What does the national curriculum state?
That there is weaknesses in problem solving despite teachers knowing its importance.
How children should have varied and frequent practice with more complex problems over time to develop their conceptual understanding.
Increased focus is needed on the use and application aspect of mathematics.
What did ofsted find in 2012?
They found that there is weaknesses in problem solving despite teachers knowing its importance. Children’s investigative skills need to be developed as problem solving is integral to teaching.
That children should have varied and frequent practice with more complex problems over time to develop their conceptual understanding.
What does the Cockcroft report 1982 argue?
That more investigational work is needed and mathematic knowledge needs to be better applied to everyday situations within the curriculum.
What may have caused the move away from problem solving?
The national numeracy strategy which introduced the three part numeracy lesson but problem solving was seen as an add on and not integral to everyday mathematics.
The new curriculum
What did the Williams review n 2008 argue?
That investigative skills need to be developed as problem solving is integral to teaching.
That increased focus is needed on the use and application aspect of mathematics.
What is the general look of problem solving today?
Wide variety of problems
Currently problem solving is featured on a Friday where children apply their skills in word problems or at the end of the lesson during a plenary. Children often struggle as they have not got the problem solving skills they need.
Used occasionally
Not present
What needs to be the assessment within problem solving?
How children solve problems
Teachers need to know whether they want to assess their multiplication ect or problem solving in which they may not necessarily get their mathematics correct.
What did ofsted find in 2013?
That problems are mainly word problems within the classroom
That assessing problem solving is a weakness in trainee teachers practice.
That there is not enough problem solving
What is the importance of spoken language in problem solving?
It is essential to develop mathematical vocabulary
It allows justification
Helps children discuss and choose a method
It allows an arguement
What is a question?
A question which has a solution which involves routine procedures.
A task that can be expected to be carried out and is a generic term.
When the route to the answer is not clear.
What is an exercise?
What is a problem?
A problem can be a problem for some people and not for others depending on their prior understanding. 11 + 3 may be a problem in reception for example, but not a problem in year 2
What is problem solving?
It is engaging in a task for which the solution for the method is into known in advance
It requires a cognitive process to move from not knowing how to solve the problem to a state of knowing how to solve it.
What are the advantages of problem solving?
It provides insights into the structure of the subject matter
It develops a disposition towards mathematics through attitudes and beliefs.
It allows for higher order thinking
It is seen to be effective through inspection evidence
It allows children to improve their interest in mathematics
It is considered the real essence of mathematics (Orton, 1987)
It is the highest form of learning as children are likely to go on and solve similar problems (Gagne, 1970)
Burton (1984) It extends knowledge, is creative, interesting and provides confidence, enthusiasm and enjoyment.
How many types of problems are there?
3
4
5
6
What is an investigation?
It is a sustained exploration of a mathematical situation, it is distinguished from problem solving because it does not have one clear solution.
What are the advantages of investigations?
Improves mathematical attainment
Suitable for a wide range of attainment levels
Sustains pupils interests
It allows a creative stand from the pupil
What are the disadvantages of investigations?
Requires complex thinking processes
Difficult to plan for abilities
Time consuming
What are the key ideas when children are problem solving?
Begin in with important information.
Not rushing into problems
Metacognition
Self-regulation
Being stuck is good
Standing back and reflecting
Why is RUCSAC not sufficient or good to teach problem solving?
It it complex to understand
Only applys to selected word problems
Children can be stuck as they cannot read and therefore they cannot understand
It has different meanings
What is Polya 1957s model of problem solving?
I – Identify the problem D – Define and represent the problem E – Explore possible strategies A – Act on the strategies L – Look back and evaluate the effects of your activities
- Understanding the problem - Devising a pan - Carrying out the plan - Looking back
- Entry (how can I gets started, what does the problem tell me, extract information, test guesses, introduce a representation or form of recording) - Attack (is there a pattern, can I break the problem down/work backwards/reformulate the problem). - Review-Extension (check/is the solution acceptable/can I extend the solution/communication)
What is Brandford and Stein 1984s model of problem solving?
What is Burtons 1984s Entry level of problem solving?
How I can get started
What does the problem tell me
Is the solution correct
Test guesses
Introduce a representation and form of recording
Is there a pattern
What is Burtons 1984s Attack level of problem solving?
How can I get started
Can I break the problem down
Can I extend the solution
Can I work backwards or reformulate the question
What is Burtons 1984s Review level of problem solving?
Is the solution acceptable
Can I work backwards and reformulate the question
What sis Davis 1990 identify within problem solving?
Two simultaneous processes within problem solving, the first being building representations and the second being meta-analysis (Assessment of progress)
Reflective enquiry is seen as a key part of the problem solving process, this allows children to understand them more fully.
Children must practice problem types
What did Mayer 1985 identify?
That children should practice recognising problem types.
Practice recording
Practice representing problems
Practice reading
Practice selecting relevant information
