It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…

Each year a high school math club selects an applications topic for a year-long study. This year the club members chose the study of Mars in its orbit from the perspective of Johannes Kepler's laws of orbital motion, which they applied to data available on the Jet Propulsion Laboratory Horizons Web site. Although not apparent at the time, the math…

We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

Using different representations and having flexibility of transition between representations throughout the definite integral problem-solving process are thought to be effective on the development of conceptual understanding and students' performance. The study aims at considering the effects of representations used in the definite integral on…

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Games can be a valuable tool for a mathematics teacher. Students who dislike mathematics and are not engaged in class never get to experience the exhilaration that accompanies hard work and real accomplishment in mathematics; they usually experience only the frustration that accompanies enforced and futile effort. Game playing is a way to engage…

Many authors suggest that incorporating the history of mathematics in the classroom leads to a heightened awareness and appreciation of mathematics, aids in looking at problems from a different perspective, and helps students understand why mathematics is important. Introducing students to the history of mathematics provides them with a chance to…

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in…

The first pretest-posttest hypothesis was tested using the dependent t test. Null hypotheses for test score improvement over time were rejected for the end of fifth-grade pretest compared to ending sixth-grade posttest math Essential Learner Outcome scores converted to standard scores for randomly selected sixth-grade girls meeting measured test…

This paper presents our initial work to develop trajectories of preservice teachers' knowledge of teaching algebra for equity. We have developed two overlapping hypothetical learning trajectories (HLTs) for teachers' learning to engage and motivate diverse students to solve algebra problems. These HLTs are being used to guide the development of…

In recent years, the "street teachers" issue has caused social concern in Taiwan. This study estimates the retirement of and needs for newly hired and public primary school teachers in 2010 using an algebraic model from the paper by Husssar (1999). This recursive methodology predicts the number of newly hired public primary school…

A peer mentoring program has been implemented to support a group of at-risk students enrolled in two sections of an elementary algebra course at an urban community college. Peer mentors were recruited from advanced mathematics classes and trained to provide individualized tutoring and mentoring support to at-risk students. The results show that…

This paper presents the results of a study focused on the issue of how proctored testing affects the learning outcomes and integrity in an Intermediate Algebra course setting. The study follows a model of assessment where students in one group have taken two of their five unit exams as proctored tests along with a proctored Comprehensive Final…

The concept of "function" spans elementary school through high school. When introducing the topic to elementary school and middle school students, the authors ask them to work with a variety of examples and representations of functions, since a formal definition of a function is rather abstract. They give the most accessible geometric functions…