Report

PROBLEM SOLVING A PILOT PROGRAMME WITH SECOND-YEAR STUDENTS SEAMUS KNOX (DES) FIONA LENNON (PMDT) TONY KNOX (PMDT) JOHNNY FLAHERTY (PMDT) Introduction Background • Purpose • Introduce students to collaborative problem solving • Motivate curricular content • Establish student response to the process • Project Design & Organisation • Partnership • Workshops • Laois Education Centre • School-Based • Project Website mathsprojectlaois.weebly.com • Content • Chat Student Profile • 18 students in total-9B,9G • 14 Average or Just above average • 4 Well above average • Half of the students listed Mathematics as one of their two favourite subjects • 14 enjoyed mathematics ‘most of the time’ in school • When asked if they liked mathematics all agreed or strongly agreed Workshop Structure • Minimal Instruction • Group work • Unseen Problems • Collaboration • Discussion • Internet Access • Presentation of Solutions • Homework • Research Topics • Feedback Workshop Content Workshop 1 • Introduction to GeoGebra • Car Park Problem • Paper Folding Workshop 2 • Constructions • The Euler Line • Napoleon’s Theorem Role of GeoGebra in facilitating a problem-solving approach • Strengths • Weaknesses Expanding Car park A client wants to double the area of his car park. He insists on retaining a square shape and as many of the trees as possible. • What is the best solution? Why Choose This Problem? • Interesting. • Many approaches. • Accessible. • Layers. • Linked to syllabus. • Lends itself to group work and promotes discussion. • Requires students to explain their thinking. Workshop Content Workshops 3 &4 • Basic Number Theory • Properties of number • Divisibility Tests • Sequences • Building on the students’ prior learning • Algebra • Factors • Place Value • Basic Expansions School Workshops Four in Total • Designed and delivered by students • Content • Delivery Model • Outcomes • Positives • Student Engagement • Response from the Delivery Teams • Response from Schools • Shortcomings • Too ambitious • Too much content • Too little exploration Student Responses Strongly Agree/ Agree I enjoyed participating in the project Disagree/ Strongly Disagree (%) 18 100% 0 0% Participating in the project increased my understanding of mathematics 17 94.5% 1 5.5% Participating in the project increased my appreciation of mathematics 18 100% 0 0% My approach to school work and homework in mathematics is different now 14 78% 4 22% I liked the way the workshops were organised (group work etc.) 18 100% 0 0% I enjoyed using GeoGebra to solve problems 16 89% 2 11% Student Responses Strongly Agree/ Agree I enjoyed solving problems in number theory (residue classes, divisibility tests etc.) Disagree/ Strongly Disagree (%) 17 94.5% 1 5.5% 16 89% 2 11% I enjoyed delivering the workshops to my fellow students 17 94.5% 1 5.5% Presenting the material in the workshops helped me to understand the material better. 17 94.5% 1 5.5% I would be prepared to participate in a further project in problem solving 18 100% 0 0% Participating in the project will help me when I meet difficult mathematics problems in future Student Responses Using GeoGebra (7) Doing the Sierpinski Patterns Group work, sharing opinions, collaborating (6) Problem solving Food (2) Discovering new material Divisibility Tests Describe the part (or parts) of the project you enjoyed most Applying the skills outside of school Creating worksheets for our class mates Looking at maths in a different way Presenting, (more time should be allowed) The Puzzles Residue Classes (simple and useful) The presenting, the puzzles, the use of GeoGebra Student Responses Waking up on Saturday morning (2) Nothing Euler Line (2) Solving very difficult algebra problems Number theory When it Ended Describe the part (or parts) of the project you enjoyed least Having to miss a class due to my brother’s confirmation There wasn’t any part I didn’t enjoy Having to present to my class mates I Didn’t enjoy the modular arithmetic that much Residue Classes-but I still enjoyed them Presenting to the class (2) GeoGebra (2) Student Responses Napoleon’s theorem, prime numbers, Circumcentre etc. How to work out problems to the full extent To read the question carefully I learned how to use algebra to prove things My problem-solving improved as a result How GeoGebra works and just thinking about numbers Not to overreact when faced with a problem but to take my time and figure it out What did you learn most as a result of participating in the project That with determination and hard work along with group work you can solve problems easily Have a better understanding of Maths It’s not about the answer it’s the approach you adopt How to approach problems It’s not about the end answer (sic) it’s about trying to figure it out. There are different ways of looking at maths There are multiple ways of looking at problems To approach questions differently and to figure out how I got the answer before writing down the answer If you want to do well at maths you have to work at it Would you like to see the approach used in the project being more widely used in mathematics lessons in schools ‘Yes’ responses @ 100%