Problem Solving in Mathematics
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Transcript Problem Solving in Mathematics
PROBLEM SOLVING
IN
MATHEMATICS
Presented by
Dot Shea
2013
PROBLEM SOLVING
Newman’s error analysis states that a student
wishing to solve a written mathematics problem
typically has to work through five basic steps:
1. Reading the problem
2. Comprehend what is read
3. Carrying out a transformation from the words of
the problem to the selection of an appropriate
mathematical strategy
4. Applying the process skills demanded by the
selected strategy
5. Encoding the answer in an acceptable written
form.
http://www.curriculumsupport.education.nsw.gov.au/se
condary/mathematics/numeracy/newman/index.htm
1. READING THE PROBLEM
It is very important to always remember to read
the questions to the students when doing word
problems in mathematics.
What are you assessing?
The emphasis should be on the mathematics
understanding not the ability to read.
All testing of Mathematics (NAPLAN, PAT-M)
allows you to read the words (not numbers) to the
students.
There will always be students in your class who
have more ability in maths than reading.
It is important for these students to show their
full potential.
2. COMPREHEND WHAT IS READ
For a student to understand what they have read and know
what to do they need to understand what the words in the
problem mean.
Mathematical language can be very difficult to understand
and can be easily misinterpreted.
Students may:
not understand the spoken or written instructions-such as
‘draw a line between’..’ring’....or ‘find two different ways to’
Not be familiar with mathematical vocabulary-that is, words
such as difference, equation.......
be confused about mathematical terms-such as ‘odd’ or ‘table’
which have a different meaning in everyday language.
be confused about other words-like ‘area’, ‘fraction’ or ‘divide’
which are used everyday and have similar though more
precise contextual meanings in mathematics
It is vital to teach mathematical language explicitly and
have the words displayed so the students can refer to them
if necessary
3. TRANSFORMATION (STRATEGIES)
To work out a word problem the student needs to be
able to transform the words of the problem through
an appropriate mathematical strategy to solve the
problem.
Students need to be explicitly taught different
strategies they can use to approach a word problem.
Strategies such as:
Draw a picture
Guess and check
Act it out
Write a number sentence
Find a pattern
Work backwards etc
4. PROCESS SKILLS
Most teachers are very good at teaching skills
and the majority of students are able to do
process skills such as addition or multiplication.
Can they apply these skills?
“Research using Newman’s error analysis has
shown that 50% of errors occur before students get
to use their process skills. Yet many attempts at
remediation in Mathematics have in the past
over-emphasised the revision of standard
algorithms basic facts”
•
NSW Government Education & Communities
5 ENCODING THE ANSWER
When testing a student on their mathematical ability
the question may be in one format and the answers in
another format.
This means that the student often has to use their
prior knowledge to interpret the answer in the right
format.
Sometimes this is interpreted for you, such as in a
key in Graphs or maps but often there is an
assumption of prior knowledge such as the question
in grams but the answer in kilograms.
Students can make mistakes purely because the
answer is in a different format. The question might be
in a specific format such as a calendar but the
answers are in a different format such as a date.
NEWMAN’S PROMPTS
1. Read the question.- We need to read for meaning.
What word do you think it could be?
Is there another word you know?
2. What is the question asking you to find out? Locate the question.
What do you think it means?
What do you think you should do?
3. What could you do to get the answer?
What strategy could you use?
What information have you been given?
What do you know?
Can you record this in some way?
4. Can you solve it now?
What are the steps to your solution?
How do you record these steps so that it is understood by others not just you?
Carry out those steps.
5. Can you write your solution?
Have you answered the question?
Is your solution understood by others?
Is your answer in the right format
FISH
There are many different resources out there on how
to teach problem solving. It is important to
specifically teach problem solving, some students will
not know how to do it just by practicing.
Problem solving should be continually revised and
could be used as a 10 minute warm up exercise once it
has been taught.
The FISH strategy is a good way to teach problem
solving.
F- What am I asked to FIND? (include What do the
words mean?)
I- What INFORMATION do I already have?
What STRATEGIES and SKILLS do I have to solve
/do this task?
How reasonable is my solution. How do I know?
WHY TEACH PROBLEM SOLVING?
RESEARCH LINKS
Research based strategies for problem solving in maths
http://floridarti.usf.edu/resources/format/pdf/Classroom%20
Cognitive%20and%20Metacognitive%20Strategies%20for%
20Teachers_Revised_SR_09.08.10.pdf
Research paper on Problem solving strategies in
Mathematics-ACER
http://research.acer.edu.au/cgi/viewcontent.cgi?article=1022
&context=aer&seiredir=1&referer=http%3A%2F%2Fwww.google.com.au%2F
url%3Fsa%3Dt%26rct%3Dj%26q%3Dmath%2520problem%
2520solving%2520teaching%2520strategies%26source%3D
web%26cd%3D8%26ved%3D0CFEQFjAH%26url%3Dhttp%
253A%252F%252Fresearch.acer.edu.au%252Fcgi%252Fvie
wcontent.cgi%253Farticle%253D1022%2526context%253D
aer%26ei%3D_gSxUrvhMMWikwWviIDgCg%26usg%3DAF
QjCNGuMyq3cYKgXB4l1uSE_vbJPl8CKw#search=%22ma
th%20problem%20solving%20teaching%20strategies%22
WEB LINKS FOR TEACHING
PROBLEM SOLVING
Problem solving strategies
http://pred.boun.edu.tr/ps/
The Singapore Maths teacher- Maths problem solving
strategies
http://thesingaporemaths.com/stratf.html
New Zealand Syllabus- Problem solving activities and
teaching sequences
http://nzmaths.co.nz/problem-solving
The Franklin Institute-Open ended maths problemsnew ones each month
http://www.fi.edu/school/math2/
Problem solving in Maths- thinkquest
http://library.thinkquest.org/25459/learning/problem/