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SanGiovanni, John J.; Bay-Williams, Jennifer M.; Serrano, Rosalba – Corwin, 2021
Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…
Descriptors: Mathematics Instruction, Elementary School Mathematics, Mathematics Skills, Teaching Methods
Peltier, Corey; VanDerHeyden, Amanda M.; Hott, Brittany L. – Beyond Behavior, 2022
Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this…
Descriptors: Mathematics Instruction, Problem Solving, Word Problems (Mathematics), Addition
Ebby, Caroline B.; Hulbert, Elizabeth T.; Fletcher, Nicole – Teaching Children Mathematics, 2019
Assessing student learning traditionally involves determining whether students can solve a certain percentage of problems correctly, under the assumption that this achievement indicates they have the knowledge and understanding they need to progress to new topics. This article explores what teachers can learn from looking closely at student…
Descriptors: Mathematics Instruction, Problem Solving, Mathematical Logic, Learning Processes
Lamb, Lisa A.; Bishop, Jessica Pierson; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Journal for Research in Mathematics Education, 2018
In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…
Descriptors: Problem Solving, Grade 2, Grade 4, Grade 7
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P. – Mathematics Teaching in the Middle School, 2016
Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…
Descriptors: Mathematical Logic, Mathematics Instruction, Instructional Materials, Numbers
Liu, Fuchang – Routledge, Taylor & Francis Group, 2017
Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students…
Descriptors: Teaching Methods, Mathematics Instruction, Elementary School Mathematics, Mathematics Teachers
van Klinken, Eduarda – Australian Primary Mathematics Classroom, 2012
This article outlines how a Brisbane independent school, Clayfield College, improved the ability of its Year 3 students to solve addition and subtraction word problems by utilising a schematic approach. It was observed that while students could read the words in the text of a written problem, many had difficulty identifying the core information…
Descriptors: Private Schools, Problem Solving, Word Problems (Mathematics), Subtraction
Mosrur, Ridwanul – Online Submission, 2011
Word Problems those are also named as "Story Problems" which are well known to the students around the world. In this book there are 26 chapters which encompass diversified problems of four basic mathematical rules--addition, subtraction, multiplication and division. These problems may help students to practice more and more as well as…
Descriptors: Mathematics Education, Word Problems (Mathematics), Elementary School Mathematics, Mathematics Skills
Dixon, Juli K.; Tobias, Jennifer M. – Mathematics Teaching in the Middle School, 2013
What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…
Descriptors: Computation, Arithmetic, Preservice Teacher Education, Preservice Teachers
Karp, Karen; Caldwell, Janet; Zbiek, Rose Mary; Bay-Williams, Jennifer – National Council of Teachers of Mathematics, 2011
What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…
Descriptors: Subtraction, Mathematics Instruction, Addition, Mathematical Concepts
Taylor-Cox, Jennifer – Eye on Education, 2009
Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…
Descriptors: Feedback (Response), Intervention, Number Concepts, Mathematics Teachers
Kartambis, Kathy – Australian Primary Mathematics Classroom, 2007
Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…
Descriptors: Mental Computation, Number Concepts, Subtraction, Arithmetic
Callahan, Leroy G.; Charles, Desiree – Focus on Learning Problems in Mathematics, 1985
Previous studies indicate that many early elementary school children have the misconception that whole number subtraction is a commutative operation. The degree and character of this subtraction error was investigated in this longitudinal study. Results obtained from three groups of students with different number abilities provided further…
Descriptors: Arithmetic, Cognitive Processes, Elementary Education, Elementary School Mathematics

Thompson, Charles S.; Hendrickson, A. Dean – Arithmetic Teacher, 1986
Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)
Descriptors: Addition, Computation, Elementary Education, Elementary School Mathematics
Femiano, Robert – 1998
This guide contains classroom-tested problems designed to introduce and reinforce mathematical concepts in a quick, "fun" way. Activities emphasize the logic and reasoning skills needed to build a strong foundation in mathematics. The problems are thinking activities and require only elementary level mathematics skills. Activities are…
Descriptors: Addition, Arithmetic, Elementary Education, Mathematics Activities