Societal Beliefs Effect The Math Student

Accodring to Curtis McKnight's book, The Underachieving Curriculum......

A survey of eighth- and 12th-grade students, researchers found that 40% of students at both grade levels agreed with the statement that mathematics is a set of rules, while 50% of the eighth-graders and 25% of the 12th-graders stated that mathematics involves mostly memorizing. Lending further credence to this rule-bound conception of the field, eight out of 10 eighth-graders and two out of three 12th-graders held the opinion that there is always a rule to follow in solving a mathematics problem.  In the real world of mathematics, nothing could be further from the truth.

    Society's negative view of math is adversely affecting students. In essance  the preconceptions about math are closing student's minds regarding the subject.

    Math is not simply a set of rules for the student to memorize. Instead, as Imre Lakatos in the book  Proofs and Refutations: The Logic of Mathematical Discovery points out:

Mathematicians participate in a problem-solving process that is interactive and often quite fluid. Some individuals have described this process as a "zigzag path" from conjectures to explorations of the conjectures through refutations and back to reformulated conjectures. Mathematicians offer hypotheses, or educated guesses, changing their ideas and their approaches in response to new arguments and discourse.

In other words, mathmatics can lead to discovery just like science. New arguments, and new facts are learned in the study of mathmatics, just as science does.  This poses a great challange to math teachers.

     How does one present mathmatics as a method of discovery and experimentation??