Before we get into the philosophies of mathematics, I would like first to discuss with you your opinions of math and "Mathematics Anxiety." There is no question that many students dread their math classes and have a high level anxiety toward the very idea of solving an algrebraic equation. Why is this? Below is a section of Wikipedia's analysis of the causes of "Mathematics Anxiety." Please read it and respond in reference to the questions that follow.
Students often develop mathematical anxiety in schools, often as a result of learning from teachers who
are themselves anxious about their mathematical abilities in certain areas. Typical examples of areas where mathematics teachers are often incompetent or semi-competent include fractions, (long) division, algebra, geometry "with proofs", calculus, topology. In many c
ountries, would-be math teachers are required only to obtain passing grades of
51% in mathematics exams, so that a math student who has failed to understand
49% of the math syllabus throughout his or her education can, and often does, become a math teacher.
Math is usually taught as a right and wrong subject and
getting the right answer is paramount. Unlike most subjects, there is almost always a right answer. Additionally, it is often taught as if there is a
right way to solve the problem and
any other approaches are wrong,
even if they get the right answer. When learning, understanding the concepts should be paramount. With a right/wrong approach to teaching math, students are encouraged
not to try, not to experiment, not to find algorithms that work for them, and not to take risks.“Teachers benefit children most when they encourage them to share their thinking process and justify their answers out loud or in writing as they perform math operations. … With less of an emphasis on right or wrong and more of an emphasis on process, teachers can help alleviate students' anxiety about math.” [12]
While teaching of many subjects has progressed from
rote memorization to the current Constructivist approach, math is still frequently taught with a rote learning behaviorist approach. That is,
1. a problem set is introduced
2. a solution technique is introduced
3. practice problems are repeated until mastery is achieved
Constructivist theory says the learning and knowledge is the student’s creation, yet rote learning and a right/wrong approach to teaching math ensures that it is external to the student.
Teachers who
actually understand what they are teaching
tend to encourage questions from the students. Those teachers who
do not understand much about their subject, on the other hand,
impose fear on the students to prevent them asking questions which might expose the teacher's ignorance.
It has long been well established that
anyone (other than a tiny minority who have serious learning disabilities)
can learn any area of mathematics, given a desire to learn, a coherent presentation of the information, and adequate practice. Nevertheless, many educational administrators continue to profess the belief that anything more complex than simple arithmetic is too difficult for most people.
In spite of the unfortunate design of the modern school system, a remarkably high percentage of schoolchildren continue to find mathematics interesting, relaxing, easy, and enjoyable.
______________________________
Feel free to react openly to this selection... but also consider the following questions:
1. What is your opinion of mathematics in the classroom? Interesting? Boring? Stressful?
2. What are some other reasons you believe students fear math?
3. Do you think YOU are capable of ANY level of mathematics? If not, why?
4. Name your favorite math teacher and why he/she was your favorite.
As you can see, what starts as a simple pattern soon becomes relatively more complex and detailed simply by repeating it's pattern upon itself. This concept can be applied in great complexity and detail as to create fractal art such as these:
