The Take Action Project (TAP) was created to help middle school students take informed and effective action on science-related issues. The seven steps of TAP ask students to (1) choose a science-related problem of interest to them, (2) research their problem, (3) select an action to take on the problem, (4) plan that action, (5) take action, (6)…

While some disasters involving engineered structures are due to events in nature (e.g., tornadoes, hurricanes, earthquakes), others may be caused by inadequate materials, design flaws, and poor maintenance. These catastrophes result in the loss of human lives and cost billions of dollars. In the set of lessons described here, students design a…

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Mathematics may be inconceivable without its diagrams and symbols--its representations. Mathematical representations help individuals organize their thinking; they bring a visual component to abstract ideas and serve as templates for computation with understanding. But the inevitability of representations is no guarantee that they are used…

This material has been used twice as an out-of-class project in a mathematical modeling class, the first elective course for mathematics majors. The only prerequisites for this course were differential and integral calculus, but all students had been exposed to differential equations, and the project was assigned during discussions about solving…

Insects are fascinating creatures--especially when you and your students get up close and personal with them! To that end, the authors facilitated an inquiry-based investigation with an emphasis on identification of the different types of insects found in the school yard, their characteristics, their habitat, and what they eat, while engaging the…

This article features Sweet play math, a "math by the month" activity that involves decorating and making sugar cubes. Teachers may want to substitute straws, paper squares, alphabet blocks, or such commercially made manipulatives as Unifix[R] cubes for the real sweets. Given no allergy concerns, teachers and students alike would enjoy some sweet…

Teaching based on problem solving brings challenges for the teacher, primarily that of finding problems with multiple access points that accommodate all students. This article narrates the author's lucky day as she discovers the Four fours problem which impacted her passion for teaching math. The day she presented the Four fours problem to her…

This third edition of the best-selling "Mathematics in Nursery Education" provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics learning--number and counting, calculation, pattern, shape, measures and data handling--it summarises the research findings and underlying key concepts…

In the advent of the development and mass adoption of the common core state standards for English language arts and mathematics, state and local agencies have now expressed a need to the Council of Chief State School Officers (CCSSO or the Council) for assistance as they upgrade existing social studies standards to meet the practical goal of…

Students with autism spectrum disorders (ASD) present unique programming challenges to school personnel because of the wide variability of clinical symptoms and the high rates of emotional and/or behavior disorders (EBD) that can affect learning outcomes. Currently, there is little empirically based guidance to assist in determining the support…

Too often, teachers scratch their heads and ask, "What were my students thinking?" then answer, "I don't want to know." But teachers should want to know, and students should question their own thinking, as well. Critical thinking involves not just problem solving, creativity, analysis, and synthesis but also self-awareness of learning and learning…

Biographies, which are popular among young people, can stimulate interest in the past when students investigate the historical contexts in which individuals lived. Creating biography webs offers students structured opportunities to investigate how other people and groups influenced the personal development of specific individuals (NCSS Strands II,…