Reaction timer
Problem
In this problem, you will meet two different ways to test your reactions.
This reaction timer will enable you to collect data on the time it takes you to respond to an image on your computer.
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Note: You can copy/paste the results table into a spreadsheet
Here is a second experiment you can use to test your reactions.
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.
The pictures below show this experiment being carried out:
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.
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.
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.
Here are some questions you might like to consider:
- I think I respond more quickly with my right hand than with my left - are you the same?
- Do your reactions vary depending on the time of day or the sort of thing you are being asked to react to?
- Do your reactions improve with training/practice?
- Do boys react more quickly than girls?
- Do young people react more quickly than older people?
- What else do you think affects people's reaction times?
- 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?
- Can you think of other experiments you could do to test your reactions?
You may also wish to explore how accurately you can estimate time.
Getting Started
Student Solutions
We received a number of observations and conjectures.
Octavia from Fowlmere suggested the following
- Right handers are better at reacting with their right hand and left handers vice versa
- At night you are more tired so your reactions are slower
- Males tend to be quicker than females because they play more computer and playstation games
- The older you are the more time it takes for you to react because your body doesn't work as fast
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.
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.
Michael from Lancaster Grammar experimented with a moving star. He made the following acute remark: "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."
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.
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 always do better with their left hand. Keeley claimed that boys have better reactions than girls while under stress, but otherwise girls are quicker!
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.
To learn more about collecting data and making conjectures, we suggest reading Understanding Hypotheses.
Teachers' Resources
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.
- 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.
Another similar activity where students can make hypotheses and test them is Estimating Time.
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 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.
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?