Keeping it Real!Taking a fresh look at Problem Solving in the Primary School Classroom

Tracy CurranINTO Consultative Conference – Sat 16th November 2013

Key Objectives

1. To examine the evolution of problem solving as a national concern

2. To take a fresh look at IMC – constructivism & problem solving

3. To examine some components of an effective problem solving lesson

4. To explore pedagogical challenges & changing role of the teacher

5. To provide a space for professional reflection on your practice.

References & Sources (include)

Anthony, G &, Walshaw, M (2009) Effective Pedagogy in Mathematics, International Academy of Education

English, L. and Halford, G. 1995. Mathematics Education Models and Processes, Hove: Laurence Erlbaum Associates.

Irish Primary Mathematics Curriculum & Teacher Guidelines (1999), Department of Education & Science

Matthews, M.R. 2000. Constructivism in Science and Mathematics Education. In D.C. Phillips (ed.) National Society for the Study of Education, 99th Yearbook, Chicago: University of Chicago Press.

National Council of Teachers of Mathematics, 2000. Principles and Standards for School Mathematics, Virginia: The National Council of Teachers of Mathematics.

Ng Wee Leng. (2008). Problem Solving Heuristics for Primary School Mathematics, A Comprehensive Guide. Singapore: Pearson Prentice Hall.

OECD (2010), PISA 2009 Results: What Students Know and Can Do – Student Performance in Reading, Mathematics and Science

Polya, G., 1945. How to Solve It. NJ: Princeton University

Charles and E.A. Silver (Eds), The Teaching and Assessing of Mathematical Problem Solving, USA: National Council of Teachers of Mathematics.

Sahid (2011), Mathematics, Problem Solving and Problem-Based Learning for Joyful Learning in Primary Mathematics Instruction, Seameo Qitep in Mathematics, Indonesia

www.pcsp.ie, www.pdst.ie

Mathematics vs. Numeracy?

Numeracy encompasses the ability to use mathematical understanding and skills to solve problems and meet the demands of day to day living in complex social situations

Literacy & Numeracy for Learning & Life 2011 p.9

Wordle

As a response to…

International Reports – PISA (2009)

26th out of 34 OECD Countries

National Standardised Testing Results (2009)

49% of 2nd class pupils performed least well in Applying & Problem Solving.

DES Incidental Inspection findings (2010)

Less than half (48.4%) of problem solving lessons observed involved collaboratively group work among students

The National Strategy to Improve Literacy & Numeracy among children and Young People 20011-2020 p.25

We need to equip teachers to develop student’s numeracy skills…Develop their own understanding of how mathematical concepts may be used in a range of

everyday applications Their ability to understand and communicate information presented in mathematical terms Their ability to explore, hypothesise and reason logically; and Their ability to use a variety of methods to solve problems

Ensure the development of young people’s skills in carrying out procedures flexibly and accurately

Infuse language, thought and meaning into mathematics teaching

Use open-ended challenging tasks that motivate young people to engage with problem solving in a meaningful way.

Enable young people to understand, appreciate and enjoy mathematics.

DES Recommendations

Schools should promote a stronger social constructivist perspective, including using problem solving to develop mathematical thinking.

Pupils should spend more time solving substantial problems, analysing and discussing problems with other pupils and their teacher.

Schools should make greater use of aggregated data (particularly standardised tests) to identify strengths and weaknesses across grade levels and curricular areas

So what’s the problem with problem solving?

‘‘The real voyage of discovery

consists not in seeking new landscapes

but in having new eyes’’

Marcel Proust

(French Novelist and Author, 1871-1922)

How many?

Constructivism

“A constructivist approach to mathematics learning involves the child as an

active participant in the learning process. Existing ideas are used to make

sense of new experiences and situations. Information acquired is interpreted

by the learners themselves, who construct meaning by making links

between new and existing knowledge”.

(Irish Mathematics Curriculum)

“…..This makes consultation, discussion and co-operation essential.”

(Teacher Guidelines p.3)

Ma & Pa Kettle http://www.youtube.com/watch?v=Bfq5kju627c

Common Misconceptions

Keeping It Real!

When students can use mathematics as a

tool for solving significant problems in

their everyday lives they begin to view it

as relevant and interesting

Anthony, G &, Walshaw, M (2009) Effective Pedagogy in Mathematics, International Academy

of Education. p16

Problem Solving in a nut shell

What is problem solving?

What are Word Problems?

Word Problem Strategieshttps://sites.google.com/a/pdst.ie/region5problemsolving/home/additional-materials-1/problem-solving-strategies-and-role-card

Word Problem Strategies https://sites.google.com/a/pdst.ie/region5problemsolving/home/additional-materials-1/problem-solving-strategies-and-role-cards

Mediums for teaching problem solving

Word Problems

Oral problems

Story Books

Mathematical games

Puzzles, brain teasers, mind-benders…

Mathematical trails

Problem solving and investigation using ICT

Practical tasks

Open-ended investigations

PROBLEM – BASED LEARNING – ‘I have a problem…’

TOOLKIT OF STRATEGIES

Giving a representation to a problem

• Draw a Diagram

• Make a systematic List

Making a calculated guess

• Trial & Error

• Look for Patterns

• Make a supposition or ‘reasonable guess’.

Going through a Process

• Act it out

• Work backwards

• Create a model

Modifying the Question

• Restate the problem

• Simplify the problem

• Solve part of the problem

Observation Task

Problem Solving Learning Environment

Active

Constructivist

Student-Directed

Dynamic

Centre of Creativity & Critical Thinking

Students construct their own understanding

Students build their own theories and ideas

Integration of Skills

Integrating Skills Development

Successful achievement of curriculum objectives will need a fresh approach to the interconnectedness between both

Framework for Problem Solving – Polya (1945)

1 •Understand the Problem

2 •Devise a Plan

3 •Carry out the Plan

4 •Look Back

1. Understand the Problem

Students must understand what the problem means by

identifying what the question needs to be addressed.

What information is already provided in the question?

What information is missing?

What assumptions and conditions must be satisfied?

Can you describe your understanding of the problem in your own words?

2. Devise a Plan

Students proceed to design a plan to solve the problem using a strategy from their toolkit.

Estimate the quantity, measure or magnitude of the solution

Look for a solution pattern

Select the appropriate strategy or strategies to solve the problem more effectively from your toolkit.

Is there a particular strategy or strategies that might help you? Why?

3. Carry out the Plan

Students implement the selected solution plan to find the actual solution of the problem.

Identify the calculations and apply the strategy that has been designed in the previous step.

Check for any mistakes as you work.

Have your selected the correct strategy? Is there a different strategy that might work better?

4. Look Back

Students reflect on the problem solution by asking the following questions

Was all the given information used?

Has the question in the problem been answered?

Does the answer make sense or is it reasonable? Have I made any computational mistakes?

Is the answer unique, or are there others?

Am I satisfied with the approach I used? Do I need to seek another solution strategy?

Changing Role of Teacher

Content Expert

Knowledge Imparter

Facilitator of Learning

Motivator

Problem Constructor

Self Reflection

What have been key messages for you from this presentation?

Contact Details

Tracy CurranTel: (087) 4101955

Email: tracy.curran@hotmail.com

In exponential times…

“There is no road…. We make the road by walking……”

Antonio Machado (1875-1939)