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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.
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.
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.
For many students, learning mathematics in the middle grades represents a watershed activity. If they fall behind or fail at this point, they are unlikely to recover and to pursue a career in the sciences or other mathematics-dependent occupations. The authors reveal at least two of the reasons for this watershed experience. First, the content itself is much more complex than that at the primary grades, a complexity that is only now being fully appreciated. Second, conventional instruction often is based on faulty assumptions about the way in which the content is learned. The chapters present the latest understanding of the nature of the mathematics content in the middle grades and the processes by which it is learned.
Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
"A multimedia professional learning resource"--Cover.