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Pedagogic Enquiry Presentation - Threshold Concepts in Statistics as a Discipline - Dr Richard Diamond
 

Pedagogic Enquiry Presentation - Threshold Concepts in Statistics as a Discipline - Dr Richard Diamond

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    Pedagogic Enquiry Presentation - Threshold Concepts in Statistics as a Discipline - Dr Richard Diamond Pedagogic Enquiry Presentation - Threshold Concepts in Statistics as a Discipline - Dr Richard Diamond Presentation Transcript

    • Threshold Concepts in Quants Dr Richard Diamond Enquiry Presentation 18th May 2011Postgraduate Certificate in Learning and Teaching in Higher Education University College London
    • Enquiry Aims and Activities• Disciplinary application of the threshold concepts approach to analyse quants (statistics and finance)• Identification of threshold concepts and effective learning pathways to navigate the webs of concepts• Analysis of VLE data (grades and time spent)• Analysis of student feedback (CATs and informal)• Reflection on and improvement of techniques for teaching, engagement and support
    • Threshold Concepts Approach Literature ReviewKey ReferencesCousin (2006), Davies and Mangan (2007), Meyer andLand (2003, 2005), Land et al. (2005) and Meyer et al.(2008)
    • What Is Threshold Concepts Approach About?• Recognising and focusing on central concepts in contemporary ‘stuffed’ curriculum• Linking thinking and practicing through re-working of prior naive or premature understandings (common sense vs. science)• Dealing with the troublesomeness of knowledge that stems from (a) opening up concepts deemed understood and (b) uncertainty about future understanding
    • Surface Learning Issues in Economics• Students acquire formal knowledge of a discipline but seem unable to use it when making sense of experience in work or their everyday lives• Students struggle with underpinning theory and resort to verbatim learning of isolated aspects of the subject that they are unable to juxtapose Davies and Mangan (2007:18)
    • Initial Findings from Assessment DataDesign and Sampling• Three subsequently delivered modules of 14, 51 and37 participants• Curriculum made ‘simpler’ from one run to next• Same textbook (Barrow 2009) and MathXL questions• Scores had a range of 1 to 100, presenting categorialand finely ranked data
    • Grades DistributionHighly discretised data bins give approximate Normal
    • Where is the mean?10% bins provide more difference between students
    • Surface DeepLearners Learners Distribution is Multi-Modal Fitting to the Normal still leaves a problem with bins
    • Histogram Surface 20 18Learners 16 14 Deep Frequency 12 10 Learners 8 6 4 2 0 30 40 50 60 70 80 90 0 e 10 or M Bin Distribution is Bi-Modal Reflects a transition through troublesome knowledge
    • Group One28 SectionsGroup Two20 sections Amount of time spent indicates problem, not result
    • Initial Findings from Significant Correlations I• Total time spent by students had no significant correlation with their results. Time spent per section had negative correlation with the section’s score• In order to score high overall, the students needed to score high for all chapters (grading emphasised particular chapters)
    • Initial Findings from Significant Correlations II• Scores in Chapters 1-3 have significant correlation with subsequent results (procedural thresholds being learned, especially in Chapter I)• Normal Distribution - Hypothesis Testing - Regression Modelling showed the strong triangle relationship. They are threshold concepts and procedures of Statistics
    • Threshold Concepts forKnowledge Integration
    • Example of a conceptual map Notice multiple dimensions that link concepts
    • Webs of Threshold Concepts• Two kinds of maps: local and grand• Learners should have some basic and threshold concept knowledge before being guided through the mapping• Maps are drawn in front of and together with learners and questions get answered
    • Technique Improvement:What has been tried in class
    • Visualisaiton• Visual simulations for complicated matters. Examples: Type I and Type II errors in justice system. Thousands of weight combinations to show the Efficient Frontier of a financial portfolio• Sketches of probability distributions. Example: finding any area under the Normal Distribution curve
    • Improvisation• Improvising with different meaningful data sets on the go: downloading data from the Internet, applying a statistical technique then soliciting interpretations and acknowledging or providing the most sensible.• Example: sorting hamburgers and coffee drinks in percentiles for the amount of fat
    • Experiments with Assessment• Giving an integrating document such as a final exam early, during the first workshop• Exam design: calculation question plus several interpretation questions (could be multiple choice)• Questions on interpretation aim to check the deeper understanding
    • Exam Design Pendulum in Quantitative Disciplines• From solely multiple choice questions to sections of several related questions that require calculation and interpretation• This was the case in how I developed my own exams (over three years) and exams done by colleagues elsewhere
    • This only scratched a surface of insight which thresholdconcepts approach can offer
    • Technical Slides
    • Type of Change Type of Transformation Examples in Business Statistics The concepts that have relevance to everyday Central tendency and dispersion experience. Mean vs. medianBasic Calculation skills and ability to identify a Standard Deviation statistical measure Probability (sources, ways of definition) Probability Distribution Acquisition of theoretical perspective--ability to Continuous vs. discrete see the world as a statistician. Hypothesis Testing. Significance Basic concepts are related to the outside worldDiscipline using discipline threshold concepts (e.g., mean Correlation and standard deviation can be plugged in to Regression probability distribution in order to describe a specific situation). Time Series Data Index (Same description as in quantitative finance, a Essential mathematical notation (summation with indexes) more intense area) Operation with equations. Polynomials Operations with percentages An understanding and mastery of the subject’s modelling procedures that enable the Meaning of greek lettersProcedural construction of discipline-specific models, Normal Distribution Tables arguments and ways of practising. Ability to visualise a distribution (use a sketch) “Mathematical Transformation” - “Magic of working through a proof” (there could well be other, lower level procedural threshold not covered) Types of Conceptual Change Discipline: Business Statistics