Transcript Inset - 22 March 2010 - Presentation (PPT, 132KB)

Thinking &
Reasoning Skills
Problem Solving
Aims of Session
• To develop a taxonomy of problem solving
skills relating to the specification
• To explore a range of problem solving
exercises related to the specification
• To understand the sorts of problem
solving exam questions which could evolve
from the specification
Key Starting Points
• Problem solving exercises and exam questions
can be in both word and numerical form
• Mathematical skills will never be above KS2
• Exam papers are likely to reflect the skills in the
specification more closely than the SAMs
• Problem solving questions can appear on both
papers, but are likely to have a greater emphasis
in unit 1
Skill 9 Specification
• Information processing and
problem solving
What information do we need to
extract in order to answer the
question or solve the problem?
Skill 9 Specification Content
• Scanning and skimming sources for relevant
information
• Identifying relevant data
• Recognising and identifying patterns
• Using simple matrices to organise data in
order to solve a problem
• Drawing conclusions from data
A Simple Taxonomy for Skill 9
Information Processing
• Scanning and skimming sources
for relevant information
• Identifying relevant data
• Recognising and identifying
patterns
Problem Solving
• Using simple matrices to organise
data in order to solve a problem
• Drawing conclusions from data
Scanning and skimming sources for
relevant information
Sorting Data
• Jigsawing activities where different pieces of
data are jumbled up.
• Sorting evidence according to which side of
an argument it supports.
Jigsaw Puzzle
• Take any two or three arguments and jumble
them up. The problem is to piece them back
together into two separate arguments.
• This can be extended by requiring argument
indicator words to be added into the arguments
or producing argument maps, thus also
requiring students to identify reasons and
conclusions.
Evidence Sorting Problem
• Take any dispute where evidence exists to
support either side of the dispute.
• Mix up the evidence and present the problem
to sort it into which pieces support which side.
• This can be extended to consider which
evidence is the stronger, which is the more
credible, etc.
Identifying relevant data
Extracting Data
• Selecting data from a range of items presented
Data Extraction Problem
• Students can be presented with any table of
data and asked to extract some key
information.
• Examples could be train timetables, exam
results, sport league tables, etc.
• The key skill is to identify the correct piece(s)
of data from amongst elements of irrelevant
data.
Recognising and identifying patterns
Analysing Data
• Odd-one-out puzzles
• Compare graphs with numerical data
• Number code puzzles
Odd One Out Puzzles
• These puzzles should require reasoning skills,
so the secret is being able to explain why it is
the odd one out.
• Try to present puzzles which can have more
than one correct solution.
• Puzzles should not require specific subject
knowledge to solve them.
Graphical Puzzles
• Present a table of fairly simple data.
• Turn this data into a graph (bar chart,
histogram, pie chart, etc.)
• Produce three or four similar looking graphs
and the puzzle is to work out which is the
correct one.
Using simple matrices to organise
data in order to solve a problem
Processing Data
• Matrix puzzles
Matrix Puzzles
• A matrix can be used to solve a puzzle where
a number of clues are given to match-up two
variables.
• Normally this will be in the form of identifying a
certain set of characteristics with a group of
named people.
• The puzzle is best solved by a process of
elimination
Drawing conclusions from data
Synthesising Data
• Data Synthesis puzzles
Data Synthesis Puzzles
• These are puzzles which require students to
use two or more pieces of data to solve a
problem.
• The skill is in synthesising the data, not in
mathematical calculation