While progressive teaching methods can be and are employed in all subject areas, secondary mathematics classrooms are begging for new and innovative methods. All too often, students cannot see relevance to their present or future lives in the topics covered at school. Many teachers explain that learning math is important, but do not or cannot tell the children why. Thus, learning often becomes motivated entirely by extrinsic rewards rather than the intrinsic personal value of the knowledge to the students and, hence, retention of the material is severely reduced. Traditionally-instructed students use drills, memorization and practice, practice, practice to learn theorems and formulas rather than thinking critically about underlying concepts and principles of a problem and deducing the formulas for themselves. Consequently, an opportunity for students to buy into the educational process and take personal ownership of knowledge is missed. Students become pawns of the institutions rather than independent entities with the power and means of self-determination.
How then can one combat these problems in the schools of today and tomorrow? The first step is to look to the past: adopt the philosophies and methods that did work, discard those that did not and understand the reasons for both. The next step is to adopt existing methods to include new technology and tools available today. Finally, progressive education professionals must look to the future and envision the opportunities and the possibilities that will become available, in order to be prepared for their arrival.
It seems almost impossible to argue against the ideas presented in the progressive education philosophy. As a nation, we strive to uphold democratic principles and so, then, should our schools also embody those ideals. Students should be allowed to help determine the curriculum beyond state mandates, based on their own interests in the subject. Aside from developing class rules, there may also be opportunity for pupils to help set some class policies (e.g., take weekly quizzes or bi-weekly quizzes worth half as much) and there should be a process for students to appeal those policies they believe to be unfair. Critical pedagogs foster this questioning of class, school or societal rules and encourage students to become active in the process of change through talks with parents, educators, administrators and even legislators if necessary. By allowing all students to have an equal voice while still upholding egalitarianism in his classroom, a teacher empowers students of minorities (and minority opinions) to instigate change while also fostering cooperation or compromise between students of differing ethnicities, races, genders, cultures, religions or socio-economic classes.
Truly egalitarian teachers endeavor to preserve ethnic diversity. One simple way to do this in any classroom is to celebrate all holidays (not just Judeo-Christian holidays) and/or discuss the history behind them. It is important that, within these discussions, students and teachers alike attempt to examine the past through different cultural perspectives and not just their own. In addition, critical pedagogs encourage their pupils to discuss why different cultures (i.e. American Indians and European-descended Americans) have different views of these holidays (e.g. Thanksgiving) and also the reasons why one view is more widely accepted (e.g. oppression, disinformation and control of the education system). Specifically, math teachers have the opportunity to celebrate diversity when introducing significant mathematicians. While the great western thinkers of the past were mostly European and upper-class, the mathematical advancements of today’s world are made in all corners of the globe by all types of people. In addition, many of the first mathematical developments (i.e., Arabic numerals, calendar systems, etc.) were developed in non-white cultures. It is quite important for modern teachers to represent the entire student population in the material presented, in order to help students personally identify with the subject and also to give them hope that they are not precluded from the field based on sex, race, gender, etc.
Progressive teachers also strive to facilitate different learning styles and abilities in one classroom. Because no two classes are the same, there is not one perfect way to present different students with the same material. A good teacher is not only creative, but is also mindful of students’ reactions to his methods, uses reflective inquiry to help determine if the methods are having the desired effect and adapts them immediately if they are not successful. In addition to incorporating diverse learning styles and abilities, creative presentations of mathematics also serve as means integrate the curriculum and to discuss greater social problems. For example, students asked to calculate comparisons of the demographics, local funding and matriculation rates of their urban school and a nearby suburban school (or vice versa) could springboard into discussions of statistics, economics (e.g., taxes), history (e.g., reasons for migration of minorities to urban centers), civics (e.g., legislative mechanisms to change school funding policies) and social commentary (e.g., de facto segregation and “white flight”).
Math teachers also incorporate different learning styles and abilities into the classroom by presenting material in ways atypical of the traditional blackboard lecture and pen-and-paper practice. Geometers give students Tango toys to help them discover the relationships between shapes for themselves and through hands-on play activity or have students read novels, such as Flatland: A Romance of Many Dimensions. Students are asked to draw their own tessellating shapes and display the art in the classroom. Instructors show students how to build three-dimensional geometric kites or origami in order to lead into discussions the physics of flight or modular math. Other teachers allow individual students or small groups to research a topic on their own and then present the material to the rest of class. While building the research and public speaking skills of children, this method also helps students to realize what they do not know about their topic during the presentation stage. Through reflective inquiry facilitated by the teacher, students can identify for themselves how their research or presentation skills need to be improved for future endeavors. In addition, students may possess unique insights into the material that other students will appreciate and the instructor may not have otherwise presented. Some teachers also have students write self-analyses to help both teacher and student properly identify where the student, teacher and curriculum are lacking. By integrating methods (e.g., reading, writing, drawing, building, public speaking, playing music) and topics (science, economics, music, art, etc.) traditionally used in other classrooms, math teachers can help students to build upon existing problem-solving skills while exhibiting real-world applications of mathematics to other subject areas.
Regarding the philosophical approach to the inclusion of all types of students in the classroom, the most important ideas to take from progressivism are pragmatism, empiricism, democracy and egalitarianism. However, as public schools are the defense of democracy in society as a whole, teachers must also employ reconstructive practices of critical inquiry and activism to empower students as instruments of social change and rightful heirs to civic duty. Also, through the application Eastern philosophical ideas, individual responsibility, self-determination and self-reliance can be cultivated in future generations. Teachers themselves must learn to be mindful of hidden and null curriculums as well as gaps in messages sent to and received by students, so that inequalities will not be tacitly perpetuated by their curriculum. Most importantly, though, educators must always be mindful of ways to link the study of mathematics to the students’ home lives. Progressive teachers can relate math skills to pay checks, interest accumulation, price-per-unit comparisons, building a house, filling a swimming pool, etc. Critical pedagogs may problematize situations and discuss the mathematics behind pay inequities, gender/race performance differences, taxation, welfare programs or even the No Child Left Behind Act.