Traditional vs Progressive

Chapter Three of Jo Boaler’s, Experiencing School Mathematics, describes two schools that have the same demographics, however, are at completely different ends of the education spectrum. 

First, Boaler identifies the very traditional and conventional school, Amber Hill.  As you walk through the school “icons of traditionalism were located throughout the reception area, presenting strong messages about the way in which the school was intended to be perceived” (Boaler, 2002, p.13).  The school’s Principal was an authoritarian figure and the school was “unusually orderly and controlled” (p.13).  Numerous rules managed students’ behavior of “obedience and conformity” (p.13).

Teaching at Amber Hill followed the traditional, long-established custom of chalk and talk.  Teachers would teach for about 15-20 minutes.  Writing notes and examples on the chalk board and then students would be assigned work in their text books for the remainder of class.  While students were completing their work teachers would take time to help individuals who need it.  This teacher centered approach focused on rote learning and memorization (Tradition Education). 

The second school Boaler describes is Phoenix Park.  Phoenix Park seemed to have a positive feel to the school, a “relaxed and cheerful atmosphere” (Boaler, 2002, p.19).  The school had a “long tradition of progressive education, placing emphasis on self-reliance and independence” (p.18).  It was relaxed and peaceful and student behavior was a “product of the school’s overall ambiance” (p.18). 

Teaching at Phoenix Park followed the progressive approach; it focused on individual students’ needs and self-exploration.  Many departments used project based instruction where students could generate knowledge based on their experiences and ideas.  Students were given choice as to the nature and direction of their work.

This opens up the age old debate of traditional versus progressive approach to education.  At a time when the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics calls for “reform to both curriculum and classroom instruction,” placing particular emphasis “constructivist learning, student-centered classrooms, worthwhile tasks, and reflective teaching” (White-Fredette, 2009/2010, p.21).  

Although the NCTM wants to redefine the vision of mathematics instruction, many mathematics teachers are still entrenched in the traditional method of teaching.  When the new junior high mathematics curriculum was being implemented in Newfoundland and Labrador I taught at a school where I was teaching grade 7, 8 and 9 Mathematics.  I implemented all three new curriculums, and when discussing the implementation with the high school mathematics teacher (this was a K-12 school); he completely rejected the majority of the ideas and values that were in the new mathematics program.  He believed in instruction that was teacher centered.  He did take his students needs into consideration and was a very admirable teacher, however, within the restraints our current system (time, amount of material, etc…) he believed chalk and talk was the most efficient method of instruction.  At this point in time he had not taught the new high school curriculum (Level I was only implemented this year), so I must make note I am not sure what his beliefs are now.  As well, I am not aware of the teaching expectations in the new high school curriculum.    

This being said, I have to agree White-Fredette when she point out that if we want to change the vision of mathematics the “theoretical framework must include a re-examination of teachers’ views of mathematics as a subject of learning” (p.21).  She concludes that teachers need to reflect on their own mathematics philosophies. Some questions for self reflection she suggests are:

1.       What are teachers’ beliefs about mathematics as a field of knowledge?

2.       Do teachers believe in mathematics as a problem-solving discipline with an emphasis on reasoning and critical thinking, or as a discipline of procedures and rules?

3.       Do teachers believe mathematics should be accessible for all students or is mathematics only meant for the privileged few?” (p.21).

To initiate change teachers must ask themselves and question their own philosophies of mathematics to recognize the importance of student centered instruction and engagement. 

This relates back to Reuben Hersh’s interview “What is Mathematics, Really?”  He argued as well that many individuals in the field of mathematics do not have a philosophy regarding the subject or have never spent time thinking about it.  As I have said previously, before this course I never thought about my own mathematics philosophy.  Looking back now, I think this is one of the most important things one should evaluate before teaching the subject.  The more I read and research the more I can affirm that my philosophy is rooted in constructivism.  I do believe learning is a social activity where communication is key; it is something you do, not something you gain (Forman, 2003). 

How to best teach mathematics is a very touchy, hot topic.  “Strong feelings exist in the debate on how “best” to teach mathematics in K–12 schools, feelings that are linked to varying perceptions about the nature of mathematics (Dossey, 1992).  Many parents and conservatives are concerned with the maintenance of educational standards based on testing.  However, there are many questions regarding students’ ability to apply the knowledge they retain through rote learning and memorization. 

Can students learn best in real life situations with other people that can be mimicked through project based instruction?  OR Can students’ learn best through abstract knowledge that is fed to them mindlessly by a teacher?  And the debate continues…

We only think when confronted with a problem.

- John Dewey, quoted in Harper’s Quotes

References:

Boaler, J.  (2002).  Experiencing School Mathematics.  New York: Routledge.

Dewey, John.  (n.d.).  Retrieved at http://www.mrlsmath.com/download-materials/math-quotations/ on October 10, 2011. 

Dossey, J. (1992). The nature of mathematics: Its role and its influence. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 39–48). New York: Macmillan.

Forman, E. A. (2003). A sociocultural approach to mathematics reform: Speaking, inscribing, and doing mathematics within communities of practice. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.). A research companion to Principles and Standards for School Mathematics (pp. 333–352). Reston, VA: National Council of Teachers of Mathematics.

Hersh, Reben.  (1997).  “What kind of thing is a number?  A talk with Reuben Hersh.”  Retrieved from http://www.edge.org/3rd_culture/hersh/hersh_p1.html on September 29, 2011.

Traditional Education.  Wikipedia.  Retrieved at http://en.wikipedia.org/wiki/Traditional_education on October 10, 2011.

White-Fredette, Kimberley.  (2009/2010).  “Why Not Philosophy? Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform.”  The Mathematics Educator, 19(2), 21-31.