The top
navigation bar will remain the same no matter where you are in the
program: Welcome: 
Returns you
to your Welcome Page
Comments:Since
CyberTutor is still in development, we recognize that there are many
changes that might be made in order to improve its look and feel,
content and functionality. Please use this button to input suggestions
or questions you have about the program as you proceed.
Logout: Allows you
to logout of CyberTutor.
Help:Not
presently enabled. Provides written help tailored to the task on which
you are working.
Left Navigation Bar
The left
navigation bar will change as you navigate within
CyberTutor.Essentially, this navigation bar displays all of the
features that are available for your use from any particular page in
the program:
Assignment Assistant: Allows you
to create assignments for your class.
| Problem Manager: | | Allows
you to review the Problem Library, edit existing problems, and create
new problems. |
| Syllabus: | | Allows
you to create a syllabus for your class using
HTML. |
| Gradebook: | |
Allows you to view the gradebook for your class. Additional
details on setting up and using the gradebook are provided later in
this document. |
| Assignment List: | |
Provides a list of all assignments that you have created for
your class along with due date. Allows you to edit the assignment
list to reorder assignments and/or add additional explanatory text.
Also allows you to edit specific assignments to reorder problems
and/or add additional explanatory text. |
| Current Assignment: | |
Returns you to the last assignment you selected when you've
moved to other pages within the program. |
| Current Problem: | |
Returns you to the last problem you selected when you've
moved to other pages (e.g., Assignment List, Problem
Library). |
Problem Framework
CyberTutor problems are
composed of main parts, hints and subparts. Students may begin by
answering the main parts of a question directly. However, if they have
difficulty, they may request that each problem be broken down into
simpler problems (subparts) requiring skill in a narrower range of
topics. The program also allows students to request further help, in
the form of hints, on these subparts. Students are not heavily
penalized for wrong answers (with the exception of multiple choice
questions); instead, they can try again, occasionally after being
given specific feedback about their previous incorrect responses. The
outcome on any particular problem or subpart is either that the
student answers it to CyberTutor's satisfaction or that they click
"Hint" to get help in the form of a hint or a subpart or, if the hints
are exhausted, the solution.
This branched logical structure is the key to CyberTutor's
approach to interactive online education.This approach will assist
students in developing the skills which they already have acquired
(e.g., from lecture, the textbook or earlier homework problems)
and learning how to apply them to more advanced topics. In the
future, CyberTutor will use this multi-part framework to allow us to
assess each student's skill level on each of the topics involved in
the subparts. Ultimately, this skill profile will be used to select
the most appropriate subsequent problem for the individual student,
which maximizes their learning.
Answering CyberTutor
Problems
Understanding CyberTutor's answer engine is
important to understanding how the program works overall. The answer
types currently supported by CyberTutor are:
|
Pull-down
|
Multiple choice
problems with a pull down menu listing options
|
|
Radio
|
Multiple choice
problems with options that you must click to select
|
|
String
|
Fill in the blank with
text
|
|
Symbolic answers
|
Analytic expressions
involving numbers, variables, and special functions (e.g.,
sin(x)).
|
|
Vector
|
Evaluates student
drawn vectors (see below, Section X)
|
|
Diagram
|
Evaluates student
drawn curves (see below, Section X)
|
Pull-down, Radio and String
Answers
Multiple choice answers function as you might expect; students must
select one of the answer options provided. Fill-in-the-blank responses
call for a text or "string" response, i.e., a word, phrase
or simple number with no operators. String answers are evaluated using
a Perl pattern matcher; this allows problem authors to determine which
answers they deem acceptable on a problem-by-problem basis.The
"string" answer type is case-insensitive and automatically strips
white space from the student's response.
Symbolic Answers
Symbolic answers involve numeric input by the student using one or more mathematical operators and can also involve special functions.The input syntax used in CyberTutor is similar to that which is used in programs such as Maple or Matlab.Numeric answers are entered normally, prefixed by a negative sign where appropriate.Vector components are indicated by adding "Xunit", "Yunit", or "Zunit" as needed, e.g., "14*Xunit + 4*Yunit."Notation for mathematical operations is similar to that used in most computer math programs or programming languages.
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-
|
Subtraction
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Order of Evaluation: CyberTutor uses the calculator-standard rules for the order in which mathematical operators are evaluated in situations where multiple operators are included in an expression:
1. For terms inside parentheses, the most deeply nested terms are evaluated first (Therefore always use an extra pair of parentheses when in doubt).
2. ^ stands for exponentiation and is the top priority after parentheses.
3. * and / for multiply and divide have next priority
4. + and - have lowest priority and are done last
5. Within each priority class, evaluation proceeds left to right, except exponentiation.
These rules sometimes produce counterintuitive results, e.g. 16/ 2*2^1/2 is 16 (exponentiate first, * and / left to right).Additional examples are provided in the assignment covering mathematical notation on the CyberTutor Tutorial.
Implicit Multiplication: implicit multiplication is generally not recognized in standard mathematical notation (e.g. x(t) is a function, not x*t).However, CyberTutor interprets a number preceding a variable (with or without a space) to indicate multiplication, e.g. 2m2 = 2 m2 = 2*m2. Generally, the units for a numerical answer will be provided in a text box following the answer box.However, the above rule means that 7N will be interpreted as 7 * N, correctly indicating 7 newtons.
Variables: Variable names in symbolic answers must first appear in the problem text, and must start with letters.(Exceptions are G, g, and PI, which are Newton's Universal gravitational constant, local gravitational acceleration, and 3.14159 respectively). Symbolic answers and special functions are case-sensitive; M and m, for example, may indicate two different masses in a problem.
Greek symbols will be written out in the problem if you must include them as part of your answer.
Subscripting is quite commonly used in physics to indicate a close relationship between two variables (e.g. i and f for initial and final values; 1,2,and 3 for three times, or three similar things).CyberTutor will use the simple notation, e.g., Ei and Ef; theta1 and theta2 for single subscripts, but will use the TeX convention for longer subscripts, e.g., p_init for the initial momentum.
The answer engine also supports special trigonometric functions.In most cases, the syntax for these functions is provided in problems when it is needed.For easy reference, the supported trigonometric functions are listed below (Note: they are case-insensitive; sin(x) and Sin(x) are both correct notation):
Fractions are input using the / sign and parentheses where appropriate, e.g., (5+4)/(3+1)
Exponents are entered using the ^ sign and parentheses where appropriate, e.g., (2+1)^3
Helpful Features:
Hot Equation Editor: Since using parentheses, multiple operators, a variety of variables and special functions can become confusing for the student, CyberTutor's answer engine includes a "Hot Equation" editor that will interpret their input and display it as a more clear visual representation, using Greek symbols, sub- and super-scripts, and fraction notation. This editor is displayed at the top of the screen, above the top navigation bar. When students enter a symbolic answer, to update the Hot Equation Editor, they must push the "Tab" button. This will allow them to review the notation and determine if they input their answer as desired.
Variable Checking: In evaluating a symbolic response, CyberTutor checks for variable names that do not appear in the solution and informs you of their names. This feature will find both misspellings and some misunderstandings. Cybertutor then evaluates students' responses to determine if they are algebraically equivalent to the correct solution(s).
Challenging the Answer: CyberTutor programmers and problem authors have attempted to make CyberTutor's answer engine as robust as possible. Nevertheless, students will undoubtedly find problems that don't accept responses that seem to be correct.If a student enters an answer that they feel should be graded correct but it is rejected by CyberTutor, they have the opportunity to submit the same response again.CyberTutor will compare their response to the correct solution.If the response is rejected again and the student still feels that their answer should have been accepted, CyberTutor will ask allow them to submit a problem report.
Multiple Solutions: String and Symbolic answer types may also require multiple solutions. These must be input in question order, alphabetical order (or, for vectors, xcomponent, ycomponent), followed by commas.For example, for the following question:
"Which of the following is true?
a) red is a color
b) string is a color
c) blue is a color
The correct response would be a, c
Vectors
Many problems in mechanics involve free-body diagrams and manipulation of vectors.CyberTutor's vector module enables students to create such diagrams and perform the necessary manipulations.The vector module consists of two regions: the diagram and the vector list.
To draw a vector on the diagram, students first select a vector from
the list by clicking on the desired vector.This vector should then be
drawn on the diagram with the mouse; a blue vector arrow will follow
the mouse cursor.The tail of the vector will be anchored at the
position of the initial click.To stop drawing, they will simply
release the mouse button. To draw additional vectors, students will
simply select them from the list and use the same method.If students
select a vector from the list that has already been drawn, the
existing vector will be highlighted in blue on the diagram. If they
wish, they may modify or delete the vector. To modify it, simply click
and drag in the diagram to redraw the vector.To delete the vector,
click the "clear this arrow" button at the bottom of the vector
module.
For many problems, the vector module may display a continuously
updated red "vector sum" arrow to indicate the sum of the vectors
(both preexisting and student-drawn) on the diagram. When the sum of
vectors is zero, the red arrow shrinks to a red dot on the
diagram.
When students are satisfied with their vector diagram,
they will press the "Submit" button to submit the diagram to
CyberTutor.If any of the vectors are incorrect, CyberTutor will inform
them of this immediately.They will be given the option to correct the
diagram by redrawing or deleting vectors (as described above) or to
continue to the next problem part.Full details for creating answers to
problems using the Vector Module are provided under Problem Manager
below.
Curves and Diagrams
Answers that
take the form of a curve or diagram are evaluated using the Curve
Evaluator.Curves that are included as CyberTutor problems are composed
of three layers of images.The first, background, image is the diagram
that will display to the student.The second image is the correct
curve, as input by the problem author.The third image is the weight
curve; on this curve, problem authors will have specified key
points
on a student's curve that will be evaluated and the
relative importance of these areas in determining the correctness of
the response.The weight is indicated visually by problem authors; the
default is uniform weighting (indicated by a complete, straight
line).Authors could also have a weight curve with missing gaps,
indicated that only certain parts of the curve (where the line is
shown) should be evaluated in determining if a curve is correct.
For example, students may be given the following question: "An object
at rest accelerates at a constant rate of 1 meter per second per
second.Plot the velocity of this object versus time."
They will
also be given a graph indicating the x and y axes on which to diagram
their answer.
When a student draws and submits a curve, the curve
grader compares the pixels in their curve to the nearest pixels on the
correct image.If the solution had been set up as a standard,
unweighted, curve, evaluation would be performed only where the
solution curve existed, and each portion would be evaluated equally in
grading the curve.In a weighted curve, the more highly weighted
portions of the solution curve would figure in to a greater extent in
the grade given to the curve.
D.Grading
You must specify
one of three grading options for each problem assigned:
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Practice
|
This problem will not be graded.It is included for the student only for review.Students will be given feedback about whether their answers to subparts and the main part are correct as they proceed, and they may request solutions.
|
|
Cyber-graded
|
Students' performance on this question will be factored into their homework grade.They will receive immediate feedback on their answers to subparts and main parts, and they may request solutions.
|
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Hand in
|
Students must submit written solutions that will be factored into their homework grade.They will not be given immediate feedback about whether their answers to the main parts of the question are correct.They will still be given feedback about the subparts.
|
Credit for problems
Each
problem is composed of a number of main parts, hints and subparts. The
total possible points for a problem is the determined by tallying the
number of main parts and hints plus twice the number of subparts.If a
student answers all main parts of a problem correctly without
requesting any 'Hints", they will receive all of the possible
points.If they request a "Hint" (which will be either a problem
subpart or hint text), they will lose whatever fraction of a point you
specified when creating the assignment.The subparts are designed to
provide students with checkpoint information as they attempt to answer
the main part; they do not have to answer the subparts IF they
correctly answer the main part below. However, if a student requests
the solution for any subpart or for the main part below (without first
having answered that subpart), they will lose an additional fraction
of a point.
Class Management
4
CyberTutor will eventually support an entire array of class management tools to assist you in organizing course information using the Web.The beta version includes only a basic online syllabus and gradebook, as well as additional tools to allow you to edit assignments and your class assignment list.
Syllabus
Clicking
the "Syllabus" button on the left navigation bar will allow
you to create a basic online syllabus for your class.This may be used
to display a course description, course goals, and a listing of
topics, reading, homeworks and upcoming quizzes and exams by date.A
sample syllabus has been set up for you to use as an example. Click
"edit" to customize the syllabus for your use.If you are
happy with this format, you can simply paste in your own content. If
you would like to edit the template extensively, you must use HTML to
do so.You may preview your syllabus at any time by clicking the
preview button.When you are satisfied with your syllabus, simply save
the syllabus to exit editing mode.This syllabus will be accessible to
your students when they press the "Syllabus" button on their
left navigation bars.
Gradebook
The gradebook will allow you to review your students' performance on CyberTutor homeworks and any quizzes or exams you have set up.CyberTutor will automatically create a class roster by collecting the names of your students as they register with their class code and access code you provide to them.The gradebook will display their names in alphabetical order.Grades will be listed by assignment, with the total possible points and the number received by each student on an assignment recorded.To review student's performance on the specific problem making up an assignment, you would simply click on the assignment to receive a display showing total possible points per problem and the credit received per problem.
Assignment List
The Assignment List button displays a listing of all assignments you have created for your class to date.This information is displayed in a form identical to that in which the students will view it, with the exception of two editing tools provided for your convenience.The "Edit Assignment List" button at the top of the page allows you to reorder your list of assignments and add explanatory test.The "Edit particular assignment" button allows you to reorder the problems included in a specific assignment and add explanatory text if you wish. Clicking either of these options will bring up an HTML editor listing all of the files included in the assignment list or problem list.Important: you must be careful not to alter the actual filenames for your assignments or problems (e.g., <assignment file=one title="NV - Vectors"> or <prob NV.dr.1>), as these are automatically generated by CyberTutor.To reorder assignments or add explanatory text, use the normal cut and paste commands and any HTML tags that you wish.
III.Using CyberTutor
A.Welcome Page
After you log in or register as a new user, CyberTutor will display a brief Welcome Page.The first time you log in, at the top of the page will be displayed a brief message from CyberTutor administration.On subsequent logins, announcements specific to your class will display in this space.To edit announcements, simply click the "Edit" button, input the desired text, preview it if you desire, and then click "Save" to return to the Welcome Page.(Note: you will have to click "Reload" in order for your changes to display in this window.)
In the future, the remainder of the page will display a full range of options for class management.At present, this page serves as the starting point for setting up assignments for your class.The tasks involved in setting up your class are:
Creating assignments for your class using existing problems from the Problem Library and/or problems that you yourself have authored(the Assignment Assistant)
Reviewing, editing and creating additional problems (the Problem Manager)
B.Assignment Assistant
To begin creating assignments for your class, from the Welcome Page, click on "Assignment Assistant."This will bring you to a page on which you can specify details about an assignment for your class.
1) Input a File Name for the assignment.In the future, this step will be unnecessary.However, for now it is necessary for you to specify a file name for data storage purposes.This file name may be any combination of alphanumeric characters that wish, but you should enter it without any spaces, e.g., "kinematicsone" or "SeptFifteenth".
2) Input a name for your assignment.This will be the text that will show up on the Assignment List as a link, so be certain that it conveys useful information.
3) Use the pull down menu to select when you would like the assignment to be displayed to students:
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Now
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Displays the assignment when it is saved
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When previous assignment due
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Displays the current assignment after the previous assignment (as determined by due date) is due
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When previous assignment is finished
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CyberTutor automatically determines when an assignment is "finished," i.e., when the student has gotten correct answers for all of the problems in an assignment.This option will display the current assignment when the student has completed all problems in the previous assignment.
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One week before assignment is due
|
Displays current assignment one week before due date.
|
4) Enter the due date for the assignment.
5) Specify the points or fraction of a point that you would like students to lose for each Hint they request.
6) Provide a brief description of the assignment.This can be viewed by students, and will also be useful to CyberTutor in analyzing the manner in which instructors teach topics.
7) Indicate "after due date and time" preferences:
How will credit be assigned?*
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No credit
|
Late problems (turned in after the due date and time) receive no credit.
|
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No change
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Late problems receive full credit.
|
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½ credit
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Late problems receive half credit.
|
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Falls to ½
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Credit for late problems decreases linearly with time, reaching 1/2 12 hours after due date and time.
|
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Falls to zero
|
Credit for late problems decreases linearly with time, reaching zero 24 hours after due date and time.
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How will problem display options change?*
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No change
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After the due date and time, the problems will be displayed to students as they were originally specified.
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Hints available
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Hints will be displayed to students.
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Subpart answers available
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Subpart answers and hints will be displayed to students.
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All answers available
|
Hints, subpart and main part answers will be displayed to students.
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*Note: although these features are not yet enabled, your preferences will be stored and will be implemented when the feature is turned on.
8) Click "Begin Making Assignment" to begin selecting problems for inclusion on the assignment.This will take you to a Problem Library displaying all of the available problems, categorized by section and topic.For a complete list of topics (see below, Section X), you can click the Topic List button.
9) Click on a topic to go to the Problem List for that topic.Click on a problem name to review that particular problem.The "Do This" pulldown menu allows you to view a number of problems simultaneously for purposes of comparison.Select the problems that you would like to view by checking the boxes to the left of the problem.Select "View these problems" from the "Do This" pulldown, and then click "Do This."You will be shown the full text of the selected problems in printable format at the bottom of the screen.
10) When you are on the problem page for a particular problem, a number of viewing options are available to you."Student View" will display the problem in the format that it is visible to the students."Author View" will allow you to view all parts of the problem, including hints, subparts and solutions.##
11) After reviewing a problem, if you decide that would like to add it to your assignment, select"Add to Assignment" on the "Do This" pulldown menu and then click the "Do This" button.The problem will be added to your assignment.To add additional problems, follow the same procedure.
12) When you have added all the problems you wish for a topic, click on "Assignment Assistant" on the left navigation bar.This will return you to the Assignment Assistant page, where a list of your selected problems is displayed.If you would like to return to the Problem Library, a button linking you directly to the library should appear above the problem list.
13) For each problem, you must specify a grading option: practice, cyber-graded or hand in.
14) Click "Save Assignment" when you are finished.The assignment will be added to the Assignment List for your class as specified.You will remain in the Assignment Assistant, and may create additional assignments if you wish.
## For teachers with problem editing or authoring privileges, "Author View" will also allow you to review and edit all of the problem parts."Resume" will return you to Student View from any other mode."Click to Edit" displays the parts of the problem in a manner similar to student view, but will allow you to click on any particular problem part to edit itFull authoring and editing instructions are provided below.
5
Problem Manager: creating, editing and managing problems in CyberTutor
Users with author privileges are permitted to edit problems in the CyberTutor Problem Library and to create new problems using the Problem Manager.If you are a user with authoring privileges, there are two methods by which you can access the Problem Manager.
1) While you are reviewing problems for inclusion in an assignment, you will have the option to edit problem files while you are reviewing them.When you are on an individual problem page, the tool bar at the top of the screen will display editing options (described below under Editing Existing Problems), rather than simply asking if you would like to include this problem on an assignment (see Step 8, Assignment Assistant).
2) You can access the Problem Manager from the left navigation bar at any point in the program.
To effectively author problems using CyberTutor, you should begin by familiarizing yourself with the Topic List, which indicates the various categories, sections and topics into which problems are organized.To view this listing, click the "Topics List" button provided on the Problem Manager page.You should also review the existing library of problems to familiarize yourself with problem availability and typical problem structure.
Layout of Problem Pages
Whether you are editing an existing problem or creating a new problem, the format of problem pages remains the same.At the top of an existing or blank problem page are three check boxes that refer to the status of the problem, i.e., how close it is to completion.These boxes will be useful to you in keeping track of the status of your problems, and are also useful to us, since CyberTutor maintains a full inventory of problems in each stage of completion.The meaning of the boxes is straightforward:
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Wording
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Indicates that the way in which the problem is written is clear and correct.
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Solutions
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Indicates that the solutions you have input are, in fact, correct and can be reached given the information provided in the problem.
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Complete problem
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Indicates that all problem details including any supporting graphics have been included and that the problem is correct and complete and should be added to the Library.[COMMENT1]
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Below these boxes is a tool bar with a variety of viewing and editing options:
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Author View
|
Allows you to view all parts of the problem, including hints, subparts and answers in an expanded format.In this view, you may edit any of the fields that you choose.
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Click to Edit
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Essentially an expanded Student View.You may click on any of the parts of the problem to see an expanded view that will allow you to edit that problem part.
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Student View
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Shows you the problem in the format that it is visible to the students.Also allows you to work through the problem to attempt to answer it.
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Resume
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Returns you to Student View from any other mode.You will reenter the problem at exactly the point that you left it, i.e., if you had answered the first two subparts initially, you would be returned to the problem at the same point.
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Save Changes
|
After you have edited a problem, allows you to save your changes.
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Below the toolbar is the problem itself, including main parts, subparts, hints and comments, plus any supporting images; the text boxes will be empty in the case of a new problem.Problems may be composed of any combination of main parts, subparts and hints that you desire.The general problem format includes the following components:
Filename: For example, MFS.31.0.The format of filenames corresponds to the breakdown of topics as specified in the Topic List.Also see Filename Conventions (Section X, below).
Problem description: This description is for the benefit of problem authors and teachers; you should input any information here that will remind yourself and indicate to others the primary purpose of the problem and its general classification.
Problem Title: This will be displayed in the Problem Library and in any assignments for which it is selected, so be certain it is useful and suitable for public viewing.
Problem Setup: You should enter a basic description of the details of the problem in the first box. Note: you will need to use HTML tags to format the text of the problem setup and to include any images with the problem.This is true for the parts of the problems as well.Using HTML is fairly straightforward, and we try to walk you through most of the basic commands that you will need in Section X, HTML for Problem Authors, below.
Problem Part: This can be a main part or subpart to a problem.They are both composed of a variety of components, as listed:
Question Text:The first question to be presented to the student.This should be input in the large box.Once again, HTML tags should be used to format this text. Where possible, type the = sign before the answer box.
Answer Box: Input the text for the answer.The format of the text will vary depending on the Answer Type selected with the pull-down menu on the far right of this line:
Answer Type
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Input Format
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Example
|
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Pull-down
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Multiple choice answers must be input with commas to separate them
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"the table, gravity, inertia"
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Radio
|
Multiple choice answers must be input with commas to separate them
Formatting tags may not be used.
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"the table, gravity, inertia"
|
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String
|
Text answers must be entered in plain text.
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"the table"
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Symbolic answers
|
Answers must be entered using standard input notation (See Section X, Mathematics and Hypertext, below).Answers will be reinterpreted and displayed above in Hot Equation.
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see below
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Vector
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The name of the saved vector diagram must be input in the answer box (see below, Section X, Creating Vector Answers)
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If we created a vector diagram named "partJ," we would input this in the answer box to display the vector diagram in Student View.
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Diagram
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The name of solution image, weight image and background image must be input in the answer box (see below, Section X, Creating Diagram Answers)
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The images should be input as follows: "solution.gif, weight.gif, background.gif"
|
Answer Post Box: To the right of the answer box.This is usually used to input the units in which the answer should be returned, e.g., meters/second.This text will be displayed when the problem part is loaded.
Solution Button: Used in Student View only to give the answer to this part of the problem.
Answer Type Pull-Down: Allows you to select from the available answer types.
Topics Box: Not currently in use.Will be used to classify the problem part (as opposed to the entire problem) according to its section, topic and difficulty for closer monitoring of student performance.
Add Pull-Down:
The Add Pull Down specifies additional problem parts that can be created.In understanding problem structure, it is useful to view a problem as a logical tree.The main parts of the problem (the siblings) will always be on screen when the problem is loaded.For all intents and purposes, they are equals.Each main part (or sibling) can have branches (hints or subparts) extending from them, and the subparts can have new branches extending from them.
Hint Above
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This allows you to specify text for a Hint that will appear above this problem part when the student clicks on the 'Hint" button.
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Subpart Above
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This allows you to add a Subpart (with an answer box and solution) that will appear above this problem part when the student clicks on "Hint."
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After Problem Below
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This button specifies that after a student finishes this problem part, either by successfully answering the part or asking for a solution, a new problem part (requiring a solution) will appear below the current part.
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AfterComment Below
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This button specifies that after a student finishes a problem part, again either by successfully answering the part or asking for a solution, a comment will appear below the part.
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New Part Below (sibling) (parent part or subpart is first opened)
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This button allows you to add a new problem part that will display when the problem is loaded.You would edit this problem part as specified below under Creating a New Problem.
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New Hint Below (comment) (sibling)
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This button is poorly named at present. It allows you to add a comment referring to the part above that will display when that part is opened.
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Delete Branch
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Allows you to delete a branch of the problem.Deletion would begin with the part on which you currently are located.Using the metaphor set up above, a branch could include a main part and all of the subparts and hints that are associated with it.
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Copy
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Allows you to copy a branch of a problem.This is particularly useful when you want to rearrange a problem.This function also allows you to paste between problems.
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Cut
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Allows you to delete a branch of a problem and then paste it elsewhere.
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Paste Over
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Allows you to paste cut text into an empty problem part.Note: it is entirely possible to overwrite useful problem parts with this function if you are not cautious.
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B.Editing Problems
Editing an existing problem involves most of the same steps as creating a new problem.As we mentioned earlier, this is primarily due to the fact that CyberTutor considers these tasks to be essentially identical.To begin editing existing problems, select Problem Manager from the left navigation bar.
1) Select a problem that you would like to edit, either by clicking on the Problem Library and browsing the problems or, if you know the filename of a specific problem, entering this in the "load this problem" box.
2) When you are on the problem page, select either "Click to Edit" or "Author View" to begin editing.
3) Save this problem with a new filename (see File Name Conventions, below) immediately.If you fail to do so and make changes to the problem, when you attempt to save them, you will receive an alert informing you that the problem that you are working with is a Library file and cannot be edited.
4) Edit the problem parts as you wish (see Authoring Conventions below for guidelines).
5) Save your changes to the problem.Indicate the problem status using the check boxes.If you change the problem status (i.e., check a box that was previously unchecked), you must select "Update status" from the "Do This" pulldown and then click "Do This" to submit the problem status change.
6) If you wish to add this problem to an assignment, you have two options:If the assignment to which you wish to add it was the last assignment in which you were working, you can select "Add to Homework" from the "Do This" pulldown.The problem will be added to that assignment.Otherwise, you should click on the Assignment Assistant and follow the procedure outlined above.
C.Creating New Problems
To begin writing or editing existing problems, you should first click on the Problem Manager.This will take you to a page displaying a number of options for creating, editing and managing problems, as well as links to the Problem Library and the Topics List.
1) To begin creating a new problem, from the Problem Manager, you should click on the "Create New Problem" button.This will bring up a blank problem file, displayed in Author View.
2) Input the file name for the new problem (see File Name Conventions, below).Our new problem, for example, is going to be saved as file: MFS.3l.n, meaning Mechanics (M), Force and Statistics (FS), Newton's third law: real force pairs (3l), lowest number available (n).
3) Input Problem Description.In this case, our description will be "conceptual third law problem."
4) Input the Problem Title. Our problem will be entitled: "Weight on Floor."
5) Write the Problem Setup in the next box.Remember to include the appropriate HTML tags. For our problem we'll use more advanced HTML than is normally necessary to illustrate how simple it actually is:
<table><tr><td><img src="/probhtml/MFS.3l.3.gif"align="left"></td><td>A 5N weight rests on the floor.<br>Fill in the blanks in the following sentences.<br><b>Use lower case letters (except N for 'newtons'') and only one word for each answer.</b></td></tr></table>
Note: the <table><tr> and <td> tags are not always necessary.However, tables make it possible to have greater control over the display of your information.In this case, the table makes it possible to return adisplay with an image aligned on the left and a block of text on the right.
6) Enter the first part of the question. (Once again, you will need to use HTML to format the text and to include any necessary images.)In our example, the first problem part is:
[COMMENT1]
Note: this is completed by CyberTutor administration.
6
A downward force of magnitude 5N is exerted on the floor by the force of...<br>
7) On the next line, in the Answer box, we will input the answer to this part.For our problem, the answer type chosen is radio.To input the multiple choice answer options, the author must enter the choices in the left hand box separated by commas, as follows: "the weight, gravity, inertia"These responses will show up as a multiple choice answer with clickable circles.
8) Since our answer does not have applicable units, we would leave the Answer Post Box empty. (Note: you should not enter anything in the "Topics" box as this feature is not yet being supported.In the future, this will be used for problem inventory purposes).
9) Once you have completed the first part of the problem, you have several options.If this is a simple, one part problem and you are finished, you would click "Save Changes" to save the file.
10) If you would like to add additional parts, you would select the appropriate step from the Add Pull Down, as specified above.
11) When you have finished writing your problem, you should click "Save Changes" to save your new problem.Note: It is also good practice to "Save Changes" occasionally while in the process of authoring a problem.
12) You should make it a practice to scrutinize problems that you create quite closely.To encourage you to do so, we've created three checkboxes at the top of the problem page to indicate the authoring status of a problem: If the wording of the problem is correct and has been double-checked, you should check this box, select "Update status" from the "Do This" box, and click "Do This." The same holds true for the solutions to the problem.Finally, when the problem is correct and complete, you should indicate this and update the status again using the "Do This" button.
D. Authoring Guidelines and Conventions
File Names
Problem filenames should indicate the general category, primary syllabus section and topic of the problem (from the Topic List).CyberTutor will provide a numbered extension (e.g., MUG.co.4) to distinguish them from all other problems under the same topic.As an example, consider a problem that deals with the calculation of moments of inertia.On the topics list, "Moments of inertia" falls under the category "Mechanics" (M), section "Mechanics, Rigid Body Rotation and Energy" (MRB), and the topic "moment of inertia" (.mi).If this is the first problem created under this topic, the filename should be "MRB.mi.1."Similarly, if this problem is the nth problem under this topic, replace "1" with "n," "MRB.mi.n."
Images
Images that will be used in problems, including simple graphics and graphics or diagrams to be used with the curve evaluator and vector module, must be created in an outside graphics program.The image files must then be uploaded to CyberTutor.Only normal web formats (.gif, .jpg, .png) are supported.However .jpg should not be used for the curve evaluator, as it is a "lossy" compression algorithm and does not recreate the image as exactly as necessary.
Uploading an image:
1) It is currently necessary to open a open a new window in your browser (by clicking on "File" on the browser menu bar, and then selecting "New Window").
2) Input the address:
http://cybertutor.mit.edu/upload.html.
3) If you know the path and filename (e.g., c:/classdocs/physics.gif) leading to your image, enter it directly.Otherwise, click "Browse" to look through the files on your computer to find the image you wish to upload.
4) Enter the filename you wish to use to save the image in CyberTutor's files.Note: we recommend you use the same filename with which you've stored the image on your own computer, and that you keep a list of uploaded files.
5) Click "Upload File" to import the file.
6) If you were successful, CyberTutor will return a message indicating that you have been successful and displaying the image.You will then have the option to upload additional files by clicking on "GIF upload page."
When setting up a problem that will include an image, you will need to reference the image using HTML as follows:
<img src=/probhtml/yourimage.gif>
This tells your browser that you would like to insert an image, and that the directory source (src) is as follows.Note: /probhtml is the default directory for all images.If you would like to align the image in a particular position, for example, to ensure that the image is on the left and the text on the right, you can include align=left(or right or center) after the src command.
Vector Diagrams
To create a vector diagram to use for a vector answer type, you must do the following:
First, create the image that you will use for your background using any graphics program.Upload this image to CyberTutor using the instructions above.Open a new browser window and input the address
http://cybertutor.mit.edu/au.html.This will take you to the Vector Creation page.
Load your background image by inputting the file name and clicking on load.The image should show up in the diagram box.
Below the diagram box, select what you would like to add to the diagram.
Vectors:
1) Click "real" to draw a vector that you would like a student to input as part of the answer.Click "provided" to draw a vector that will be provided to the student on the diagram when they open the problem.
2) Specify the symbol or text that you would like to be associated with the vector in the problem and, if the vector is provided, shown on the diagram.
3) Using the mouse, draw the vector on the diagram.When you are finished, click "Add these fields" to add the vector to the diagram.
Regions
Click "region" to draw a polygon specifying acceptable starting points for a vector; this is useful if you would like to define a starting point and have this factored into the grading.
1) Click "define region" to begin creating a region.
2) Go to the diagram and define the region by clicking on points to define a polygon.
3) Input a symbol explaining what the region is if desired.
4) Click "add fields"
5) To make a vector with the region as a starting point, you would now add another starting in this region as above.When this is complete, this will specify that the student must start the vector in this region for it to be judged correct.
Center:
Clicking "center" allows you to define the starting point for a sum vector arrow; a red dot will appear at this point when the vector sum is zero.
When you have completed all vectors, regions and a center, write a name for this vector file. Go to the bottom of the file and click "Submit" to create the vector diagram.When you are creating a problem file, you will add in the vector diagram by selecting the vector answer type and specifying the file name.
Curves and Diagrams
The process for creating curves and diagrams to use with the curve evaluator is currently under revision.As soon as the new process has been finalized, instructions will be sent to all problem authors and included in the help documentation.
For the time being, those of you familiar with Xfig who would like to create diagrams for use with the curve evaluator using Athena can find an older set of instructions can be found at the following link:
http://cybertutor.mit.edu/docs/curvegrader.html
Variables
In selecting the manner in which to display variables in your problems, it is important to remember that students are able to input only plain, unformatted text.When naming variables, you should name them in a manner which makes it easiest for the student to answer the problem, that is, they should be able to input the name of the parameter precisely as it is displayed in the problem text.This may mean forgoing bold type or italics in cases where you might generally prefer to use them or writing out Greek symbols or subscripts.Also, remember that the answer engine is case-sensitive; for example, ``g'' will not be interpreted as being the same quantity as "G."
Use standard mechanics symbols when you are authoring problems.For example:
|
Distances (use d for a smaller distance than D, etc.)
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1, L, d, D
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Vectors
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Use bold to name vector variables and emphasize that it is a vector in your wording, e.g., "the vector F_AB, the force that object A exerts on object B".
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Angles
Angular velocity
Angular acceleration
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Theta, phi, etc.
Omega
Alpha
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If you would like to include a variable name in bold or italics, you can do so using the following HTML tags:
Bold text<b>text</b>Text within brackets displays in bold.
Italicized text<i>text</i>Italicizes text between brackets.
Greek symbols: In general, for Greek symbols, write out the word if students will have to input this as part of their answer.Otherwise, it is fine to use the symbol.
Sub and super scripts: If the sub or superscript is only a single number or variable (e.g., p1 for initial momentum), it is the convention not to use the TeX subscript symbol.For longer subscripts, if students will need to include this as part of their answer, you should use notation that they might easily input, e.g., p_init.
If the subscript will not be part of the answer, you can include subscript notation.In HTML, you do so as follows:
Superscript<sup>text</sup>Text within brackets displays as superscript.
Subscript<sub>text</sub>Text within brackets displays as subscript.
To display a single sub- or super-scripted number, you might use the ⊂ or &sup' tags (the ambersand and semi-colon are necessary).For example, to display m² using HTML tags, you would use:
m²
The superscripts for squares and cubes come up so often that they have shortcut tags. That is, x² may be obtained by entering:<var>x</var>²
while to get x2, you would enter:<var>x</var><sup>2</sup>
The tags ¹ and ³ do analogous things.
Square roots: Square roots are generally entered in one of three ways, as follows:
sqrt(2*y/g) or(2*y/g)^0.5or(2*y/g)^(1/2
Coordinates and Signs:
Cartesian coordinates (perhaps even two sets) should be shown on your figures.For example, you may want to ask students to identify the coordinate system that has the most unknown quantities along the coordinate axes.In this way, you can force the issue of which way to orient the coordinate system.If it is a clear-cut selection, you should simply instruct them to use the coordinate system shown, since it aligns all of the unknowns along a coordinate axis so that they appear in only one equation.
+ direction:+ direction: Always up and to the right, even for bodies moving down or to the left.Outwards for radial coordinates.
+ for angles and angular momentum: Always counterclockwise for positive, which is pretty standard for angles.And importantly, always positive counterclockwise for angular momentum. (The opposite convention for angular momentum is inconsistent with the right hand rule and violates the rule torque = x*p_y - y*p_x.)
Origin for torque problems, orientation for Cartesian coordinates.For the present, guide the students to the best choice (e.g., by stating that "most unknown forces act through it," etc.).
Vector Notation: If you would like students to answer a problem using vector notation rather than a vector image, it is important to keep in mind that any answer must take the form in which it would appear in a paper problem, i.e., the answer will be either in terms of components or in terms of magnitude and direction.
For answers that are given in terms of components, Cybertutor can handle at least two formats: ordered pair or ordered triple.For example, an answer might be entered as: (15,5,5).The answer engine will accept this either with or without parentheses.
Magnitudes and directions can be handled in a number of ways, most easily by having two parts
For the first part, you will select the symbolic answer type and have them input a simple number for the magnitude.For the direction, you could use either a multiple choice pull-down or string answer type.
You can also use unit vectors, but you need to tell students in the context of the problem what they must type for the unit vectors.The convention that has emerged is to use x_unit, y_unit, z_unit'.If this is done, the text of the problem should include instruction to the effect of use x_unit for i, the unit vector in the x-direction," etc. Students would input an answer as follows: 15*x_unit+5*y_unit+5*z_unit.
Typing Equations: You should ensure that your equations do not break in the middle, as this can be confusing.The easiest remedy is to use the non-breaking space commands.There are two options:
1) may be used in situations where you'd like to avoid one non-breaking space.Note: the ambersand and semi-colon are necessary.For example, if you are specifying units, m² / kg², you would want to ensure that this remains on the same line.You could use as follows: m²$nbsp;/ kg²
2) The <nobr></nobr> tags are an easier way to ensure that unwanted breaks do not occur.
For example, consider the equation for Netwon's gravitational constant:
G = 6.67 x 10-11 N · m² / kg².
To ensure that this equation does not break, you could simply enclose it in the following tags:
<nobr>G = 6.67 x 10-11 N · m² / kg²</nobr>.
Non-breaking space tags should be used whenever you are including an equals sign and with ``>'' and ''<," and it is recommended that you use it with binary operators (+, -, *, /, etc.).
Really long equations, in any form, should be centered; this is done using the following tags:
<p align=center>equation</p>
Paragraph tag<p> text</p> Denotes the beginning and end of a paragraph of text
alignment attributealign=left/right/centerAligns the text within the tags to the left, rightor
center of the page.
To input fractions, you use the ½ tag.This tag, for example, gives you ½.This tag can be used with any numbers, e.g.,
¼¼
¾ ¾
Additional useful HTML tags for equations:
Less than<
Greater than>
middle dot·As used between N and m²in this equation: G = 6.67 x 10-11 N ·
m²/kg²
degree°Will insert a circle as superscript for a degree sign, e.g. 32°
±±
x×
/÷
E.Using HTML for CyberTutor
HTML, as used in CyberTutor, will consist primarily of HTML tags that will accomplish the following tasks:
1) formatting text
2) displaying mathematical and physics symbols
3) displaying inserting images where needed
4) setting up tables to provide greater control over text display.
For a much more thorough Quick Reference to HTML, please refer to the following site:
http://www.frc.ri.cmu.edu/~mcm/tags.html
You can also refer to the HTML Character Set Guide at
http://www.natural-innovations.com/boo/doc-charset.html
Formatting Text and Displaying Symbols
Most of the important tags for formatting text and displaying mathematical and physics symbols werecovered above.However, they will be recapped here for your convenience.Note: all letters in HTML tags (the letters between the brackets ``<'' and ``>'' are case-insensitive.However, in these notes, lowercase will generally be used.
Bold textText within brackets displays in bold.
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<b>text</b>
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Displays text between brackets in bold.
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Italicized text
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<i>text</i>
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Italicizes text between brackets.
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Superscript
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sup>text</sup>
&subx;
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Text within brackets or number (denoted by x) displays as superscript
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Subscript
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<sub>text</sub>
&subx;
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Text within brackets or number (denoted by x) displays as subscript
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Paragraph tag
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<p> text</p>
<p align=left/center/right>…</p>
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Denotes the beginning and end of a paragraph of text.Alignment options align the text within tags to the left, center and right or the page.
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Line break
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text<br>
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Inserts a line break in your text.We've found that to make a problem display best, you often should include a line break after the problem statement and answer, as well as after hint text.
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No break
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<nobr>…</nobr>
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Text or graphics with this tag will always display on one line.The line may run beyond the right edge of the browser window, requiring horizontal scrolling.
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Non-breaking space
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Prevents text from breaking at the point where the tag is inserted.
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Fractions
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&fracxx;
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x denotes a number.Allows you to create any fraction you choose, e.g., ¾ for ¾
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Middle dot
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·
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As used between N and m²in this equation: G = 6.67 x 10-11 N · m²/kg²
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Degree
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°
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Will insert a circle as superscript for a degree sign, e.g. 32°
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Plus-minus
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±
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Inputs the ± symbol.
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Times sign
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×
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Inputs the x sign.
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Divide sign
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÷
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Inputs the / sign.
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Images
The <img> tag places a graphic on a page.As explained above, to insert an image into a problem part, for example as part of the problem setup, you would include the following tag as part of the text of the problem setup.
<img src=/probhtml/yourimage.gif>
You can also select alignment options for your image, which will help to determine where it displays.
align=typespecifies the alignment of the image using one of the following attributes:
leftAligns the image on the left margin and allows subsequent text to wrap.
centerCenters the image horizontally on the page and aligns the text baseline with the middle of the image.
rightAligns the image on the right margin and allows subsequent text to wrap.
The alignment option is displayed within the brackets, as follows:
<img src=/probhtml/yourimage.gif align=center>
Tables and Formatting
Table tags may be used in CyberTutor to ensure that images and text blocks are aligned in a way that is visually pleasing. It is important to keep in mind that the pages in CyberTutor are generated dynamically, and that different users will in general have different browser windows and font sizes.When we want a block of text, most often the introductory material, next to a figure, and we don't want problem parts or hints to end up being "squeezed" by the figure, we can use a table.
The basic table tags are as follows:
<table>…</table>Defines the beginning and end of a table. The end tag is required.
Attributes:
align=left/right/centeraligns the table within the text flow, similar to align in the <img> tag. The default alignment is left.
<tr>…</tr>Defines a row of cells within a table.A table row as delimited by <tr> tags
contains no content other than a collection of table cells <td>. The end tag is
optional.
<td>,,,</td>Defines a table data cell.The end tag is not required, but is recommended.
Attributes:
align=left/center/rightAligns the text or other elements (such as graphics) within a table cell.The default value is left.
width=numberSpecifies the width of the cell in pixels or by a percentage value relative to the table width, e.g., width=25%.The width specified in the first row will apply to the rest of the cells in the column.
To demonstrate how to use these tags to create a table, we'll return to the example we provided in "Creating New Problems."The HTML for this table was as follows:
<table><tr><td><img src="/probhtml/MFS.3l.3.gif"align="left"></td><td>A 5N weight rests on the floor.<br>Fill in the blanks in the following sentences.<br><b>Use lower case letters (except N for 'newtons'') and only one word for each answer.</b></td></tr></table>
This table would display the image on the left, with the text on the right.There would be a gap between the first and second sentences, as specified by the <br> tag, as well as between the second and third.The third sentence would display in bold text, as specified by the <b>…</b> tags.
Using tables is not always necessary to make problems display well.However, you may find it to be helpful.If you do plan to use tables, you can expect a bit of trial and error until you understand the way in which the tags interact. For a more complete description of how to use table tags, refer to the Quick Guide to HTML, referenced above.
IV
.Topic Listtc \l1 "Topic List
CyberTutor's Physics content is currently divided into three general categories: Necessary Math(N), Mechanics (M), and Statistical Mechanics and Elementary Thermodynamics (S).The topics list is further divided into sections, e.g., Algebra (NA) and topics, e.g., linear - one variable algebra (11).As explained below, these divisions are used in specifying filenames for problems when authoring as well as for understanding where problems fall in the topic tree when reviewing existing problems.
NECESSARY MATH (N)
NA: Algebratc \l1 "NA: Algebra
11linear - one variable
l2simultaneous linear - two variables
lnsimultaneous linear - n variables
apadding polynomials
mpmultiplying polynomials
dfdivision and factoring
rfroots and the factor (x-r)
csquadratic equations, completing square
qfquadratic formula
dsdiscriminant
rdeliminating radicals
cfcombining fractions
spseries and progressions
bebinomial expansion
NX: Exponents, Logs, Scientific Notationtc \l2 "NX: Exponents, Logs, Scientific Notation
es a^(n+m) = a^n * a^m tc \l2 "es a^(n+m) = a^n * a^m
ena^(-n) = 1 / (a^n)
eza^0 = 1
eddefinition of e
snexponential scientific notation
sfsignificant figures
gpgraphs and properties of exponents
elx = b^[log_b(x)]
lnln(x), logarithms to base e
lplog(x*y) = log(x) + log(y)
lqlog(x/y) = log(x) - log(y)
lwlog(x^p) = p*log(x)
pspower series for e^x and ln(x)
NG: Geometry and Analytic Geometrytc \l1 "NG: Geometry and Analytic Geometry
stsimilar triangles
paperimeter and area
avarea and volume
ocorthocenter & centroid
aspolygon angle sum
lelinear equations
csconic sections
7
asasymptotes
NT: Trigonometry
ptPythagorean Theorem
stspecial triangles
rmradian measure
tffunctions: sin, cos, tan, csc, sec, cot
tetrigonometric function expansions
titrigonometric identities
dhdouble and half angle formulas
oeodd & even functions
aaangle addition formulas
sclaws of sines and cosines
NCD: Calculus - Differential
dpdifferentiate polynomials
dfdifferentiate special functions
prdifferentiate products
crchain rule
tsTaylor series
NCI: Calculus - Integral
ipintegrate polynomials
itintegrate special functions
bpintegrate by parts
NV: Vectors
drdefinition and representations
cccartesian coordinates
pcpolar coordinates
uvunit(base) vectors
ctcomponents and trig
asaddition and subtraction
spscalar product
vpvector product
liline integrals
grgradient
NF: Functions
fxfind f(x)
dndefinition: ind var, dep var, etc.
grgraphing f(x)
smsimple manip: x = x-3, -x; -f(x)
MECHANICS (M)
MPM: Physics and Math
ppSolving physics problems
vpVariables, parameters, constants
8
kuThe answer: knowns vs. unknowns
pnWhen & where do we plug in numbers?
scSpecial cases (to test answer)
caChecking the answer
MDU: Dimensions and Units
pdphysical dimensions: t,l,m
siSI system - def'n of base units
duDerived units (e.g. force, energy)
mwMass vs. Weight
dvWriting dimensioned variables
cuConverting units
daDimensional analysis
omorders of magnitude
esEstimation, Fermi Problems
M1K: Kinematics in One Dimension
avAverage velocity
aaAverage acceleration
dvdefinition & concept v = dx/dt
dadefinition & concept a = dv/dt
gigeneral integrals
gmGraphing motion vs time
caConstant a: x(t), v(t)
clconstant $\alpha$
vdv(t)^2 = v0^2 + 2 a*(x(t)-x0)
papiecewise constant acceleration
2btwo body problems
MAK:Kinematics - Angular
om$\omega=d\theta/dt$
al$\alpha=d\omega/dt$
otomegaf^2 = omegai^2 + 2*alpha*theta
M2K: Kinematics - Two Dimensions
dvDefinition & concept v = dx/dt
daDefinition & concept a = dv/dt
giGeneral integrals - 2d
caConstant a: r(t)
pmProjectile Motion
cmr(t)=R(t)[cos(wt)x^ + sin(wt)y^]
caCentripetal acceleration
rmRelative Motion
MFS: Force and Statics
3lNewton's 3rd law: real force pairs
1lNewton's 1st law: sum(F) = 0
ffFundamental forces of physics
cfContact forces (normal, friction, viscous drag)
9
fxf(x): springs
spSprings in parallel and series
naa = 0, no acceleration
MTS: Torque and Statics
ToTorque = r x F
stStatics (a = $\alpha$ = 0)
popicking the origin
MLD: Linear Dynamics: F=ma IN 1 & 2-d
1dF = ma in one dimension
2lNewton's 2nd law: sum(F) = ma
dyDynamics (selecting coord system)
coConstraints in 2-d: track, string
cmForces in circular motion
MWE: Work and Kinetic Energy
weWork-Energy Th'm from kinematics
keKinetic Energy of point body
wiWork Integral: definition & meaning
cwCommon work integrals
ckconservation of kinetic energy
poPower = dW/dt
MPE: Potential Energy
cnConservative vs Non-conservative
uxDef'n: U(x)= -line int F.ds to x=-W>x
grF = - Grad U(x,y)
Common Potentials:
uguniform gravity
spspring
cgcentral force gravity
MME: Mechanical Energy Conserved
ceUf + Kf = Ef = Ei + Wnc = Ui + Ki + Wnc
cmconservation of mechanical energy
peU(x) Diagrams, equilibrium and KE
MLM: Linear Momentum
mvp = mv F = dp/dt
siSystems and internal forces
cmCenter of Mass F = M acm
imImpulse: J = delta p
mcConservation of Momentum
rfCenter of mass reference frame
rmreduced mass $\mu$ = m1*m2/(m1+m2)
ininelastic collisions
e1elastic, 1-d general
10
erelastic 1-d, m2 initially at rest
e2elastic 2-d general
fmFlowing mass - Rocket Eqn.
fdForm Drag f = -CD A v^2
MRB: Rigid Body Rotation and Energy
rrRigid Body Rotation, $\omega^\rightarrow$
rmRolling Motion without slipping
miMoment of Inertia
keRotational Kinetic Energy
paParallel Axis Theorem
wpRotational Work and Power
pePerpendicular Axis Theorem
MAD: Angular Dynamics
iaT = Ia
iwL = Iw + Rcm X p
dlT= dL/dt
clConservation of L
aiAngular Impulse
d3T=dL/dt in three dimensions
pgPrecession of Gyroscope
ngNutation of Gyroscope
MUG: Universal Gravity, Kepler
klKepler's Laws
urU(r)=-mMG/r
frF(r)=-mMG/r^2
coCircular Orbit
evEscape Velocity and Cons of Energy
clCons of L and Apogee and Perigee
eoElliptical Orbits
ssF(r) and U(r): shells and spheres
MHM: Simple Harmonic Motion
fpFrequency (w and f), Period
deDifferential Equation, w = sqrt(k/m)
xtx(t) = A sin(wt + delta)
vav(t) and a(t)
icInitial conditions
x2x(t) = xo cos(wt) + vo/w sin(wt)
cmRelation to circular motion
ehEnergy in Harmonic Motion
pmPendulum Motion (simple, physical, torsional)
dmDamped Harmonic Motion
drDriven Harmonic Motion, Resonance
tqTime constant, Q factor
11
MRM: Real Materials
ssStress and strain
moModulus: Young's, shear, bulk
psPoisson ratio
tsTensile Strength
teThermal expansion
MAR: Accelerating Reference Frames
ffFictitious forces
lflinear fictitious
ceCentrifugal force
coCoriolis force
MWV: Waves
maMath description of waves on a string
sfWave speed, frequency, wavelength
weWave equation
siPrinciple of superposition, interference
swStanding waves: boundary conditions (1 or both ends fixed)
etEnergy transmitted by waves
lwLongitudinal waves: pressure
swSound waves, beats
deDoppler effect
S:
STAT MECH AND THERMODYNAMICS
SFL: Fluids
rorho = mass/volume, States of Matter
ffFluid Flow, v1 A1 = v2 A2
apArchimedes Principle
plPressure and Pascal's Law
beBernoulli's Equation - Cons of Energy
stSurface tension
viViscosity
SIG: Ideal Gases
pgpressure of particle gas
ieInternal Energy of gas
eqequipartition theorem
pvPressure of Ideal Gas, pV=NkT
vwvan der Waals Equation
fpMean free path
STH: Thermodynamics
teDef'n of Temperature, Heat, Equilibrium
1lFirst Law of Thermo
2lSecond Law of Thermo
cpCp = Cv + R, gamma = Cp/Cv
dwdW(by gas)=p dV
12
plp vs V plots
aeAdiabatic Expansion of Gas
tcThermodynamic Cycles (Carnot, etc.),
heHeat Engines, heat pumps, etc.
enEntropy, of Ideal Gas
pdPhase diagrams
ptPhase transitions
crThermal conductivity & resistance
13
| Annotation Author Key |
| Initials | Full Name |
| COMMENT | COMMENT |
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