This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

Today's building level instructional leader is faced with an enormous challenge in ensuring that all students are meeting end-of-year proficiency targets. The current climate of accountability, particularly in regards to high-stakes end-of-year assessments has placed the burden of assessment upon students, parents, teachers, team or department…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

This study was conducted to determine the views of high school students about proof and these students' levels of proof. Case study method was used in this descriptive study. The data of the study were obtained by conducting a questionnaire which consists of eight open-ended questions to total 125 10th grade students studying in two different…

Since teachers always teach area and perimeter together--and they are both introduced soon after the definition of a rectangle--it is not surprising that students mix up the notions of area and perimeter. Changing the investigation on maximising the area of a fixed perimeter from the traditional, but boring, "Sheep pens" to the much more…

In late 2009, the National Council of Teachers of Mathematics released "Focus in High School Mathematics: Reasoning and Sense Making" (NCTM 2009). This new NCTM policy publication is designed to offer guidance for high school mathematics teachers in providing focus and coherence that parallels what "Curriculum Focal Points for Prekindergarten…

Since 2002 the authors have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper the authors describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities they have…

As the recession that began in 2008 continues to impact schools at every level, collaboration among educational entities is a matter of survival because public schools and universities are strapped for resources. Therefore, they must reach out and combine their efforts to provide needed services at a minimum cost. A natural partnership exists…

At the suggestion of a colleague, I read "The Code Book", [32], by Simon Singh to get a basic introduction to the RSA encryption scheme. Inspired by Singh's book, I designed a Ball State University Honors Colloquium in Mathematics for both majors and non-majors, with material coming from "The Code Book" and many other sources. This course became…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

The choice of pedagogy in statistics should take advantage of the quantitative capabilities and scientific background of the students. In this article, we propose a model for a statistics course that assumes student competency in calculus and a broadening knowledge in biology. We illustrate our methods and practices through examples from the…

When students are asked to write original story problems about fractional amounts, it can illustrate their misunderstandings about fractions. Think about the situations students would describe to model 1/2 + 2/3. Three elements, in particular, challenge students: (1) Which of three models (region, or area; measure; or set) is best suited for a…

Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics…

The authors describe ways in which a history of mathematics course can help prospective teachers of mathematics develop knowledge they will need for teaching. The types of knowledge include content knowledge of mathematics, knowledge of mathematics for teaching, and pedagogical knowledge.

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…