A Research on the Strategy of Integrating PBL with Curriculum Ideological and Political Elements-Taking College Mathematics as an Example

Taking college mathematics as an example,a questionnaire was designed for college mathematics teachers and students to fully comprehend the teaching situation.This paper mainly discusses the problems existing in the teaching of college mathematics and proposes the strategy of integrating PBL with curriculum ideological and political elements in college mathematics,so as to change the teaching process and improve the teaching quality.

Analysis of Mathematical Modeling Thought in College Mathematics Teaching

The mathematical analysis enters the higher mathematics as the mathematics specialized student from the general elementary mathematics the initiation curriculum, its content and middle school mathematics still exist relate very much, while it during the expansion knowledge as also has many transformations. Under this basis, this paper proposes the analysis of the mathematical modeling thought in college mathematics teaching. Mathematics modelling teaching uses the open style teaching method also to wait for consummates regards the concrete course content the main point, the function as carries on each kind of variant to the open style mathematics educational model enable this kind of pattern to have pointed. We propose the novel paradigm for the education that will then be essential for the further development of the systems, in the future, we will then apply more of the methodologies to enhance the current proposed model.

A Procedure for Trisecting an Acute Angle (Method 2)

This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.

A Procedure for the Squaring of a Circle (of Any Radius)

This paper presents a graphical procedure for the squaring of a circle of any radius. This procedure, which is based on a novel application of the involute profile, when applied to a circle of arbitrary radius (using only an unmarked ruler and a compass), produced a square equal in area to the given circle, which is 50 cm2. This result was a clear demonstration that not only is the construction valid for the squaring of a circle of any radius, but it is also capable of achieving absolute results (independent of the number pi (π), in a finite number of steps), when carried out with precision.

A Key to Solving the Angle Trisection Problem

This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.

A Method for the Squaring of a Circle

This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm2, it produced a square having an area of 12.7 cm2, using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.