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====== How students learn ======

In this section we describe what we have learned about how middle-division students learn:
    * [[.:features:start|Features of the Paradigms Curriculum]]
    * [[.:Sequences:start|Sequences of Activities]]
    * [[.:Labs:start|Upper-Division Labs]]
    * [[.:AAPT09Cognitive|Cognitive Issues in Upper-Level Physics Courses]]
    * [[.:Narratives:start|Narratives of Classroom Practice]]
    * [[.:Writing:start|Writing]]
    * [[.:Harmonic:start|Geometric & Harmonic Reasoning]]
    * [[.:bridge:start|The Geometry of Vector Calculus]]
    * A Short List of [[.:DontKnow:start|Things Students Don't Know]]
    * [[.:Notation:start|Student Problems with Notation]]
    * [[.:Spoonfeed:start|Spoonfeeding?]]
    * [[.:Variables:start|Variables v. Constants]]
    * [[.:Current:start|Student Understanding of Current]]
    * [[.:PhiHat:start|What's Right with $\hat{\mathbf{\phi}}=\phi/|\phi|$ : Student Understanding of Vectors and Scalars]]
    * [[.:CylSph:start|Cylindrical and Spherical surface integrals]]
    * [[.:MultipleRepresentations:start|Multiple Representations and Touchstone Examples]]
    * [[.:typical:start|Typical Upper-Division Problems]]

The rest of these are drafty-drafts.  Read at your own risk:
    * [[.:AssessNonCotent:start|Assessing Non-Content Goals]]
    * [[.:Differentials:geometry:start|Differentials: Sensemaking and Geometry]]
    * [[.:Representations:UpperDiv:start|Representation Issues in Upper-Division Physics]]
    * [[.:Representations:QM:start|Representation Issues in Quantum Mechanics]]
    * [[.:Representations:Thermo:start|Representation Issues in Thermodynamics]]
    * [[.:Representations:EM:start|Representation Issues in E&M]]
    * [[.:Representations:CM:start|Representation Issues in Classical Mechanics]]
    * [[.:IntroContent:start|Intro Physics Content that Students Still Struggle with in Upper-Divison Courses]]
    * [[.:Content:start|Content Order]]
    * [[.:Curriculum:start|Constructing Curriculum]]
    * [[.:Sensemaking:start|Sensemaking]]
    * [[.:SayingDoing:start|Saying vs. Doing]]
    * [[.:ProblemSolving:start|Problem-solving]]
    * [[.:Reflection:start|Importance of Reflection]]
    * [[.:Logic:start|Importance of Logical Argument]]
    * [[.:Story:start|Storytelling]]
    * [[.:Concept:start|Concept Maps]]
    * [[.:Laughter:start|Importance of Laughter]]
    * [[.:Touchstone:start|Touchstone Problems]]
    * [[.:Hostility:start|Enjoy Temporary Hostility]]
    * [[.:ChopAndAdd:start|Integration as Chopping, Multiplying, and Adding]]
    * [[.:ChopCorrelateDivide:start|Derivatives as Chopping, Correlating, and Adding]]
    * [[.:FieldRepresentations:start|Relationship between electric field vectors, electrostatic potentials, and electric field lines]]
    * [[.:Conversations:start|Classroom Conversations]]
    * [[.:Mathdecision:start|Mathematical Decision Making]]
    * [[.:PCK:start|Pedagogical Content Knowledge]]
    * [[.:Ways of Posing Questions]]
    * [[.:Relation between small group conversations and reports]]
    * [[.:Cuing mini-lectures]]
    * [[.:mmm:start|Teaching the Murder Mystery Method]]
    * [[.:conventions:start|Our Choices of and Reasons for Conventions]] 

    * [[.:Miscellaneous comments from 100107PrefaceCorinne]]
    * [[.:PDM:start|Partial Derivative Machine]]