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''The uncommon value of this book is found in the way it treats teaching as an object of study. It engages all teachers in studying and improving teaching. It focuses directly on the details of teaching and on the methods used to interact with students about the content.''
-- From the Foreword by James Hiebert, Robert J. Barkley Professor of Education, University of Delaware
''Readers will gain insight about how to foster a challenging classroom that propels students toward a deeper understanding of mathematics.''-- Journal for Research in Mathematics Education
Now in its second edition, this essential textbook and professional development resource offers a new foreword by James Hiebert. Drawing on the authors' work over the past decade, two important new chapters focus on the ways in which the book can be used to support the learning of teachers and administrators. Chapter 11 illustrates the various ways in which teacher educators and professional developers might use the materials in the book to aid in the professional growth of teachers, including how to directly improve teachers' instruction practices. Chapter 12 discusses ways in which principals and school leaders can use the book to become better instructional leaders of teachers who are attempting to teach with cognitively demanding tasks.
This essential book:
* Describes the Mathematical Tasks Framework, a tool that has been proven effective in evaluating instructional decisions, the choice of materials, and learning outcomes.
* Provides narrative cases of actual classroom instruction that include Discussion Questions and Teaching Notes.
* Includes a link to a downloadable PowerPoint presentation containing an expanded overview of the research for use with teachers, parents, and other interested stakeholders.
- Sales Rank: #258459 in Books
- Brand: Brand: Teachers College Press
- Published on: 2009-04-04
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x 6.00" w x .50" l, .66 pounds
- Binding: Paperback
- 208 pages
Features
- Used Book in Good Condition
About the Author
Mary Kay Stein is Professor of Learning Sciences and Policy at the University of Pittsburgh. Margaret Schwan Smith is a Professor in the Department of Instruction and Learning in the School of Education at the University of Pittsburgh. Marjorie A. Henningsen is the Head of School at Wellspring Learning Community in Beirut, Lebanon. Edward A. Silver is the William A. Brownell Collegiate Professor of Education and Professor of Mathematics at the University of Michigan.
Most helpful customer reviews
2 of 3 people found the following review helpful.
A limited take on teachers' views of tasks
By Phillip A. Towndrow
Introduction
International comparative research identifies the maintenance of cognitively challenging tasks during instruction as a central distinguishing feature of high performing mathematics classrooms. The question is: how can mathematics teachers provide challenging and worthwhile learning opportunities for students? The answer lies in the purposeful combination of specialized teacher education, appropriate school-based leadership, and relevant tools and materials.
Description
The book is divided into three sections. The first part (Chapters 1-3) presents and explains the concepts and findings that support the ideas and recommendations made throughout the book. The central notion concerns instructional tasks--understood as the activities selected and set up by teachers, and implemented by students resulting in student learning. What is vitally important here is teachers' ability in determining "... the kind and level of thinking required of students to successfully engage with and solve ... task[s]" (p. 1). The authors propose the Mathematical Tasks Framework (MTF) as a way to draw teachers' attention to what students are actually doing and thinking about during lessons, and provide explicit standards against which to judge practice. The MTF is necessary, we learn, because, "[o]pportunities for student learning are not created simply by putting students into groups, by placing manipulatives in front of them, or by handing them a calculator. Rather, it is the level and kind of thinking in which students engage that determines what they will learn" (p. 1).
The second part of the book (Chapters 4-10) features six cases based on real teachers and events for use in teacher development classes, seminars and/or other instructional settings (p. xix). In each instance, the cases are meant to illustrate what happens when tasks are implemented by students as intended by teachers. The various scenarios also exemplify task `decline', that is, when there is `slippage' (for numerous reasons) from high-level cognitive demands to classroom work where there may be: procedures without connection to meaning (p. 18), unsystematic exploration (p. 19) and even no mathematical activity at all (p. 20). The format of the cases includes a (mathematical) task description (recommended to be done before the discussion of the case starts), discussion questions and teaching notes for teacher educators covering, among other things, what can be learned and discussed in the case in question.
Part three (Chapters 11-12) is new to the second edition. Chapter 11 deals with the issue of how mathematics teachers can actively and meaningfully transfer learning from professional development sessions into practices that improve pedagogy and practices in their classrooms. And Chapter 12 discusses how school principals, in particular, can better lead [mathematics] teachers in teaching with cognitively demanding tasks (pp. xx-xxi).
Example 1
Without exception, the authors craft their cases carefully to make specific pedagogical points with reference to the MTF. For example, the case of Ron Castleman (Chapter 5) describes two attempts to teach a lesson in linking fractions, decimals, and percents using an area model. We're told in the teaching notes that Ron "... is discovering ... that ... students sometimes prefer simpler, more straighforward tasks and can react anxiously to the uncertainty associated with not knowing immediately how to tackle a more complex, less structured task" (p. 47). Further, the case tells how in the first lesson, "Ron inadvertently simplifies the problem by suggesting that the students start with finding the fraction, [but] he does not repeat this mistake in the later class ... (p. 49). Significantly, the teacher sustains the complexity in his problem-solving task in his second attempt through a number of assisting factors including, scaffolding, building on student knowledge and thinking, making conceptual connections, modeling high-level thinking, and the provision of enough time (p. 50).
Example 2
In another 'dual' teacher case (Chapter 6) Fran Gorman and Kevin Cooper set-up the same interesting and challenging task in their respective classes to do with multiplying fractions with pattern blocks. This time, Kevin stays at the level of `procedures with connections' and notably uses a pair of high-level performing students to model problem-solving at the point when most of the other students in the class were not engaging sufficiently well with the task (pp. 70-71). In contrast, Fran's task slips from `procedures with connections' to 'procedures without connections'. Strategically, she does not allow her students to struggle on their own. Instead, she does all the thinking and reasoning herself and so initial challenges become nonproblems.
Critique
Given its size, just 163 pages excluding the references, Implementing standards-based mathematics instruction: A casebook for professional development could be a rich, thought-provoking and practice-changing resource in the hands of competent, theoretically informed, and caring educators. Yet, there are, in my opinion, a number of limitations in the authors' approach and conceptualizations worth considering. Although the MTF is positioned from the outset as "... a fluid representation of how tasks unfold during classroom instruction" (p. xviii) it is, fundamentally, a linear, non-recursive, teacher-only cut on what tasks are and how they evolve. Crucially, there's little or no consideration of how tasks are `redesigned' or reinterpreted by students as they implement them. In other words, I think students can, when allowed, play the role of joint-task designers but this possibility isn't represented in the MTF
The casebook repeatedly shows how teaching is a complex, highly-nuanced endeavour that should require detailed planning and skillful enactment. Teachers are required to keep multiple factors in play some of which are directly task-related and others are more general in orientation relating, for example, to classroom management, student motivation and affect. However, at times, for me, the cases, lack detail or raise issues not covered adequately in the teachers' notes. For instance, while Ron (Chapter 5) "... believed that diagrams, although not a panacea by any means, provided a tool for reasoning" (p. 38), we don't know what this belief is grounded on. Further, we don't know to what extent his insistence on his students' use of a particular resource (a 4x10 grid) made his task more difficult than it needed to be. In fact, I'd say, given the differential affordances of various modes of representation, one person's perceived usefulness of a `tool for reasoning' is another's barrier to knowledge building and understanding. On occasions, it makes sense, prototypically to let students decide for themselves how to represent their knowledge in ways they think are best. A couple of the cases provide scope for this to happen.
For me, the biggest issue not covered in sufficient detail in the text concerns critical reflection. This is not to say its importance and centrality are not mentioned but that its purposes and practices are not specified and explained. How is reflection altered by making it `critical'? And whose interests are served by reflecting critically on practice. I strongly sense Stein and her colleagues haven't devised their cases as ways to understand, for example, how considerations of power underpin, frame, and distort mathematical processes and classroom interactions (cf. Brookfield, 1995).
My Recommendation
In sum, the greatest strengths of this book lie in two areas. First, it highlights a range of factors that can account for student learning or not in mathematics classrooms where mandated standards exist. Second, the materials are adaptable to various teacher education contexts and could--in the right hands--assist in making decisions about which tasks to use to accomplish particular student learning outcomes (pp. 131-132). The chief weakness of the cases in my opinion is that they only present a limited take on teachers' views of tasks. A fuller account of task planning and implementation needs to hear multiple voices and pay greater attention to a larger set of considerations including but not restricted to identifying and articulating goals, choosing appropriate tools and resources, planning appropriate support, task evaluation and lesson-level assessment.
Reference
Brookfield, S. D. (1995). Becoming a critically reflective teacher. San Francisco: Jossey-Bass Publishers.
0 of 0 people found the following review helpful.
Great book for Secondary Math Teacher!
By Catwoman
This book is a great reference for Secondary Math Teachers. The chapters are a manageable length and deal with issues pertinent to secondary level mathematics, especially time management. I carried the book around in my purse for the better part of a summer and read it when I was waiting on a line at the grocery store or at the airport. You will find many ideas that change how you think about teaching secondary math in this book.
2 of 3 people found the following review helpful.
Essential reading
By D. Clark
Every teacher should read this. The framework for maintaining the cognitive level is important for all mathematics instruction, whether or not it is claimed to be Standards-based.
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