Capturing Undergraduate Learning An Ako Aotearoa/TLRI Project Bill Barton, Judy Paterson, Greg Oates, Caroline Yoon The idea behind the Project #1 The team consists of 31 people, mostly from this department, and the funding body. We share the assumption that things can be improved. Indeed, we share an assumption of continual, rational development. How would you improve undergraduate learning? Think for a moment what you would do to enhance students’ undergraduate mathematics experience. How would you know that an improvement had taken place? The idea behind the Project #2 In this project we are turning our attention to learning ata class level. We want to understand how the way we deliver a course affects the student learning that results. The idea behind the Project #3 Yes, we do believe that we can significantly enhance learning in an undergraduate mathematics degree. Sources of this belief are: (i) research knowledge1 (ii) the questioning of the dominance of traditional lecturing2 (iii) our observations of the conservative response to the changing educational environment (technology3a, student body3b, economic pressures3c). 1. 2. 3a. 3b. 3c. D Holton (Ed.) (2002) The Teaching & Learning of Mathematics at University Level. The 11th ICMI Study. Kluwer Academic Pubs. A Ryan (2012) Massive Black Mirror. Times Higher Education, 4 October, 2012. This Department E. Anderson (2003) Changing US Demographics and American Higher Education, New Directions for Higher Education, No. 121 The assumption that lecturing to larger audiences is the only way to increase student/staff ratios. The idea behind the Project #4 But we do not believe in change for change’s sake. So, we want to establish a rational basis for the improvement of undergraduate teaching. That is the main idea behind the project. We aim to develop a way to know how a course contributes to the desired learning outcomes for undergraduate mathematics. Only if we can do this do we have a reason for changing the way we do things now. The idea behind the Project #5 NOTE: We do not expect that this research will result in fundamental change to all courses, or, say, the demise of lecturing. Rather, we expect that we will obtain evidence that different types of courses contribute to student learning in different ways, and therefore the department might decide to arrange things so that students have a range of opportunities to meet the learning expectations of lecturers and employers. Components of the Project Developing a Course Learning Profile 1. Identify the broad spectrum of desired learning outcomes 2. Find ways to observe these learning outcomes 3. Analyse and report learning outcomes for courses as a Course Learning Profile (CLP) Course Innovations 1. Team-based learning 2. Intensive Technology 3. Low lecture Project Extensions 1. Canterbury & Victoria Mathematics & Statistics Departments 2. Law, English, Psychology and Dance at Auckland Main Component of the Project Developing a Course Learning Profile 1. Identify the broad spectrum of desired learning outcomes 2. Find ways to observe these learning outcomes 3. Analyse and report learning outcomes for courses as a Course Learning Profile (CLP) Developing a Course Learning Profile Our first task is to identify, and categorise, ALL the learning outcomes desired in an undergraduate mathematics course. 1. 2. 3. 4. Those desired by the lecturers of the course Those desired by lecturers of subsequent and graduate courses Those desired by the university in Graduate Profiles Those desired by employers of mathematics graduates For Example 1. 2. 3. 4. 5. 6. 7. 8. Mathematical content Mathematical skills Mathematical processes Mathematical habits Attitudes towards mathematics Mathematical communication General thinking and learning behaviours ……. ???? Observing & Reporting Learning Outcomes 1. Mathematical content—examinations, assignments 2. Mathematical skills—examinations, assignments 3. Mathematical processes—observation in tutorials? specially designed tasks? 4. Mathematical habits—observations? self-report? 5. Attitudes towards mathematics—surveys 6. Mathematical communication—observations in tutorials? assignments? 7. General thinking and learning behaviours—self-report? class participation observations? 8. ……. ???? ???? Other Components of the Project Course Innovations 1. Team-based learning 2. Intensive Technology 3. Low lecture A Team-Based Learning model of delivery: 1. Shifts responsibility towards the students. 2. Provides feedback to students and lecturers. 3. Uses some lecture time for students to work in teams on tasks that apply ideas and concepts. 4. Allocates students to teams as fairly as possible for the duration of the course This approach is used in Maths 326 See www.teambasedlearning.org/ The Readiness Assurance Process (RAP) The students do a multiple choice test on the pre-reading. They then do the same test in their team. How? IF-AT scratch and win score cards Immediate feedback for students … the instant feedback makes sense - to learn from our mistakes and adapt to our environment this kind of testing is far more beneficial than a number out of 10 you receive a week later. Feedback to lecturers Feedback is most powerful when it is from the student to the teacher. When teachers are open to feedback from students, then teaching and learning can be synchronized and powerful. Feedback to teachers helps make learning visible. (Hattie 2009) Hattie J (2009) Visible Learning; a synthesis of over 800 meta-analyses relating to achievement London; Routledge • Business as usual for much of the course • What to do with the lecture time we saved? • Take a holiday? • Students do tasks in teams – apply ideas • What sort of tasks have proved successful? Example of a Maths 326 task – the team hands in one A4 sheet. • A parliament with 99 seats has three parties, A, B and C. Laws can be passed by a coalition of parties with at least 50 seats. • The largest party, C, splits into two factions. Investigate what happens to the power of the parties when party C splits into two smaller parties. • You might ask these or other questions about the shifts in power when a party splits: – Will the power of the two factions add to the pre-split power of Party C? – Can a dummy player gain power because of the split? – How much shifting in power can occur? A good solution to this task will ask and answer further questions about the effects of the split of Party C. What sorts of things do we want to take a long, hard look at? • What sort of questions do we hear students ask as they work? Are they good questions? • What evidence can we find of mathematical behaviour that we value – “I wish my students would……” • I am sure they are behaving more like mathematicians but how can I convince other people that it is happening? Other Components of the Project Course Innovations 1. Team-based learning 2. Intensive Technology 3. Low lecture Intensive Technology Innovation • We are talking about “Effective” use of technology, not indiscriminate use; • Its here, and its use is growing rapidly – we cannot ignore it if wish to prepare our students for mathematics in a modern age; • TSG 13: ICME-12: Teaching & Learning of Calculus - 17 presentations (12 countries); Technology was a major theme, even though two large Technology-specific TSG’s Ponce-Campuzano & Rivera-Figuero (Delta 2011): Value of CAS (various technologies) to reveal particular aspects, especially when considering domains of antiderivatives, where CAS may provide inconsistencies and alternatives to by-hand solutions. Compared the solutions provided by a variety of CASsoftware (Derive 6.0, Scientific Work Place 5.5, Mathematica 8.0, Wolfram Alpha) when used to compute antiderivatives of functions. The many examples where different CAS-technologies and by-hand computations yield different results are very interesting. Tasks & Assessment: Definitions Technology Trivial: 1999 Maths 102 2x 5 If f ( x) , find f ( x) 3x 1 Can still ask such questions in the skills tests for skills deemed necessary. Technology Neutral: 2007 Maths 108 Technology Neutral…… Thomas & Klymchuk (Delta 2011) Sketch the graph of a function f(x) such that it is continuous on 0 x 3 and 3 x 5, and f ( x) 0 for 0 x 5, x 3. Does limx3 f ( x) exist for your function? Technology Active (CAS-positive) Lin & Thomas – Proceedings of Delta 2011. Technology can help from an exploratory perspective, which will help understanding, but it will not answer the question directly. This is neither a technology neutral or technology trivial question. Technology Active – more examples Thomas & Klymchuk (Delta 2011) 1. If a 0 (2x 1) dx 2 find the possible values of a. 2. Find the derivative of the function: y ln2 sin(3x) 4 3. Find the derivative of the function: 1 1 dx 1 x Tobin & Weiss (Delta 2011): Use of CAS in differential equations in course examinations, ways of posing questions to be CAS-active. Question 1 Solve dy xy 2 y 2 x 4 for y as a function of x dx This question involves solving a first order separable differential equation which can be trivially done with just one command using CAS. Question 1A Show that the following DE is separable and hence or otherwise solve for y as a function of x. dy dx xy 2 y 2 x 4 This allows the testing of separability and still gives a chance for an answer to be found or checked by CAS, using an appropriate marking schedule. “Activating” technology trivial questions This can be quite time-consuming if you have a data-base of existing questions, and can take a while adjusting. However, it becomes easier & you gradually build up a new database. Example: Standard definite integration problems: Find 7 2 (3x 2 2 x)dx What might we do to transform such a question? Consider: If 7 2 7 ( fx)dx 20, find ( fx 4)dx How about: Still trivial? 2 b a b ( fx)dx c, find ( fx 4)dx a Often, technology-positive questions are more conceptually difficult than the standard skills-style questions we may have posed in the past; Other Components of the Project Course Innovations 1. Team-based learning 2. Intensive Technology 3. Low lecture Low Lecture Innovation The three key ideas behind this innovation are that: (i) lectures are not the best means of imparting information or developing skills, although they are useful for overviews, “colour”, and modelling; (ii) the best learning takes place when students are themselves engaged, both individually and together; (iii) responsibility for content and skills learning will be handed back to students using print and web resources, but with the means for self- and lecturer-monitoring of progress. Low Lecture Innovation A voluntary stream (max 32 students) of MATHS 108 will be established in Semester 2, 2013, taught by the research team as extra to load. One lecture per week. Five Engagement Sessions of 2hrs plus pre- and post-work. These substitute assignments. Tutorials, tests, exam all the same. Significant on-line resources and monitoring systems. Timelines Nov/Dec 2012 Identifying Learning Outcomes Observing Learning Outcomes Analysing & Reporting Outcomes Developing Innovative Courses Teaching & Observing Courses Summer 2013 Sem 1 2013 Sem 2 2013 Summer 2014 Sem 1 2014 Sem 2 2014 Summer 2015 ILIUM Investigating Learning In Undergraduate Mathematics LUMOS Learning in Undergraduate Mathematics and Other Subjects (or Operationalising the Spectrum) PLUMP Profiling Learning in Undergraduate Mathematics Project CLUMSY Capturing Learning in Undergraduate Mathematics Spectrum MULLET Mathematics Undergraduate Learning Lectures Engagement Technology CALCIUM CApturing Learning Concepts In Undergraduate Mathematics Learning Undergraduate Mathematics Capturing Profile Low Lectures Technology Team Based Learning Project Investigating Research Spectrum Send entries to Caroline ([email protected]) by midday 29th November Thank you for your attention … … and your future assistance. Bill, Judy, Mike, Greg, Caroline, Louise, Fiona, and Barbara and 23 others.