This easy to use exercise displays the key functions of the Measurement
Tutor. Once this exercise is completed, students will be familiar and
comfortable with the Tutor, giving them maximum benefit as they progress
with their scientific studies.
The best opportunity to learn occurs when mistakes are made – and that
is when the full power of the Quantum Tutor is realized. To demonstrate
the Tutor's capabilities and features, some of the more common errors
made by students are a key focus of this exercise.
The Measurement Tutor is one of the most flexible of all of the Quantum
Tutors – it does not depend on knowing in advance the object being measured,
therefore it is designed to help you with anything you would
like to measure.
Similar to a human tutor, the Quantum Tutor deliberately offers a variety
of wordings and numbers in its examples and explanations every time you
use it. The ideas and concepts are the same. So, be prepared – you
may not see the exact same words or numbers that appear in these sample
screens. Know that you are learning the concepts and the why
behind the answers, not just memorizing facts and procedures.
Teachers may choose to print out this document and use it as an assignment
in the classroom or for homework. Space has been provided for students
to write in their responses.
- Students will be able to determine the precision and assess
the accuracy of their own original measurements using the Measurement
- Students will learn to ask the Tutor questions in order
to learn more about the nature of measurement and measuring instruments.
Overview of Exercise:
Steps 1 through 5: Students enter a measurement, receive
tutoring, and ask the Tutor questions relating to precision, accuracy,
and the nature of measurement.
Steps 6 and 7: Students take a measurement (or make an
approximation) and use the Tutor to help them explore common errors.
Step 1: Getting Started
To use this Activity, you will need to toggle back and forth between
this page and the Measurement Tutor. You will have multiple
windows open, and some windows may be hidden from view. If you are
using a PC,
look at the Windows toolbar to see which windows are running. Find
the title of the window that you want, and click on the title to
make that window the active window. If you are using a Mac, you
may need to minimize all of the browser windows to find the one
that you want. At any time you may click Instructions
at the upper left of your screen for information about the operation
of the Tutor. The main window will look like this:
Figure 1: Measurement Tutor main window. You must "Choose a Measuring
The Tutor begins by asking what measuring instrument you are using. The
menu allows you to select the instrument. For this exercise, let's select
the meter stick. If you have an actual meter stick available, it would
be helpful (though not essential) to have it with you for this exercise.
In the menu, click on (highlight) meter
stick and then click the green OK
button to the right. You will see a window that looks like this:
Figure 2: We're taking measurements with a meter stick. The Tutor is
ready for your measurement.
Step 2: Ask a question
Now that the Tutor knows that you are using a meter stick, it immediately
gives you information. Even though you haven't entered a measurement yet,
the Tutor can answer general questions about the meter stick you are using.
In the Ask a Question box click once on
"What is the maximum length in centimeters that should be measured using
a meter stick?" and then click the green
Ask button to the right. The results will look
Figure 3: Ask a Question. The Tutor answers your question.
In addition to helping you with actual measurements, the Tutor answers
questions about the measuring device and the fundamental nature of measurement.
Step 3: Enter your measurement
The Tutor allows you to enter your own measurement
exactly as you would record it on your paper or lab report. Let's
say we were measuring the width of your computer screen and we found it
to be 39 centimeters. In the Enter your
measurement box, enter 39:
Figure 4: Entering your measurement. Enter the numbers exactly as you
would on your lab report.
There is nothing apparently wrong with the number "39" as it is entered,
but is it in the proper form for a measurement? Let's see how the
Tutor responds. Click the green OK
button and the Tutor will assess your measurement.
Figure 5: The Tutor responds to your entry.
To find out why this is wrong, we can go to the Ask a Question
box and click once on "How does the general form
of my measurement look?" Click the green Ask
button and you will see the Tutor's response.
Figure 6: The Tutor answers the question: "How does the general form
of my measurement look?"
Now ask the question "Why is it necessary always
to write the units with a measurement?" and see what the Tutor has to say.
Figure 7: The Tutor answers the question: "Why is it necessary always
to write the units with a measurement?"
Reenter the measurement by typing 39 cm
in the box and click the green OK
Figure 8: The Tutor responds to your entry. Notice how the Ask
a Question menu has changed.
Step 4: Using the Tutor to revise and correct your measurement
The Tutor now provides a much longer list of questions it is ready to
answer for you. This is encouraging, but the measurement you entered still
has problems. For more detailed information about the remaining problem
with the decimal places, ask the question:
"How many significant figures does my measurement have?"
Then ask the Tutor:
"Is the precision of my measurement appropriate for a meter stick?"
Reenter your measurement by typing 39.47 cm
and clicking the green OK button.
You will see a window that looks like this:
Figure 9: The Tutor helps you determine the accuracy of the measurement.
Step 5: Determine the accuracy of your measurement
Even though the Tutor doesn't know the actual object you are measuring,
it provides information to assist you. Decide if the width of your computer
screen is indeed near the diameter of an automobile steering wheel. The
fact that the size of the object you measured matches very closely with
the size of the item listed by the Tutor increases your confidence that
your measurement has the accuracy necessary for a science activity.
Step 6: Start a new problem
To try a new problem, click on the New Problem
button, located in the upper left corner of the screen. Select meter stick as the measuring device and click the
green OK button. If available,
use your actual meter stick to measure some object near you, perhaps the
height of the table where the computer sits. If you don't have a meter
stick with you then make your best estimate of the height. This activity
will be equally useful either way.
The height of your computer table will be near the 73 mark on the
meter stick. Let's suppose you were unfamiliar with the meter stick
and were uncertain of the units used here. This device can be used
to measure meters, centimeters, or millimeters so let's use the
Tutor to help us decide which unit is correct. To see if the units
are meters, enter 73 m in the box and click the green
OK button. From the questions menu ask the
question "Give me something I can compare
to my measurement." (It may also be worded something like
"How can I estimate the size of 73 m?") You will
see a screen that looks like this:
Figure 10: The Tutor answers the question: "Give me something I
can compare to my measurement."
From the Tutor's response, it is clear that the 73 units are not meters.
The height of the table is obviously nowhere near the length of two basketball courts.
Now enter 73 cm and click the green OK
button. Ask the same question again and review the Tutor's response.
The Tutor replies that 73 cm is approximately twice the diameter
of a large pizza. Centimeter is definitely the correct unit. The
choice of unit this time probably wasn't in doubt, but as you progress
in your study of the metric (or SI) system of measurement you are
certain to have problems from time to time. Even more importantly,
you will, from time to time, mistakenly record the wrong unit or
misplace a decimal point. This is to be expected for beginning students,
especially when you are making several measurements with different
measuring devices for the same activity.
Now that you are finished, scroll down to the bottom of the screen.
There, you will see a record of every step you took and every question
you asked of the Tutor.
Figure 11: The Tutor always displays the transcript.
This record is a "transcript" of the work you did so far. It is
always there if you need to review a question or step when you use
the Tutor. You will find that reviewing this transcript is a very
good use of your time.
Step 7: Identifying other common errors
Let's see how the Tutor will help you identify some other common errors.
Enter any measurement you wish and experiment with the Tutor until you
feel completely comfortable with it. Entering intentional errors is one
of the best ways to become familiar with the Tutor's features. Knowing
in advance exactly what the error is enables you to interpret the Tutor's
explanations much more quickly. After you have explored as many of the
Tutor's features and questions as you need, try the following activities:
Click the New Problem button,
select meter stick as the measuring
device, click the green OK button
and enter 6.937 cm.
Do you think there is a problem with this measurement or is the form correct?
On the first line try to predict what the Tutor's response will be and
click the green OK button. On
the second line, summarize the Tutor's actual response.
What about this measurement: 0.3 m? Your ability to make good observations
about measurements should be improving by now. Again, on the first line
try to predict what the Tutor's response will be and click the green OK
button. On the second line, summarize the Tutor's actual response
It is very important to remember that the form you are learning to use
to record your measurements is the same one used by all scientists everywhere.
It is a system that was developed over a long period of time and has been
thoroughly tested. These tests have shown this technique to be completely
appropriate for all applications. Isn't it interesting to know that you
are using exactly the same system as the scientists at NASA who are recording
detailed measurements from multi-million dollar space vehicles?
The problems you have just completed illustrate many of the major features
of the Quantum Tutors. The program has tutored you through an in-depth
examination of measurement by encouraging you to bring together all related
background information and concepts from both mathematics and science.
As you entered your measurements you were tutored on choosing a measuring
device, choice of dimensions, choice of units, the number of decimal places
(significant figures), and the broader concept of the nature of measurement.
The Tutor has encouraged you to think about the choice, application, and
especially the limitations of the common measuring devices you are likely
to have in your classroom.
Your challenge is to continue to consider all factors encompassing the
concepts of precision and accuracy before, during and after the process
of making each measurement. This becomes especially important when assessing
measurements recorded by another student. With these skills and concepts
now clearly associated in your thinking you are much better equipped to
handle problems involving scientific measurement. As you use the Tutor
to assist you with other problems, begin to predict what the computer
will do next and attempt to become increasingly aware of the various errors
that may lurk in even the simplest measurements. When your predictions
and explanations begin to match those of the Tutor, then you have mastered
the concept of measurement.