TAILIEUCHUNG - The Mathematics Pre-Service Teachers Need to Know

Skill and automaticity with numbers is only part of the story. Students must also bring abstraction into play. This is also very commonly an uncon- scious process. There are huge numbers of choices for what to emphasize and what to exclude in real problems so as to focus on the core of what matters. Indeed, it is often far from clear what the core actually is. As was the case before, one has to practice to facilitate abstraction. How? One explores the situation, focusing on one area, then another, and accu- mulates sufficient data so that non-verbal tools in the brain can sort things out and focus on. | The Mathematics Pre-Service Teachers Need to Know R. James Milgram Department of Mathematics Stanford UNivERSiTy Stanford California 94305 E-mail address milgram@ The author was supported in part by a Grant from the . Department of Education. Any opinions findings conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the United States Department of Education. Copyright 2005 R. James Milgram. Permission granted to reproduce for educational purposes and distribute for cost of reproduction and distribution. For my students at the University of New Mexico and Skip Matthes. To my wife Judy my son Jules my daughter Jean and dedicated to the memory of Martha my .

• Toán học
• Business Edition
• provides multiple
• layers of protection
• unmatched defense
• against email
• borne threats
• Small business
• Accounting and finance for your small business
• Industrial management
• Business enterprises
• Small Business management
• New business enterprises management
• Operating the business
• Essentials of business communications
• Business communications
• Communications skill
• Business message
• Creating business message
• Proofreading business message
• 21st Century business entrepreneurship
• Business entrepreneurship
• 21st Century business series
• Business plan
• Business opportunity
• Careers for entrepreneurs Google
• Ebook Business process management
• Business process management
• Business process modelling
• Process choreographies
• Properties of business processes
• Business process management architectures
• Paul Smithson
• busines
• business document
• business ebook
• business specific study
• business research
• Social responsibility
• Strategic planning
• The business plan
• Existing business
• New business
• Evaluating the operations of the business
• Brown Smashwords Edition
• International small business
• Professional small business management
• Operations management
• Small business marketing
• Financial Statements
• Making business decision
• Business decision tool
• Lecture Accounting
• Business organization
• Business activities
• Foundations of business
• Being ethical
• Socially responsible
• Exploring global business
• Business ownership
• The management process
• Business communication
• Drafting business messages
• Revising business messages
• Planning business messages
• The digital age
• Intercultural communication
• Power system analysis
• Formal business reports
• Business presentations
• Business plans
• Sales messages
• Informal business reports
• Ebook Business research method
• Business research methods
• Information systems
• Theory building
• The business research process
• Enterprise systems architectures
• Business process modelling foundation
• Process orchestrations
• Decision Support Systems
• for Business Intelligence
• 2nd Edition
• r Business Intelligence
• DSS design
• DSS
• Careers for entrepreneurs LRMR
• Market your business
• Human resource management
• Marketing business
• Business environment
• Ebook The business environment
• Business organisations
• Political environment
• Macroeconomic environment
• Cultural context of business
• Business and Information
• integrated expertise
• business discipline
• broad based
• flexible business degree
• business or provide
• Smashwords Edition
• Rob Palmer