All learners, including those who qualify for special education services, should have access to learning mathematical concepts. This study examined the efficacy of using hands-on sets of materials to teach two high school students with mental retardation the four situations for subtraction. This is a mixed methods study using a simple…

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

Much has been written on the subject of linking math and literature. However, the focus is usually on the incorporation of reading into a math class--how a teacher might use picture books, problems, or stories, in general, to bring enthusiasm and engagement into the math classroom. In this article, the authors propose that teachers think about…

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and…

There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards…

Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…

The PD program evaluated in this study is designed to address the problem of low student achievement in topics in rational numbers. The study focuses on seventh grade, the culminating year for teaching those topics. The study randomly assigned 77 mid- and high-poverty schools from 12 districts to treatment and control conditions and collected…

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

In this book, Bob Hogan and Char Forsten introduce American mathematics educators to the model drawing process adapted from the much-acclaimed Singapore approach. They explain what model drawing is and why it's such an effective problem-solving tool. They show exactly how teachers can guide their students through the process, tell which key points…

There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)

The use, learning and transfer of workplace numeracy skills, as well as current understandings of the term numeracy, are examined in this study. It also highlights the importance of numeracy as an essential workplace skill. "Thinking Beyond Numbers: Learning Numeracy for the Future Workplace" challenges the training system and training…

The Pre-Kindergarten Inventory of Demonstrated Skills (Pre-KIDS) is designed to be used before the school year begins so that teachers and staff can obtain information about incoming kindergarten students. This information is intended to give teachers insight about what skills a student may or may not have before entering their classrooms. This…