Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
Math Methodology is a three part series on instruction, assessment, and curriculum. Sections contains relevant essays and resources.
This page continues part 1 on Instruction, providing Instruction Resources, including for special needs students (e.g., deaf, visually impaired, learning disabilities, English language learners).
Part 1: Math Methodology: Instruction
The Instruction Essay An Introduction to Teaching Challenges, Bloom's Taxonomy and Levels of Understanding; Teaching Mathematics Right the First Time: Learning for Understanding; and Addressing the Needs of Students with Math Difficulties
Part 2: The Role of Assessment and resources
Part 3: Curriculum: Content and Mapping and resources
HOT: The Alabama Department of Education has provided a series of video clips related to the Common Core State Standards for Mathematics, which "provide additional insight into how the College and Career Ready Standards change instruction and the implications of the Standards for the classroom."
HOT: The U.S. Department of Education started the Doing What Works (DWW) website to assist teachers in the implementation of effective educational practices. The DWW website contains practice guides developed by the Department’s Institute of Education Sciences that evaluate research on the effectiveness of teaching practices described in the guides. The website also contains examples of possible ways this research may be used, but not necessarily the only ways to implement these teaching practices. Content addresses English language learners, psychology of learning, early childhood education, math and science with more to come on other topics.
Much of the content is based on the work of the What Works Clearinghouse (WWC), which also has a set of practice guides. Note: Practice guides "consist of actionable recommendations, strategies for overcoming potential roadblocks, and an indication of the strength of evidence supporting each recommendation. IES practice guides are subjected to rigorous external peer review," according to the WWC.
Instruction resources here are grouped into sections:
Hook your students on The Beauty in Numbers in Math Wonders to Inspire Teachers and Students by Alfred S. Posamentier (2003), an ASCD publication. Chapter 1, available online, is an amazing discussion of some surprising number patterns, power relationships, beautiful number relationships, strange equalities, perfect numbers, friendly numbers (Yes, there is a definition of friendly numbers), palindromic numbers (e.g., 12321), number associations with geometric figures, Fibonacci numbers (i.e., 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,...) and more. As examples:
Note the digits of these special numbers and the consecutive exponents (p. 12)
598 = 51+92+83
1,676 = 11+62+73+64
A palindrome, which is a number that can be read the same in both directions, can be generated from any number by making successive additions of the number with its reversal (p. 27). This might take a few such additions.
67 + 76 = 143; 143 + 341 = 484, a palindrome
There are only five numbers (i.e., 1, 153, 370, 371, and 407) in which the number is the sum of the cubes of its digits as in 153 = 13+53+33 (p. 36).
Buy additional resources via CT4ME.
The Amazon widget below shows books using the search phrase: mathematics teaching. You can also use the widget to search with other key words. Suggestions include:
Achievethecore.org provides Where To Focus: Math Shifts, Key Fluencies, and Major Work of Grade. This document is of particular relevance for K-8 mathematics as it provides guidance for focusing instruction at each grade level for implementing the Common Core State Standards in Mathematics. Content emphases are identified by major clusters, supporting clusters, and additional clusters.
Adding It Up: Helping Children Learn Mathematics (2001) is a longer book (over 400 pages), available online, by the Mathematics Learning Study Committee and editors Jeremy Kilpatrick, Jane Swafford, and Bradford Findell of the Center for Education at the National Research Council. Its focus is school mathematics from pre-kindergarten to eighth grade. Much of this report attends to the learning and teaching of number, but authors emphasize that their perspective is considerably broader than just computation. Authors say, "Three kinds of knowledge are crucial for teaching school mathematics: knowledge of mathematics, knowledge of students, and knowledge of instructional practices" (p. 370).
Algebra 4 All (A4A) Social Network is a "community of educators committed to sharing resources and supporting one another in the practice of teaching Algebra." A4A is sponsored by the Michigan Learnport. You'll find a group discussion forum, a project and lesson sharing area, blog posts, videos on multiple topics, an extensive collection of resources organized by function families, and more.
The Art of Teaching Resources from TeacherVision.com.
21st Century Problem Solving, by H. McAllister of the University of Hawaii, is devoted to providing teachers and students with training in how to solve problems. The methodology described is useful for all students from grade school to grad school and beyond. Begin with an understanding of why students can't solve word problems reliably. Learn to use the 3 R's of problem solving, Request-Response-Result, and a verification of the result. The examples and theory given at this site deal specifically with subjects that use mathematics for problem solving, including algebra, physics, and chemistry. The problem-solving principles apply equally well to problems which require non-mathematical tools or a mixture of mathematical and non-mathematical tools.
Centre for Innovation in Mathematics Teaching (CIMT) was established in 1986 at the University of Exeter in the UK and is now housed at the University of Plymouth. Content is focused on research and curriculum development for mathematics teaching and learning. K-12 educators will be particularly interested in the CIMT curriculum resources, such as "pupil texts, lesson plans, classroom resources, assessment materials and on-line interactive resources." There is also a section for math misconceptions. Don't miss the project, The Mathematics Enhancement Programme, which offers school curriculum and teaching material (posted online) for mathematics for all grade levels with lesson plans, copymasters, and tests. Read articles from the International Journal for Mathematics Teaching and Learning.
Classroom Instruction that Works (2001) by Robert Marzano, Debra Pickering, and Jane Pollock includes nine research-based instructional strategies that have a high probability of enhancing student achievement for all students in all subject areas at all grade levels:
Identifying similarities and differences--graphic forms, such as Venn diagrams or charts, are useful
Summarizing and note taking--provide guidelines for creating a summary; give time to students to review and revise notes; use a consistent format when note taking
Reinforcing effort and providing recognition--you might have students keep a weekly log of efforts and achievements with periodic reflections of those. They might even mathematically analyze their data. Find ways to personalize recognition, such as giving individualized awards for accomplishments.
Homework and practice--vary homework by grade level; keep parent involvement to a minimum; provide feedback on all homework; establish a homework policy; be sure students know the purpose of the homework
Nonlinguistic representation--incorporate words and images using symbols to show relationships; use physical models and physical movement to represent information
Cooperative learning--consider common experiences or interests; vary group sizes and objectives. Core components include positive interdependence, group processing, appropriate use of social skills, face-to-face interaction, and individual and group accountability.
Setting objectives and providing feedback--set a unit goal and help students personalize that goal; use contracts to outline specific goals students should attain and grade they will receive if they meet those goals; use rubrics to help with feedback; provide timely, specific, and corrective feedback; consider letting students lead some feedback sessions
Generating and testing hypotheses--a deductive (e.g. predict what might happen if ...) , rather than an inductive, approach works best.
Cues, questions, and advance organizers--these should be highly analytical, should focus on what is important, and are most effective when used before a learning experience.
The authors caution, however, that instructional strategies are only tools and "they should not be expected to work equally well in all situations."
Concrete and Virtual Manipulatives Research: The George Mason University Mathematics Education Center focuses on the study of concrete and virtual manipulatives. You will find a list of published articles and abstracts on this topic.
Critical Thinking: Glazer, E. (2001). Using Web-Based Resources to Promote Critical Thinking in High School Mathematics. Wellington, New Zealand, NZAMT Annual Conference, July 3-6, 2001 Available: http://math.unipa.it/~grim/AGlazer79-84.PDF
The Critical Thinking Community comprises The Center for Critical Thinking and Moral Critique and the Foundation For Critical Thinking. "The work of the Foundation is to integrate the Center’s research and theoretical developments, and to create events and resources designed to help educators improve their instruction" (Mission). Resources are numerous at this site, particularly articles that define critical thinking and elaborate on the dimensions of critical thought. See Sample Teaching Strategies for K-12 Teachers and For Students, for example. Articles are relevant for teaching critical thinking within the mathematics classroom.
EduCore from ASCD is a free resource for "professional development, lesson plans and modules, and other materials—that you will need to successfully implement the Common Core State Standards for Mathematics and Literacy." The Math Tools section "features formative assessment lessons and instructional videos for mathematics aligned to the Common Core." Classroom challenges (formative assessment lessons developed by the Mathematics Assessment Project) are provided for middle and high school, concept development, problem solving, and include supplemental and related resources.
Everyday Mathematics algorithms for grades 2-6 and their animations from the publisher are among free resources and are also good for family use.
Helping Children Learn Mathematics (2002) is a short book (52 pages), available online, by the Mathematics Learning Study Committee and editors J. Kilpatrick and J. Swafford of the Center for Education at the National Research Council. The authors stress that mathematics proficiency involves five intertwined strands: understanding mathematics, computing fluency, applying concepts to solve problems, reasoning logically, and engaging with mathematics, seeing it as sensible, useful, and doable. Mathematics in grades K-8 should be taught for an hour a day. Time should be divided so that all of the strands receive adequate attention--the key being that instructional materials should integrate the five strands. All students can and should be proficient in mathematics.
Houghton Mifflin Math Education Place has teaching models and tools (glossary, online manipulatives, graphic organizers, games) associated with each of the chapters in their K-6 texts to help you teach concepts--excellent resource for methodology.
IMAGES: Improving Measurement and Geometry in Elementary Schools contains a discussion of cognitive and developmental issues related to designing and teaching an instructional unit to elementary students. Of particular interest are the Van Hiele Levels of Geometric Reasoning. Teaching strategies and assessment issues are addressed with how-to's, lesson plans and activities:
Inside Mathematics, which grew out of the Noyce Foundation's Silicon Valley Mathematics Initiative, is exemplary as "a professional resource for educators passionate about improving students' mathematics learning and performance. This site features classroom examples of innovative teaching methods and insights into student learning, tools for mathematics instruction [organized by grade level and subject] that teachers can use immediately, and video tours of the ideas and materials on the site" (Welcome section). The Ohio Department of Education developed a Correlation of Inside Mathematics Tasks to CCSS (Common Core State Standards) as of June 2010.
Instructional Methods Information by Dr. Bob Kizlik includes advantages, disadvantages, and required preparation related to using direct teaching, cooperative learning, lecture, lecture with discussion, a panel of experts, brainstorming, video tapes/slides, discussion, small group discussion, role playing, worksheets/surveys, guest speakers, and values clarification.
Instructional Strategies from Prince George's County Public Schools (MD) lists a variety of instructional strategies and research-based best practices, including performance-based instruction, portfolios, questioning, dimensions of learning, and cooperative learning.
Instructional Strategies Online from Saskatoon Public Schools (CA) includes five categories of instructional strategies and explanation of these five categories: direct instruction, indirect instruction, experiential learning, independent study, and interactive instruction. There are additional sections for instructional skills, and instructional methods by strategy.
Instructional Tools Related to Mathematics from Special Connections at the University of Kansas. Tools relate to building initial mathematical understanding and then extending it, building math proficiency (e.g., via instructional games), evaluating student needs and making effective math decisions.
Iowa Education Agency 267: Curriculum, Instruction, Assessment contains specific sections on content, instruction, assessment and alignment of all three.
Knowing and Teaching Elementary Mathematics is a 1999 book by Liping Ma, which includes examples from teachers explaining what it means to know and be able to teach elementary school mathematics. Richard Askey has an article by the same name in the Fall 1999 edition of American Educator in which he explains the relevance of this book. You'll be introduced to typical scenarios in the classroom, such as teaching subtraction and regrouping, multidigit multiplication, division by fractions, and the relationship between area and perimeter. The anniversary edition of the book was published in 2010 by Routledge; there is an excerpt in Google books.
LINKS Learning is an "E-learning site, [which] has involved Washington's Office of Superintendent of Public Instruction and partner organizations including the Technology Based Learning and Research Project at Arizona State University; the Washington school districts involved in the Washington Alliance for Better Schools; Carkhuff Thinking Systems; Limelight Technologies, Inc.; Fairfax County, Virginia schools; and Educational Service District 113 in Olympia, Washington." The Teacher Section for Math is designed to provide information and resources to assist teachers and others in understanding and providing high quality instruction for all students. You will find:
The math concept maps in Curriculum Planning are superb with examples of the key concepts for each of the five math content areas. When you click on the bolded concepts, you will see a definition and, in some cases, examples.
Mathematics Education: The Math Forum from Swarthmore College contains information on topics as assessment, block scheduling, calculus reform, collaborative learning, curriculum development, grouping and tracking, interdisciplinary math, math education reform, mathematicians, NCTM standards, and the WWW and pedagogy. See math resources for people with disabilities. Read about teaching issues/strategies and technology in math education.
Mathematics Models, by Paul Griffith, illustrates how teachers can use mathematical modeling as a methodology in a 4th-8th grade curriculum. Each page on this site includes a concept and basic models that accompany a lesson from Math Alive! (formerly known as the Visual Mathematics), which is a hands-on, concept-building curriculum that emphasizes exploration and discussion. The curriculum has been published by the Math Learning Center at Portland (Oregon) State University since about 1989. Teachers, parents, and students will benefit from the models that illustrate concepts. This is a very complete site to accompany your lessons.
National Center for Improving Student Learning & Achievement in Mathematics & Science has researched and produced documents of relevance for improving math achievement. Among those are: Algebraic Reasoning in the Elementary Grades (Grades K-5), Classroom Assessment as the Basis for Teacher Change (Grades 5-8--addresses role of formative assessment) Statistics in the Middle Grades (Grades 6-8)
The Most Common Errors in Undergraduate Mathematics have been articulated by E. Schechter of Vanderbilt University's Math Department, along with the likely causes of those errors, and their remedies. Dr. Schechter presents errors in communication, algebra errors, confusion with notation, errors in reasoning, unwarranted generalizations, and common calculus errors. Any teacher of upper level secondary mathematics will also benefit from this presentation, which should be shared with students--they make the mistakes after all. Pointing out these common errors as part of your teaching methodology might help students to become more successful in learning algebra and calculus.
Mathwire.com has a section on instructional strategies addressing active participation, cooperative learning, assessment, classroom management, and differentiation.
Northwest Regional Educational Laboratory Math Problem Solving Model "helps educators meet the challenges of teaching and assessing open-ended problem solving. The model includes a scoring guide for problem solving, open-ended tasks, and examples of student work for practice in scoring." The design of the model was informed by Robert McIntosh and Denise Jarrett's (2000) TEACHING MATHEMATICAL PROBLEM SOLVING: IMPLEMENTING THE VISION, which is a review of recent research and literature on the essential traits and processes of teaching and learning mathematics through open-ended problem solving.
Promoting Reading Strategies for Developmental Mathematics Textbooks by Anne E. Campbell, Ann Schlumberger, and Lou Ann Pate of Pima Community College presents three reading and study strategies designed to facilitate student comprehension of and learning from developmental mathematics textbooks. The discussion includes a preview, predict, read, and review reading strategy; concept cards; and a Question Answer Relationship technique. For example, concepts cards can include definitions, characteristics, examples, and nonexamples. Common kinds of concept cards in math include: (a) strategy cards for solving problems; (b) fact cards that include rules, laws, or theorems; and (c) cards for symbols and specialized vocabulary.
Supporting the Math Classroom through Literacy Development posted at Knowledge Loom: http://www.knowledgeloom.org . Strategies that support literacy development and understanding of math concepts include "Think Alouds, graphic organizers, word problems, brainteasers, math journals, Inquiry Models, Quick Writes, Word Walls, concept maps, flow charts, computer or graphic programming, creation of texts, Socratic Questioning, and WebQuests." The Northeast and Islands Regional Educational Laboratory at Brown University, Center for Resource Management, presents a series of articles illustrating how those strategies can be used in the high school mathematics classroom.
Teachersnetwork.org has a series of articles on how to teach math. Among resources are lesson plans, podcasts, and curriculum units for elementary, middle, and high school math.
Teachers' Domain states that it "is a free digital media service for educational use from public broadcasting and its partners. You’ll find thousands of media resources, support materials, and tools for classroom lessons, individualized learning programs, and teacher professional learning communities." You can search by content area, including mathematics, or by state standards, national standards from leading organizations such as NCTM, and Common Core State Standards. There is a section on teaching strategies.
Teaching Math to Young Children by Rick Garlikov is "one of a series of Web pages to help students understand math, and to help parents teach their children math -- especially to help children have a good foundation." Some other essays in this series include:
Access Center contains a number of information briefs on strategies for teaching K-8 math to all learners, and specifically for those with mild learning disabilities. For example, read about using mnemonic instruction, peer tutoring, computer-assisted instruction, the Concrete-Representational-Abstract Instructional Approach, direct/explicit instruction, learner accommodations and instructional modifications for students with learning disabilities, math differentiation, problem-solving strategies, graphic organizers, and more. Presentations such as Research Based Math Interventions are included. The Access Center is a national technical assistance (TA) center funded by the Office of Special Education Programs.
Center on Instruction: Mathematics offers materials and resources "to build educators’ knowledge of instruction for students with low achievement in mathematics, improve professional development models for math teachers, and build teachers’ skills in monitoring student growth toward important math outcomes." The Center on Instruction maintains a collection of scientifically based research for reading, math, science, special education and English language learners, and exemplars of best practice. It is one of five content centers serving as resources for the 16 regional U.S. Department of Education Comprehensive Centers.
Clearinghouse On Mathematics, Engineering, Technology, and Science (COMETS). http://www.rit.edu/~comets. National Science Foundation Grant HRD-9550468. Dr. Harry Lang of COMETS says, "Much of the information on this website has been developed from 20 years of teaching a methods course to prepare teachers for effective instruction of deaf students in science and math." K-12 teachers will appreciate the section on teaching tips and preparing a lesson for deaf students. Educators will appreciate the classroom teaching tips, lesson plans, links to science/math projects for deaf students, and bibliography of science/math education for deaf students. Additional resources are provided for pre-service teachers, college faculty, high school and college students, parents, administrators, and support personnel.
Citing work from Marsha C. Stevens and Madeline Hunter, Dr. Lang elaborates on the essential components of a lesson, which include:
- Check for Understanding
Dyscalculia.org addresses teaching and learning strategies for learners with dyscalculia (math LDs) and dyslexia (reading LDs). A diagnostic is available (fee attached), along with special education resources.
Learners with dyscalculia might benefit from a special calculator called the Dyscalculator. It is designed to assist with arithmetic by offering four different representations of quantities: as digits, as words, graphically, and spoken aloud. It can also round numbers. This app is designed for iPad, iPhone, or Android. Due to support from the Danish Ministry of Education, it is free until July 2013.
Education for All: The Report of the Expert Panel on Literacy and Numeracy Instruction for Students With Special Education Needs, Kindergarten to Grade 6 (2005) was financially supported by the Ontario Ministry of Education in Canada. The report recommends practices, based on research, "to improve and reinforce effective instruction of reading, writing, oral communication, and mathematics to students from Kindergarten to Grade 6 who have special education needs" (p. 1). However, practices discussed can enhance the learning of all students in mathematics and literacy. Chapters address Universal Design and Differentiated Instruction, Assessment and Evaluation, Developing Learning Profiles, Professional Learning Communities, Research to Practice: What Works for Both Literacy and Numeracy; Effective Instructional Approaches for Numeracy, Effective Instructional Approaches for Literacy, Organization and Management, Computer-based Assistive Technology, and Professional Development.
Learning Disabilities Online contains a series of articles with strategies for teaching mathematics to students with learning disabilities, but those strategies are suitable for use with all students. Read how to modify mathematics instruction to promote success and understanding in the areas of mathematical readiness, computation, and problem-solving; how use cooperative learning in the math classroom, and how to break math difficulties down into different types. Another article discusses techniques that have been demonstrated to be effective with secondary students who have learning disabilities in mathematics.
Learning Toolbox from the James Madison University Special Education Program contains tools and resources to enable students with learning difficulties to become better learners. Sections are devoted to secondary learners, teachers of middle and secondary students, and parents. Academic areas and strategies include organization, test taking, study skills, notetaking, reading, writing, math, and advanced thinking. Advanced thinking addresses organizing information sequentially, comparing and contrasting ideas, understanding categories, determining cause and effect relationships, and problem solving.
Math VIDS! "MathVIDS is an interactive website for teachers who are teaching math to students who are having difficulty learning mathematics. The development of MathVIDS was sponsored through funding by the Virginia Department of Education" (sec: Introduction). The site contains Foundational Information, Instructional Strategies, and Teaching Plans. Foundational Information is devoted to Math Disabilities and Metacognitive Strategies. The Instructional Strategies section describes and models fifteen, research-based effective math instructional strategies for students with learning difficulties. The Teaching Plans section provides detailed instructional plans and selected video models for teaching specific K-5 math concepts/SOL.
National Center on Accessible Instructional Materials: Learn about accessible media, policy, and practice.
National Center for Learning Disabilities includes a section on Dyscalculia--what it is, symptoms, how it is treated.
Signing Math Dictionary (SMD) is a math app by Vcom3D, compatible with iPhone, iPad, and iPod Touch. It is described as "an illustrated, interactive 3D sign language dictionary with 705 math terms defined in both American Sign Language (ASL) and Signed English (SE). The SMD is one in a series of fully animated, illustrated and interactive 3D signing dictionaries. The SMD is designed for grade 4-8 students who are Deaf or Hard-of-Hearing and use ASL or SE in the classroom. The SMD supports access to standards-based math content among elementary and middle school students" (Description section). While not free (about $15), it would also be a valuable tool for teachers and parents.
Special Connections, according to the Web site, "is a Project of National Significance (CFDA #84.325N) funded through the federal Office of Special Education Programs (OSEP) and coordinated through the University of Kansas. The ultimate goal of the project is to provide educators, both classroom teachers and university faculty, with tools and resources that support students with special needs in general education settings and in accessing the general education curriculum in meaningful ways. Four main areas of focus include Instruction, Assessment, Behavior Plans, and Collaboration." Tools for mathematics address building initial mathematical understanding, extending that understanding, building proficiency through games, evaluating student needs and making effective mathematics instructional decisions.
Teaching Math to Visually Impaired Students: S. Osterhaus of the Texas School for the Blind and Visually Impaired offers strategies and resources for teaching mathematics to visually impaired students. She provides links to math education and Nemeth code, tactile math graphics, calculators, current research in math for VI students and more.
TIPS for English Language Learners in Mathematics (2005) from the Ontario (CA) Ministry of Education includes grade-level support materials for those working with English language learners in Grades 7 to 10. "This resource contains models for adjustment of instruction for pairs, small groups, or the entire class and ways of differentiating instruction and assessment for English language learners so they can achieve literacy and mathematics goals. These adjustments in student groupings, teaching strategies, timing, and materials are based on recent research of ways to support English language learners" (Introduction, p. 1).
Center for Effective Collaboration and Practice has several miniwebs in relation to preventing behavior problems and appropriate interventions: Functional Behavior Assessment, Prevention Strategies that Work, Prevention and Early Intervention, and more. Several issues (e.g., cultural competence, school safety) are included with extensive resources.
Committee for Children addresses programs for prevention of bullying and violence, and includes a personal safety curriculum.
You Can Handle Them All, a Web site on discipline help for teachers and parents, lists over 100 behaviors (e.g., arrogant, class clown, cheater, disorganized, overly aggressive, whiner), the affect of each, actions to take to change the behavior, and mistakes in dealing with the behavior.
Connect Math to Everyday Life
As you strive to learn methods for presenting math concepts to students, don't neglect your need to connect math to your learners' everyday lives. Consider Scholastic MATH, an award-winning math magazine with 12 issues each year designed specifically for middle school and early high school students. Each issue also includes articles on real-world uses of math and how math is used in various careers.
Plus is an internet magazine which is free for educational and non-commercial purposes. It would appeal to learners aged about 15 and above. It aims to introduce readers to the beauty and the practical applications of mathematics. You'll find "articles, which describe applications of maths to real-world problems, games, and puzzles; reviews of popular maths books and events; a news section, showing how recent news stories were often based on some underlying piece of maths that never made it to the newspapers; a puzzle for you to sharpen your wits against; a lucky dip of mathematical curiosities; and opinions on various maths-related topics and news stories. [Plus also has] a regular interview with someone in a maths-related career, showing the wide range of uses maths gets put to in the real world." (About Plus section)
Need books on Math Methodology?
Association for Childhood Education International Among publications of interest is the book: Mathematics for All: Instructional Strategies To Assist Students With Learning Challenges, Editors: Nancy L. Gallenstein and Dodi Hodges, 2011. To purchase, call 1-800-423-3563.
ERIC (Education Resources Information Center). Search an extensive database using such keywords as mathematics, teaching methods, and mathematics instruction. ERIC offers over a million records for journal articles, books, research syntheses, conference papers, technical reports, policy papers, and other education- related materials.
isbn.nu has mathematics books at all levels. Use search phrases such as mathematics study teaching secondary or mathematics study teaching elementary. This site will then link you to a resource for purchasing the book.
National Academies Press: http://www.nap.edu/topics.php?browse=1 has over 4,000 books online, which you can read for free. For example, math educators might be interested in How Students Learn: History, Mathematics, and Science in the Classroom (2005) by Committee on How People Learn, A Targeted Report for Teachers, Center for Studies on Behavior and Development, National Research Council.
National Council of Teachers of Mathematics: http://www.nctm.org/catalog/. You might be particularly interested in the Navigations Series: http://www.nctm.org/catalog/product.aspx?id=13742, which translates NCTM's Principles and Standards for School Mathematics into action. The books highlight major math content areas in appropriate preK-12 grade-bands: algebra, data analysis, geometry, probability, measurement, problem-solving and reasoning.
Questia.com: http://www.questia.com/ promotes itself as the world's largest online library. Search using phrases like: teaching mathematics.
See other Math Methodology pages: