PAcree

     The final chapters of Van de Walle's book, Teaching Student Centered Mathematics grades 5-8, addresses and provides activities for algebraic reasoning, understanding equations and functions, analysis of data, and probability. The activities in chapter 9 look specifically at reasoning skills and the development of language and an understanding of symbolism that allows students to communicate their mathematical ideas. Activities range from the very simplest pf patterning to number tricks and equations. In chapter 10, the author moves from algebraic reasoning activities to activities that teach equations and functions, including graphing proportional relationships. "Real world" problems are used for student investigations into these relationships. Chapters 11 and 12 focus on the analysis of data,  describing of statistical information and finally developing the concepts of probability. The activities for learning probability include both theroerical and experimental probability.

     All of the chapters in this book provide activities with instructions on how to teach them to students with the goal in mind that our students need to think, do, and communicate mathematics. This book is a great resource for the teacher because it is filled with activities geared to help plan student-focused activities for teaching the rigorous mathematics that students are being asked to do. Additionally, the author also includes remediation and assessment ideas.

     In chapters 5-8, Van de Walle presents futher lessons which delve deeper into teaching concepts related to number theory, ratios and proportions, geometry, and measurement. Each chapter is organized around the basic goals of the lessons (Big Ideas) and provides basic information for the teacher on the concepts and sample activities to use to teach students. The lessons and activities are specifically geared for the upper elementary and middle school learner and at the end of each chapter are expanded lessons which would be appropriate to use for differentiation. The author also provides picture models, step by step instructions, examples of manipulatives, and notes on how to use technology for the activities listed.

     As schools attempt to meet state and federal guidelines of student achievement, teacher need resources to help students master the concepts at an ever increasing depth of understanding. Van de Walle's ideas and activities can be one of the resources. The book is user friendly and provides a great deal of information on the very math concepts that students need to know.  I have enjoyed re-acquainting myself with some of the mathematical concepts and have found many great activities which increase student involvement in math through Van de Walle's books.  

     In Van de Walle's book, Teaching Student Centered Mathematics in Grades 5-8, the author explains that teachers need to understand that effective mathematics teaching is based on the understanding of how children learn, how we as teachers promote learning, and how teachers can plan and assess student learning on a daily basis. In chapter 1, the authors discusses how people learn new things. Students give meaning to new ideas by connecting them to the things they already know. Understanding is defined as the quality and quantity of the connections of new ideas to the existing ideas. This idea provides the foundation of the book that student centered problem solving allows students to construct their own ideas and become learners that understand mathematics. Chapter 1 further explains problem solving is a vehicle to teach the math that students are required to know.

     The benefits of Problem-Based teaching are: focusing students attention on ideas and making sense of mathematics, developing students' belief in themselves as problem solvers, on-going assessment, students are having fun and thus engaged, and it requires students to communicate, reason, and justify their own ideas about mathematics.

     Chapters 2-4 discuss strategies for teaching whole number computations, fraction concepts and computations, and decimals and percents. These chapters highlight the concepts and offer strategies and activities for teaching the concepts through problem solving tasks.

   The use of a problem based approach to teaching mathematics is different from the traditional approach of the teacher showing how to do the steps to solve problems and students repeating the steps to produce an answer. I have used tasks to allow students the opportunity to "play" with a problem and come up with original ways and often multiple ways of solving it. I have found that facilitating while students work together, helps me to assess understanding of "big ideas" and to provide some redirection when misconceptions arise on a one-on-small group basis. Students are more confident and less afraid to ask questions or admit to not knowing what to do when working in a small group. The challenge of teaching using tasks is to have numerous tasks available and constantly revising plans based on the previous days work. Grading and scoring have also been a challenge. Rubrics are a good way to score understanding, however, must be made in advance and be geared toward a specific task.

    Craft Lessons, the final reading covers the topics which will further enhance student writing. Students can learn through the sample lessons to refine and improve their writing. The topics include lessons on character conflict, using flashbacks to make plot more interesting, improving setting descriptions, shaping and slowing down the actions, improving transitions, and experimenting with irony and symbolism. In every lesson, the tie between reading and writing is evident and lessons have been based in quality children's literature.

     The information gained in Craft Lessons has caused some thought about the importance of creating an environment where writing is frequent and rewriting is a natural part of the writing process. Students need to practice daily writing and work on a piece of writing to improve it. Student conferences about their writing has helped to focus my students this year on the importance of creating a publishable product that fits the purpose of the assignment. Having students correct each others and their own writing with verbal feedback has created better written works. Entertwining reading and writing and creating a opportunity for students the read and respond to quality literature and to identify and discuss the literary devises of authors is absolutely essential in enhancing student writing.

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Posted by: PAcree
Modified on February 28, 2006 at 4:00 PM

Craft Lessons (pages 79-92) continues with examples of what to teach and how to teach writing to the upper elementary student. The authors have focused on topics which will create improved writing by students. Subjects such as finding a focus, manipulating time in a story, "pruning", selecting a lead, using descriptions, creating interesting characters and making them come alive, using recurring lines, and writing "low on the food chain" are suggested as necessary topics which will teach students to engage readers. The authors suggest that teaching these topics requires a great deal of interaction with good literature and models of writing created by the teacher. Students need to experience good and poor writing to compare and revise. The authors link writing heavily with reading and give examples of literature to use to cover writing topics.

The list of topics covered by the authors are the very things that we wish our students would use in their writing. For example, frequently, students have a difficult time finding a focus  and creating the details that support that focus.  Pruning writing to get rid of any unnecessary parts could be part of the revision process. Teaching students to write "low on the food chain" helps them to make their writings detail specific and more appealing to readers (described by the authors as the bottom feeders).

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Posted by: PAcree
Modified on February 21, 2006 at 4:31 PM