For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

Many middle school students approach math with caution, often trepidation, and generally less-than-complete confidence. Several factors contribute to their views of what math actually is (a system of rules to follow and formulas to apply) as well as who might be good at it (people who can see the path to an answer and calculate quickly). A few say…

The purpose of this study was to deconstruct the relationship between visual static models and students' written solutions to fraction problems using a large sample of students' solutions. Participants in the study included 162 third-grade and 209 fourth-grade students from 17 different classrooms. Students' written responses to open-ended tasks…

This paper describes the results achieved by high school seniors on an item which involves translation of the equation P = kT into a corresponding pictorial external representation. The majority of students (the classes of 2011, 2012 and 2013) did not give the correct answer to the multiple choice part of the translation item. They chose pictorial…

The old myth about the ability and variability of potential in children is a comforting myth, for those who are uneasy with the degree of inequality they see and would rather seek to justify it than confront it. The myth of inherent potential helps some explain to themselves why they are privileged. Extend the myth to believe in inherited ability…

The purpose of this paper is to present a conceptual framework for diagnosing teaching difficulties of a science topic in the science classroom. The development of the framework is presented as well as descriptions of the features of the framework. How the framework can be used is also elaborated? Furthermore, there is a detailed indication of an…

Students' ability to effectively study for an exam, or to manage their time during an exam, is related to their metacognitive capacity. Prior research has demonstrated the effective use of metacognitive strategies during learning and retrieval is related to content expertise. Students also make judgments of their own learning and of problem…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

Holidays and seasonal activities provide excitement and a change of pace for teachers and students alike. They also offer perfect backdrops for mathematical tasks that can be related to other topics and themes in the classroom. "Problem Solving in All Seasons, Prekindergarten-Grade 2" delivers thirty-two appealing, real-world situations,…

Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…

Many teachers experience the tension between using published curriculum materials and teaching in ways that are responsive to children. Teachers are often expected to use a particular mathematics curriculum series, but they still want to be able to build on and connect to children's multiple mathematical knowledge bases (MMKB).…

A small number of studies have investigated student understanding of vector addition and subtraction in generic or introductory physics contexts, but in almost all cases the questions posed were in the vector arrow representation. In a series of experiments involving over 1000 students and several semesters, we investigated student understanding…

Using a constructivist framework, eight senior chemistry majors were interviewed twice to determine: (i) structural inferences they are able to make from chemical and physical properties; and (ii) their ability to apply their inferences and understandings of these chemical and physical properties to solve tasks on the reactivity of organic…

A web-based two-tier test (WTTT-NS) which combined the advantages of traditional written tests and interviews in assessing number sense was developed and applied to assess students' answers and reasons for the questions. In addition, students' major misconceptions can be detected. A total of 1,248 sixth graders in Taiwan were selected to…