PRACTICING and ASSESSING BASIC MATHEMATICS SKILLS

HOW TO USE THIS NOTEBOOK:
To access any of the topics presented below, double click on the far ight-hand vertical blue line with the solid triangle at the bottom.  When \finished with the selected topic, double click on the far right-hand verical \blue line without the solid triangle at the bottom to close that topic.

PROJECT AUTHOR

\tProject designed by Adele Miller - Summer 1998		at jmmiller@ultranet.com\>

PURPOSE

The purpose of this notebook is to present an example of how Mathematica might be used in the college developmental mathematics classroom for \drill work and for assessment.  Because many traditional and non-traditional \students arrive at college with weak mathematics skills, there is frequently \a need for these students to work on building basic mathematics skills in \order to be successful in some college-level mathematics course.  It is also 
ecessary for students' instructors to assess the competencies of each \student as the course progresses.  This notebook provides a tool that can be \used either for drillwork or for students' assessment or for both.

CONTENTS OF NOTEBOOK

This package provides practice exercises in adding signed integers.  It is \made up of ten exercises.  The first five exercises give two integers to be \added, the next three exercises give three integers to be added, and the last 	wo exercises give four integers to be added.  The integers are generated andomly and have values between -100 and 100.  Therefore, if a student goes 	hrough the ten exercises and wishes to practice the concept again, (s)he \will be given different integers with which to work on each subsequent \encounter with the package.  The number of exercises presented will remain 	he same and the number of integers given in each of the exercises will also emain the same unless this Mathematica notebook is modified.
Once the student has completed answering the \exercises, the notebook will inform the student which answers are correct and \which are incorrect.  For the exercise responses that are incorrect, the \student will also be told what the correct answer is.

OTHER CONCEPTS

\While this notebook is  an example of providing practice or assessment in \adding signed integers, practice or assessment in an indefinite number of \other concepts might be made available. Other topics that developmental \mathematics students frequently struggle with that might have parallel 
otebooks include, but are not limited to: subtracting, multiplying and \dividing signed integers; adding, subtracting, multiplying and dividing \fractions; using exponents; finding the least common multiple and finding the \greatest common factor.     \>

MODIFICATIONS TO EXERCISES

Modest modifications can be made to the exercises in this notebook quite \easily with little or no knowledge of Mathematica.  In the cell that contains the lines
SumQuestion[n_]:=
(k=Table[Random[Integer,{-100,100}],{n}];response=	
and the line			
quiz=BuildQuiz[{2,2,2,2,2,3,3,3,4,4}]		
three different changes may be made to provide some variation to the \exercises presented.
	1. In the brackets {-100,100}, the integers may be \modified to smaller or larger values. E.g. {-250,1000} would present integers \between -250 and 1,000 to be added in the exercises.
	2. In the brackets \{2,2,2,2,2,3,3,3,4,4}, the integers may be modified so that a different 
umber of integers are presented for addition.  E.g. {2,3,4,5,6,7,8,9,10,11} \would present 2 integers to be added in the first exercise, 3 integers in the \second exercise, and one additional integer to be added in each successive \exercise until the tenth exercise where there would be eleven integers to be \added.
	3. In the brackets {2,2,2,2,2,3,3,3,4,4}, the number of integers \could be reduced or increased so that a different number of exercises are \presented to the student.  E.g. {2,2,3,3,4} would present only 5 exercises to 	he student.

REVIEW OF RULES FOR ADDING SIGNED INTEGERS

\1. To add two integers with the same sign, add the two integers and keep 	heir sign.2. To add two integers with different signs, find the difference of their \absolute values and keep the sign of the integer with the larger absolute \value.\>

Further Help

***************************************************************************\************** I seem to get the color red no matter what I put into \RGBColor.  Why?  I also get the same size font no matter what size I set and \it looks awful.  Why can't I get something very small when I set the font \size to 1?   I tried naming PrintInColor as PrintInGreen so that I could set \up 2 different colors.   PrintInGreen won't work.   When I do that you can \see that I can't see any output.  Why?
I agree with you that I don't want \students to have to evaluate a lot of cells.  I know that I should have the \10 evaluations of the student's performance in one place instead of 10 \separate evaluations, but I don't have a clue as to how to do that.  I just \don't understand that part of Mathematica at all well.  Especially since I am using Part[Part]], I am confused as 	o how I might do the 10 evaluations at once.                                 \                     *********************************************************\********************************

ACCESSING AND ANSWERING EXERCISES

In order to use the exercises in this notebook, double click on the far ight-hand vertical blue line at EXERCISES.  Once you have "opened" the \exercise section, you will see a mustard colored box with Mathematica instructions in it.  You must now initiate the instructions for Mathematica to generate exercises for you to complete.  This may be done by clicking 	he left-hand vertical blue line on the right side of the box.  Once you have \clicked on the line and it becomes black, hold down the shift key and hit the \enter key.  The first exercise will appear in a Local Kernel Input box, and \you will enter the answer in the white box within that Local Kernel Input box \and then click on OK.   The next exercise will then appear in a Local Kernel \Input box.  At this point you must move the cursor into the box and click on \it.  Now you will be able to type in your response for the second exercise.  \Then click on OK.  You may answer the remaining exercises in the same fashion \as you answered the second exercise.  Once you have completed all ten \exercises you will see a new box in this notebook containing information from \your work.  You may ignore this box and simply double click on the far ight-hand vertical blue line to close the exercise section.

EXERCISES

\(SumQuestion[n_] :=       \((k = Table[Random[Integer, {\(-100\), 100}], {n}];         response =           Input["What is "<>ToString[Plus@@Map[ToString, k]]<>"?"]; 
        \ mathans := Plus@@k; 
rightwrong = \((response == mathans)\);         
{k, response, mathans, rightwrong})\)\)PrintInColor[s_String, c_, size_] :=       NotebookWrite[EvaluationNotebook[],         Cell[s, "Output", FontColor -> c, FontSize -> size]]correct[m_] :=       (PrintInColor[          "Your answer to number "<>ToString[m]<>" is correct.",           RGBColor[0, 0.5, 0.7], 12])wrong[m_, {nums_, reply_}] :=       PrintInColor[        "Your answer "<>ToString[reply]<>" to number "<>ToString[m]<>          " is incorrect.  "<>ToString[Plus@@Map[ToString, nums]]<>          " = "<>ToString[Plus@@nums], RGBColor[0.6, 0, 0.6], 14]BuildQuiz[{nvalues___}] := Map[SumQuestion, {nvalues}]quiz = BuildQuiz[{2, 2, 2, 2, 2, 3, 3, 3, 4, 4}]

ACCESSING AND EVALUATING EXERCISE RESPONSES

You may use the following EXERCISE EVALUATION section to determine whether \your responses to the exercises are correct.
In order to evaluate the \exercise responses, double click on the far right-hand vertical blue line at \EXERCISE EVALUATION.  Once you have "opened" the exercise evaluation \section, you will see a mustard colored box with Mathematica instructions in it.  You must now initiate the instructions for Mathematica to generate the exercise evaluations.  This may be done by clicking the \left-hand vertical blue line on the right side of the box.  Once you have \clicked on the line and it becomes black, hold down the shift key and hit the \enter key.  The evaluations will take place then.

EXERCISE EVALUATION

Map[      If[Part[Part[quiz, #], 4], correct[#],           wrong[#, {Part[Part[quiz, #], 1], Part[Part[quiz, #], 2]}]]&,       Range[1, Length[quiz]]]

REVISITING ADDITION OF SIGNED INTEGERS

If you should wish to complete another practice session of adding signed \integers, click on this message.

QUESTIONS

If you have any questions about how to perform calculations using signed 
umbers, you might want to contact Dr. Math on the Internet at -
 http://forum.swarthmore.edu/dr.math/dr-math.html.
You may leave a question for Dr. Math, and Dr. Math will respond to your \question.

EXITING NOTEBOOK

When exiting the notebook you will be asked whether you wish to save this 
otebook.  If this is a practice session, click on DON'T SAVE before exiting. \ If this is an assessment session, clink on SAVE before exiting.  To exit 	his notebook, click on the X in the upper right-hand corner of the notebook.