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Author: TERC (Firm)
Publisher:
ISBN: 9781559537230
Category : Algebra
Languages : en
Pages : 292
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Book Description
Author: TERC (Firm)
Publisher:
ISBN: 9781559537230
Category : Algebra
Languages : en
Pages : 292
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Book Description
Author: Alisa Belzer
Publisher: Routledge
ISBN: 1135601313
Category : Education
Languages : en
Pages : 335
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Book Description
This volume revisits, problematizes, and expands the meaning of quality in the context of adult basic education. Covering a wide range of relevant topics, it includes contributors from the realms of both policy and practice and encompasses both the major instructional areas-reading, writing, and mathematics-as well as larger issues of literacy, learning, and adulthood. Each chapter focuses on what improving quality in the field might look like through the particular lens of the author's work. As a whole, the broad scope of topics and ideas addressed will raise the level of discussion, knowledge, and practice regarding quality in adult basic education. In this book, the term adult basic education refers to the broad range of services for adults who wish to improve their literacy and language skills, including beginning and intermediate writing, writing and numeracy, preGED, GED/Adult Secondary Education, and ESL instruction that takes place in a range of contexts including schools, community-based programs, and workplace development programs. The volume is organized around three themes: *Accountability, Standards, and the Use of Documentation and Research; *Program Structures and Instruction; and *Rethinking Our Assumptions and Concepts. Coming at a time of increasing pressure to standardize, to be accountable, and to improve outcomes, and when calls for evidence-based practice are fueling stakeholders' interest in the relationship between research and practice at all levels of the system, Toward Defining and Improving Quality in Adult Basic Education is particularly timely for scholars, graduate students, and professionals in the field of adult basic education.
Author: TERC (Firm)
Publisher:
ISBN: 9781559537209
Category : Graphic methods
Languages : en
Pages : 172
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Book Description
Author: N. Bednarz
Publisher: Springer Science & Business Media
ISBN: 9400917325
Category : Education
Languages : en
Pages : 342
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Book Description
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Author: Peter Liljedahl
Publisher: Corwin Press
ISBN: 1544374844
Category : Education
Languages : en
Pages : 454
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Book Description
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.
Author: Robert Femiano
Publisher:
ISBN: 9781601442765
Category : Mathematical recreations
Languages : en
Pages : 48
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Book Description
Author: John Mason
Publisher: Paul Chapman Educational Publishing
ISBN: 9781412911719
Category : Business & Economics
Languages : en
Pages : 342
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Book Description
'Mason, Graham, and Johnston-Wilder have admirably succeeded in casting most of school algebra in terms of generalisation activity? not just the typical numerical and geometric pattern-based work, but also solving quadratics and simultaneous equations, graphing equations, and factoring. The authors raise our awareness of the scope of generalization and of the power of using this as a lens not just for algebra but for all of mathematics!' - Professor Carolyn Kieran, Departement de Mathematiques, Universite du Quebec a Montreal Algebra has always been a watershed for pupils learning mathematics. This book will enable you to think about yourself as a learner of algebra in a new way, and thus to teach algebra more successfully, overcoming difficulties and building upon skills that all learners have. This book is based on teaching principles developed by the team at The Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning algebra. Written for teachers working with pupils aged 7-16, it includes numerous tasks ready for adaption for your teaching and discusses principles that teachers have found useful in preparing and conducting lessons. This is a 'must have' resource for all teachers of mathematics, primary or secondary, and their support staff. Anyone who wishes to create an understanding and enthusiasm for algebra, based upon firm research and effective practice, will enjoy this book. This book is the course reader for The Open University Course ME625 Developing Algebraic Thinking
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309131987
Category : Education
Languages : en
Pages : 53
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Book Description
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.
Author: Center for Science, Mathematics, and Engineering Education
Publisher: National Academies Press
ISBN: 0309522455
Category : Education
Languages : en
Pages : 206
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Book Description
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
Author: National Research Council
Publisher: National Academies Press
ISBN: 0309131979
Category : Education
Languages : en
Pages : 386
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Book Description
First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€"to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.
