They are basically an "overhaul of mathematics instruction," (611). The major points Alsup discusses in his article include the background information as to why traditional instruction falls short of the ideal, and includes the seven new rules for preservice elementary teachers' mathematics instruction. These seven rules are based on the National Council of Teachers of Mathematics and on what Alsup calls a "constructivist view of mathematics learning." According to the constructivist view, the teacher does not directly "transmit" mathematical knowledge and facts to the students; rather, students construct their own set of mathematical knowledge through active and creative problem solving (611).

Alsup suggests that the progressive, constructivist approach to teaching preservice elementary school teachers will lead to a "learning community." Students interact with one another and with the instructor, rather than having the instructor always stand before the class in a lecture format. The...

Emphasis is on problem-solving. Alsup also distinguishes mathematics exercises from math problems, which demand creative problem-solving skills: the student reaches a conclusion and thus remembers the underlying math theories better. With the constructivist approach, the teacher does not solve problems for the students, and often there is no one right answer. In fact, with Alsup's plan, students would work on many math problems for which even mathematicians do not necessarily agree. Moreover, students must present their solutions openly to the class and defend them.
Alsup's suggestions, I believe, are highly likely to eliminate the anxiety regarding math that many educators experience. Moreover, if progressive means of teaching math are employed in the classroom, elementary students are more likely to enjoy math. I would highly recommend Alsup's article to others because it presents a positive and constructive new approach to…