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Promoting active learning in Mathematics – a ‘Problems First’ approach.

Promoting active learning in Mathematics – a ‘Problems First’ approach. Donal Healy Martin Marjoram Ciaran O’Sullivan James Reilly Paul Robinson. 5 th Annual Conference in Mathematics and Statistics Service Teaching and Learning IT Carlow 24 th and 25 th May 2010.

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Promoting active learning in Mathematics – a ‘Problems First’ approach.

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  1. Promoting active learning in Mathematics – a ‘Problems First’ approach. • Donal Healy • Martin Marjoram • Ciaran O’Sullivan • James Reilly • Paul Robinson 5th Annual Conference in Mathematics and Statistics Service Teaching and Learning IT Carlow 24th and 25th May 2010 ITT Dublin May 2010

  2. ‘Problems First’ project Overview of Talk Problems First Brief background to project The 3 sub- projects: ‘Problems First’ for Mechanical Year 1 Group ‘Problems First’ for Pharmaceutical Science Year 1 Group Reflective Sheets in Key Skills Testing in Electronic Engineering Year 3 Layout for each description: Implementation Student Feedback Effectiveness of approach Lessons Learnt ITT Dublin May 2010

  3. ‘Problems First’ Project - Background • Motivation: ongoing challenge engaging students in active learning in mathematics • Move from traditional to total enquiry based approach daunting • Approach of incremental change in delivery is under investigation at the ITT Dublin. • Funded by SIF CONTINUE Innovations in Teaching, Learning, and and/or Inclusive Education Project • Main aim - encourage active learning ITT Dublin May 2010

  4. ‘Problems First’ Project - Background • Staff identified areas or aspects of 3 existing Mathematics module to be modified to • improve student engagement with the module • increase student reflection on their learning • hence lead improve learning • Designed questionnaire for evaluation of student experience of this approach ITT Dublin May 2010

  5. ‘Problems First’ for Mechanical Year 1 GroupWhy? • Mathematics 1 module, 1st semester level 7 degree in Mechanical Engineering • 6 review sections at beginning of module. • 40% of the overall course • Lecturer unhappy with traditional approach for review part • New approach(Christenson input at 2008 SEFI 14 (MWG) conference) • materials to be studied are introduced via problem sets given to the students to work on first • followed with a subsequent lecture session to deal with any issues arising and to recap the material. ITT Dublin May 2010

  6. Implementation: (Mechanical Year 1) • For each of the 6 review sections: • students first given a problem sheet; this was augmented where necessary by input from the lecturer • What Happened: • Most sessions studentsworked on problems, lecturer helping individuals or small groups when his help was sought. • Some sessions were devoted to recapping and summarising key concepts that had arisen from the review problem sheets. • What was needed: • Class materials to enable this approach • Problem Sheets ( modified and added detailed solutions), • Topic notes ( Gap notes edited and filled) • Reflective diary template for the lecturer. ITT Dublin May 2010

  7. Student Feedback: (Mechanical Year 1) • Questionnaire • 4 point Likert scale: • Agree Strongly, Agree, Disagree and Disagree Strongly • 5 areas ITT Dublin May 2010

  8. Questionnaire ResponsesMechanical Year 1 (n =21) • most students agreed or agreed strongly in most statement categories. • In particular there was strong agreement regarding the materials used, the ease of asking questions and confidence in answering exam questions in these topics. ITT Dublin May 2010

  9. Effectiveness of approach: (Mechanical Year 1) • Comparisons of student performance between: 2009 ‘Problems First’ group and 3 previous academic years. • Benchmark prior attainment using Leaving Certificate Mathematics grade (points): • Mathematics 1 • Same lecturer • Method and standard of assessment components kept equivalent • All questions compulsory on the end of semester examination. ITT Dublin May 2010

  10. Effectiveness of approach: (Mechanical Year 1) • Two measures. 1. improvement in student mark between a one hour diagnostic test (administered at the first lecture) and an equivalent diagnostic test re-take (administered after the review material has been completed) 2. student performance on the end of semester examination Mechanical Engineering student performance comparisons. ITT Dublin May 2010

  11. Lessons learnt: (Mechanical Year 1) • Food for thought ! No short term improved learning of the review material Overall improvement in module performance. • Variation in test improvement scores and in examination performance was significant at p =1% level. • Used one–way ANCOVA (analysis of co-variance with for example year as factor , leaving certificate mathematics points as co-variate and test improvement score as response ) ITT Dublin May 2010

  12. Lessons learnt: (Mechanical Year 1) • Observations • an improved level of engagement by the 2009 student cohort • Evident continued student effort late in the semester • Statistically significant improvement at a p =1% level examination questions for topics covered later in semester, for example: • Future plan • Repeat the Problems First approach, • But refine of the materials and approach for the review sections using Insights recorded in the reflective diary key in informing changes. ITT Dublin May 2010

  13. ‘Problems First’ for Pharma Science Yr 1 Group Why? • Mathematics 1 module 1st semester level 8 degree in Pharmaceutical Science • Section traditionally ignored by this class • Not attempted by many in exam • Poor marks from those who did the question • Encourage students to engage with lecturer outside class hours • One hour less per week, class size doubled ITT Dublin May 2010

  14. Implementation: (Pharmaceutical Science Year 1) • Unseen problem • Groups of 4 • Terms not explained • 10 weeks • Series of introductory tasks • Regular opportunities to meet with lecturer ITT Dublin May 2010

  15. Questionnaire ResponsesPharmaceutical Science Year 1 (n =26) • There was strong agreement with the following statements: • The structure of the project enabled me to take more responsibility for my own learning • I felt comfortable asking questions relating to the project ITT Dublin May 2010

  16. Questionnaire ResponsesPharmaceutical Science Year 1 (n =26) • There was strong disagreement with the following statement: • I found the problem presented to be easy to follow ITT Dublin May 2010

  17. Effectiveness of approach: (Pharmaceutical Science Year 1) • Comparisons of student performance between: 2009 ‘Problems First’ group and previous academic year. • No significant difference in marks at 5% level • Perhaps not a bad thing given the circumstances! • Mathematics 1 • Same lecturer • Method and standard of assessment kept equivalent ITT Dublin May 2010

  18. Lessons learnt: (Pharmaceutical Science Year 1) • Introductory tasks completed to a very high standard • Main aims not achieved by most • Lack of engagement until shortly before deadline. Preliminary deadlines to be implemented in future • Final deadline earlier in semester. Most students who did finally engage seemed surprised and encouraged by the benefits ITT Dublin May 2010

  19. Mathematics Key Skills – Why? • Students do not bring key knowledge with them from one semester to the next • Students do not master the basics • Students need to refresh their key mathematics knowledge continuously BUT • Students will not concentrate on anything with no marks attached • In later semesters, the basics are not tested directly ITT Dublin May 2010

  20. Mathematics Key Skills – What? • Key Skills consists of • many categories of multi-choice questions • Designed to test material our students MUST be able to do. • Each question comes with immediate feedback and reference to a book chapter and an electronic resource. • the tests draw randomly from particular categories of questions • The tests are Moodle multichoice quizzes • We allow the tests to be repeated several times over a semester • Only a high mark is rewarded with credit • different tests • For different groups and in different semesters. • We test material from earlier semesters that we consider to be “Key Skills” for the current semester. ITT Dublin May 2010

  21. Key Skills Reflection Sheets Absence of Reflective Learning? While there was no systematic survey, many students admitted not working on Key Skills topics between tests and not having any record of the question categories they got wrong. We want students to be active learners and enforce a delay (usually of several days) between tests to allow students to consider question feedback and review their test attempts. Reflection Sheets Since September 2009 a structured reflection sheet has been piloted in 3rd Year Electronic Engineering to prompt students to identify and record areas in which they need to do revision work ahead of their next test attempt. Actions must be filled in against some or all of the question categories they got wrong and the sheet returned before their next attempt. ITT Dublin May 2010

  22. Reflection Sheets - Implementation Reflection Sheets Piloted since September 2009 Sheet must be returned to the lecturer before the student may repeat the test Actions must be filled in against some wrong answers Examples: 4 reflection sheets for 2 students (who sat 5 tests each). Student 1: Mark sequence: 8  8  8  13  13 Student 2: Mark sequence:6  6  8  10  13 ITT Dublin May 2010

  23. Student 1 Sheet 1(see handout ) ITT Dublin May 2010

  24. Reflection Sheets: Student Feedback • The reflection sheets themselves are a record of student feedback • Some students (as above) filled the sheets in very diligently giving detailed actions • Others were careless about which questions they got wrong and gave only generic actions, such as “studied” or “revised” • No detailed study done on content of sheets – the focus was on ensuring that a sheet was returned by every student before every repeat attempt and that every student scoring less than full marks on a test was provided with a sheet immediately and encouraged to mark the wrong answers immediately ITT Dublin May 2010

  25. Reflection Sheets: Effectiveness • For students taking more than one test • A much larger proportion of the group with reflection sheets reached the threshold level of 10 right answers (where they begin to get more than 0% for Key Skills). • Since the introduction of Reflection Sheets, there have been increases in: • The mean best score • The mean increase (1st test to best test) • The proportion of tests better than the previous test • The mean mark in the semester examination • [However, these increases for the most part are not large enough to be considered statistically significant.] ITT Dublin May 2010

  26. Reflection Sheets: Effectiveness Complication in Assessing Effectiveness In 2007 (the first year of Key Skills), students were allowed to compensate for poor Key Skills marks with their performance in their midterm test and semester examination. This led to some students not engaging fully in the process. Since 2008, the 15% for Key Skills is based solely on Key Skills performance. 2009 students (with reflection sheets) are compared to 2007 and 2008 students combined and to 2008 students only (where the reflection sheets were the only difference in approach). ITT Dublin May 2010

  27. Proportions Passing “Threshold” Fisher’s Exact Test: 2 × 2 Contingency Table of Passing Threshold of 10 Right Answers p-value: the probability that all of the students are from the same population and the proportions observed occurred randomly. ITT Dublin May 2010

  28. Mean Increase Mann-Whitney Test of the Hypothesis that the Mean Increase is Unchanged Notes: • “Increase” for each student = Best score – First Score. • Two sample t-test gives lower p-values. ITT Dublin May 2010

  29. Reflection Sheets: Lessons Learnt • It is strongly recommended that the reflection sheet be viewed as an essential element in implementing key skills testing. • The combination of using reflection sheets and offering no compensation for poor key skills performance seems to offer the best approach. Future Implementation • Efforts to improve the quality of students’ entries under “Actions” will be considered. ITT Dublin May 2010

  30. Any Questions? Thank you 30 ITT Dublin May 2010 ITT Dublin 2009

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