"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…

The purpose of this study was: (1) to analyze increasing students' learning activity and learning outcomes. Student activities which were observed include the visual, verbal, listening, writing and mental visual activity; (2) to analyze the improvement of student learning outcomes using "Round Table" and "Rally Coach" Model of…

Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher…

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing…

Understanding frames of reference is critical in describing planetary motion and learning astronomy. Historically, the geocentric and heliocentric models were defended and advocated against each other. Today, there are still many people who do not understand the relationship between the two models. This topic is not adequately treated in astronomy…

Though it is generally believed that doing homework promotes better learning, no consensus has been achieved concerning its importance and relevance to students' achievement. The historical up-and-down status of public attitudes toward homework indicates that understanding about the role of homework in students' learning is far from comprehensive…

Recent studies on professional development programs indicate these programs, when sustained, have a positive impact on student achievement; however, many of these studies have failed to use longitudinal data. The purpose of this study is to understand how one particular instructional practice (STEM PBL) used consistently influences student…

This article describes a cooperative project between eighth graders and first graders called "Going Green in the Neighborhood." The project entailed the first grade students sketching home designs on paper to make a model community, and the eighth grade students taking those drawings and making them into 3D computer models and then…

If we want our students to become capable practitioners of scientific inquiry, we should not stop at providing opportunities to do inquiry. We need to be intentional about assessing and teaching the competencies necessary for inquiry. However, the ability to conduct scientific inquiry can be difficult to assess. Therefore, the author created The…

The No Child Left Behind Act of 2001 calls for improving test scores of minority students in third through eighth grades, making middle level schools a key venue for closing the racial gap in achievement. This study, by analyzing data on the 15,000 eighth graders who took the 2000 National Assessment of Educational Progress (NAEP) in mathematics,…