---

Teaching Student-Centered Mathematics by Van de Walle/Lovin

Chapters 9-12

Chapters 9-12, give an overview of mathematical concepts. These chapters include measurement, algebraic reasoning, exploring data analysis, and exploring concepts of probability. Two appendices are provided that give principles and standards for school mathematics, as well as a guide to blackline masters. In Chapter 9, the authors discuss student-centered goals for measurement. Helping students understand the "meaning and process of measuring," is a key objective of student centered mathematics when pertaining to measurement. The authors also discuss how to develop measurement concepts and skills, including making and using measurement instruments. Chapter 10 deals with algebraic reasoning, which includes repeating patterns, "growing" patterns, patterns with numbers representing ideas, variables and equations, and functions. An expanded lesson on predicting is also included. In Chapter 11, the authors explore data analysis. The key concepts here are: gathering data to answer questions, understanding the mean, two concepts graphical and representations. In Chapter 12, an overview of exploring concepts of probability, such as probability on a continuum, sample spaces and probability, and short run versus long run results, is given. An expanded lesson on "testing Bag Designs" is given. The NCTM Content Standards are provided in the Appendix for Teachers Reference. I found this book to be most informative, and it provided many activities I can use with my students.

Teaching Student-Centered Mathematics by Van de Walle/Lovin

Chapters 9-12

Chapters 9-12, give an overview of mathematical concepts. These chapters include measurement, algebraic reasoning, exploring data analysis, and exploring concepts of probability. Two appendices are provided that give principles and standards for school mathematics, as well as a guide to blackline masters. In Chapter 9, the authors discuss student-centered goals for measurement. Helping students understand the "meaning and process of measuring," is a key objective of student centered mathematics when pertaining to measurement. The authors also discuss how to develop measurement concepts and skills, including making and using measurement instruments. Chapter 10 deals with algebraic reasoning, which includes repeating patterns, "growing" patterns, patterns with numbers representing ideas, variables and equations, and functions. An expanded lesson on predicting is also included. In Chapter 11, the authors explore data analysis. The key concepts here are: gathering data to answer questions, understanding the mean, two concepts graphical and representations. In Chapter 12, an overview of exploring concepts of probability, such as probability on a continuum, sample spaces and probability, and short run versus long run results, is given. An expanded lesson on "testing Bag Designs" is given. The NCTM Content Standards are provided in the Appendix for Teachers Reference. I found this book to be most informative, and it provided many activities I can use with my students.

Teaching Student-Centered Mathematics by Van de Walle/Lovin

Chapters 9-12

Chapters 9-12, give an overview of mathematical concepts. These chapters include measurement, algebraic reasoning, exploring data analysis, and exploring concepts of probability. Two appendices are provided that give principles and standards for school mathematics, as well as a guide to blackline masters. In Chapter 9, the authors discuss student-centered goals for measurement. Helping students understand the "meaning and process of measuring," is a key objective of student centered mathematics when pertaining to measurement. The authors also discuss how to develop measurement concepts and skills, including making and using measurement instruments. Chapter 10 deals with algebraic reasoning, which includes repeating patterns, "growing" patterns, patterns with numbers representing ideas, variables and equations, and functions. An expanded lesson on predicting is also included. In Chapter 11, the authors explore data analysis. The key concepts here are: gathering data to answer questions, understanding the mean, two concepts graphical and representations. In Chapter 12, an overview of exploring concepts of probability, such as probability on a continuum, sample spaces and probability, and short run versus long run results, is given. An expanded lesson on "testing Bag Designs" is given. The NCTM Content Standards are provided in the Appendix for Teachers Reference. I found this book to be most informative, and it provided many activities I can use with my students.

Teaching Student-Centered Mathematics by Van de Walle/Lovin

Chapters 4-8

Chapters 4-8 discuss various strategies for mathematical computational concepts. Rather than one fixed method of computation, various methods are discussed. Flexibility is seen as a key component. Three types of computational strategies the authors discuss are: (1)Direct Modeling, (2)Invented Strategies, and (3)Traditional Algorithms It has been shown that students are more likely to use and understand strategies they have invented themselves. Specific activities for different computational skills are given. I will be able to use many of these with my students. Technology notes and assessment notes are also provided. Effective instruction includes providing activities that will involve students in the mathematics they must learn. Students who are let "struggle" and "interact" with math, by using their own ideas and their own strategies have been shown to develop better understanding, as well as an enjoyment of mathematical concepts. As the authors continually state, "It makes sense to them."

Teaching Student-Centered Mathematics, by Van de Walle/Lovin

Chapters 1-4

The authors, in this book, discuss student-based as well as problem based activities to aid students in developing confidence in their ability to understand mathematical concepts. Approximately two hundred activities that are grade level appropriate are given, as well as a website that contains more than 50 reproducible blackline masters. Helping students learn that math makes sense is a primary goal of the authors in this book. It is important that teachers provide an environment that encourages students to solve problems themselves as well as working together, sharing ideas and knowledge in order to solve problems. A student centered approach is seen as the key to helping students learn that math makes sense. An important aspect of the student centered approach is to permit students to "struggle" with mathematical concepts. A table is provided that gives mathematical "activities at a glance," divided by chapters. I found this table to be very helpful. In these chapters, the authors continue by discussing the basic foundations of student centered instruction. This includes understanding how students actually learn and how to incorporate problem solving into the learning environment, to be assessed on a daily basis. The authors discuss the four main foundational components: children learning constructively, teaching with problems, planning lessons and assessing where students are. Expanded lessons are also included which I found to be especially interesting, and useful

Differentiation In Practice by Tomlinson and Eidson

Parts 1 and 2

In this book, the authors discuss how teachers intertwine differentiation principles and strategies throughout an entire instructional unit, that applies, to any grades, but focusing on grades K-5. the basic components of differentiation in instruction are discussed, allowing teachers consistency in planning. Differentiated instruction is viewed by the authors as "just common sense." The example is given of parents differentiating to meet the individual needs of their own children. Effective teachers know how to take these fundamental principles of differentiation and adapt them to meet the individual needs of their students. A fundamental component of differentiated instruction is the teacher's understanding of how teaching and learning occur. It is an adaptation to the student's individual needs concerning "structure and independence, more practice or greater challenge, etc." The teacher's main goal should be to help each student "bridge gaps in understanding and skills, " and grow as much as is feasible. The authors give an example of Ms. Johnson, who is guided in her teaching by four classroom elements: Who she teaches, Where she teaches, What she teaches, and How she teaches. The differentiated classroom is composed of a "strong link between assessment and instruction,", the teacher's clarity about learning, flexible use of time, space and materials, sharing responsibility for the classroom environment, and emphasis on individual student's growth. A chart is given explaining how to use the student traits and curricular elements to plan differentiation. In chapters one through six, the authors provide actual, complete various differentiated units of instruction. These units include reading, language arts and math.  An extended glossary along with recommendations for further readings is also provided. I was very impressed with the units, and believe they can be of real help to me with meeting the individual needs of my students.

Mosaic of thought by Keene/Zimmerman

Chapters 6-10

 In these chapters, the authors discuss the use of sensory images to enhance comprehension, as well as inferring and synthesis. Questions are seen as a way to "generate" writing topics. Modeling is an important aspect on order for students to become  aware of the questions they naturally ask as they are listening or reading. Some of the key ideas proficient readers exhibit are: asking questions before, during and after reading, and the comprehension skills that are enhanced by asking questions. Proficient readers have also been shown to "spontaneously and purposefully create mental images" during and after reading, using all five senses and emotions, and are based on a reader's prior knowledge. Again, modeling by the teacher is seen as vital in helping students learn how to create images, thereby, improving comprehension. Inference is seen as a way to expand the "literal  confines of reading a page" and is viewed as an important part of improving comprehension when related to the reader's prior experiences. Synthesis is seen by the authors as the "process of ordering, recalling, retelling and recreating in a coherent whole, the information with which our minds are bombarded every day." This is the basis the comprehension mosaic the authors are trying to create. Equally important is teaching children the ability to solve reading concerns themselves. The authors discuss the "tray of reading instruments" proficient readers can use to operate on comprehension problems, to be used "flexibly and interchangeably." Cueing systems that the authors have found to be most useful in helping students solve reading problems are the Grapho- Phonic System, the Lexical or Orthographic System, Syntactic System, Schematic System and Pragmatic System. These cues are discussed in detail by the authors. The authors include appendices which address some questions that they have been asked and the authors responses. I found this to be especially interesting and helpful.

Mosaic of Thought by Keene/Zimmerman

Chapters 1-5

The authors in this book, discuss teaching comprehension in a reader's workshop. Research on reading comprehension is highlighted, and we are shown how we can apply it to our students. Comprehension is an area of real weakness for a lot of my students, and I found this book to be very helpful and informative. In this section, the "Mosaic of Thought" concerning comprehension, begins to take shape. The various ways in which we "construct meaning as we read" are explored. Readers and writers workshops are seen as an integral part of teaching children comprehension skills. Giving children extended time to read, making them feel "ownership" for the selection of many of their books, and elaborating on what they have read by talking to others, and writing about their "reaction, " are sen as an important components of comprehension. Successful reading programs in various schools are discussed. Reading workshops are seen as "inviting places" for students to learn to love to read.  Children are taught to love to read.  I have found this love of reading to be a very successful strategy in helping my students develop their reading skills.Various successful cognitive strategies are also discussed.

Whatever It Takes by DuFour, Eaker, and Karhanek

Chapters 8-10

 

The authors in the preceding chapters discussed four very distinct schools that, seem to have more differences than things in common. In these chapters, the authors emphasize the important concepts these schools do share. These are: clarity of purpose, collaborative culture, collective inquiry into best practice and current reality, action orientation, commitment to continuous improvement, focus on reality, strong principals who empower teachers, commitment to face adversity, conflict and anxiety, the same guiding phrase. The details of an individual school's plans for non-responding learners, may vary from school to school, but the final step is the same, "Whatever It Takes." The authors continue by stating the importance of "monitoring each student's learning on a timely basis," and creating a plan for additional support and time when students demonstrate difficulty in learning. A system of interventions needs to be put in place. The importance of making special education "last resort rather than a first response," is emphasized. I enjoyed this discussion very much! Philosophical challenges for systematic interventions are discussed and expanded upon. The authors in these final chapters, continue to stress the importance of changing the focus of schools from a "focus on teaching to a focus on learning." "Failure is not an option," is seen as an important concept in the student's learning process, as well as building shared knowledge and working together collaboratively as a school to do whatever it takes to ensure that all students do learn.

Whatever It Takes by DuFour, Eaker, and Karhanek

Chapters 5-7

 

In these chapters, the authors discuss the importance of providing time and support for middle school students. A brief history of the middle school concept is reviewed, as well as specific examples of successful middle school programs. Boones Mill Elementary School is given as a model of providing time and support at the elementary level. How Boones Mill responded to the three critical questions discussed in the previous chapters, is also critiqued. The "team learning" process is shown to be an efficient time management concept. Peer Tutoring/Buddy programs as well as grade-level parent workshops are also effective programs to help non-responsive learners. A section I was especially interested in, was the discussion of the importance of "connecting special and regular education" programs. This is especially true in my field.

 

Next page >>