Intro; Preface; Acknowledgement; Contents; List of Figures; List of Tables; Chapter 1: Introduction; How Did IBecome Interested inStudying Mathematical Content Understanding?; Swimming Upstream: My Research Path; Putting It All Together: This Book; References; Chapter 2: K-12 Mathematical Learning Experiences; Following theTeaching ofaBasic Mathematics Idea AcrosstheElementary, Middle, andHigh School Classrooms; First 2nd Grade Class: Tens andOnes: Are Students Provided Opportunities toLearn theDecimal Counting System andtheConcept ofPlace Value?
A High School Class: Honors Algebra 2-Do Students See Different Forms ofRepresentations (Equation andIts Graph) andAre They Able toSolve aProblem that Involves thePlace Value Concept?Nine Hundred Observations: No Teaching forMathematical Understanding; References; Chapter 3: Teachers' andMath Coaches' Understanding ofBasic Mathematical Ideas; Elementary Teachers' Responses; What WastheFocus ofTeachers' Responses?; Why WasThere aNeed toRegroup?; How Would Teachers Normally Teach This Topic?; Secondary Math Teachers' Responses
Response totheSlope Question: ASample Response Exhibiting Deep UnderstandingDefining Slope Formulaically asConsistent withtheK-12 Textbooks (Rise OverRun); Taking What Needs toBeProven asGiven (i.e., Circular Reasoning); When Similar Triangle Is Mentioned, How WasIt Used andforWhat Purpose?; Variation inStudents' Responses; What Do WeObserve Comparing Students' Responses totheResponse Exhibiting Deep Understanding?; Implications forMathematics Teachers' Content Training attheCollege Level; References
Second Grade Class: Two-Digit Subtraction withRegrouping-Do Students Understand theApplication ofthePlace Value Concept inThis Context?Fourth Grade Class: Four-Digit Addition andSubtractions withRegrouping-Do Students See theSame Application ofthePlace Value Concept with"Bigger" Numbers?; Beyond x's andy's: Dynamics oftheMiddle andHigh School Algebra Classes; An 8th Grade Class: Algebra 1-Do Students See theDifferent Forms ofRepresentations (Numbers andNumber Line; Symbols andDefinitions)?
What WasTeachers' Interpretation ofWhy Students Made Errors?What Were Teachers' Teaching Strategies?; Mathematics Coaches' Responses; What WastheFocus ofElementary Coaches' Responses?; Why WasThere aNeed toRegroup?; How Would Coaches Normally Teach This Topic?; What WastheFocus oftheSecondary Coaches' Responses?; References; Chapter 4: Undergraduate STEM Majors' Understanding ofSlope; Scenario Question Assessing STEM Majors' Understanding ofSlope; Why Slope?; What Is Slope? Review ofState Standards, Textbooks, andResearch; CCMS Approach toSlope
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Springer Nature
com.springer.onix.9783319712079
9783319712062
Engineering-- Study and teaching (Elementary)-- United States.
Mathematics-- Study and teaching (Elementary)-- United States.
Science-- Study and teaching (Elementary)-- United States.
Technology-- Study and teaching (Elementary)-- United States.