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Threshold Concepts      in Quants               Dr Richard Diamond               Enquiry Presentation                 18th...
Enquiry Aims and Activities•   Disciplinary application of the threshold concepts    approach to analyse quants (statistic...
Threshold Concepts Approach      Literature ReviewKey ReferencesCousin (2006), Davies and Mangan (2007), Meyer andLand (20...
What Is Threshold Concepts    Approach About?•   Recognising and focusing on central concepts in    contemporary ‘stuffed’...
Surface Learning Issues in         Economics• Students acquire formal knowledge of a  discipline but seem unable to use it...
Initial Findings from       Assessment DataDesign and Sampling• Three subsequently delivered modules of 14, 51 and37 parti...
Grades DistributionHighly discretised data bins give approximate Normal
Where is the mean?10% bins provide more difference between students
Surface                                          DeepLearners                                         Learners   Distribut...
Histogram Surface                            20                            18Learners                    16               ...
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 r...
Initial Findings from  Significant Correlations II• Scores in Chapters 1-3 have significant  correlation with subsequent res...
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 kno...
Technique Improvement:What has been tried in class
Visualisaiton• Visual simulations for complicated matters.  Examples: Type I and Type II errors in justice  system. Thousa...
Improvisation• Improvising with different meaningful data  sets on the go: downloading data from the  Internet, applying a...
Experiments with Assessment• Giving an integrating document such as a  final exam early, during the first workshop• Exam des...
Exam Design Pendulum in  Quantitative Disciplines• From solely multiple choice questions to  sections of several related q...
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 ...
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

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

  1. 1. Threshold Concepts in Quants Dr Richard Diamond Enquiry Presentation 18th May 2011Postgraduate Certificate in Learning and Teaching in Higher Education University College London
  2. 2. 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
  3. 3. Threshold Concepts Approach Literature ReviewKey ReferencesCousin (2006), Davies and Mangan (2007), Meyer andLand (2003, 2005), Land et al. (2005) and Meyer et al.(2008)
  4. 4. 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
  5. 5. 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)
  6. 6. 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
  7. 7. Grades DistributionHighly discretised data bins give approximate Normal
  8. 8. Where is the mean?10% bins provide more difference between students
  9. 9. Surface DeepLearners Learners Distribution is Multi-Modal Fitting to the Normal still leaves a problem with bins
  10. 10. 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
  11. 11. Group One28 SectionsGroup Two20 sections Amount of time spent indicates problem, not result
  12. 12. 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)
  13. 13. 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
  14. 14. Threshold Concepts forKnowledge Integration
  15. 15. Example of a conceptual map Notice multiple dimensions that link concepts
  16. 16. 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
  17. 17. Technique Improvement:What has been tried in class
  18. 18. 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
  19. 19. 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
  20. 20. 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
  21. 21. 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
  22. 22. This only scratched a surface of insight which thresholdconcepts approach can offer
  23. 23. Technical Slides
  24. 24. 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

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