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| depth of knowledge math: Open Middle Math Robert Kaplinsky, 2023-10-10 This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking. |
| depth of knowledge math: Making Every Maths Lesson Count Emma McCrea, 2019-05-01 In Making Every Maths Lesson Count: Six principles to support great maths teaching, experienced maths teacher and lecturer Emma McCrea takes away the guesswork as she sums up the key components of effective maths teaching. Maths classrooms are incredibly complex places. At any given time, the factors influencing the effectiveness of your teaching are boundless and this can lead to relying on intuition as to what might work best. This book aims to signpost a route through this complexity. Writing in the practical, engaging style of the award-winning Making Every Lesson Count, Emma McCrea helps teachers to move beyond trial and error by sharing evidence-informed tips and suggestions on how they can nudge the impact of their teaching in the right direction. Making Every Maths Lesson Count is underpinned by six pedagogical principles challenge, explanation, modelling, practice, feedback and questioning and presents 52 high-impact strategies designed to streamline teacher workload and ramp up the level of challenge in the maths classroom. The book draws out the key findings from the latest research on memory, learning and motivation and each chapter features numerous worked examples to demonstrate the theory in action, together with a concluding series of questions that will help maths practitioners relate the content to their own classroom practice. Furthermore, Emma's writing offers clarity around the language of maths teaching and learning, and also delves into the finer points of how to identify and address any misconceptions that students may hold. Written for new and experienced practitioners alike, this gimmick-free guide provides sensible solutions to perennial problems and inspires a rich, challenging and evidence-based approach to the teaching of maths. Suitable for maths teachers of students aged 11 to 18 years, and for primary school maths specialists. |
| depth of knowledge math: A Taxonomy for Learning, Teaching, and Assessing Lorin W. Anderson, David R. Krathwohl, 2001 This revision of Bloom's taxonomy is designed to help teachers understand and implement standards-based curriculums. Cognitive psychologists, curriculum specialists, teacher educators, and researchers have developed a two-dimensional framework, focusing on knowledge and cognitive processes. In combination, these two define what students are expected to learn in school. It explores curriculums from three unique perspectives-cognitive psychologists (learning emphasis), curriculum specialists and teacher educators (C & I emphasis), and measurement and assessment experts (assessment emphasis). This revisited framework allows you to connect learning in all areas of curriculum. Educators, or others interested in educational psychology or educational methods for grades K-12. |
| depth of knowledge math: Now That's a Good Question! Erik M. Francis, 2016-07-22 In this book, Erik M. Francis explores how one of the most fundamental instructional strategies—questioning—can provide the proper scaffolding to deepen student thinking, understanding, and application of knowledge. You’ll learn: *Techniques for using questioning to extend and evaluate student learning experiences. *Eight different kinds of questions that challenge students to demonstrate higher-order thinking and communicate depth of knowledge. *How to rephrase the performance objectives of college and career readiness standards into questions that engage and challenge students. Francis offers myriad examples of good questions across content areas and grade levels, as well as structures to help teachers create and use the different kinds of questions. By using this book to fine-tune your approach to questioning, you can awaken the spirit of inquiry in your classroom and help students deepen their knowledge, understanding, and ability to communicate what they think and know. |
| depth of knowledge math: 5 Principles of the Modern Mathematics Classroom Gerald Aungst, 2015-10-09 Students pursue problems they’re curious about, not problems they’re told to solve. Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration. Aungst shows you how to Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment. Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended! Cindy Johanson, Executive Director, Edutopia George Lucas Educational Foundation Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today. Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces |
| depth of knowledge math: Activating Math Talk Paola Sztajn, Daniel Heck, Kristen Malzahn, 2020-09-24 Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning. |
| depth of knowledge math: Teaching Numeracy Margie Pearse, K. M. Walton, 2011-03-23 Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts. |
| depth of knowledge math: Knowing and Teaching Elementary Mathematics Liping Ma, 2010-03-26 Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work. |
| depth of knowledge math: How To Enhance Your Mathematics Subject Knowledge: Number and Algebra for Secondary Teachers Jemma Sherwood, 2018-07-12 Written by an award-winning teacher, this guide equips teachers with the depth of knowledge they need to talk confidently and competently about maths to students of all attainment levels - in short, to be an expert in secondary-level mathematical concepts, regardless of how recently they studied themselves, or their own subject specialism. How To Enhance Your Mathematics Subject Knowledge: - Explores a broad range of the trickiest concepts and misconceptions in the number and algebra topics of secondary maths - Packed with diagrams and questions to allow readers to check their own understanding of concepts - Supports a mastery approach by laying bare the underlying architecture in Secondary maths, giving teachers the confidence to pass on that understanding to their students - Builds on teachers' knowledge and experience, supporting them in answering those awkward but brilliant questions that crop up in class. |
| depth of knowledge math: Every Math Learner, Grades K-5 Nanci N. Smith, 2017-02-01 Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website. |
| depth of knowledge math: Knowing and Learning Mathematics for Teaching National Research Council, Mathematical Sciences Education Board, Center for Education, Mathematics Teacher Preparation Content Workshop Program Steering Committee, 2001-02-25 There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place. |
| depth of knowledge math: Building Thinking Classrooms in Mathematics, Grades K-12 Peter Liljedahl, 2020-09-28 A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling non-thinking student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before. |
| depth of knowledge math: What Matters? Research Trends in International Comparative Studies in Mathematics Education Ji-Won Son, Tad Watanabe, Jane-Jane Lo, 2017-03-03 This book provides a unique international comparative perspective on diverse issues and practices in mathematics education between and among the US and five high-performing TIMSS education systems, Japan, China, Singapore, South Korea, and Taiwan. The book offers multiple perspectives on the important factors that contribute to mathematics teaching and learning in different educational systems and cultural contexts. Using large scale data generated by numerous international comparative studies, the book analyzes and provides context for various methodological perspectives. The book raises compelling questions and issues for mathematics education researchers, leading to a critical examination of what can be learned from other education systems. Authors address four major research perspectives by critically examining cross-national similarities and differences, such as research on the influence of curriculum on student learning; research on institutional systems of mathematics teacher education; research on improving teacher knowledge and pedagogical approaches; and research using large-scale data. This collection of perspectives serves as a foundation for reviewing and analyzing the international comparative studies introduced in the book. |
| depth of knowledge math: Guided Math Lessons in Third Grade Nicki Newton, 2021-11-29 Guided Math Lessons in Third Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, fractions and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So throughout these lessons you will see students working with manipulatives to make meaning, doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense to them! |
| depth of knowledge math: Guided Math Lessons in First Grade Nicki Newton, 2021-07-15 Guided Math Lessons in First Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial, and abstract. The lessons are based on the priority standards and cover fluency, word problems, operations and algebraic thinking, and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates, and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way! |
| depth of knowledge math: Understanding and Teaching Primary Mathematics Tony Cotton, 2014-04-29 How would you teach the concept of odd and even numbers to a child? What is the probability of throwing a three on a six-sided die? How could you help a child who is confusing ratio and proportion? By seamlessly combining subject knowledge and pedagogy, the second edition of Understanding and Teaching Primary Mathematics will not only build your own confidence in mathematics, but also equip you with the curriculum understanding and pedagogical know-how to excel at teaching maths to children of any age. Written in a clear and accessible way, the book guides you through the fundamental ideas which are at the heart of teaching and learning maths, with special focus on observation and assessment of primary and early years children. Hallmark features Links to the classroom and research are provided throughout to help you relate educational theory to your own teaching practice. Portfolio and audit tasks allow you to assess your own subject knowledge and build up a portfolio of evidence to gain Qualified Teacher Status. The accompanying extra resources offers topic-specific self-audits for you to monitor your progress, exemplar lesson plans, a range of Portfolio Tasks mapped directly to current teacher standards and web-links to up-to-date online resources. New to this edition Resource Inspiration boxes give inviting examples of different activities to do with your class to provide inspiration for your own teaching. High quality videos with corresponding discussion, have been expertly selected from Teachers TV help to widen your skills and develop your practice, offering tips, lesson ideas and classroom resources. |
| depth of knowledge math: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| depth of knowledge math: Visible Learning for Mathematics, Grades K-12 John Hattie, Douglas Fisher, Nancy Frey, Linda M. Gojak, Sara Delano Moore, William Mellman, 2016-09-15 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. |
| depth of knowledge math: Rethinking the Teaching Mathematics for Emergent Bilinguals Ji Yeong I, Hyewon Chang, Ji-Won Son, 2019-11-09 This book focuses on the role of cultural background in Korean public schools, and provides essential insights into how Korean teachers perceive and respond to the transition of their classroom situations with Korean language learners. It reveals the perspectives and the practices of Korean teachers, especially with regard to multicultural students who struggle with language barriers when learning mathematics. The information provided is both relevant and topical, as teaching mathematics to linguistically and culturally diverse learners is increasingly becoming a worldwide challenge. |
| depth of knowledge math: Concept-Based Mathematics Jennifer T.H. Wathall, 2016-01-14 Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind! — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students. — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant |
| depth of knowledge math: Deconstructing Depth of Knowledgw Erik M. Francis, 2021-10-29 Depth of knowledge (DOK) has become a priority for many schools. But if your understanding of DOK is a little cloudy, you're not alone. This resource is your one-stop-shop for learning what it is, who it's for, and how to use and sustain it. Ultimately, you will discover how to plan and provide learning experiences that are academically rigorous, socially and emotionally supportive, and student responsive. Learn how DOK is a different, deeper way of approaching teaching and learning. Explore the different DOK levels and how they relate to instruction. Understand DOK's relationship with standards and assessment. Designate correct levels based on learning needs. Acquire strategies for helping students engage with DOK on a deeper level. Contents: |
| depth of knowledge math: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| depth of knowledge math: Guided Math Lessons in Kindergarten Nicki Newton, 2021-11-29 Guided Math Lessons in Kindergarten provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of three—concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, counting and cardinality, and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can more work effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So throughout these lessons you will see students working with manipulatives to make meaning, doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense to them! |
| depth of knowledge math: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 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. |
| depth of knowledge math: K-8 Digital Citizenship Curriculum Ask a Tech Teacher, 2019-09-21 9 grade levels. 17 topics. 46 lessons. 46 projects. A year-long curriculum that covers everything you need to discuss on internet safety and efficiency. Digital Citizenship–probably one of the most important topics students will learn between kindergarten and 8th and too often, teachers are thrown into it without a roadmap. Well, here it is–your guide to what our children must know at what age to thrive in the community called the internet. It’s a roadmap for blending all pieces into a cohesive, effective student-directed cyber-learning experience that accomplishes ISTE’s general goals |
| depth of knowledge math: Learning Mathematics in a Mobile App-Supported Math Trail Environment Adi Nur Cahyono, 2018-07-28 This brief presents the results of a study on the development of the mobile app-supported math trail program for learning mathematics. This study is a part of the MathCityMap-Project, a project of the MATIS I Team from IDMI Goethe-Universität Frankfurt, Germany, that comprises math trails around the city that are supported by the use of GPS-enabled mobile phone technology. The project offers an activity that is designed to support students in constructing their own mathematical knowledge by solving the prepared mathematical tasks on the math trail and interacting with the environment, including the digital environment. The brief focuses specifically on the development of a model for a mobile app-supported math trail programme and the implementation of this programme in Indonesia. It offers both an empirical exploration of its implementation as well as critical assessment of students’ motivation in mathematics, their own performance, as well as teachers’ mathematics beliefs. It concludes with a future-forward perspective by recommending strategies for implementation in schools, among the general public of the existing math trails (including its supporting tool). It also discusses strategies for developing and designing new trails and suggests further research in other geographical regions and contexts for continued project development and implementation. Learning Mathematics in a Mobile App-Supported Math Trail Environment articulates an innovative and exciting future for integrating real mathematical tasks and geographic and digital environment into effective mathematics education. |
| depth of knowledge math: Mathematics Teaching and Learning Rina Kim, Lillie R. Albert, 2015-03-24 The purpose of this research is to identify the categories of South Korean elementary teachers’ knowledge for teaching mathematics. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers’ knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. This study also demonstrated that Mathematics Pedagogical Procedural Knowledge might play a pivotal role in constructing Mathematics Pedagogical Content Knowledge. These findings are connected to results from relevant studies in terms of the significant role of teachers’ knowledge in mathematics instruction. |
| depth of knowledge math: The Math Teachers Know Brent Davis, Moshe Renert, 2013-07-18 What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms. |
| depth of knowledge math: Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016-11-10 An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors. |
| depth of knowledge math: Probabilistic Graphical Models Daphne Koller, Nir Friedman, 2009-07-31 A general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions. Most tasks require a person or an automated system to reason—to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality. Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs. |
| depth of knowledge math: The Common Core Mathematics Companion: The Standards Decoded, High School Frederick L. Dillon, W. Gary Martin, Basil M. Conway IV, Marilyn E. Strutchens, 2017-09-12 Your User’s Guide to the Mathematics Standards When it comes to mathematics, standards aligned is achievement aligned... In the short time since The Common Core Mathematics Companions for grades K–2, 3–5 and 6–8 burst on the scene, they have been lauded as the best resources for making critical mathematics ideas easy to teach. With this brand-new volume, high school mathematics success is at your fingertips. Page by page, the authors lay out the pieces of an in-depth explanation, including The mathematical progression of each conceptual category, starting with modeling as a unifying theme, and moving through number & quantity, algebra, functions, geometry, and statistics and probability, building from the 8th grade standards The mathematics embedded in each conceptual category for a deeper understanding of the content How standards connect within and across domains, and to previous grade standards, so teachers can better appreciate how they relate How standards connect with the standards for mathematical practice, with a focus on modeling as a unifying theme Example tasks, progressions of tasks, and descriptions of what teachers and students should be doing to foster deep learning The Common Core Mathematics Companion: The Standards Decoded, High School has what every high school teacher needs to provide students with the foundation for the concepts and skills they will be expected to know . |
| depth of knowledge math: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1927 The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century. |
| depth of knowledge math: ISC Mathematics for Class XI (2021 Edition) O P MALHOTRA, S Chand's ISC Mathematics is structured according to the latest syllabus as per the new CISCE(Council for the Indian School Certificate Examinations), New Delhi, for ISC students taking classes XI & XII examinations. |
| depth of knowledge math: Proven Programs in Education: Science, Technology, and Mathematics (STEM) Robert E. Slavin, 2014-05-12 Proven Programs in Education is a series of books that draws on the best of Better: Evidence-Based Education, a unique magazine that provides leadership teams in education with the information they need. The series includes four titles: Proven Programs in Literacy Proven Programs in STEM Proven Programs in Social Emotional Development Proven Programs in Classroom Management and Assessment The Proven Programs in Education series is about research-proven strategies and programs that can be applied in practice. The authors distill their work and research into succinct, easily-digestible articles highlighting the practical implications that teachers, principals, and administrators can use. Each article includes links to further reading and resources that allow readers to delve more deeply into particular issues. |
| depth of knowledge math: Ditch That Textbook Matt Miller, 2015-04-13 Textbooks are symbols of centuries-old education. They're often outdated as soon as they hit students' desks. Acting by the textbook implies compliance and a lack of creativity. It's time to ditch those textbooks--and those textbook assumptions about learning In Ditch That Textbook, teacher and blogger Matt Miller encourages educators to throw out meaningless, pedestrian teaching and learning practices. He empowers them to evolve and improve on old, standard, teaching methods. Ditch That Textbook is a support system, toolbox, and manifesto to help educators free their teaching and revolutionize their classrooms. |
| depth of knowledge math: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| depth of knowledge math: The Mathematical Universe William Dunham, 1997-02-18 Dunham writes for nonspecialists, and they will enjoy his piquantanecdotes and amusing asides -- Booklist Artfully, Dunham conducts a tour of the mathematical universe. . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are. -- Nature If you want to encourage anyone's interest in math, get them TheMathematical Universe. * New Scientist |
| depth of knowledge math: The Great Mental Models, Volume 1 Shane Parrish, Rhiannon Beaubien, 2024-10-15 Discover the essential thinking tools you’ve been missing with The Great Mental Models series by Shane Parrish, New York Times bestselling author and the mind behind the acclaimed Farnam Street blog and “The Knowledge Project” podcast. This first book in the series is your guide to learning the crucial thinking tools nobody ever taught you. Time and time again, great thinkers such as Charlie Munger and Warren Buffett have credited their success to mental models–representations of how something works that can scale onto other fields. Mastering a small number of mental models enables you to rapidly grasp new information, identify patterns others miss, and avoid the common mistakes that hold people back. The Great Mental Models: Volume 1, General Thinking Concepts shows you how making a few tiny changes in the way you think can deliver big results. Drawing on examples from history, business, art, and science, this book details nine of the most versatile, all-purpose mental models you can use right away to improve your decision making and productivity. This book will teach you how to: Avoid blind spots when looking at problems. Find non-obvious solutions. Anticipate and achieve desired outcomes. Play to your strengths, avoid your weaknesses, … and more. The Great Mental Models series demystifies once elusive concepts and illuminates rich knowledge that traditional education overlooks. This series is the most comprehensive and accessible guide on using mental models to better understand our world, solve problems, and gain an advantage. |
| depth of knowledge math: Manifolds, Tensors and Forms Paul Renteln, 2014 Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences. |
| depth of knowledge math: International Reflections on the Netherlands Didactics of Mathematics Marja van den Heuvel-Panhuizen, 2019-08-13 This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education. |
Unwrapping Depth-of-Knowledge - Oklahoma.gov
Unwrapping Depth-of-Knowledge Oklahoma State Department of Education Unwrapping Depth-of-Knowledge 2 DOK Considerations DOK is not the same as difficulty. Difficulty refers to the …
Mathematics Item Specifications - Arizona Department of …
in alignment with the standards for English language arts and math. These item specifications for AASA are intended to provide information regarding standards, item formats and response types. …
Understanding Depth of Knowledge and Cognitive …
information as well as the charts, Pennsylvania educators are asked to determine the depth of knowledge of each item and to verify that the depth of knowledge of each item is in alignment …
A Guide for Using Webb’s Depth of Knowledge - CT.gov
for ELA-Social Studies, Writing, and Math-Science developed by Karin Hess, at the Center for Assessment; Norman Webb’s Alignment Tool from Wisconsin Center of Educational Research; …
Using the Depth of Knowledge Model to Create High School …
purposefully assessing students’ depth of knowledge, math teachers are incorporating the Common Core Standards into their teaching and assessments for learning. According to the 2012 Kappan …
Depth and Complexity Question/Statement Stems
Find examples of _____ in science, social studies, math, and language arts. Find the relationship between _____ and ideas in science, social studies, math, and language arts. Explain the …
HESS COGNITIVE RIGOR MATRIX (MATH-SCIENCE CRM):
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Depth of Knowledge Matrix - Elementary Math - Portland …
Depth of Knowledge Matrix - Elementary Math Topic Adding 1-Digit Numbers (< 5) Equality Interpreting Data Money CCSS Stand. K.OA.5 1.OA.7 1.MD.4 2.MD.8 DOK 1 Example Solve. 3+1= …
Kindergarten Mathematics Instructional Toolkit - Florida …
course descriptions, formative assessment resources, mathematical practices, depth of knowledge ratings and FloridaStudents.org resources. Kindergarten Mathematics Course Description Course …
Depth of Knowledge Matrix - Elementary Math - Robert …
Depth of Knowledge Matrix - Elementary Math Topic Subtracting 3-Digit Numbers Operations with Time Comparing Fractions Multiplying Decimals CCSS Stand. • 3.NBT.2 • 3.MD.1 • 4.NF.2 • …
Microsoft Word - CRM_math.doc - pdesas.org
Hess’ Cognitive Rigor Matrix & Curricular Examples: Applying Webb’s Depth-of-Knowledge Levels to Bloom’s Cognitive Process Dimensions – M-Sci ... o Represent math relationships in words, …
Depth of Knowledge (DOK) Levels - hannatli.weebly.com
From Depth of Knowledge – Descriptors, Examples and Question Stems for Increasing Depth of Knowledge in the Classroom Developed by Dr. Norman Webb and Flip Chart developed by Myra …
DOK Question Stems - Arizona Department of Education
From Depth of Knowledge – Descriptors, Examples and Question Stems for Increasing Depth of Knowledge in the Classroom Developed by Dr. Norman Webb and Flip Chart developed by Myra …
Appendix B Cognitive Rigor Matrix/Depth of Knowledge (DOK)
the depth(s) of knowledge (DOK) that the student needs to bring to the item/task has been identified, using the Cognitive Rigor Matrix shown below. This matrix draws from two widely …
Depth-of-Knowledge Levels for Four Content Areas
Depth-of-Knowledge Levels for Four Content Areas Norman L. Webb March 28, 2002 Language Arts Levels of Depth of Knowledge Interpreting and assigning depth-of-knowledge levels to both …
Depth of Knowledge (DOK) Overview Chart - Michigan's …
Depth of Knowledge (DOK) Overview Chart Level ofComplexity (measures a student'sDepth of Knowledge) Level 1 Recall/Reproduction Recall a fact, information, or procedure. Process …
Depth of Knowledge (DOK) Levels - CASPOnline
Depth of Knowledge (DOK) Levels Level One Activities Level Two Activities Level Three Activities Level Four Activities Recall elements and details of story structure, such as sequence of events, …
Depth of Knowledge Matrix – Algebra 1 (Integrated 1)
Depth of Knowledge Matrix – Algebra 1 (Integrated 1) Topic Solving Equations with Variables on Both Sides Factoring Quadratics Quadratics in Vertex Form Adding polynomials CCSS Stand. • A …
Webb’s Depth of Knowledge Question Stems - Solution Tree
REPRODUCIBLE Teaching With the Instructional Cha-Chas 2019 Solution Tree Press • SolutionTree.com Visit go.SolutionTree.cominstruction to download this page. Webb’s Depth of …
Hess’ Cognitive Rigor Matrix & Curricular Examples: Applying …
Hess’ Cognitive Rigor Matrix & Curricular Examples: Applying Webb’s Depth-of-Knowledge Levels to Bloom’s Cognitive Process Dimensions ... o Represent math relationships in words, pictures, or …
Get to ALIFORNIA DOK Levels 3 and 4! - Houghton Mifflin …
Below is an example of a math problem for each Depth of Knowledge (DOK) level based on Norman Webb’s model. Webb’s DOK Levels Recall and Reproduction (DOK 1) Skills and Concepts/ Basic …
Depth of Knowledge Matrix - Elementary Math - Robert …
Depth of Knowledge Matrix - Elementary Math Topic Adding 1-Digit Numbers (< 5) Equality Interpreting Data Money CCSS Stand. • K.OA.5 • 1.OA.7 • 1.MD.4 • 2.MD.8 DOK 1 Example Solve. …
DIGGING DEEPER INTO DEPTH OF KNOWLEDGE - Michigan …
•Assigning depth-of-knowledge to content standards and assessment items is an essential requirement of alignment analysis •There are four levels of depth of knowledge: Recall and …
Developing Higher Order Thinking Questions - wrschool.net
Using Webb’s Depth of Knowledge (DOK). A scale of cognitive demand (thinking)to align standards with assessments Defines the òceiling or highest DOK levelfor each Core Content standard for …
Applying Webb’s Depth of Knowledge and NAEP Levels of …
Descriptors of Levels for Mathematics (based on Webb, “Depth-of-Knowledge Levels for Four Content Areas,” March 2002 and Webb, Technical Issues in Large-Scale Assessment, report …
What is Depth of Knowledge (DOK)? - WebbAlign
Wisconsin Center for Education Products & Services 1213 N. Sherman Ave., #322 Madison, WI 53704 877-272-5593 WebbAlign@wceps.org www.webbalign.org
Build Depth of Knowledge with RAFT Activities
Take Depth of Knowledge (DOK) to New Levels with Hands-on Activities SUMMARY The new education standards encourage students to use the higher-level thinking skills ... Level 1 = Share …
Depth of Knowledge Matrix - Secondary Math
Depth of Knowledge Matrix - Secondary Math Topic Geometric Proofs Complex Numbers Trigonometric Functions Definite Integrals CCSS Standard(s) • G-CO.11 • N-CN.2 • F-TF.3 • N/A …
GED Test - Assessment Target Comparison Table
GED® Test - Assessment Target Comparison Table This table is provided by GED Testing Service to help you understand the information test-takers will see in their GED® test score reports. The …
Cognitive Rigor: Blending the Strengths of Bloom's Taxonomy …
Depth of knowledge (DOK) forms another important perspective of cognitive complexity. The best-known work in this area, that of Norman Webb (1997, 1999), compelled states to rethink the …
Depth of Knowledge handout for PD with stems on front and …
Microsoft Word - Depth of Knowledge handout for PD with stems on front and possible activities with roles on back-2.docx Created Date: 4/21/2015 12:01:13 AM ...
Copyright 2009 Hess, Carlock, Jones, & Walkup
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Depth of Knowledge (DOK) Levels - The Institute for Arts …
Depth of Knowledge (DOK) Levels Level One Activities Level Two Activities Level Three Activities Level Four Activities Recall elements and details of story structure, such as sequence of events, …
Table 2: Hess’ Cognitive Rigor Matrix with Curricular Examples ...
Bloom’s Revised Taxonomy Webb’s Depth-of-Knowledge (DOK) Levels of Cognitive Process Dimensions Level 1 Recall & Reproduction Level 2 Skills & Concepts Level 3 Strategic Thinking/ …
Summative Item Specifications - Alabama State Department of …
Depth of Knowledge (DOK): Depth of knowledge involves the cognitive complexity or the nature of thinking required for a given item. Most recently, Webb’s Depth of Knowledge levels are used in …
IncreasingCognitive Complexity: Webb’s Depth of Knowledge
Webb’s Depth of Knowledge 3 3 www.projectbumpup.education.uconn.edu Webb’s Depth of Knowledge (Webb, 1997) •Related to number of connections of concepts and ideas a student …
Hess’ Cognitive Rigor Matrix & Curricular Examples: Applying …
Hess’ Cognitive Rigor Matrix & Curricular Examples: Applying Webb’s Depth-of-Knowledge Levels to Bloom’s Cognitive Process Dimensions – Math/Science Revised Bloom’s Taxonomy Strategic …
Everyday Mathematics the Common Core State Standards
1.1.4 Depth of Knowledge The Common Core’s calls for greater focus, coherence, and rigor in school mathematics all aim at promoting greater depth of knowledge. The idea of depth of …
HESS COGNITIVE RIGOR MATRIX (MATH SCIENCE CRM)
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Mathematics depth-of-knowledge levels - Wisconsin …
Depth-of-Knowledge Levels for Four Content Areas Norman L. Webb March 28, 2002 Language Arts Levels of Depth of Knowledge Interpreting and assigning depth-of-knowledge levels to both …
Mathematics Item Specifications - Arizona Department of …
in alignment with the standards for English language arts and math. These item specifications for AASA are intended to provide information regarding standards, item formats and response types. …
SUMMARY DEFINITIONS OF DEPTH OF KNOWLEDGE (DOK) …
SUMMARY DEFINITIONS OF DEPTH OF KNOWLEDGE (DOK) LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4 Mathematics Requires students to recall or observe facts, definitions, ... • Recall or recognize a …
THE PEDAGOGICAL CONTENT KNOWLEDGE IN …
can possess an in-depth knowledge of how to represent the subject matter to learners (Parker & Heywood, 2000). Shulman (1987) also stated that pedagogical content knowledge must ... in …
Test Specifications - Ohio Department of Education
Depth of Knowledge is used for ELA, Math, and Social Studies and Cognitive Demand is used for Science. Depth of Knowledge/Cognitive Demand. Planning Instruction Dig Deep into Learning …
Teaching with Webb's Depth of Knowledge in Mind for High …
Depth of Knowledge (DOK) is like the finish line for learning. It shows the type of thinking ... DOK Level 2 Rationale: The student must interpret the graph, do math operations, and find a solution . …
Grade 4 Mathematics - coassessments.com
CMAS CPR Answer Key and Scoring Rubric– Grade 4 Math | 3 ITEM INFORMATION Colorado Academic Standard (CAS) Evidence Outcome Describes the evidence that demonstrates that a …
Microsoft Word - Appendix_B.6_FINAL rigor-math-sci
Represent math relationships in words, pictures, or symbols)-attend to precision f. Read, write, compare decimals in scientific notation - attend to precision; repeated reasoning a. ... Applying …
MCA Mathematics Grade 3 Teacher Guide 2016-2017
Cognitive Complexity/Depth of Knowledge (DOK) Cognitive complexity refers to the cognitive demand associated with an item. The level of cognitive demand focuses on the type and level of …
PA STANDARDS and COMMON CORE : FREQUENTLY ASKED …
standards framework in reading and math. Using Webb’s Depth of Knowledge (DOK) framework, the April subsequent report to be released in May will define the degree of alignment of CC …
Depth of Knowledge (DOK) Levels - PA Adult Education …
Depth of Knowledge (DOK) Levels. Title: Microsoft Word - Notes page - Assessment in PLC.doc Author: kbailey Created Date: 1/10/2011 8:34:42 AM ...
