Tracy Curran, Cloneen NS - INTO

Keeping it Real!
Taking a fresh look at Problem Solving
in the Primary School Classroom
Tracy Curran
INTO 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 Strategies
https://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
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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
Going through a
Process
Modifying the
Question
• Trial & Error
• Look for Patterns
• Make a
supposition or
‘reasonable guess’.
• Act it out
• Work backwards
• Create a model
• 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 Curran
Tel: (087) 4101955
Email: [email protected]
In exponential times…
“There is no road…. We make the road by walking……”
Antonio Machado (1875-1939)