The Idea Of A Coherent Curriculum For Mathematics And Science
Today we are awash in reports and recommendations, commissions and boards, standards and frameworks all striving to improve American education across the curriculum, and especially in science, mathematics, and technology. From those various sources, several common themes emerge: a belief in the importance of powerful ideas that provide all students with true scientific and mathematical literacy, ideas that enable them to use, not merely possess, knowledge; an emphasis on significant, ambitious content embedded in contexts that are meaningful to the students; and a recognition of the connections that permeate the disciplines and that link them one to another.
When it comes to mathematics and science, virtually no one contests the assertion that the fields are closely related. Statements like “mathematics is the language of science” and “science provides real-life applications of mathematics” have become educational cliches. Yet what we say and what we implement in our educational programs frequently bear little resemblance to one another.
Yet we have perpetuated an educational system in which mathematics and science are as separated from each other as they are from history, literature, the arts, or any other part of the curriculum. It is from this milieu that the cries for reform arise, cries that include a crescendo of voices calling for connection, integration, application, unification, alignment, and a litany of similar “innovations.” The mathematics and the science education communities are, more often than not, closely allied in this quest for literacy, although they may express their goals in slightly different terms.
Throughout history, science and mathematics have long enjoyed a symbiotic relationship: mathematics provides the analytic tools and theoretical models upon which science depends while science brings forth interesting problems and applications that contribute to an understanding and appreciation of mathematics. The intrinsic relationship between mathematics and science needs to be made explicit in our educational programs, or we shall fail to achieve our goals in either field. Our challenge becomes one of shaping learning experiences that reflect the spirit and value of science and mathematics and that respect the subject matter of both science and mathematics while at the same time building a common core of understanding that strengthens students’ knowledge, appreciation, and power to do science and mathematics.
To achieve the outcomes put forth in the current vision of educational reform will require an environment for learning science and mathematics that redefines our expectations for students and teachers, the ways in which we teach the subjects, and the means by which we evaluate success. It also requires that we clarify what it is that we mean by “integration.” Frequently we discuss topics using words familiar to all of us, yet we are each describing a different aspect of the education.
The situation with integration of science and mathematics is not much different: we find varied interpretations of what it means to “integrate” the disciplines and the methods we employ in teaching them.
The integration of mathematics and science is a reflection of what we believe about the nature of mathematics and science; it is not an organizational scheme. Integration can be approached through a variety of alternative curricular and instructional structures, but no one of them guarantees that integration will be achieved. The labels used to name various curricular approaches are neither well-defined nor important. Dossey used terms that included simultaneous, braided, topical, unified, and interdisciplinary to describe approaches in which one can find both similarities to and differences from Ost’s categorization. Any of the approaches can contribute to a revitalization of the curriculum; none will guarantee any particular results. Subsequent explorations build on that foundation by having the students investigate other phenomena that give rise to linear functions, thus simultaneously developing an understanding of the physical systems while also enhancing and expanding the concept of linear function. In activities such as those outlined above, students are engaged in investigations that help them to construct understanding both of significant mathematical relationships and of significant science concepts and to do so in an environment that models scientific inquiry and mathematical problem solving.
Throughout history, humans have invented tools-technologies-to extend their capabilities and enable them to accomplish goals that were previously outside their reach. The technology of the industrial age enabled humans to extend their physical and psychomotor skills, but industrial-age technology employed inanimate, non-interactive tools. By contrast, the technologies of our current information age include “intelligent” tools capable of extending human mental capacities in interactive and cooperative ways. In a very real way, humans now can enter into partnership with their tools. To the mathematics and science educator, this means that we can transfer many of the “old basics” to our tools, our technology. What was once necessary to be transferred to students in the form of memorized information or practiced skill is now stored in machine memory, or is accessed on the Internet. Students carry in their pockets technology more powerful than the largest computers of a generation ago. Such technology has profound implications for teaching and for curriculum. Modern technology makes possible the deep exploration of problems of real significance not only to science and mathematics, but to the learner as well. Describing a vision for integrating science and mathematics gives no assurance that such vision will lead to systemic change in classrooms, as the record of the past century has shown. The literature reports numerous attempts at integration over the years, but few traces are found in most schools today. Yet systemic change is precisely the goal that permeates all of the current reform efforts. If we hope to realize it, we must also attend to several critical issues and concerns. Each merits extensive exploration and discussion; a few of the most serious ones are identified briefly below.
What the framers of the reform documents understand about the nature of science and mathematics and what the public at large believes paint two very different scenarios. We believe that the essence of mathematics and science is inquiry: observing, experimenting, conjecturing, testing, verifying, even creating. The public believes that the essence of mathematics and science is memorizing disconnected bits of inert information and developing proficiency in the rote performance of mechanized tasks. We believe that mathematics and science are dynamic human enterprises that can and should engage the interest and abilities of contemporary students and adults. The public believes that virtually all mathematics and most science is “all finished,” having been done long ago by persons of another era with nothing for the contemporary student except to read about what others have completed. We believe that all persons are capable of engaging in significant mathematical and scientific inquiry. The public believes that only a small minority of “very smart” people, who have inherited their ability genetically, are capable of anything beyond the lowest levels of computation and factual recall.
If we hope to mount and sustain any significant reforms, we must first change the beliefs and expectations for mathematics and science held by teachers, students, parents, and the public. When that occurs, the absolutely close connections between the disciplines, their shared goals and processes, will come into focus and then, perhaps, educators will at last wonder why we have so long kept them isolated. The slogan “less is more” is becoming an anthem of the science education reform movement, and similar notions permeate the mathematics efforts. The message is that, in order to engage students in constructing significant, powerful understanding and useful knowledge, the curriculum will, of necessity, need radical overhaul. In particular, we cannot perpetuate an educational system in which teachers broadcast information to students who are then expected to commit it to memory. If students are to engage in real inquiry, then the amount of “material covered” will be decreased as emphasis shifts from transmitting as much information as possible to developing deep conceptual understanding and useful knowledge centered around powerful unifying ideas.
The above is easier said than done. Teachers and curriculum developers are reluctant to “leave anything out” of the curriculum, and it will require a dedicated effort to bring about curricular reconstruction. One major challenge will be to reach consensus on what concepts, principles, and processes of science and mathematics are best developed in an integrated setting, and which are more appropriately studied as separate disciplines.
The reform documents in both mathematics and science call for ambitious content for all students. There is more to that goal than meets the eye. We don’t like to admit it, but our educational system in science and mathematics has historically been a caste system: reasonably significant learning for a few, minimal learning for the rest. It is a situation with which society could cope in a time when advanced levels of science and mathematics were the province of a relatively small number of careers and fields of study. But it is a situation which we can no longer tolerate. This is not merely a call for schools to require more hours or years of mathematics and science classes that continue the separate-but-unequal tradition of ambitious content for a few, low-level outcomes for the majority. Literacy and power for all demands that we change from the ground up what we expect all students to learn, how we expect them to achieve it, and how we assess their attainment. Such literacy will reflect the fact that knowledge of both mathematics and science, and the connections between them, is essential for participation in our technological society, not only as professionals in one of the disciplines, but as consumers, taxpayers, voters, decision makers, and caretakers of the environment.
Improving our educational system in either science or mathematics, and most assuredly in the integration of science and mathematics, will demand significant changes in the realm of teacher education and professional development. Presently, few science teachers are equipped to teach the broad range of science courses, and even fewer are prepared to teach mathematics at anything but a rudimentary, computational level. Conversely, few mathematics teachers can teach even one branch of science, and elementary school teachers are in the main only marginally prepared to teach either discipline. Achieving the vision of systemic reform of science and mathematics education, including the vision of integration of the disciplines, will require a radical departure from traditional teacher education models that foster specialization in one field, a specialization that becomes more narrow with succeeding levels of advanced study.
The idea of a coherent curriculum for mathematics and science presents a rich image of what the current reform movements strive to accomplish. The documents that delineate that reform do not carry with them prescriptions for implementation; instead they are described as standards, frameworks, and benchmarks. The reform documents present us with a diamond in the rough accompanied by a vision of what brilliance can emerge if that diamond is placed in the hands of an imaginative and skilled craftsperson — and they challenge us to bring forth educational brilliance in our programs so as to enhance the literacy and power of all of our students.
Megan Wilson is a teacher, life strategist, successful entrepreneur, inspirational keynote speaker and founder of https://Ebookscheaper.com. Megan champions a radical rethink of our school systems; she calls on educators to teach both intuition and logic to cultivate creativity and create bold thinkers.
