Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

Project-based learning (PBL) is an effective approach to STEM education because it allows students to experience scientific inquiry by using their knowledge and skills in science, technology, engineering, and mathematics (STEM) to solve realistic problems. PBL consists of four components: (1) posing and comprehending a driving question; (2)…

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…

The difficulty in observing, recording, and examining internal representations has been well documented (Goldin & Shteingold, 2001). However, the important role that these internal representations play in the learning and understanding of mathematical concepts has been noted (Yackel, 2000). This study sought to develop a framework for…

In Taiwan, teaching focuses around lecturing, with students having little opportunity to interact with each other. Problem-based learning (PBL) is a means of instruction where students learn the subject by being active participants in the pedagogical process, with the emphasis on problem-solving. In this study, the authors investigated whether PBL…

Gain a new perspective on the sharing of erroneous solutions in classroom discussions. Based on their research in grades four and six, the authors reveal how student-to-student correction of errors promotes mathematical reasoning and understanding. Tips for teachers include strategies for using students' errors to encourage reasoning during…

Background: Adventure education is an instructional model where students participate in adventurous activities to acquire physical, cognitive, and affective skills. It also has strong connections with cooperative learning. Parkour is a fast-growing sport practiced by thousands of youngsters all over the world. The media does not portray it as an…

This article describes an interdisciplinary project that created awareness of female scientists in a public Montessori classroom. Every spring, the author's sixth-grade students write an educational play in which the entire class participates. Following an underwhelming response to asking students who are their favorite female scientists, the…

Research has suggested that different strategies used when solving fraction problems are highly correlated with students' problem-solving accuracy. This study (a) utilized latent profile modeling to classify students into three different strategic developmental levels in solving fraction comparison problems and (b) accordingly provided…

This paper examines two factors that have been shown in previous literature to enhance students' interest in learning mathematics--personalization of problems to students' interest areas, and the addition of visual representations such as decorative illustrations. In two studies taking place within an online curriculum for middle school…

This paper examines two factors that have been shown in previous literature to enhance students' interest in learning mathematics--personalization of problems to students' interest areas, and the addition of visual representations such as decorative illustrations. In two studies taking place within an online curriculum for middle school…

This study examined whether developing earlier forms of knowledge in specific learning environments prepares students better for future learning when they are placed in an unfamiliar learning environment. Forty-one students in the fifth and sixth grades learned to program robot movements using abstract concepts of speed, distance and direction.…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

As part of a 3-year longitudinal study, 136 sixth-grade students completed an engineering-based problem on earthquakes involving integrated STEM learning. Students employed engineering design processes and STEM disciplinary knowledge to plan, sketch, then construct a building designed to withstand earthquake damage, taking into account a number of…

Numerous research articles and curricula standards maintain that learning is optimized when students are actively involved in the learning process by assimilating information and constructing their own meanings. The authors' experience with teaching probability concepts has shown that students struggle with concepts of counting. These…