Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…

This case study describes a congenitally blind undergraduate student who successfully completed a basic statistics course. Accommodations specific to his blindness included: a textbook on tape and review tapes before examinations; a talking calculator; graphs made on Braille paper and other tactile teaching aids. Affective problems encountered…

Shares an experience from a mathematics methods course for elementary teachers that used concrete materials to teach the concept of rounding in different bases. Discusses how this experience modeled recommendations by the NCTM "Professional Teaching Standards" in creating classroom climate and conducting discussion. (MDH)

Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)

Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

An example is given of how to help students who have obtained a correct answer by a wrong method. They are asked to suppose that a child has found an easy method for division, and eventually write a computer program to show the correct method. (MNS)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

In dynamical theory, mathematical understanding is considered to be that of a person (or group) of a topic (or problem) in a situation or setting. This paper compares the interactions between the situations and the mathematical understandings of two students by comparing the growth in understanding within a Fibonacci sequence setting in which…

The teaching of numeral representations other than decimals is seen as a necessary and important step in the education of pupils in computing. Basic arithmetic procedures for binary, octal, and hexidecimal bases are discussed. (MP)

Numerous studies indicate that performance in solving single step multiplicative word problems is influenced by both problem structure and the types of numbers involved in the problem. For example, including numbers less than one often increases the difficulty of a problem. What remains unclear is how problem structure and number type interact in…

Analyzes the concept "growth" by investigating the logic core of the concept, using systems theory, and testing it employing free definitions. Determines the associative framework using free association tests. Shows that a shift takes place in the logic core and in the associative framework from a growth in terms of geometric dimension towards a…

Programs are listed for integer powers and fractional powers, with discussion of how to use them in instruction. (MNS)