6044
/www/nrich/html/content/id/6044/
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2011-02-01T00:00:01
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<ul id="stemLinks">
<li><a href="http://nrich.maths.org/6172">Warm-up</a></li>
<li><a href="http://nrich.maths.org/505">Try this next</a></li>
<li><a href="http://nrich.maths.org/7033">Think higher</a></li>
<li><a href="http://nrich.maths.org/6178">Read: mathematics</a></li>
<li><a href="http://depts.washington.edu/rural/RURAL/design/scimethod.html">Read: science</a></li>
<li><a href="http://faculty.washington.edu/chudler/chreflex.html">Explore further</a></li>
</ul>
<div> </div>
<p>In this problem, you will meet two different ways to test your reactions.<br></br>
<br></br>
This reaction timer will enable you to collect data on the time it takes you to respond to an image on your computer.<br></br>
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<span style="font-weight: bold;">Note:</span> You can right click (or control-click if your mouse has only one button) on the 'Times' panel to select, clear or copy the times. This allows you to paste them into a spreadsheet or text document.<br></br>
<br></br>
Here is a second experiment you can use to test your reactions.<br></br>
Ask a friend to hold a ruler by the end, above your hand. Open your hand below the ruler and be ready to catch it. Your friend will drop the ruler without saying when they're going to let go. Catch the ruler as fast as you can after it's been dropped.<br></br>
The pictures below show this experiment being carried out:<br></br>
<mdo:image alt="hand holding ruler" height="365" src="reactions.jpg" width="362"></mdo:image><br></br>
Record the level (in centimetres) at which you caught the ruler, and repeat the experiment several times. If you have quick reactions, the ruler will not have travelled far when you catch it.<br></br>
<br></br>
<span style="font-weight: bold;">Taking only one measurement in either of these experiments will not give you a reliable, accurate measure of speeds of reaction that could be used to rank a group of people.</span><br></br>
<br></br>
<span style="font-weight: bold;">Decide how many measurements you will take, and what you will do with them to provide an accurate measure of reaction speeds. Make sure you can justify your decisions.</span><br></br>
</p>
<h4>Here are some questions you might like to consider:</h4>
<ul>
<li>I think I respond more quickly with my right hand than with my left - are you the same?</li>
<li>Do your reactions vary depending on the time of day or the sort of thing you are being asked to react to?</li>
<li>Do your reactions improve with training/practice?</li>
<li>Do boys react more quickly than girls?</li>
<li>Do young people react more quickly than older people?</li>
<li>What else do you think affects people's reaction times?</li>
<li>Are both experiments testing the same ability? If you perform both experiments with a group of people and rank them in order, will the rankings be the same for both experiments?</li>
<li>Can you think of other experiments you could do to test your reactions?</li>
</ul>
<div>Test any hypotheses you come up with, and send us your analysis and conclusions.</div>
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<p class="editorial">We received a number of observations and
conjectures.</p>
<p class="editorial">Octavia from Fowlmere suggested the
following</p>
<br></br>
<ul>
<li>Right handers are better at reacting with their right hand and
left handers vice versa</li>
<li>At night you are more tired so your reactions are slower</li>
<li>Males tend to be quicker than females because they play more
computer and playstation games</li>
<li>The older you are the more time it takes for you to react
because your body doesn't work as fast</li>
</ul>
<p class="editorial">Meghan from AHS suggested that if you change
the properties of the star, it is harder to click it quickly. She
also added that males are actually no quicker than females. We
already have conflicting conjectures, and this is where providing
real data in support of your argument is important.</p>
<br></br>
<p class="editorial">Maria and Katie from St Mary's conducted an
experiment, in which they found that the average reaction time for
their left hand was 0.2s, while for their right hand it was 0.15s.
Rosie, Natalie and Gabby, also from St Mary's provided similar data
which supports the argument that we react quicker with our better
hand.</p>
<br></br>
<p><span class="editorial">Michael from Lancaster Grammar
experimented with a moving star. He made the following acute
remark:</span> "If you are right handed have the mouse at the right
side of the screen, so when a star does come it is easier to get to
the star because your right hand can move faster and more easily to
the star if it is at the left."</p>
<br></br>
<p class="editorial">This raises an important issue - that factors
other than reaction time (such as strategy) can affect our results.
In conducting a fair experiment it is essential to make sure that
these other factors are controlled.</p>
<div><span class="editorial">Some students from Hampton School
suggested some other factors that may affect reaction
time:</span></div>
<div> </div>
<div>Your reactions are always faster if you limit the number of
things you have to be aware of <span class="editorial">-
Harry</span></div>
<div>People with better eyesight have quicker reaction time <span class="editorial">- Matt</span></div>
<div>The time you get varies depending on whether you pay close
attention or not <span class="editorial">- Nick</span></div>
<br></br>
<p><span class="editorial">In response to our demand for
experimental data, a number of students from Chalkstone Middle
School sent in their findings. Sithabile and Shannon sent in some
data and concluded that we react fastest with our best hand. Kelly,
however, claimed that people</span> <span class="editorial" style="font-style: italic;">always</span> <span class="editorial">do better with their left hand. Keeley claimed
that boys have better reactions than girls while under stress, but
otherwise girls are quicker!</span></p>
<br></br>
<p class="editorial">The data were well organised and clearly
presened, but in many cases we were concerned that there were not
enough data to truly back up your claims. A number of you based
your conclusions on testing each individual in your sample just
once. Aaron and Eshter made an effort to get more accurate results
by repeating individual experiments three times.</p>
<br></br>
<p><span class="editorial">To learn more about collecting data and
making conjectures, we suggest reading</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6178" class="editorial">Understanding Hypotheses</a><span class="editorial">.</span></p>
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<h3>Why do this problem?</h3>
<div>The skills of making and testing hypotheses and analysing data
are important both in mathematics and in scientific enquiry. <a href="http://nrich.maths.org/public/viewer.php?obj_id=6044">This
problem</a> is an ideal starting point for developing these
skills.</div>
<br></br>
<div>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.</div>
<div></div>
<h3>Possible approach</h3>
<div>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 <span style="font-style: italic;">varying the shape</span> or <span style="font-style: italic;">varying location</span> + <span style="font-style: italic;">click on shape</span> make it
harder).</div>
<br></br>
<div>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.</div>
<br></br>
<div>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.</div>
<br></br>
<div>Ask students, perhaps working in pairs, to select a hypothesis
and discuss:</div>
<ul>
<li>whether they think it is true or false</li>
<li>how they could use the experiment(s) to test their views</li>
<li>what data (and how much data) they would need to collect</li>
</ul>
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.<br></br>
<br></br>
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.
<h3>Key questions</h3>
How many times do you think it would be useful to carry out the
experiment(s)?<br></br>
How will you represent and analyse your data to test your
hypothesis?<br></br>
Can you justify that your experiment is a valid way of testing your
hypothesis?<br></br>
Are your results reliable - could someone else replicate your
results with their own experiment?<br></br>
<h3>Possible extension</h3>
<div>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.</div>
<br></br>
<div>A Stage 4 follow-up problem that investigates how to turn the
results from the second experiment into reaction times can be found
at <a href="http://nrich.maths.org/7033&part=">How Do You
React?</a> </div>
<br></br>
<h3>Possible support</h3>
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.<br></br>
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<mdoxml version="1.0">Present your plans to someone else before you start any data
gathering, and request feedback on what is good and what might need
improving. <br></br></mdoxml>
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Reaction timer
This problem offers you two ways to test reactions - use them to
investigate your ideas about speeds of reaction.
Handling, Processing and Representing Data
Measures of spread
Handling, Processing and Representing Data
Comparing data
Handling, Processing and Representing Data
Averages
Using, Applying and Reasoning about Mathematics
Making and testing hypotheses
Handling, Processing and Representing Data
Interpreting data
Applications
STEM - physical world
Applications
STEM - living world
Admin
Experiment
Secondary Mapping Document
Statistics – planning
Secondary Mapping Document
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