Problem Solving

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.

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.

That more investigational work is needed and mathematic knowledge needs to be better applied to everyday situations within the curriculum.

That there is weaknesses in problem solving despite teachers knowing its importance.

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

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.

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

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.

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

It is essential to develop mathematical vocabulary

It allows justification

Helps children discuss and choose a method

It allows an arguement

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.

When the route to the answer is not clear.

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.

A task that can be expected to be carried out and is a generic term.

When the route to the answer is not clear.

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

When the route to the answer is not clear.

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.

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.

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When the route to the answer is not clear.

It is a sustained exploration of a mathematical situation, it is distinguished from problem solving because it does not have one clear solution.

Improves mathematical attainment

Suitable for a wide range of attainment levels

Sustains pupils interests

It develops a disposition towards mathematics through attitudes and beliefs.

It allows a creative stand from the pupil

Requires complex thinking processes

Difficult to plan for abilities

Time consuming

Begin in with important information.

Not rushing into problems

Metacognition

Self-regulation

Being stuck is good

Standing back and reflecting

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

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)

- 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)

- Understanding the problem - Devising a pan - Carrying out the plan - Looking back

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

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

How can I get started

Is there a pattern

Can I break the problem down

Can I extend the solution

Can I work backwards or reformulate the question

Is the solution acceptable

Can I work backwards and reformulate the question

Can I extend the solution

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

That children should practice recognising problem types.

Practice recording

Practice representing problems

Practice reading

Practice selecting relevant information