Thinking & Reasoning Skills

1. Thinking & Reasoning Skills Problem Solving

2. 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

3. 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

4. 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?

5. 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

6. A Simple Taxonomy for Skill 9 • Problem Solving • Using simple matrices to organise • data in order to solve a problem • Drawing conclusions from data Information Processing • Scanning and skimming sources for relevant information • Identifying relevant data • Recognising and identifying patterns

7. 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.

8. 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.

9. 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.

10. Identifying relevant data Extracting Data • Selecting data from a range of items presented

11. 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.

12. Recognising and identifying patterns Analysing Data • Odd-one-out puzzles • Compare graphs with numerical data • Number code puzzles

13. 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.

14. 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.

15. Using simple matrices to organise data in order to solve a problem Processing Data • Matrix puzzles

16. 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

17. Drawing conclusions from data Synthesising Data • Data Synthesis puzzles

18. 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