as used when explaining the
mathematical foundation of music (see Fig.1 [1,2]), where musical notation is a time-frequency relationship with vertical position being the frequency of the note to be played.
function tone=note(keynum,dur) % A4 is the key #0 with frequency 440 Hz fs=8000; tt=0:1/fs:dur; freq=440*2^(-keynum/12); tone=sin(2*pi*freq*tt); end Fig. 2. Matlab code of Twinkle, Twinkle Little Star by W. A. Mozart. VISUALIZATION AND ARTS Solving a simple system of three differential equations (Matlab code in Fig.3) can bring some enjoyment to a class, particularly when chaos is discussed in a differential equations or nonlinear dynamics class and the response is as shown in Fig.4.
Fig. 1. (Above) Layout of a piano keyboard with 3 octaves. (Bottom) First few measures of Twinkle, Twinkle Little Star by A. W. Mozart. Let us proceed a bit further and write a rather simple Matlab code (see Fig.2) that plays the first several measures of Twinkle, Twinkle Little Star [2] from Fig.1 in a somewhat artificial way. Would this be appealing to a person who had not previously found the mathematics and programing disciplines to be interesting at all? Will an aspiring musician perhaps now turn his or her attention to mathematics and begin to look at it from a different perspective, as something that is actually helpful in understanding music and important in this person’s musical endeavors? % "Twinkle, Twinkle Little Star" by W. A. Mozart keys=[ -3 -3 -10 -10 -12 -12 -10 -10 ... -8 -8 -7 -7 -5 -5 -7 -3 -10 -10 -8 ... -8 -7 -7 -5 -5 -10 -10 -8 -8 -7 -8 ... -7 -5 -7 -8 -7 -5 -3 -3 -10 -10 -12 ... -12 -10 -10 -8 -8 -7 -7 -5 -7 -5 -7 ... -5 -7 -3]; dur=0.1*[4 4 4 4 4 4 4 4 4 4 4 4 4 3 ... 1 8 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 ... 3 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 ... 1 1 3 1 8]; fs=8000; xx=zeros(1,168000); n1=1; for kk=1:length(keys) keynum=keys(kk); time=dur(kk); tone=note(keynum,time); n2=n1+length(tone)-1; xx(n1:n2)=xx(n1:n2)+tone; n1=n2; xx(n1:n2+175)=zeros(1,176); n1=n1+76; end soundsc(xx,fs)
function out = chaotic_jane(t,y) out= ... [-y(2,:).*(3*y(3,:).*y(3,:)-y(2,:)); ... y(1,:).*(3*y(3,:).*y(3,:) ... y(2,:))+sin(pi*t); ... -y(3,:).*y(3,:).*y(3,:)+ ... 0.9936633369*y(2,:).*y(3,:)+y(1,:)]; Fig. 3. Matlab code of a system of three nonlinear ODEs.
Fig.4. Solution of the system from Fig.3 for the matrix of the coefficients of the first derivatives diag[1,1,0.01] and initial conditions [-0.5 0.2 0.5]. Visualization, drawings, and images always seem to help in conveying the important features and findings when presenting what some students find otherwise dull and boring topics in engineering, science and mathematics. Adding a “human touch,” as in our next example, works quite well in most signal and image processing classes. Therefore, inserting the well-known “Lenna Story” (see Fig.5,[3,4]), and discussing how the story developed over the period of the last few decades is a welcome moment by most students trying to understand and implement complicated image filtering algorithms. Not only that. Using a digitized photo of one of the students of an image processing class makes the whole topic even more
interesting and engaging. That’s exactly what was done in a signal processing class at our university, when, with her permission, a digitized photo of Sandy, one of the students in that class was used (Fig.6).
[5,6] (the Lenna story) and the war-and-research drama of Doeblin [7,8] contribute to the overall process of university education that shapes the mind of the whole person. An integration of wide aspects of human activities and discoveries – interdisciplinary studies - not only those specified in STEM course syllabi, seems to be important in today’s academic landscape. A RECONSIDERATION OF A CLASSIC ON EDUCATION FOR ITS VALUE IN OUR TIME
Fig. 5. The Lenna digitized picture. Finally, history has taught us that famous and important science, technology and mathematics discoveries could not be accomplished without the amazing wills and perseverance of otherwise ordinary human beings. We all, or at least those of us who show interest in mathematics, were stunned by the latest (2000) discovery of a sealed envelope (from 1940) at the headquarters of the French Academy of Sciences in which Wolfgang Doeblin [7,8] presented his discoveries on the Chapman-Kolmogorov equation before he committed suicide when German troops were about to capture a small village in France which Doeblin’s French unit was trying to defend. In his last moments, he burned his mathematical notes and ended his life at the age of 25. Doeblin’s life is the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. The Bernoulli Society, to honor the scientific work of Wolfgang Doeblin and to recognize and promote outstanding work by researchers at the beginning of their mathematical careers in the field of probability, established the Wolfgang Doeblin Prize in 2012.
Fig. 6. The Sandy digitized picture. In summary, we would like to argue that the examples given above, both of our own classroom endeavors, other people’s touching examples of unexpected turns of events
In support of this position, we recommend a review of one of the classic treatise’s of educational philosophy in modern literature: John Henry Newman’s The Idea of a University [9,10]. Newman, a nineteenth-century English philosopher, theologian, and controversial convert, had an aesthetic vision – a vision of the whole, as that word is truly interpreted. This vision culminated in his concept of what he called the “imperial intellect,” or the development of the mind through university education, fostering the education of the “whole” person. “When Newman wrote The Idea of a University,” writes Martin Svaglic, “higher education was in the early stages of its long trend towards secularism, on the one hand, and toward utilitarian specialization on the other” [10]. Today, some fifty years after Svaglic’s comment, education is arguably even more engrossed in the secular – specialist trend observed by Svaglic, as technology-focused education has radically transformed the educational landscape. Personally, we are particularly interested in Newman’s educational philosophy, since we are instructors at a university that specializes in technical education with a substantial liberal arts core. Thus, a reexamination of Newman’s thoughts on education in the university setting is quite relevant and appropriate for us today. For Newman, the university is the locus for the “cultivation of the intellect,” and not a “foundry” or “treadmill.” Thus it is important to review how Newman addressed these issues for the value of his insights today. For example, Newman’s ideal of the integration of all disciplines into a “wholeness of vision” and a “true enlargement of the mind” inspires the rediscovery of the proper role of a university as that of educating the whole person. This raises two major issues challenging STEM education today: what is the role of the university, and what does it mean to educate the whole person? For our purposes, there is also the question of how this applies to STEM education: is such education based on the integration of all disciplines necessary for STEM education? Is it helpful? The first question provokes examination as to what extent Newman’s philosophy of education is relevant to these questions, especially in regard to three particular points: his ideal of the integration of all disciplines, notion of producing a wholeness of vision, and the goal of an enlargement of the mind. “What I would urge upon everyone,” Newman writes, “whatever may be his particular line of research – . . . . is a great and firm belief in the
sovereignty of Truth.” Indeed, this was a lifelong preoccupation with Newman, about which he wrote as a young man, “I think I really desire the truth, and would embrace it wherever I found it.” Newman presents his argument from two perspectives: a philosophy of mind and a philosophy of knowledge. The result of his reflections is his concept of the imperial intellect, which he describes as follows: “I observe, then, and ask you, Gentlemen, to bear in mind, that the philosophy of an imperial intellect, for such I am considering a University to be, is based, not so much on simplification as on discrimination.” We assert that a student’s ability to discriminate in the perception, analysis, judgment, harmonization, and synthesis of data is foundational to all learning and advancement of knowledge. Therefore Newman’s philosophy of mind and of knowledge, and his concept of the “imperial intellect,” are valuable for their relevance for those of us today who are engaged in the process of ever-expanding technological and scientific education as it bears on such ultimate questions as the search for truth and the education of the whole person. Such aspects critical to learning, as mentioned in the first part of our paper – the creation of a new perspective that promotes the motivation to seek ever deeper levels of knowledge, how this relates to the will and perseverance necessary to maintain the enigmatic search for such knowledge, and the literal effect of such sensory experiences as the visual perspective which can alter the search for, and judgment of, truth – are examples of but a few of the many intellectual dynamics generated by interdisciplinary learning.
electronic synthesized compositions of the present, the whole and the part are inseparably interrelated. In another area, wave-particle duality, a contemporary insight into a reality that has existed for billions of years, is another example of learning that depends upon such appreciation of the relationship of parts to whole, grounded in the mental act of discrimination which is developed by interdisciplinary study. We suggest that the dynamics of “paradigm shifts” as identified by Thomas Kuhn [11], who draws upon Michael Polanyi’s “tacit knowledge” [12], are grounded in this grasp of relationships, which is evidence of aesthetic knowledge – knowledge of the whole - wrought through interdisciplinary education as expressed, for example, in the writing of Richard Feynman [13]. These contemporary scientists are intellectual kinsmen of Newman, which supports our claim that a revisitation of Newman’s perspective on higher education can be fruitful for STEM education in out time. In addition, the noted contemporary philosopher and epistemologist, Bernard Lonergan, a disciple of Newman, advocated such interdisciplinary learning because of the current trend of field specialization, which results in the specialist who “knows more and more about less and less.”[14] This is especially relevant with the advent of such seismic shifts in higher education as the rise of MOOCs and their forced reconsideration of the nature of higher education. The content and delivery of higher education courses is changing rapidly due to technology and economic pressures, and a solid ground, a philosophy of what higher education should be, is needed as never before. Newman’s philosophy of education is one answer to that need.
CONCLUSION
REFERENCES
To this end, we advocate the educational philosophy of interdisciplinary studies espoused by Newman, which we assert is necessary for the education of the whole person. A major assumption of our reflections, consistent with Newman, is that all knowledge is interconnected. Thus, in an essential “aesthetic educational philosophy,” parts must be grasped in their relation to the whole. To do less would be to diminish understanding of that part. Our example of the relationship of mathematics to music is one such case in our argument for the widest possible scope of interdisciplinary education in order to grasp a subject in its fullness, and thus to be a truly educated whole person. The more such relationships one perceives, the more one discriminates – THE essential mental act at the heart of discovery and the advance of knowledge – and the more one understands the specific subject at hand. The more one knows of the whole in which that part exists, the more one understands the part in its fullness. The journey from the mathematics of the ancients to the computations of quantum mechanics is historical evidence of this interrelatedness. Let us recall that the mathematician Pythagoras discovered the laws of musical structure! From early mathematics to the beauty of the music created by the structural knowledge of Bach to the
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