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Matti Pauna SOED 2016
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- 5. Online Calculus Each module contains • YouTube videos • Reading materials •Quizzes (Automatic assessment) • Workshops (Peer assessment) • Discussion forum, calendar, gradebook, etc.
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- 9. Course Design Supports individualstudy paths
- 10. Online Calculus Courses • Single Variable Calculus 2004 • Calculus I & II •Advanced Calculus 2013 (Real analysis) Completeness property of real numbers with ℇ - 𝛿 proof method • Option to take UH undergraduate Calculus curriculum completely online and in English 2014
- 11. Online Course Content Credits Traditional Course ContentCredits Calculus I Limits, Differentiation, Antiderivatives, Riemann Sums 8 Limits Completeness, Supremum, Theory of Limits 5 Calculus II Advanced Integration, Improper Integrals, Convergence of Series, Taylor Series 8 Differentiation Continuity, Bolzano’s Theorem, Differentiation 5 Advanced Calculus Completeness, Continuity, Bolzano- Weirstrass Theorem 6 Integration Riemann Sums, Antiderivatives, Improper Integrals 5 Series Convergence of Series, Taylor Series 5 Total ECTC credits 22 20
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- 13. Mathematical Competencies (Pointon & Sangwin 2003, Rämö, Oinonen, Wikberg2015) 1. Factual recall 2. Carry out a routine calculation or algorithm 3. Classify some mathematical object 4. Interpret situation or answer 5. Proof, show, justify (general argument) 6. Extend a concept 7. Construct example/instance 8. Criticize a fallacy 9. Information transfer
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- 17. Automatic & Immediate Feedback • Systems such as STACK and WeBWorK take student’s answer as a mathematical object •Evaluate whether the answer satisfies the mathematical properties required • Give feedback also about common misconceptions • Assessment is objective: The same criteria are consistently applied to all answers
- 18. Peer Feedback Workshop module in Moodle: 1. Students are given homework problems asking a complete and clear presentation of a solution. 2. After the submission deadline, an example solution is provided 3.According to the model solution and assessment instructions, students grade and give constructive feedback to other students even to yourself Pedagogical goals: • Students study example and other studens’ solutions • Learning from other ways to solve, common mistakes and provide corrective feedback • Creates interaction between students in an online course • Scalable to MOOCs
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- 21. Assessment Data • Each action is logged: Clickstream data about behavior in an online course • Attempts, answers, scores in quizzes •Workshop submissions, grades & feedback given and received • Questionnaires about learning styles, self-efficacy, motivation
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- 30. Conclusions • E-Assessment is becoming more popular in Finland • Digitalizing teaching not in the core of the institution or because of lack of resources •Imaginative ways to assess higher competencies automatically • More data becoming available (Spring 2016: statistics courses 900 cases)