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Kosko, Karl W. – School Science and Mathematics, 2019

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…

Descriptors: Grade 3, Elementary School Teachers, Mathematical Concepts, Mathematics Instruction

Fonger, Nicole L.; Davis, Jon D.; Rohwer, Mary Lou – School Science and Mathematics, 2018

This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

Descriptors: Mathematics Instruction, Mathematical Concepts, Algebra, Problem Solving

Riggs, Iris M.; Fischman, Davida D.; Riggs, Matt L.; Jetter, Madeleine E.; Jesunathadas, Joseph – School Science and Mathematics, 2018

Efforts to measure teacher self-efficacy beliefs have built upon the theories of Albert Bandura. Continuing in that vein, the purpose of this study was to develop a measure that assesses teachers' efficacy and expectancy beliefs regarding teaching mathematics with an emphasis on conceptual understanding and mathematical practices, and to use this…

Descriptors: Teacher Attitudes, Beliefs, Correlation, Mathematics Instruction

Yee, Sean P. – School Science and Mathematics, 2017

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Descriptors: Figurative Language, Mathematics Instruction, Teaching Methods, Mathematical Concepts

Amador, Julie M. – School Science and Mathematics, 2016

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers…

Descriptors: Mathematics Instruction, Grade 4, Elementary School Mathematics, Elementary School Teachers

Popovic, Gorjana; Lederman, Judith S. – School Science and Mathematics, 2015

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…

Descriptors: Mathematics Instruction, Mathematics Skills, Relevance (Education), Problem Solving

Cady, Jo A.; Hodges, Thomas E.; Collins, R. Lee – School Science and Mathematics, 2015

In the United States, fractions are an important part of the middle school curriculum, yet many middle school students struggle with fraction concepts. Teachers also have difficulty with the conceptual understanding needed to teach fractions and rely on textbooks when making instructional decisions. This reliance on textbooks, the idea that…

Descriptors: Textbooks, Mathematics Instruction, Mathematical Concepts, Teaching Methods

DeJarnette, Anna Fricano; Walczak, Marissa; González, Gloriana – School Science and Mathematics, 2014

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric…

Descriptors: Mathematical Concepts, Fundamental Concepts, Middle School Students, Geometric Concepts

Bieda, Kristen N.; Lepak, Jerilynn – School Science and Mathematics, 2014

Students learn norms of proving by observing teachers generating proofs, engaging in proving, and generalizing features of proofs deemed convincing by an authority, such as a textbook. Students at all grade levels have difficulties generating valid proof; however, little research exists on students' understandings about what makes a…

Descriptors: Middle School Students, Mathematics Instruction, Mathematical Concepts, Concept Formation

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan – School Science and Mathematics, 2014

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

Descriptors: College Mathematics, Calculus, Mathematical Concepts, College Faculty

Timmerman, Maria A. – School Science and Mathematics, 2014

If teachers make few connections among multiple representations of division, supporting students in using representations to develop operation sense demanded by national standards will not occur. Studies have investigated how prospective and practicing teachers use representations to develop knowledge of fraction division. However, few studies…

Descriptors: Elementary School Teachers, Mathematics Instruction, Word Problems (Mathematics), Pedagogical Content Knowledge

Wood, Marcy B.; Olson, Amy M.; Freiberg, Elizabeth J.; Vega, Ruby I. – School Science and Mathematics, 2013

A sample of third-, fourth-, and fifth-grade student responses to the question "What is a fraction?" were examined to gain an understanding of how children in upper elementary grades make sense of fractions. Rather than measure children's understanding of fractions relative to mathematically conventional part-whole constructions of…

Descriptors: Elementary School Mathematics, Elementary School Students, Mathematics Instruction, Mathematical Concepts

Bahr, Damon; Monroe, Eula E.; Shaha, Steven H. – School Science and Mathematics, 2013

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30-minute peer-teaching sessions, while…

Descriptors: Preservice Teachers, Student Attitudes, Mathematics Instruction, Teaching Methods

Improving Algebra Preparation: Implications from Research on Student Misconceptions and Difficulties

Welder, Rachael M. – School Science and Mathematics, 2012

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of…

Descriptors: Symbols (Mathematics), Mathematical Concepts, Middle School Teachers, Arithmetic

Walcott, Crystal; Stickles, Paula R. – School Science and Mathematics, 2012

This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to…

Descriptors: Mathematics Achievement, National Competency Tests, Problem Solving, Calculators