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identifier"ӬDX X 0x YP 1YD Y P k(The) Analysis of High-School Freshmen's Mathematics Textbooks According to The Types of Induction by Polya1996P!Y YP!
tTŐYP P!YMasterMaster's Thesis~Many scholars have claimed that inductive reasoning plays a very important role in the course of how to 'do' mathematics and discoveries to guess. A research of high-school students' cognitive level shows that many of them haven't reached the stage of formal operation yet. That suggests that the contents of their textbook should be instructed more concretely and inductively in proportion to their cognitive level. It is very important that should be the core element of the contents in their textbooks.
I think it is very meaningful to find out how much high school freshmen's textbooks deal with inductive reasoning, we will study the way how the textbooks deal with inductive reasoning in this research. They are as follows:
1) How are the textbooks of the students who stand in concrete operational stage and the transition period to be instructed?
2) Are the current textbooks instructed according to the process of (l)?
The followings are the results concerning those issues:
1) The textbooks must be instructed in a concrete way, which leads the students to have various mathematical experiences, as many of the freshmen haven't reached the stage of formal operation.
On the one hand, it is very evident that inductive thinking plays a very important role in providing the students with these experiences, on the ground that inductive method means a way to investigate all the phenomena empirically. Consequently, it is very important that the textbooks must be instructed centered on inductive thinking. That results in the way that the textbooks contain the contents concretely in proportion to the students' cognitive level.
2) Current mathematics textbooks of high-school freshmen hardly employ I_(1) or I_(1) -1. That gives the students little opportunity to do inductive reasoning by generalization. I can scarcely find I_(2). That causes the students not to figure out accurately the meaning of theorem. The same story goes to I_(3). Concrete examples or similar ways approaching to proof and the solution of the problems lead the students to understand what theorem is. However, the textbooks scarcely contain those ways and that makes the students difficult to study. The analysis of the current mathematics textbooks of high-school freshmen according to the 6th education reform shows that the textbooks have contents which lead the students to deductive thinking, rather than inductive thinking. That doesn't fit students' cognitive level. Also, the textbooks have little contents motivating inductive thinking, preventing them from improving their skills of thinking inductively and deductively in harmony.;YD XՔ ) !D \ D XՔ 买 ɔ\ `D \䲔 @ YՐ Xt ȥ T. YX x D pȬ\ l 0tt ι@ Yt D pȑ0 tt \ <\ 'И Ǵ YX x ʹ Yյ D T l<\, <\ ` DՔ . 0| PX t | ĳXՔ )<\ | h@ 买 ɔ\ |t.
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