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Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.
Mental calculations and estimations are basic, everyday skills that are essential for real-life arithmetic operations and number sense. This book presents a much needed overview and analysis of mental computation and estimation, drawing on contemporary research and empirical studies that were conducted on students, teachers and adults to cover all aspects of this complex field. Mental Computation and Estimation analyses the implications that are involved in the research, teaching and learning of mathematics and delivers effective practices that will enhance everyday learning for students. Focusing on a range of international research and studies from the School of Nature and Life Mathematics in Greece, it answers a number of important questions including: What mental calculations and estimations are, why they are important and what other mathematical concepts and cognitive behaviors are they related to? What strategies are used on mental additions, subtractions, multiplications and divisions and how are multiplication tables learned? What are the new trends in the teaching of mental calculation and estimation? An invaluable resource for all those involved in the practice and research of mathematics education, Mental Computation and Estimation will also be a useful tool for researchers, policy makers and developers of educational programs.
These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
The study sought to investigate how Grade 3 students from two separate schools learned mathematics. The study explores the role of mental computation when students are engaged in sharing their invented strategies. I observed students sharing ideas and teachers implementing mental computation lessons over fifteen sessions. Interviews with students and teachers, copies of students' journal on mental math strategies were used to collect additional data. The findings were organized around descriptive moments; as I described how students were absorbed in mathematical conversation when they were invited to think mathematically and also encouraged to use their own strategies. I drew on the epistemology of constructivism in problem solving, to understand how students develop conceptual understanding of mathematics when given the opportunity to explain their own strategies. Students' cooperation in sharing their inventions was observed in class and group discussions, as well as in pairs with classmates. It was at these levels where the students: (a) eagerly invented numerous strategies for solving addition, subtraction and multiplication problems; (b) made sound arguments in support of their ideas when discussing problem solving strategies; (c) were cooperative in presenting their strategies; (d) learned from each other by listening to one another's explanations; (e) learned from correcting their errors; and (f) used their cognitive backgrounds as useful heuristics in their discussions. The students expressed their satisfaction and enjoyment during their collaborative learning and social interactions. The teachers used questioning strategies, among other teaching principles, to help students to complete their presentations. These included leading questions, probing and follow-ups, checklisting and student-specific questioning strategies. The study informs teachers about how mental mathematics lessons were implemented in the two Grade 3 classrooms to help the students understand mathematics. Teachers should be given courses, workshops and supportive programs on implementing mental computation lessons. This will give teachers the necessary experiences to increase their understanding of how students improve their understanding of mathematics when they are encouraged to share their inventions in class. The study provides a useful template for future studies in all subject areas of mathematics related to mental computation and estimation at all grade levels.