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This single-volume reference is designed for readers and researchers investigating national and international aspects of mathematics education at the elementary, secondary, and post-secondary levels. It contains more than 400 entries, arranged alphabetically by headings of greatest pertinence to mathematics education. The scope is comprehensive, encompassing all major areas of mathematics education, including assessment, content and instructional procedures, curriculum, enrichment, international comparisons, and psychology of learning and instruction.
Is your child getting lost in the system, becoming bored, losing his or her natural eagerness to learn? If so, it may be time to take charge of your child’s education—by doing it yourself. The Well-Trained Mind will instruct you, step by step, on how to give your child an academically rigorous, comprehensive education from preschool through high school—one that will train him or her to read, to think, to understand, to be well-rounded and curious about learning. Veteran home educators Susan Wise Bauer and Jessie Wise outline the classical pattern of education called the trivium, which organizes learning around the maturing capacity of the child’s mind and comprises three stages: the elementary school “grammar stage,” when the building blocks of information are absorbed through memorization and rules; the middle school “logic stage,” in which the student begins to think more analytically; and the high-school “rhetoric stage,” where the student learns to write and speak with force and originality. Using this theory as your model, you’ll be able to instruct your child—whether full-time or as a supplement to classroom education—in all levels of reading, writing, history, geography, mathematics, science, foreign languages, rhetoric, logic, art, and music, regardless of your own aptitude in those subjects. Thousands of parents and teachers have already used the detailed book lists and methods described in The Well-Trained Mind to create a truly superior education for the children in their care. This extensively revised fourth edition contains completely updated curricula and book lists, links to an entirely new set of online resources, new material on teaching children with learning challenges, cutting-edge math and sciences recommendations, answers to common questions about home education, and advice on practical matters such as standardized testing, working with your local school board, designing a high-school program, preparing transcripts, and applying to colleges. You do have control over what and how your child learns. The Well-Trained Mind will give you the tools you’ll need to teach your child with confidence and success.
How big is a crocodile? What about a tiger, or the world’s largest spider? Can you imagine a tongue that is two feet long or an eye that’s bigger than your head? Sometimes facts and figures don’t tell the whole story. Sometimes you need to see things for yourself—at their actual size.
For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.
The title Gattegno Mathematics embodies an approach best expressed by the phrase The Subordination of Teaching to Learning. The program covered in this series envisages the use of colored rods (Algebricks) and other books and printed materials that are available from: www.EducationalSolutions.com.
Teachers have the responsibility of helping all of their students construct the disposition and knowledge needed to live successfully in a complex and rapidly changing world. To meet the challenges of the 21st century, students will especially need mathematical power: a positive disposition toward mathematics (curiosity and self confidence), facility with the processes of mathematical inquiry (problem solving, reasoning and communicating), and well connected mathematical knowledge (an understanding of mathematical concepts, procedures and formulas). This guide seeks to help teachers achieve the capability to foster children's mathematical power - the ability to excite them about mathematics, help them see that it makes sense, and enable them to harness its might for solving everyday and extraordinary problems. The investigative approach attempts to foster mathematical power by making mathematics instruction process-based, understandable or relevant to the everyday life of students. Past efforts to reform mathematics instruction have focused on only one or two of these aims, whereas the investigative approach accomplishes all three. By teaching content in a purposeful context, an inquiry-based fashion, and a meaningful manner, this approach promotes chilren's mathematical learning in an interesting, thought-provoking and comprehensible way. This teaching guide is designed to help teachers appreciate the need for the investigative approach and to provide practical advice on how to make this approach happen in the classroom. It not only dispenses information, but also serves as a catalyst for exploring, conjecturing about, discussing and contemplating the teaching and learning of mathematics.
Ask mathematicians to describe mathematics and they' ll use words like playful, beautiful, and creative. Pose the same question to students and many will use words like boring, useless, and even humiliating. Becoming the Math Teacher You Wish You' d Had, author Tracy Zager helps teachers close this gap by making math class more like mathematics. Zager has spent years working with highly skilled math teachers in a diverse range of settings and grades and has compiled those' ideas from these vibrant classrooms into' this game-changing book. Inside you' ll find: ' How to Teach Student-Centered Mathematics:' Zager outlines a problem-solving approach to mathematics for elementary and middle school educators looking for new ways to inspire student learning Big Ideas, Practical Application:' This math book contains dozens of practical and accessible teaching techniques that focus on fundamental math concepts, including strategies that simulate connection of big ideas; rich tasks that encourage students to wonder, generalize, hypothesize, and persevere; and routines to teach students how to collaborate Key Topics for Elementary and Middle School Teachers:' Becoming the Math Teacher You Wish You' d Had' offers fresh perspectives on common challenges, from formative assessment to classroom management for elementary and middle school teachers No matter what level of math class you teach, Zager will coach you along chapter by chapter. All teachers can move towards increasingly authentic and delightful mathematics teaching and learning. This important book helps develop instructional techniques that will make the math classes we teach so much better than the math classes we took.
Help students make sense of mathematics Rather than merely discussing how to improve students’ ability to do mathematics, this fifth edition focuses on helping them make sense of mathematics. Based on research on the functioning of the mind as it engages in learning, the text supports teachers as they promote mathematical understanding, strengthen students’ abilities to think, and help students to attain computational fluency. Features A rich collection of ready-to-use learning activities Fully integrated language and intent of Principles and Standards for School Mathematics (PSSM). A greater emphasis on problem solving and higher-level thinking A greater focus on teaching mathematics to diverse learners Descriptions of a variety of promising and effective mathematics programs for the K – 8 levels