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## Test & Learn – 2 ways of helping Learning

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**Test & Learn – 2 ways of helping Learning**Jon Sims Williams Mike Barry Engineering Mathematics University of BRISTOL,UK.**A Learning Cycle – Test & Learn - TAL**Attend Lecture take test Or Read Book revise Take specialised test**TAL – Test & Learn - www.tal.bris.ac.uk**• TAL is a Computer Assisted Assessment System • The Core element is an Oracle Database • The database stores questions and student data • about 2000 questions on Mathematics • Both staff and students can talk to TAL from a web browser from home or work**Delivery of Support through Tests**• Tests provide students with encouragement • Tests tell students where they do not understand • Tests can provide feedback on questions to help students who don’t understand • TAL will build sets of tests that are all on the same topics; take about the same length of time to do and are about of equal difficulty**Question :Given x, y, z are real quantities and a, b integer**powers, show that the indices in the identity (xayz-1)b(2yz2)2(x/y)a = 4(x6z)2 must be one of the following. Specify which is correct. Answer1:a = 4, b = 2 Feedback: Correct. Answer 2:a = 2, b = 4 Feedback:No. Multiply out and then equate powers of each variable x , y and z in turn Answer 3: a = 3, b = 2 …… TAL Classification: mathematics/Algebra/ Equating powers in identities Facility: 50% Time-to-do: 90 seconds Theory: 3 Function Type: Simple algebraic functions Evaluationtype: Numerical Example Multiple Choice Question**Part of Subject Classification**• Algebra • Arithmetic • Complex Algebra • Differentiation • Chain; product; ratio rules • Differentiability • Equations of lines • Function of function rule • ….. • Fourier Series • Functions • Etc.**TAL and Maths Classification**• Weissteins World of Maths – http://mathworld.wolfram.com/ • The European Society for Engineering Education, SEFI syllabus for Core Zero http://learn.lboro.ac.uk/mwg/core.html**A small sample from the SEFI syllabus**• Analysis and Calculus • Rates of change and differentiation • Average & instantaneous rates of change • Definition of derivative at point • Derivative as instantaneous change rate • Derivative as gradient at a point • Difference between derivative & derived function • Use notations: dy/dx, f(x), y etc.**A Theory of Successful Learning**successful learning = Ease_of_Learning * Motivation**A Learning Cycle – Test & Learn - TAL**Attend Lecture take test Or Read Book revise Take specialised test**A Theory of Successful Learning – revisited**successful learning = Motivation* Ease_of_Learning**The Camera’s Histogram records the number of pixels with**each of 255 illumination levels, grouped as shown.**How does the camera display the histogram**• For each of the 255 illumination levels, cj that the camera can recognise it will do a test to see if the illumination level, I satisfies: cj < I < cj+1 • count the number of pixels that satisfy this constraint. • This then forms the height of the histogram at the point corresponding to cj**Pedagogy Support 2**• Example of Motivation but suppose the students did not understand support webpage • So we need to find out why. • Pedagogy Support 2 is a trace of the syllabus back from any point. So we start from Histograms.**Trace back through syllabus**• Interpret data presented in the form of histograms Requires: • • understand the Cartesian co-ordinate system • • plot points on a graph using Cartesian co-ordinates**plot points on a graph using Cartesian co-ordinates**requires: • Algebraic expressions and formulae • add and subtract algebraic expressions and simplify the result • understand the terms direct proportion, inverse proportion and joint proportion • solve simple problems involving proportion • interpret simple inequalities in terms of intervals on the real line**Summary – 2 ways to support learning**• Automatic feedback from the question topic to a website to help the student • Trace back through syllabus to find source of problem • Contact: • Jon.sims.williams@bris.ac.uk to use TAL • Mike.Barry@bris.ac.uk for syllabus tracking