Common Mistakes and Misconceptions in Evidential Breath Testing
Learning from mistakes and misconceptions. Aims of the session This session is intended to help us...
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Transcript of Learning from mistakes and misconceptions. Aims of the session This session is intended to help us...
Learning from mistakes and misconceptions
Aims of the session
This session is intended to help us to:
• reflect on the nature and causes of learners’ mistakes and misconceptions;
• consider ways in which we might use these mistakes and misconceptions constructively to promote learning.
Assessing learners’ responses
• Look at the (genuine) examples of learners' work.
• Use the grid sheet to write a few lines summarising:– the nature of the errors that have been
made by each learner;– the thinking that may have led to these
errors.• Discuss your ideas with the whole group.
Representations of a half
• Q 8 from Sats paper
Repesentations of a half
• Misconception: – that two halves of something need to look
exactly the same
• Causes:– Lack of variety in representations to which
pupils have been exposed– Limiting of fractions to ‘pizza’ representations– Lack of experience of fractions of quantities
Parallel and perpendicular
• Q 17 from Sats paper
Parallel and perpendicular
• Believes that parallel means two lines at 90 degrees to one another
• Causes– Introduction of parallel and
perpendicular at the same time– Lack of variety of examples and
representations with parallel usually being shown parallel to the edge of the page
Co-ordinates
• Q 19 from Sats paper
Co-ordinates
• Misconception– The label of the axis refers to the value of the
label– Muddling x and y co-ordinates in ordered
pairs
• Causes– Lack of clarity in examples used– Confusing numbers and labels
Probability
• Q 23 from Sats paper
Probability and properties of numbers
• Misconception– Confusion about certain, possible and impossible
when related to events– Lack of understanding of the general rules of number
such as the sum of two odd numbers is and even number
• Causes– Lack of experiences of assessing probabilities of
ordinary events– Lack of experiences of generalising about numbers
Why do learners make mistakes?
• Lapses in concentration.
• Hasty reasoning.
• Memory overload.
• Not noticing important features of a problem.
or…through misconceptions based on:
• alternative ways of reasoning;
• local generalisations from early experience.
Generalisations made by learners
• 0.567 > 0.85 The more digits, the larger the value.
• 3÷6 = 2 Always divide the larger number by the smaller.
• 0.4 > 0.62The fewer the number of digits after the decimal point, the larger the value. It's like fractions.
• 5.62 x 0.65 > 5.62Multiplication always makes numbers bigger.
Generalisations made by learners
• Area of rectangle ≠ area of triangleIf you dissect a shape and
rearrange the pieces, you
change the area.
AB C
AB
C
Some more limited generalisations
• What other generalisations are only true in limited contexts?
• In what contexts do the following generalisations work? – If I subtract something from 12, the answer
will be smaller than 12.– All numbers can be written as proper or
improper fractions.– The order in which you multiply does not
matter.
Some principles to consider
• Encourage learners to explore misconceptions through discussion.
• Focus discussion on known difficulties and challenging questions.
• Encourage a variety of viewpoints and interpretations to emerge.
• Ask questions that create a tension or ‘cognitive conflict' that needs to be resolved.
• Provide meaningful feedback.• Provide opportunities for developing new ideas
and concepts, and for consolidation.
Look at suggestions from Maths4Life booklets
• What major mathematical concepts are involved in the activity?
• What common mistakes and misconceptions will be revealed by the activity?
• How does the activity:– encourage a variety of viewpoints and interpretations
to emerge?– create tensions or 'conflicts' that need to be resolved?– provide meaningful feedback?– provide opportunities for developing new ideas?
Follow up work
• Identify a misconception that you have seen your children show or pick a common one
• Try using some ideas from the resources to address the misconception
• Be prepared to share your experiences with the rest of the group– Note what children say and how they react– Bring some examples of their work before and after
your intervention