Beginning a teaching career and working to prepare and support beginning teachers is a roller-coaster of successes and puzzling moments. In this article, author Cassandra (Cassie) Seiboldt shares how she learned to manage her first years of teaching by purposefully planning through anticipating student thinking and solutions, and the positive…

The method of integration by parts is one of the most useful in integral calculus. Among the most important applications is the integration of differentials involving products, differentials in involving logarithms, and differentials involving inverse circular functions.

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Available research supports a belief that a high-quality mathematics education for high school students cannot be accomplished unless a highly qualified mathematics teacher is in the classroom. This author primarily addresses the need for small, rural schools in Missouri to employ such highly-qualified mathematics teachers, although he also states…

Argues that first-year algebra should be taught in eighth grade. Outlines an algebra course that could provide average students with a working kowledge of algebra. Proposes that this would require students to have experiences with variables, equations, formulas, and graphs during previous years of study. (TW)

Discusses various changes which are occuring in society in general and education in particular (including the shortage of qualified mathematics teachers). Also discusses how to teach so that people will be able to adapt to change. In addition, proposes a four-step program to improve education in schools. (JN)

Proposes a new geometry curriculum for motivating middle school students. Discusses the treatment of geometry including visual justifications of geometric phenomena, examination of the properties of various common geometric figures, use of art and architecture, and inspection of geometric transformations. Eleven references are listed. (YP)

Discussed is a high school mathematics curriculum for students pursuing majors in collegiate business programs. Proposed are different emphases in the curriculum by different career fields such as audit manager, marketing manager, and production manager. (YP)

Described are important changes that will be introduced in the mathematics sections of the new Scholastic Aptitude Test (SAT). The three main changes are (1) permission to use calculators; (2) inclusion of open-ended questions; and (3) content revisions consistent with the National Council of Teachers of Mathematics "Curriculum and Evaluation…

Presented is a summary of the actions taken by American College Testing in response to calls for reform in standardized testing. The areas of reform discussed are test development, test content, skills levels, test criteria, and new testing initiatives, such as alternative-response-format questions and calculator use. (MDH)

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.

The challenges in developing discursive classrooms in high-poverty, rural schools motivate less verbal students to communicate. Students tend to resist mathematics education reforms and classroom discourses.

Mathematical contests should be decentralized to allow access to non competitive activities so as to enable students to participate and succeed in Mathematics. These activities should be compellingly interesting so that students enjoy learning about proofs and abstract structures rather than just solving problems.

The factors responsible for the shortage of middle and secondary mathematics teachers in the U.S. are discussed. Seven strategies are suggested to reach out and recruit more mathematics teachers in the future.