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University Press of America Common Misconceptions in Mathematics
Book SynopsisThis book should be a handy tool for teachers of mathematics as they develop plans to confront the problem of misconceptions, which are common with students that often have their own notion of certain mathematical concepts, right or not. The onus is on the teacher to detect those misconceptions and help students remedy them. This book is written for that purpose. Teachers could emulate the presented strategies that the book has elucidated. Teachers may also devise their own strategies based on the source of the misconception as presented in the book. The research segment of each identified misconception will be helpful if teachers want to apprise themselves with what the literature says about the concept. In general, the book is meant for teachers who want to help students engage in mathematics that emphasize conceptual understanding.Trade ReviewOne of the book’s strengths lies in its organizational structure. Teachers can easily navigate to relevant topics because each misconception section is organized and presented in the same way. . . .The author offers a wide range of potential solutions to correct each misconception. . . .The book offers a wealth of information that would be good for K–grade 12 teachers to have at their disposal. * National Council of Teachers of Mathematics *This book would be best used in undergraduate or master’s level teacher education courses that specifically address learning mathematics. . . .The descriptions of what teachers can do are useful and straightforward, and they discuss various ways for students to understand the concept of an algorithm. The research notes are useful summaries of research that has been conducted concerning each misconception; this research can be used as a platform for further investigation. * Mathematics Teaching in the Middle School *What a great idea for a book! What I really mean is, what a great idea for reaching teachers and helping them understand and teach mathematics better!...Being able to focus on one misconception at a time will allow teachers to think about and understand concepts more than they usually do. -- Janet Beery, Ph.D., mathematics professor, University of Redlands, CaliforniaThis book is a useful resource for the classroom math teacher as it provides many examples of student errors, and also provides some practical ways to help remedy such errors. -- Ramakrishnan Menon, PhD., mathematics education professor, George Gwinnett College, GeorgiaTable of ContentsIntroduction The Purpose of the Book Issues with Misconceptions What are Misconceptions in Mathematics? How do Misconceptions Come About? Why is it Important to Correct Misconceptions? Part One: Arithmetic Misconception 1: Addition Sentence Misconception 2: Subtracting Whole Numbers Misconception 3: Addition of Fractions Misconception 4: Subtraction of Fractions Misconception 5: Rounding Decimals Misconception 6: Comparing Decimals Misconception 7: Multiplying Decimals Misconception 8: More on Multiplying Decimals Misconception 9: Division of Decimals Misconception 10: Percent Problems Misconception 11: Division by a Fraction Misconception 12: Ordering Fractions Misconception 13: Least Common Multiple (LCM) Misconception 14: Addition of Decimal Numbers Misconception 15: Subtraction of Integers Misconception 16: Converting Linear Units Misconception 17: Power to a Base Misconception 18: Order of Operations I Misconception 19: Order of Operations II Misconception 20: Simplifying Square Roots Misconception 21: Comparing Negative Numbers Misconception 22: Addition of Negative Integers Misconception 23: Scientific Notation Misconception 24: Proportional Reasoning Misconception 25: Time Problem Part Two : Algebra Misconception 26: Dividing Rational Expressions Misconception 27: Adding Rational Expressions Misconception 28: Adding Unlike Terms Misconception 29: Adding Like Terms Misconception 30: Distributive Property Misconception 31: Writing a Variable Expression Misconception 32: Simplifying a Variable Expression Misconception 33: Factoring Misconception 34: Exponents Addition Misconception 35: Zero Exponents Misconception 36: Solving Equation by Addition and Subtraction Misconception 37: Solving Equation by Division and Multiplication Misconception 38: Fractional Equations Misconception 39: One-Step Inequality Misconception 40: Absolute Value Misconception 41: Operations with Radical Expressions Misconception 42: Simplifying Polynomials Misconception 43: Systems of Equations Conclusion References Appendix A: List of Manipulatives and their Uses Appendix B: Teaching Standards
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Random House USA Inc Brysons Dictionary of Troublesome Words
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Random House USA Inc Teach with Your Heart Lessons I Learned from the
Book SynopsisThe extraordinary memoir of the #1 New York Times bestselling author of The Freedom Writers Diary, who’s been hailed as “a true inspiration” (Hilary Swank) and “simply magical when it comes to inspiring people to action” (Los Angeles Times). Don’t miss the public television documentary Freedom Writers: Stories from the Heart In this passionate, poignant, and deeply personal memoir and call to arms, Erin Gruwell, the dynamic teacher who nurtured an extraordinary group of high school students from Long Beach, California, who called themselves the Freedom Writers, picks up where The Freedom Writers Diary—and the hit movie Freedom Writers—left off and brings the reader up to date on where the Freedom Writers are today. Including their unforgettable trip to Auschwitz, where they met with Holocaust surviv
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Springer Radical Constructivism in Mathematics Education 7 Mathematics Education Library
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Springer Mathematical Enculturation A Cultural Perspective On Mathematics Education 6 Mathematics Education Library
Book Synopsis1/Towards a Way of Knowing.- 1.1. The conflict.- 1.2. My task.- 1.3. Preliminary thoughts on Mathematics education and culture.- 1.4. Technique-oriented curriculum.- 1.5. Impersonal learning.- 1.6. Text teaching.- 1.7. False assumptions.- 1.8. Mathematical education, a social process.- 1.9. What is mathematical about a mathematical education?.- 1.10. Overview.- 2/Environmental Activities and Mathematical Culture.- 2.1. Perspectives from cross-cultural studies.- 2.2. The search for mathematical similarities.- 2.3. Counting.- 2.4. Locating.- 2.5. Measuring.- 2.6. Designing.- 2.7. Playing.- 2.8. Explaining.- 2.9. From universals' to particulars'.- 2.10. Summary.- 3/The Values of Mathematical Culture.- 3.1. Values, ideals and theories of knowledge.- 3.2. Ideology rationalism.- 3.3. Ideology objectism.- 3.4. Sentiment control.- 3.5. Sentiment progress.- 3.6. Sociology openness.- 3.7. Sociology mystery.- 4/Mathematical Culture and the Child.- 4.1. Mathematical culture symbolic technolTrade Review`Taking a refreshing noneurocentric position which refutes any suggestion that `West is best' as regards the development of mathematical thinking, Bishop sees mathematical development as being a function of the needs of whatever society in which it arises.' Tony Brown (Manchester Polytechnic), in Mathematics Teaching `This book is an informed, extremely rational and objective account of some aspects of enculturation and educational activity in the field of mathematics. I would recommend the book to all interested in mathematics education and curriculum design.' Kathryn Crawford (The University of Sydney), in Educational Studies in Mathematics `What is unique about Bishop's account is his attempt to specify and describe a universal set of activities that have supported and shaped the development of mathematics throughout the world.' J. Stigler, in Journal for Research in Mathematics EducationTable of Contents1/Towards a Way of Knowing.- 1.1. The conflict.- 1.2. My task.- 1.3. Preliminary thoughts on Mathematics education and culture.- 1.4. Technique-oriented curriculum.- 1.5. Impersonal learning.- 1.6. Text teaching.- 1.7. False assumptions.- 1.8. Mathematical education, a social process.- 1.9. What is mathematical about a mathematical education?.- 1.10. Overview.- 2/Environmental Activities and Mathematical Culture.- 2.1. Perspectives from cross-cultural studies.- 2.2. The search for mathematical similarities.- 2.3. Counting.- 2.4. Locating.- 2.5. Measuring.- 2.6. Designing.- 2.7. Playing.- 2.8. Explaining.- 2.9. From ‘universals’ to ‘particulars’.- 2.10. Summary.- 3/The Values of Mathematical Culture.- 3.1. Values, ideals and theories of knowledge.- 3.2. Ideology — rationalism.- 3.3. Ideology — objectism.- 3.4. Sentiment — control.- 3.5. Sentiment — progress.- 3.6. Sociology — openness.- 3.7. Sociology — mystery.- 4/Mathematical Culture and the Child.- 4.1. Mathematical culture — symbolic technology and values.- 4.2. The culture of a people.- 4.3. The child in relation to the cultural group.- 4.4. Mathematical enculturation.- 5/Mathematical Enculturation — The Curriculum.- 5.1. The curriculum project.- 5.2. The cultural approach to the Mathematics curriculum — five principles.- 5.2.1. Representativeness.- 5.2.2. Formality.- 5.2.3. Accessibility.- 5.2.4. Explanatory power.- 5.2.5. Broad and elementary.- 5.3. The three components of the enculturation curriculum.- 5.4. The symbolic component: concept-based.- 5.4.1. Counting.- 5.4.2. Locating.- 5.4.3. Measuring.- 5.4.4. Designing.- 5.4.5. Playing.- 5.4.6. Explaining.- 5.4.7. Concepts through activities.- 5.4.8. Connections between concepts.- 5.5. The societal component: project-based.- 5.5.1. Society in the past.- 5.5.2. Society at present.- 5.5.3. Society in the future.- 5.6. The cultural component: investigation-based.- 5.6.1. Investigations in mathematical culture.- 5.6.2. Investigations in Mathematical culture.- 5.6.3. Investigations and values.- 5.7. Balance in this curriculum.- 5.8. Progress through this curriculum.- 6/Mathematical Enculturation — The Process.- 6.1. Conceptualising the enculturation process in action.- 6.1.1. What should it involve?.- 6.1.2. Towards a humanistic conception of the process.- 6.2. An asymmetrical process.- 6.2.1. The role of power and influence.- 6.2.2. Legitimate use of power.- 6.2.3. Constructive and collaborative engagement.- 6.2.4. Facilitative influence.- 6.2.5. Metaknowledge and the teacher.- 6.3. An intentional process.- 6.3.1. The choice of activities.- 6.3.2. The concept-environment.- 6.3.3. The project-environment.- 6.3.4. The investigation-environment.- 6.4. An ideational process.- 6.4.1. Social construction of meanings.- 6.4.2. Sharing and contrasting Mathematical ideas.- 6.4.3. The shaping of explanations.- 6.4.4. Explaining and values.- 7/The Mathematical Enculturators.- 7.1. People are responsible for the process.- 7.2. The preparation of Mathematical enculturators — preliminary thoughts.- 7.3. The criteria for the selection of Mathematical enculturators.- 7.3.1. Ability to personify Mathematical culture.- 7.3.2. Commitment to the Mathematical enculturation process.- 7.3.3. Ability to communicate Mathematical ideas and values.- 7.3.4. Acceptance of accountability to the Mathematical culture.- 7.3.5. Summary of criteria.- 7.4. The principles of the education of Mathematical enculturators.- 7.4.1. Mathematics as a cultural phenomenon.- 7.4.2. The values of Mathematical culture.- 7.4.3. The symbolic technology of Mathematics.- 7.4.4. The technical level of Mathematical culture.- 7.4.5. The meta-concept of Mathematical enculturation.- 7.4.6. Summary of principles.- 7.5. Socialising the future enculturator into the Mathematics Education community.- 7.5.1. The developing Mathematics Education community.- 7.5.2. The critical Mathematics Education community.- Notes.- Index of Names.
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