ED1635 Lecture Notes - Lecture 2: Problem Solving
Mathematics - Lecture 12 - Week 12
Problem Solving
Problem Solving
- Problem – a situation where there is no immediate and obvious solution
- Problem-solving is a mental process that involves discovering, analysing and solving problems. The
ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue
(Reed, 2000).
- Problem solving sits at the heart of mathematics
Features of a problem
- It must begin where the students are – socially, developmentally and mathematically.
- The problematic or engaging aspect of the problem must be due to the mathematics that the students
are to learn – content is the focus in the maths classroom but context is also important.
- It must require justifications and explanations for answers.
Levels of Cognitive Demand
Problem Solving
- Well chosen problems encourage:
Deeper exploration of mathematical ideas
Build persistence
Encourage thinking strategies
Encourage looking for relationships and patterns
Encourage sense making
Polya’s Four Step Model
- Understand the problem (See)
- Devise a plan (Plan)
- Carry out the plan (Do)
- Look back (Check)
1. Understand the problem
- Read for the meaning
- Work out what information is required
- Think about the processes that might be needed
- Reflect on other problems that are similar
- Ask what the solution might look like when the problem is solved – imagine and anticipate
Newman Analysis
Anne Newman (1977) identified that students may have difficulty
Reading the words
Understanding what they have read
Transforming what they have read so as to be able to form a course of action
Following through on procedures
Encoding the result of a procedure to answer the question
Questions that may help you lead students to an understanding of the problem
What are you asked to find or show?
What type of answer to you expect?
What units will be used in the answer?
What do you estimate the answer to be?
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Problem a situation where there is no immediate and obvious solution. Problem-solving is a mental process that involves discovering, analysing and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue (reed, 2000). Problem solving sits at the heart of mathematics. It must begin where the students are socially, developmentally and mathematically. The problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn content is the focus in the maths classroom but context is also important. It must require justifications and explanations for answers. Carry out the plan (do: understand the problem. Think about the processes that might be needed. Reflect on other problems that are similar. Ask what the solution might look like when the problem is solved imagine and anticipate. Anne newman (1977) identified that students may have difficulty.
