In this study we attempt to propose a new model of proportional reasoning based both on bibliographical and research data. This is impelled with the help of three written tests involving analogical, proportional, and non-proportional situations that were administered to pupils from grade 7 to 9. The results suggest the existence of a…

The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that instructional programs at the middle grades should enable students to "represent and analyze mathematical situations and structures using algebraic symbols" (2000, p. 222). Guess and check is a powerful problem-solving strategy that can connect a conceptual…

Algebra is considered a key gatekeeper for higher-level mathematics course-taking in high school and for college enrollment (Adelman, 2006; Gamoran & Hannigan, 2000). Yet, algebra pass rates are consistently low in many places (Higgins, 2008; Ham & Walker, 1999; Helfand, 2006), including Chicago Public Schools (CPS). This is of particular…

The most of the long distance courses are mainly based on two or three face to face meetings and printed courses or courses available on the online course web site. In this case the individual students study has attached an important amount of time. Usually the students do not receive a feed-back of their progress and do not receive answers to…

Systems of linear equations are used in a variety of fields. Exposure to the concept of systems of equations initially occurs at the high school level and continues through college. Attempts to unearth what students understand about the solutions of linear systems have been limited. Gaps exist in our knowledge of how students understand systems…

Since mathematics is found in every aspect of life, it is important for teachers to provide experiences that help students find connections and develop an appreciation for math and its use in their lives outside school. Slope is an excellent example of a math concept that is usually taught without context or connection. In this article, the…

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

The television show Deal or No Deal and an Excel spreadsheet help students see how understanding probability and mean--and the concept of expected value (EV)--can lead to game show wins.

This article describes a hands-on approach to learning proofs by induction. Students create patterns of dominos so that when the first domino is pushed, the entire design collapses, one domino at a time. Students then build designs that do not work. By constructing a list of conditions that ensure a given pattern will collapse, students discover…

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view,…

If students are in an advanced mathematics class, then at some point they enjoyed mathematics and looked forward to learning and practicing it. There is no reason that this passion and enjoyment should ever be lost because the subject becomes more difficult or rigorous. This author, who teaches advanced precalculus to high school juniors,…

One of the basic disagreements in mathematics education concerns the roles that rules and procedures, on the one hand, and concepts and principles, on the other hand, should play in students' learning of mathematics. The use of procedures and an understanding of concepts are considered to be two separate aspects of mathematical activity.…

As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

In 2010-11, Wake County Public School System (WCPSS) was in district-wide improvement as a result of failing to meet Adequate Yearly Progress (AYP) in mathematics at the district level for the second consecutive year. This report examines student outcomes in 2010-11 as well as overall teacher outcomes and longitudinal results for schools targeted…