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Designed to help pre-service and in-service teachers gain the knowledge they need to facilitate students' understanding, competency, and interest in mathematics, the revised and updated Second Edition of this popular text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Highlighting multiple types of mathematical understanding to deepen insight into the secondary school mathematics curriculum, it addresses typical areas of difficulty and common student misconceptions so teachers can involve their students in learning mathematics in a way that is interesting, interconnected, understandable, and often surprising and entertaining. Six content strands are discussed—Numbers and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability; and Proof, Functions, and Mathematical Modeling. The informal, clear style supports an interactive learner-centered approach through engaging pedagogical features: Launch Questions at the beginning of each section capture interest and involve readers in learning the mathematical concepts. Practice Problems provide opportunities to apply what has been learned and complete proofs. Questions from the Classroom bring the content to life by addressing the deep "why" conceptual questions that middle or secondary school students are curious about, and questions that require analysis and correction of typical student errors and misconceptions; focus on counter intuitive results; and contain activities and/or tasks suitable for use with students. Changes in the Second Edition New sections on Robotics, Calculators, Matrix Operations, Cryptography, and the Coefficient of Determination New problems, simpler proofs, and more illustrative examples Answers and hints for selected problems provided
This clear, interactive, learner-centered text and resource will help pre-service and in-service secondary mathematics teachers gain the deep mathematical insight they need to teach their students in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining.
What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools. Written in an informal, clear, and interactive learner-centered style, it is designed to help pre-service and in-service teachers gain the deep mathematical insight they need to engage their students in learning mathematics in a multifaceted way that is interesting, developmental, connected, deep, understandable, and often, surprising and entertaining. Features include Launch questions at the beginning of each section, Student Learning Opportunities, Questions from the Classroom, and highlighted themes throughout to aid readers in becoming teachers who have great "MATH-N-SIGHT": M Multiple Approaches/Representations A Applications to Real Life T Technology H History N Nature of Mathematics: Reasoning and Proof S Solving Problems I Interlinking Concepts: Connections G Grade Levels H Honing of Mathematical Skills T Typical Errors This text is aligned with the recently released Common Core State Standards, and is ideally suited for a capstone mathematics course in a secondary mathematics certification program. It is also appropriate for any methods or mathematics course for pre- or in-service secondary mathematics teachers, and is a valuable resource for classroom teachers.
Brought to an American audience for the first time, How I Wish I'd Taught Maths is the story of an experienced and successful math teacher's journey into the world of research, and how it has entirely transformed his classroom.
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present.This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.
Learning to Teach Mathematics in the Secondary School covers a wide range of issues in the teaching of mathematics and gives supporting activities to students to enable them to translate theory into practice. Topics covered include: mathematics in the National Curriculum different teaching approaches using ICT mathematics education for pupils with special needs in mathematics assessment and public examinations teaching mathematics post-16 professional development.
The system won’t do it for us. But we have each other. In The Imperfect and Unfinished Math Teacher: A Journey to Reclaim Our Professional Growth, master storyteller Chase Orton offers a vulnerable and courageous grassroots guide that leads K-12 math teachers through a journey to cultivate a more equitable, inclusive, and cohesive culture of professionalism for themselves...what he calls professional flourishment. The book builds from two bold premises. First, that as educators, we are all naturally imperfect and unfinished, and growth should be our constant goal. Second, that the last 40 years of top-down PD efforts in mathematics have rarely supplied teachers with what they need to equitably grow their practice and foster classrooms that are likewise empowered, inclusive, and cohesive. With gentle humanity, this book inspires teachers to break down silos, observe each others’ classrooms, interrogate their own biases, and put students at the center of everything they do in the math classroom. This book: Weaves raw and authentic stories—both personal and those from other educators—into a relatable and validating narrative Offers interactive opportunities to self-reflect, build relationships, seek new vantage on our teaching by observing others’ classrooms and students, and share and listen to other’s stories and experiences Asks teachers to give and accept grace as they work collaboratively to better themselves and the system from within, so that they can truly serve each of their students authentically and equitably Implementing the beliefs and actions in this book will position teachers to become more active partners in each other’s professional growth so that they can navigate the obstacles in their professional landscape with renewed focus and a greater sense of individual and collective efficacy. It equips teachers—and by extension, their students—to chart their own course and author their own equitable and joyful mathematical and professional stories.
A sharp mind, like a healthy body, is subject to the same ruleof nature: Use it or lose it Need a calculator just to work out a 15 percent service charge? Not exactly sure how to get the calculator to give you the figureyou need? Turn to this revised and updated edition of All the MathYou'll Ever Need, the friendliest, funniest, and easiest workoutprogram around. In no time, you'll have total command of all the powerfulmathematical tools needed to make numbers work for you. In adollars-and-cents, bottom-line world, where numbers influenceeverything, none of us can afford to let our math skills atrophy.This step-by-step personal math trainer: Refreshes practical math skills for your personal andprofessional needs, with examples based on everyday situations. Offers straightforward techniques for working with decimals and fractions. Demonstrates simple ways to figure discounts, calculatemortgage interest rates, and work out time, rate, and distance problems. Contains no complex formulas and no unnecessary technical terms.
Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.