Research-based and Best Practices strategies have shown that student achievement can be increased using a variety of methods. This is a collection of resources to help teachers wade through the research and best practices information with links to websites, articles and other resources. Please email me with sources to improve this Web Resource List.
Interactive Writing in Mathematics Class: Getting Started Ralph T. Mason and P. Janelle McFeetors
This article specific strategies for making writing in math classes authentic and purposeful by making the process interactive.
MATHEMATICS TEACHER, October 2002, Volume 95, Issue 7, Page 532
"Teaching to the Test" President's Message by Cathy Seeley, President of NCTM Quote, p.3 "Our tests are driving our teaching. This is the message from
coast to coast as pressure mounts to produce results and
meet the Adequate Yearly Progress requirements of the No Child
Left Behind (NCLB) Act. Is this good or bad, and can a good
mathematics program survive in this kind of environment?"
Originally published in the NCTM News Bulletin (January/February 2006).
Copyright 2006, The National Council of Teachers of Mathematics. All rights reserved.
NCTM President's Message, Cathy Seeley, NCTM News Bulletin, December 2005. Quote p. 3 "What does it mean to know mathematics? This is a complex
question, but there is strong agreement that facility with
numbers and skill in problem solving play important roles.
Principles and Standards for School Mathematics calls for students
to be proficient with tools that include pencil and paper
and technology, as well as mental techniques. I would like to
make a case for raising the importance of mental math as a
major component in students’ tool kits of mathematical knowledge.
Mental math is often associated with the ability to do
computations quickly, but in its broadest sense, mental math
also involves conceptual understanding and problem solving." Originally published in the NCTM News Bulletin (December 2005).
Copyright 2005, The National Council of Teachers of Mathematics. All rights reserved.
A Handbook for Classroom Instruction That Works We stand at a unique point in the history of U.S. education—a point at which the potential for truly meaningful school reform is greater than it ever has been. This is not just because we are at the beginning of a new century and a new millenium, although these are certainly noteworthy milestones. Rather, it is because we now have more than 30 years of accumulated research that provides some highly consistent answers to the question of what types of instructional strategies work best to improve student achievement. Much of that research has been synthesized and described in the book Classroom Instruction That Works: Research-Based Strategies for Increasing Student Achievement by Marzano, Pickering, and Pollock (ASCD, 2001). Briefly, based on a survey of thousands of comparisons between experimental and control groups, using a wide variety of instructional strategies in K-12 classrooms, across a variety of subject areas, we were able to identify nine categories of instructional strategies proven to improve student achievement:
1. Identifying similarities and differences
2. Summarizing and note taking
3. Reinforcing effort and providing recognition
4. Homework and practice
5. Representing knowledge
6. Learning groups
7. Setting objectives and providing feedback
8. Generating and testing hypotheses
9. Cues, questions, and advance organizers
This handbook is intended as a self-study guide to the effective use of specific strategies in each of these nine categories. Although you can use this handbook without having read Classroom Instruction That Works, we recommend that you do so, particularly if you are interested in the research that underlies the recommendations in this handbook.
Chapter 1. Introducing the Best of Times
View the print friendly version of this page. E-mail a friend the link to this page.
ASCD provides this chapter online from What Works in Schools: Translating Research into Action
by Robert J. Marzano
Communication Chapter 3 NCTM's Principles and Standards, 2000 Quote p. 60 " Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a » classmate or teacher, or when they formulate a question about something that is puzzling to them. Communication can support students' learning of new mathematical concepts as they act out a situation, draw, use objects, give verbal accounts and explanations, use diagrams, write, and use mathematical symbols. Misconceptions can be identified and addressed. A side benefit is that it reminds students that they share responsibility with the teacher for the learning that occurs in the lesson (Silver, Kilpatrick, and Schlesinger 1990).
Quote p. 61 " Written communication should be nurtured in a similar fashion. Students begin school with few writing skills. In the primary grades, they may rely on other means, such as drawing pictures, to communicate. Gradually they will also write words and sentences. In grades 3–5, students can work on sequencing ideas and adding details, and their writing should become more elaborate. In the middle grades, they should become more explicit about basing their writing on a sense of audience and purpose. For some purposes it will be appropriate for students to describe their thinking informally, using ordinary language and sketches, but they should also learn to communicate in more-formal mathematical ways, using conventional mathematical terminology, through the middle grades and into high school. By the end of the high school years, students should be able to write well-constructed mathematical arguments using formal vocabulary."
Problem Solving, Chapter 3, NCTM's Principles and Standards, 2000. Quote p. 53 "
Of the many descriptions of problem-solving strategies, some of the best known can be found in the work of Pólya (1957). Frequently cited » strategies include using diagrams, looking for patterns, listing all possibilities, trying special values or cases, working backward, guessing and checking, creating an equivalent problem, and creating a simpler problem. An obvious question is, How should these strategies be taught? Should they receive explicit attention, and how should they be integrated with the mathematics curriculum? As with any other component of the mathematical tool kit, strategies must receive instructional attention if students are expected to learn them. In the lower grades, teachers can help children express, categorize, and compare their strategies. Opportunities to use strategies must be embedded naturally in the curriculum across the content areas. By the time students reach the middle grades, they should be skilled at recognizing when various strategies are appropriate to use and should be capable of deciding when and how to use them. By high school, students should have access to a wide range of strategies, be able to decide which one to use, and be able to adapt and invent strategies. "
Quote p. 54 "Research (Garofalo and Lester 1985; Schoenfeld 1987) indicates that students' problem-solving failures are often due not to a lack of mathematical knowledge but to the ineffective use of what they do know."
David Numberman's Top 10 List: Challenges that Hinder Student Achievement in Mathematics PowerPoint: MaryJo Ormsby, Math Helping Corps, presentation at OSPI January Conference 2006
Join the members of the Math Helping Corps for this humorous look at their top 10 list of challenges that hinder student achievement in mathematics. "Expert" guests of the David Numberman Show will address best practices and research on effective mathematics instruction.
Tom Boyce "How to Reach Every Student with an Effective Mathematics Program" Handout 1 An effective mathematics program capable of reaching each and every student requires: the use of a wide range of assessment tools and data to identify areas of concern and improvement; a coordinated mathematics program that integrates all available resources; teachers with strong content knowledge and effective classroom strategies; and professional development opportunities that build a strong mathematics community. This session will provide specific examples that administrators, coaches and teachers can use to develop and strengthen the mathematics program in their school. These examples include: techniques to analyze state and classroom assessment data; methods to integrate regular and special education, LAP and Title programs; components of effective extended learning and summer school programs; and effective strategies for sustained professional development. Participants will have an opportunity to interact and discuss these and other examples with the presenter and with other participants.
Tom Boyce "How to Reach Every Student with an Effective Mathematics Program" Handout 2 An effective mathematics program capable of reaching each and every student requires: the use of a wide range of assessment tools and data to identify areas of concern and improvement; a coordinated mathematics program that integrates all available resources; teachers with strong content knowledge and effective classroom strategies; and professional development opportunities that build a strong mathematics community. This session will provide specific examples that administrators, coaches and teachers can use to develop and strengthen the mathematics program in their school. These examples include: techniques to analyze state and classroom assessment data; methods to integrate regular and special education, LAP and Title programs; components of effective extended learning and summer school programs; and effective strategies for sustained professional development. Participants will have an opportunity to interact and discuss these and other examples with the presenter and with other participants.