The Group was awe-striking, however, with a statement at the beginning of the chapter. The statement reads, "Mathematics supplies the mind with nutrients" (Adler, 1984)(p.71). There is nothing else that can be said to better summarize the importance of mathematics to our educational systems. Math is in everything that we do. Whether you know it or not, throughout the day, your mind will have to work math at some point in time. A simple example, going to the grocery store and purchasing something. When the clerk gives you back your change, if you are concerned whether or not it is correct, then you must work the math.That is the beauty of the subject, it will not fade away.
Adler states a second "beauty" of the subject when he writes, "In most things that we study, as well as in life itself, there are no certainties. An answer to a mathematical question, however, the solution of a mathematical problem, is either right or wrong - period" (Adler, 1984)(p.72). It is "black-and-white," there is no gray.
The Paideia Program does something that, in my opinion, our educational systems are making a mistake by not doing. This is making our students take math for the entire 12 years of their schooling. The Program also does a very good job of preparing its teachers to teach its students for these 12 years of school. Teachers can ask questions to students in many different ways, especially when working with math problems. Adler provides a good example of how good teachers ask good questions:
The best teachers ask many more questions than they answer; ideally, perhaps, a teacher should never answer a direct question that will aid the student to solve his own problem. Provide the students with a relatively large mass of facts to begin with - problems, examples, diagrams on the blackboard (in the case of geometry) - and let them try to figure out why things are as they are. What they learn on their own they will not forget; what they are told they are likely to forget quickly" (Adler, 1984)(p.74)
The main math subjects that are studied in the Paideia Program include: Arithmetic, Algebra, Geometry, Differential and integral calculus, Statistics (probabilistic mathematics), Computers, The history of mathematics, and The relation of mathematics to other fields.
When discussing Science, Adler states that, "Science is a search for a rational explanation of natural phenomena. It is a continuing activity" (Adler, 1984)(p.86). A continuing activity? Hmm? That sounds familiar, doesn't it? Almost like learning! Science, just like math, runs through all 12 years of school in the Paideia Program.
The goal of The Paideia Program, when teaching Science, is that, "Every student should gain a reasonable understanding of (1) the scientific mode of thought; (2) the present conception of the physical universe; (3) the nature of living systems generally and of man in particular; and (4) the development of scientific thought in the past and its implications for the future" (Adler, 1984)(p.87-88). The method used to do this is done by using a "3 Stage Approach."
In the early years of schooling, the "didactic instruction" is kept to a minimum. Most of the instruction is done by "discussing" science. Science in the middle years in taught using the "Socratic Method." This way the learners are asked to grasp the difference between an opinion and a deduction. They are also introduced to quantitative measures and taught using qualitative physical attributes. Finally, science in the "upper years" is taught by using "coaching." This is done, primarily because theory is very important here. Problems using laboratory experiments and solving should be used during this age of schooling. Physics, Chemistry, and Biology are courses that are taken during these years.
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