Pedagogical Reform of Secondary Education in the United States:
Redesigning Mathematics and Physics Curricula with Critical Pedagogy
i wrote this essay for a class i took during Spring 2015, facilitated by professor Noah De Lissovoy. he asked us to identify a problem in the education system and propose a solution using the discussions we had in class. i decide to share it here because more than a couple people asked me to read it, so here it goes.
Section 1. Introduction
One of the most notable and detrimental consequences of the American education system is the insubstantiality of students’ knowledge due to standardization and the disenfranchisement of minorities through imperialist education. Standardized tests promote traditional instructional approaches that teaches to the test, so this pedagogy focuses on memorization by requiring students to work on many practice and drill problems, and rehearse the material by working on practice tests (Savery 2006). When students coming out of this system encounter a real-world problem, or any difficult problem as for that matter, the problem becomes a source of frustration because students do not know how to approach the problem critically. This is because they are not trained to apply their knowledge to new situations in a way that requires them to exercise their imagination and think critically. Since grades are so important in the current education system, the fear of failure and ruining their GPA unsurprisingly drive students to resort to looking for the answer online, and the realization that they are really cheating themselves dawns upon them usually too late.
This is especially true in science and mathematics curriculum in secondary education in the United States. This is why I propose to reform the pedagogical foundation of physics and mathematics at the secondary educational level. My proposal is specifically aimed at this stage in a student’s education because at this point in their lives, the students are able to grasp the content of the curriculum with a more mature attitude, and it is early enough that any damage caused by past curricular failures and social conditioning can be fixed with the caring hands of critical pedagogy.
The necessity of redesigning the curricula is twofold: to give students a chance to understand physics and mathematics, and to prepare the new generation of thinkers with the tools to succeed in the fast-growing 21st century society. In many of my encounters with students of different majors, when answering the question, “What’s your major?” I am usually met with, “Oh wow, I hate physics!” Why is this? Why do most college students, after experiencing high school physics, come to dislike it so much? Surely this is not symptomatic of just the state of Texas.
The question still remains: why specifically focus on mathematics and physics? According to the American Institute of Physics, physics majors had the highest MCAT score in the physical sciences portion, and the second highest LSAT average score, behind mathematics majors by only a tenth of a point. Evidently, students of mathematics and physics, in the course of their time in college, acquire a set of skills that arm them with the ability to score extremely high in tests that require a great amount of logic and knowledge base. It is fair to consider that a good enough reason to focus on these two subjects, but a better reason to focus on mathematics and physics is a more fundamental one: every person in this world should have access to a proper mathematics and physics education because it is the language through which we interpret and make sense of this Universe. This language encompasses the technology that influence and shape the lives of billions of people across the world. As the world becomes more technologically advanced, being able to comprehend that every new technology is just the application and extension of abstract mathematical concepts takes away any feeling of intimidation toward the future, thus empowering the individual. Therefore, providing the necessary instruments to understand and appreciate the importance and beauty of these subjects really is a humanitarian service.
Section 2: Review and summary of research
How can we directly address the issues we currently face in the American education system? We must first recognize the force driving the current system: it is a white supremacist capitalist patriarchy society. But what does this mean in the context of education? This means that minorities, women, children, and anyone without an abundance of capital are marginalized and oppressed in some form or another. Wealth and power drive such a system’s economy and politics, and hence the education system takes the shape of the banking model of education as characterized by Paulo Freire in The Pedagogy of the Oppressed. This banking model of education serves to preserve the status quo—it is an oppressive model of education for it projects absolute ignorance onto those being taught, so all the decisions made regarding education are done without the consent or awareness of those being educated. This allows those in power to control what is taught at schools, giving them almost absolute control over the lives of families already suffering the consequences of such a system and their future. Therefore, we need an education model that reconciles this dichotomy, of teacher and student, and which regard students with respect, simultaneously liberating those being taught and those doing the teaching. Enter problem-based learning.
Problem-based learning (PBL) is an “instructional and curricular learner-centered approach that empowers learners to conduct research, integrate theory and practice, and apply knowledge and skills to develop a viable solution to an ill-defined problem” (Savery 2006). PBL, however, is not just about problem solving: it is about employing the methodology behind problem solving as a way to motivate teaching and learning. It is, as Freire calls it, a form of libertarian education. Savery (2006) provides an overview of the characteristics of PBL, through which the role of the teacher, referred to as tutors, and the learners are identified. The author also comments on the distinctions between PBL and different instructional strategies such as case-based learning, project-based learning, and inquiry-based learning (IBL).
The biggest distinction between problem-based learning, case-based learning and project-based learning is that in the latter two, the problems are well-structured. In characterizing problem-based learning, Savery (2006) argues that it is important for problem simulations to be ill-structured to open the door for free inquiry, because this allow students to learn the ability to identify the problem, assess what they know and what they need to know, and set the parameters to develop a solution. This ability is one of the most important skills to develop when doing research and working on open-ended questions in the real world. I have come across a few physics problems in my life that were so ambiguously worded that in decoding what these problems were asking for, I encountered many other questions that alone are questions worth exploring. For example, in investigating motion in noninertial reference frames, I was asked the question, “If you put water in a bucket and spin the bucket about its symmetry axis, what shape would the water take?” It is fair for one to immediately ask, “What’s the shape of the bucket? Does that affect the shape of the water in the bucket? Why or why not?” This is what ill-structured problem simulations mean and why it is paramount in problem-based learning: it gives the students the opportunity to come up with their own parameters to limit the scope of the question.
Another notable difference discussed in Savery (2006) between PBL and other learning pedagogies is the role of the instructor. In PBL, the instructor takes on the role of a tutor that facilitates the learning, and this renders the role not as a knowledge provider but rather as a facilitator of learning. In contrast, in case-based learning and project-based learning, the teacher takes on the role of instructors and coaches who provide guidance and “suggestions for ‘better’ ways to achieve the final product” (Savery 2006), but this diminishes the learner’s role in establishing their goals and outcomes for the problem at hand. Again we see the importance of having ill-structured problems, which is that with well-structured problems there is less incentive for the learner to set their own parameters and since the problems are well-defined, there is a well-defined answer, leaving no room for mistakes. In discussing inquiry-based learning (IBL), the author notes but one main distinction to PBL. In IBL, the instructor takes on the role of a tutor who is not only a facilitator of learning, but also a provider of information, whereas in PBL, the tutor does not provide information related to the problem because that is the responsibility of the learner. When considering the reform of mathematics and physics curricula, one must keep in mind that these subjects are inherently difficult, so I find it important and necessary to find a balance for the role of the tutor as a facilitator of learning and a provider of information.
We arrive at another important question to consider: why PBL over different styles of learning. Helle et al. (2006) provides a qualitative review of literature in project-based learning and outlines the pedagogical and psychological motives supporting this approach and its role in post-secondary education. The authors identify four principal motives for project-based learning, which supports my reasons for employing critical pedagogy: professional motives, humanitarian motives, the motive to foster critical thinking, and to foster understanding of subject matter. It is because of this article that I decided to incorporate problem-based learning as opposed to project-based learning—in project-based learning there is an end-product that the students are trying to achieve and this intrinsically creates a sense of competition between groups participating in the same project, and excessive competition, the authors argue, is not needed in classroom environments; in PBL, the end-product is simply the understanding of the subject matter.
Now, how should the classroom environment be structured? Springer et al. (1999) outlines the effects of small-group learning on undergraduate in STEM. The paper begins with a summary of education studies conducted during the 1980s by the National Commission on Excellence in Education, the National Science Foundation, and the United States Department of Education. There was a consistent recommendation among all reports: there is a need to shift the emphasis of current education from teaching to learning.
Springer et al. (1999) concludes that “what students learn is greatly influenced by how they learn, and many students learn best through active, collaborative, small-group work inside and outside the classroom.” A report by the American Association for the Advancement of Science (1989) discussed in Springer et al. (1999), points out that “scientists and engineers work mostly in groups and less often as isolated investigators,” and moreover, “overemphasis on competition among students for high grades distorts what ought to be the prime motive for studying science: to find things out.” It is in the spirit of these conclusions that I begin my proposal.
Section 3: Description of proposed project
The goal of a pedagogical reform in education is to empower all students with the knowledge necessary to develop critical thinking skills in order to realize their role in a society; to understand where they are from a historical perspective; to recognize the oppressive forces that have forced them into their current economic and geographic situation; to identify patterns of conditioned behavior in their own lives, criticize these behaviors and societal norms, and subsequently choose or create their own values and norms; and to become active learners in the classroom and beyond through extending the curriculum material to the real world by blurring the dichotomy between the real world and the classroom setting. Essentially, this form of education is meant to awaken and liberate the individual.
In reforming education, it becomes necessary to also reform the oppressive language of the old education system since language influences how we perceive something or someone. This means that the teacher should not be called a teacher—instead, they should be referred to as a facilitator. For instance, because of the etymology of the word professor, the professor figure in post-secondary education is by definition someone who professes some form of knowledge, but this invokes an authoritarian relationship between this figure and the students. On the other hand, in referring to the teacher or professor as a facilitator, we open the opportunity for teacher-student with students-teachers, and in this manner we redefine education as a practice of freedom (Freire, 1970). Keeping in mind that mathematics and physics are fundamentally difficult subjects to master, we adopt an aspect of the tutor in IBL as characterized in Savery (2006), so that in my model of education, the facilitator will additionally serve as a source of knowledge for the students. The facilitator would take the role of a passive instructor in the sense that they are ready to provide information when asked a question by the students. The reason for this is so that the facilitator would not diminish the students’ role in their education.
Another important aspect of this role is that a student may ask a question that the facilitator may not know the answer to. When this happens, the facilitator may ask the different small groups if anyone knows the answer, acknowledging his ignorance and understanding that perhaps another student might know the answer. This serves as a way for facilitators to constantly assess what they know or not know, and be in a position where they are also constantly learning. This promotes the idea of a democratic classroom by allowing students to share their knowledge with the facilitator.
What I hope to achieve with this pedagogy is simple: to make students part of the discovery process. Mathematics and physics textbooks depict a reality that is distant from the students, often too abstract, for a lot of them do not have the opportunity to ever see or play around with the objects studied in these courses. A way to overcome this would be to observe familiar objects and phenomena to explore the underlying mathematical machinery to illuminate deep, fundamental concepts of Nature. For example, in observing the behavior of light through various media, one could go further and inquire about the very nature of sight which would direct one to the study of electromagnetism; or in dropping objects from a certain height and noting how objects with different weights and shapes reach the bottom in a certain amount of time, one could begin to ponder as to why we do not fall from the surface of the Earth. In this last example, to provide a richer picture of what is happening, the facilitator would turn to general relativity and explain to them that matter curves spacetime, that this curvature of spacetime in turn dictates the gravitational field of a body, and that this field exerts a force on every object subject to this field that is always directed radially-inward.
There are many reasons for this method. Primarily, it is to build trust: facilitators would not withhold any information from the students and provide the most detailed picture to the students so they do not feel as if they are being deceived. This is part of promoting a libertarian education, where the facilitator is not in a position of power where they control what the students are allowed to know, but rather in a position alongside the students, which shows them respect by not underestimating how much the students may grasp, recognizing that they are not just students but beings who are also part of this Universe who have the right to know how their environment works. By properly depicting how something behaves, the facilitator would convey to the students the necessity of starting with simpler models to investigate the fuller, more complex picture, so that the students may begin understand how beautiful the mathematical language is and how vast its realm.
Though mostly out of the scope of the students’ knowledge, by allowing the students to ask and explore these kinds of question, the facilitator would get a clear picture of what the students know and what they want to know. This gives freedom for the facilitator to capture the students’ interest with different questions by observing different phenomena that ultimately illustrate the same concept. After captivating the students’ interest, the biggest hurdle to overcome is the mathematics. To overcome this, the facilitator would attempt to answer such questions with what the students know to motivate the need for a different mathematics, which in this case would begin with calculus. Through this method, the students would find themselves where Newton once stood right before delving into the infinite and developing calculus. Accordingly, the students would become part of the discovery process: they would be discovering known ideas through their own inquiry.
Employing this pedagogy would eliminate the oppressive capitalist companies who treat education as a business from the education system, such as publishing companies who hold monopoly over textbooks. This would be accomplished because this pedagogy is aimed at abolishing standardization and therefore creates a personalized education, since its rendition acknowledges the fact that every student is on a different page. With the notes taken from their observations, from their discussions with peers and the facilitator, and with their notes from outside research, students would compile their notes into their own textbook. This would inadvertently have students review what they learned at a much more sophisticated level. Through their research, they would reevaluate any “wrong” conclusions they might have made with their observations and learn the “correct” conclusions, and after “finishing” their textbook, students would evaluate their work by asking themselves if someone else could learn from their textbook. This form of learning would situate the students in a state of reflection where they are constantly thinking about what they have written, what they have learned, and what can they add to their textbook to make it more complete as they observe and discover new things.
However, this form of critical pedagogy poses two immediate issues: because of how extensive one’s knowledge must be in order to appropriately guide high school students through such a process, facilitators would be required to have a master’s degree in either mathematics or physics; and because of time restrictions of the daily schedule for high school, the typical high school schedule would have to be restructured completely and developed around this pedagogy. In order to implement this form of learning, it is possible to begin with a district and employ this pedagogy over a period of 4 years, beginning with a freshman group, guiding them through high school. They would then take the typical battery of tests a high school senior is put through, in order to assess how this critical pedagogy compares with the current system, and then move on to districts, then the state, and finally to the federal level if significant improvement is displayed by the students’ performance in these standardized tests.
Part 4. Conclusion
Based on the articles referenced, the authors Savery (2006), Helle et al. (2006), and Springer et al. (1999) would agree that reforming education at this level could indeed change our society. This form of teaching and learning would cease to teach students to pass a test—it would stop emphasizing extrinsic rewards such as grades as a form of merit; it would allow the students’ awareness to emerge from a cloud of toxic Western ideology into a state of wakefulness, aware of the way they exist in this fluid reality; it would help students assess social issues from a historical context from which they would realize themselves as also being oppressed, thereby entering the struggle for total liberation, recreating themselves by first liberating their minds; it would be inclusive of minorities and all those marginalized by the traditional system because facilitators would encourage those silenced to speak. The facilitator, being a humanist figure, would care to listen to the thoughts and ideas of those silenced, fostering every student’s creativity and imagination, tending to the flame that is every student, knowing well that even a small flame holds the potential of becoming a forest fire, a fire that would annihilate the monuments of capitalism.
An education system that is aware of its role in the life of a person and how it holds change on a global scale is capable of completely redefining our societies by simply adopting critical pedagogy as its philosophy. By employing the methodology of problem-based learning coupled with small-group learning, and by directing our focus from teaching to learning, we would help students think unconventionally yet critically through this pedagogy. As more and more students become educated under this new system, our society would be better suited to make humanitarian decisions that would set off a domino effect of people taking positions of power from people who should not have power, in the hope that our society would undergo a social revolution.
Freire once said, “Education as the exercise of domination stimulates the credulity of students, with the ideological intent of indoctrinating them to adapt to the world of oppression. This accusation is not made in the naive hope that the dominant elites will thereby simply abandon the practice. Its objective is to call the attention of true humanists to the fact that they cannot use banking educational methods in the pursuit of liberation, for they would only negate that very pursuit. Nor may a revolutionary society inherit these methods from an oppressor society. The revolutionary society which practices banking education is either misguided or mistrusting of people.” If we are to make real, lasting changes in our society, we must begin by reforming education by completely changing it, starting with its philosophy. We must not act out of naiveté and speak of radical changes without first addressing the obsoleteness of the current education system.
Bibliography
Freire, P. (1970). The Banking Model of Education. In Pedagogy of the Oppressed. New York: Continuum.
Helle, L., Tynjälä, P., & Olkinuora, E. (2006). Project-Based Learning In Post-Secondary Education – Theory, Practice And Rubber Sling Shots. Higher Education, 51, 287-314. doi:10.1007/s10734-004-6386-5
John, S. (2006). Overview of Problem-based Learning: Definitions and Distinctions. Interdisciplinary Journal of Problem-based Learning, 1(1).
Science for All Americans: A Project 2061 Report On Literacy Goals in Science, Mathematics, and Technology American Association for the Advancement of Science 1989. (1990). Bulletin of Science, Technology & Society, 93-101.
Springer, L., Stanne, M., & Donovan, S. (1999). Effects Of Small-Group Learning On Undergraduates In Science, Mathematics, Engineering, And Technology: A Meta-Analysis. Review of Educational Research, 69(1), 21-51.