Logic: predicting and analysing
What is logic?
Logic is the study of reasoning. The purpose of logic is to help us try and make
sense of things: it helps us establish and check facts. Whilst there are different
types of reasoning in logic, the basic principle is to draw on existing knowledge
(premises) to make a conclusion. One example of logical reasoning is when pupils
make predictions in science investigations. Here they draw on existing knowledge
to make a prediction.
Using logical reasoning to make a prediction in science. All images from www.pixabay.com. Creative Commons
Deed CC0
As pupils experiment with computers, encourage them to use logical reasoning to
develop their understanding. In the photograph below the pupil is experimenting
with the mouse and observing the output on the screen. In doing so he is
developing his understanding of how he believes the mouse works.
As pupils tinker with computer systems they reason about the relationship between input and output.
All images from www.pixabay.com. Creative Commons Deed CC0
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Examples across the curriculum
As shown in the diagram below, in design and technology pupils may use logical
reasoning to predict suitable materials for different elements of projects, giving
reasons that match materials’ properties with their function in the design.
Pupil using logical reasoning to predict suitable materials in a design and technology project. All images from
www.pixabay.com. Creative Commons Deed CC0
Philosophy for Children
The philosophy for children programme encourages pupils to develop the skill of
reasoning.
Pupils are initially encouraged to give a logical reason for choices or statements
they make. This might include reasoning why characters from films or books are
good or evil, or explaining what it is about a superhero that makes them their
favourite. In doing so, pupils are drawing upon their existing understanding to
construct their reason. Pupils progress to take part in philosophical enquiries in
which they debate open ended questions generated through stimulus material.
In such enquiries, pupils are encouraged to comment upon the points made by
others as the discussion is constructed as a group, and in doing so develop their
skills in analysing and spotting flaws in arguments.
In debating how to improve their school’s break times for example a pupil might
present the argument: All pupils should enjoy their break times (premise) and
some pupils enjoy playing football (premise), so all pupils should play football at
break time (conclusion). Here there is an inconsistency in the argument in that
the second premise states only some pupils enjoy playing football and so the
conclusion that all pupils should play football to increase their enjoyment at break
times cannot be made.
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Comprehension: logical inconsistencies
Logical inconsistencies occur in texts when two propositions contradict each other.
Whilst either of the propositions could occur individually, it is the inclusion of both
that leads to a contradiction. An example being, ‘Tom turned off the light in his tree
house and quickly fell asleep. As Tom woke in his tent the sun was shining.’ Here
it is unclear what conclusion can be drawn about where Tom has slept as there is
a logical inconsistency in the propositions. Similarly films can contain continuity
errors, whereby there are inconsistencies over time in the events, characters or
objects we see in the film. Pupils can be encouraged to spot inconsistencies in the
texts they read as this helps highlight their level of comprehension. In the example
given here the inconsistency is easy to spot as there is minimal text between
strongly contradicting propositions. With a more subtle contradiction and greater
intervening passage of text such inconsistencies can be difficult to identify.
Why is logic important?
In computer science, logical reasoning helps us to explore and explain how
algorithms and programs work.
Computers are deterministic machines, so they follow the programs they have
been given exactly, every time. This means that logical reasoning helps us to
design and analyse programs, as well as predicting their outcome.
Program design
In order for pupils to design effective simulations, they must first analyse the
system they are aiming to model. They use logical reasoning to undertake such
analyses, identifying the rules, relationships and patterns which define the system.
Pupils may then use their knowledge of a programming language to work out how
to write a program to simulate the system. For example, we might be programming
a simulation of a clock in Scratch and need the second hand to turn through 6º
each second. Combining this with our knowledge of the commands in Scratch, we
could work out that the following commands should achieve this.
The commands predicted to achieve rotation of second hand in clock simulation programmed in Scratch.
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Analysis and debugging
Logical reasoning is also used to analyse and debug programs that are not
working. Decomposing programs into sections and using logical reasoning to
think through the input, process and outcome of each of these sections helps us
pinpoint the location of a bug in our program. The process of describing what a
program should do line-by-line and comparing this to what it does do is called
rubber duck debugging, in which a programmer debugs code by explaining their
program line-by-line to a rubber duck!
By changing the input for sections of our program and observing what happens,
we can also use logical reasoning to deduce an understanding of how a block of
code works and whether it matches our requirements.
In debugging a program we may first decompose the program into sections then use logical reasoning to think
through the input, process and output of each part to help identify and correct errors.
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Predictions
Imagine a KS1 pupil programming a Bee Bot and who has entered the forward
command three times. If we ask them to predict what will happen when the
program is executed, they may use logical reasoning to predict that the Bee Bot
will move forward three steps. In arriving at this prediction, their thought process
might be:
1. Pressing the arrow key once always makes the Bee Bot move forward one
space (Premise)
2. I have pressed the arrow key three times (Premise)
3. Therefore, the Bee Bot will move forward three spaces. (Conclusion/Prediction)
Combining knowledge of the Bee Bot commands and the
inputs entered, pupils can predict an outcome using logical
reasoning.
What does logic look like in the primary
curriculum?
EYFS
Pupils start to reason about the world around them. Teachers provide scenarios
for pupils to predict and test. In water play, pupils might predict that big things
sink small things float, to test this premise teachers might model trying different
things and then leave a balloon and a stone by the water tray. Pupils play with
mechanical and electronic toys to start to build up ideas about how these work.
KS1
Use logical reasoning to predict the behaviour of simple programs.
As pupils experiment with programmable devices, they reason about the
relationship between their inputs and the observable output. When using
programs, pupils use logical reasoning to predict the outcome of their interactions
with the mouse, keyboard or screen.
KS1
activity
World Map Logic Activity
Coming soon!
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Pupils also use logical reasoning to make predictions across the curriculum.
For example, pupils might predict how the sound of a drum changes as they
hit it harder or softer, or how the distance a ball travels differs when they throw
it harder. Teachers model how to think through problems, predicting what will
happen based on what they already know, reflecting on the result to change their
understanding.
Debug simple programs.
When programs aren’t performing as intended, such as a Bee Bot not reaching
the required location, pupils use logical reasoning to think through the steps in the
program to identify and fix the error (debugging). It is important for the teacher to
model a methodical approach to the debugging process, looking at each step of
the program in turn to pinpoint the error.
KS1
activity
Bee-Bots 1,2,3 Activity
KS2
Use logical reasoning to explain how simple algorithms work.
Pupils should explore and develop a range of algorithms and use logical
reasoning to predict their outcome. Examples might include algorithms for
mathematical calculations, for solving mazes, for guessing a number or for looking
up a definition in a dictionary.
KS2
activity
Logical Number Sequences Activity
Use logical reasoning to detect and correct errors in algorithms and
programs.
When algorithms or programs aren’t functioning correctly, pupils should employ
logical reasoning to debug these. They should ‘think through’ each step of an
algorithm or a program logically to detect the root of the error. Pupils may break
the program down into smaller elements first, testing each in turn to help in the
debugging process. Once they have identified the cause of the error, pupils use
logical reasoning to work out how this should be fixed so the algorithm or program
works as intended.
At key stage 2 pupils should become more independent in debugging their
programs, adopting the methodical approach of applying logical reasoning to
‘think through’ their program and identify the bug which they have had modelled
to them. They should also be aware of the value in debugging as they go and
be independently testing short sections of their program as they construct it.
Pupils may be introduced to the concept of rubber duck debugging whereby they
use logical reasoning to explain the function of their program line-by-line to help
identify and correct any errors.
KS2
activity
Drawing 2D Shapes Activity
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Find out more about logic
Different aspects of logic
A web page from www.fibonicci.com discussing logical reasoning
Miles Berry on Computational Thinking in Primary Schools
A set of 6 animations explaining critical thinking from Bridge 8
Wikipedia article on Logic in Computer Science
Wikipedia article on Logical Reasoning
BBC material on logic: The Joy of Logic, In our Time on the History of Logic.
Peter Millican’s site exploring philosophy and computing.
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