PROBLEM SOLVING A PILOT PROGRAMME WITH SECOND-YEAR STUDENTSSEAMUS 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 ContentWorkshop 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

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?

Expanding Car park

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 ContentWorkshops 3 &4

• Basic Number Theory• Properties of number• Divisibility Tests• Sequences

• Building on the students’ prior learning• Algebra

• Factors• Place Value• Basic Expansions

School WorkshopsFour 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

 

Disagree/Strongly Disagree

(%)

I enjoyed participating in the project  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

 

Disagree/Strongly Disagree

(%)I enjoyed solving problems in number theory (residue classes, divisibility tests etc.) 

17 94.5% 1 5.5%

Participating in the project will help me when I meet difficult mathematics problems in future 

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%

Student Responses

Describe the part (or parts) of the project you enjoyed most

Using GeoGebra (7)

Doing the Sierpinski Patterns

Group work, sharing opinions, collaborating (6)

Problem solving

Food (2)

Discovering new material

Divisibility Tests

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

Describe the part (or parts) of the project you enjoyed least

Waking up on Saturday morning (2)

Nothing

Euler Line (2)

Solving very difficult algebra problems

Number theory

When it Ended

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

What did you learn most as a result of participating in the project

Napoleon’s theorem, prime numbers, Circumcentre etc.

How to work out problems to the full extent

To read the question carefullyI 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

That with determination and hard work along with group work you can solve problems easily

Have a better understanding of MathsIt’s not about the answer it’s the approach you adopt

How to approach problemsIt’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%