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Billings, Esther M. H. – Teaching Children Mathematics, 2017
Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…
Descriptors: Algebra, Thinking Skills, Mathematics Instruction, Arithmetic
Panorkou, Nicole; Maloney, Alan P. – Teaching Children Mathematics, 2016
In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…
Descriptors: Mathematics Instruction, Teaching Methods, Grade 5, Elementary School Mathematics
Store, Jessie C.; Richardson, Kerri D.; Carter, Tyrette S. – Teaching Children Mathematics, 2016
Based on a study with six elementary school teachers and 115 students in grades 3, 4, and 5, this article discusses ways that teachers might support an understanding of variable as students explore pattern-finding activities. The practices emerged from interviews with teachers and a yearlong observation of teaching algebraic thinking during an…
Descriptors: Elementary School Mathematics, Elementary School Teachers, Mathematics Instruction, Interviews
Edwards, Michael Todd; Quinlan, James; Strayer, Jeremy F. – Teaching Children Mathematics, 2016
During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…
Descriptors: Number Concepts, Mathematics, Mathematics Instruction, Addition
Philipp, Randolph A.; Hawthorne, Casey – Teaching Children Mathematics, 2015
Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…
Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Secondary School Teachers
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy – Teaching Children Mathematics, 2015
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
Descriptors: Algebra, Mathematics Instruction, Elementary School Students, Elementary School Mathematics
Swanson, Patricia E. – Teaching Children Mathematics, 2015
Elementary school mathematics is increasingly recognized for its crucial role in developing the foundational skills and understandings for algebra. In this article, the author uses a lesson to introduce the concept of "rates"--comparing two different types and units of measure--and how to graph them. Described is the lesson and shared…
Descriptors: Elementary School Mathematics, Mathematics Skills, Algebra, Skill Development
Isler, Isil; Marum, Tim; Stephens, Ana; Blanton, Maria; Knuth, Eric; Gardiner, Angela Murphy – Teaching Children Mathematics, 2014
The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…
Descriptors: Mathematics Instruction, Algebra, Mathematical Concepts, Elementary School Mathematics
Leavy, Aisling; Hourigan, Mairéad; McMahon, Áine – Teaching Children Mathematics, 2013
Quite a bit of the arithmetic in elementary school contains elements of algebraic reasoning. After researching and testing a number of instructional strategies with Irish third graders, these authors found effective methods for cultivating a relational concept of equality in third-grade students. Understanding equality is fundamental to algebraic…
Descriptors: Mathematics Instruction, Arithmetic, Elementary School Mathematics, Algebra
Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl – Teaching Children Mathematics, 2013
The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…
Descriptors: Academic Standards, State Standards, Geometric Concepts, Concept Formation
McGarvey, Lynn M. – Teaching Children Mathematics, 2013
This article describes how in early mathematics learning, young children are often asked to recognize and describe visual patterns in their environment--perhaps on their clothing, a toy, or the carpet; around a picture frame; or in the playground equipment. Exploring patterns in the early years is seen as an important introduction to algebraic…
Descriptors: Mathematics Instruction, Pattern Recognition, Mathematical Concepts, Preschool Children
Kinzer, Cathy J.; Stanford, Ted – Teaching Children Mathematics, 2013
This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…
Descriptors: Mathematics Instruction, Multiplication, Learning Activities, Mathematical Concepts
Schulman, Steven M. – Teaching Children Mathematics, 2012
The author's teaching goal is always to make certain that his students, children and adults alike, have some reason for joining him on his mathematical journeys. The lesson he describes in this article provides him with the unusual opportunity to call attention to strategies that have had a long history and remarkable results. With careful…
Descriptors: Teaching Methods, Mathematics Instruction, Grade 5, Elementary School Mathematics
Christenson, Bridget; Wager, Anita A. – Teaching Children Mathematics, 2012
One of the many challenges teachers face is trying to differentiate instruction so all students have equal opportunities to participate, learn, and engage. To provide guidelines for differentiated instruction in mathematics, staff from the Madison Metropolitan School District in Wisconsin created a pedagogical framework for teaching called…
Descriptors: Individualized Instruction, Algebra, Vignettes, Elementary School Teachers
Markworth, Kimberly A. – Teaching Children Mathematics, 2012
Over the past two decades, mathematical patterns have been acknowledged as important early components of children's development of algebraic reasoning (NCTM 2000). In particular, growing patterns have attracted significant attention as a context that helps students develop an understanding of functional relationships (Lee and Freiman 2006; Moss et…
Descriptors: Algebra, Geometric Concepts, Grade 6, Mathematics Instruction