Reaction Timer
Why do this problem?
The skills of making and testing hypotheses and analysing data
are important both in mathematics and in scientific enquiry.
This
problem is an ideal starting point for developing these
skills.
Learners need to make decisions about the information that is
required to answer the questions posed, analyse the data that is
collected, and decide whether the analysis supports the
hypothesis.
Possible approach
If you have access to a computer and data projector,
demonstrate the interactivity showing a few of the variations (e.g.
varying the size makes little difference to the task, whereas varying the shape or varying location + click on shape make it
harder).
To introduce the second experiment, ask a volunteer to come
out to the front of the class and demonstrate dropping a ruler to
test the speed of their reactions.
Once learners have seen both experiments, give them some time
to discuss in pairs some hypotheses they could test, and then share
these ideas with the whole class. There are some suggested lines of
enquiry in the problem which could be shared with learners if they
struggle to come up with good ideas of their own.
Ask students, perhaps working in pairs, to select a hypothesis
and discuss:
- whether they think it is true or false
- how they could use the experiment(s) to test their views
- what data (and how much data) they would need to collect
Give them time to collect, analyse and interpret their data and
then prepare a poster for presenting their findings to the class.
The task may take more than one lesson, so data collection could be
done as a homework task.
One way of presenting their findings to the class is for learners
to display their posters around the room and then take time to look
at everyone else's work, perhaps annotating each other's work with
post-it notes. Then the class could discuss which methods of
collection, analysis and representation were most appropriate and
effective in testing their hypotheses.
Key questions
How many times do you think it would be useful to carry out the
experiment(s)?
How will you represent and analyse your data to test your
hypothesis?
Can you justify that your experiment is a valid way of testing your
hypothesis?
Are your results reliable - could someone else replicate your
results with their own experiment?
Possible extension
All of the hypotheses suggested in the problem could lend
themselves to fairly detailed statistical analysis - there is the
opportunity for learners to explore the idea of distributions,
averages and measures of spread in order to compare data gathered
from each of the two experiments and any experiments they devise
for themselves.
A Stage 4 follow-up problem that investigates how to turn the
results from the second experiment into reaction times can be found
at
How Do You
React?
Possible support
Encourage learners to work in pairs or small groups and to support
each other in constructing clear hypotheses which are
straightforward to test. Each group could present their plan to the
rest of the class before they start any data gathering, and the
class could give feedback on what is good and what might need
improving. This could be done using post-it notes as suggested
above.