The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

Games have been used as instructional tools throughout history. Educational experiences are more effective when learners are active participants, and when teachers carefully choose fun games with appropriate game mechanics and clear curricular connections, students can engage in rigorous mental processes. At the same time, students may learn a…

Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Many elementary school curricula use folding, partitioning, shading, and naming parts of various wholes to develop children's understanding of unit and then nonunit fractions (e.g., coloring three of four parts of a pizza and…

All students should be provided with opportunities to develop conceptual understanding prior to procedural fluency. To develop students' conceptual understanding, teachers must learn such skills as how to select, plan, and enact cognitively demanding tasks (CDT) and to evaluate evidence of student learning. Therefore, teachers need opportunities…

How can a simple dot--the decimal point--be the source of such frustration for students and teachers? As the author worked through her own frustrations, she found that her students seemed to fall into groups in terms of misconceptions that they revealed when talking about and working with decimals. When asking students to illustrate their thinking…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Social studies instruction in upper elementary school (Grades 3-5) is important for building foundational content knowledge to equip students for the secondary school curriculum. Due to numerous school initiatives and demands on the time of teachers, social studies instruction can play second fiddle to reading and mathematics instruction, which…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Can middle-grades students determine which of two rectangular prisms has a larger volume? Can they do so without using a formula? Geometry, and particularly the concept of volume, is important in many subjects, such as physics and chemistry. Students greatly enhance their mathematics knowledge when they make generalizations and construct arguments…

Visual representations play an important role in science teaching. The way in which visual representations may help children to acquire scientific concepts is a crucial test in the debate between constructivist and socio-cultural oriented researchers. In this paper, the question is addressed as a problem of how to contextualize conceptions and…

The newly updated "Content-Based Curriculum for High-Ability Learners" provides a solid introduction to curriculum development in gifted and talented education. Written by experts in the field of gifted education, this text uses cutting-edge design techniques and aligns the core content with national and state standards. In addition to a revision…

Nearly 20 years after the release of The Harvard-Smithsonian Center for Astrophysics' video, "A Private Universe", much research has been done in relation to students' understanding of space-science concepts and how to effectively change these ideas. However, student difficulties with basic space-science concepts still persist. This article will…