Exam Preparation and Grades: 
A System for Addressing Questions, Challenges, and Problems


List of topics                             Outline page
    Abstract
    Introduction
    Regular Exams
    Make-up exams
    Weighting Exams
    Exam Averages
    Predicting needed grades
    Final Grades
    Links to additional strategies
    Conclusion
    References


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Abstract

The system presented solves questions, challenges, and problems with preparing exams and grading. It includes detailed instructions, rationales, web pages, examples, and EXCEL spreadsheet templates. Use these components to keep grades, show grade distributions, calculate cumulative grades, make grade predictions based on assumptions of student performance, and inform students

Introduction

I developed and use a pragmatic system for addressing questions, challenges and problems faculty and students often have about exam preparation and grades. A few examples from faculty include "How long should I make the exam?" "How can I make different but equivalent exams for all my sections?" "What level of achievement earns a grade of A, of B, etc.?" "What can I do about poor questions I asked?" A few examples you have probably heard from students include "Do you give partial credit?" "Do you grade on a curve?" "What is my average?" "Can I still get a B?" "What must I get to pass?" (Challenges and problems - Table 1)

Three of the systemís strongest attributes are adaptability, flexibility, and clear results. It works for any exams, for small or large classes, and for single-section or multiple-section classes. It also works for other student work I grade where I assign values to each answer, component, section, or characteristic, such as when I grade reports and presentations. The final products are (1) a spreadsheet grade book for recording student scores, (2) a graph for each exam or other work showing the class score distribution, and (3) a table showing the grade equivalent for each student's individual and cumulative scores plus all possible scores. The URL hyperlinks I included take you to the accompanying web pages for more complete instructions, explanations, examples, and corresponding templates you can use or adapt to meet your requirements.

This novel system may seem complicated, confusing, and labor-intensive at first, but it becomes easy and quick to use after a few tries. I believe this system can serve you and your students well. To see, just follow the directions below. You can even try it using grades you already have by skipping the marked ** steps. You will obtain clear results plus options you probably did not have before.  (Go to top of page)

Creating and grading regular exams

First exam
1.
Make up the first exam**
    a. Write all the questions possibly wanted on the exam. (When I use a test bank for an exam, I temporarily cross out all questions that may be inappropriate and add new relevant ones.)
    b. Assign appropriate point values for the answers for each question. Employ factors like the importance of the question plus the size and number of parts and complexity of a complete correct answer. If you intend to give part credit for some answers, assign these items several points so you can give partial credit while using only whole integers in grading. Assign equal numbers of points to questions that are of equal importance, even if students cannot receive partial credit for some of the questions (i.e., graded all-or-none).
    c. Decide if you want the students to know the point value for each question. If the students should know the point values, include them with the questions. I usually show the point values unless the point value hints at the number of answers (e.g., "List all chambers of the heart.")
    d. Establish how much time the students will have to take the exam.
    e. Estimate the amount of time a "representative" student would actually need to complete the exam. Decide if you want this "representative" student to be an outstanding student, a mediocre student, or a weak student. This will determine the pace at which students must work and what proportion of students will finish before time is up.
    f. Add or delete questions or points to adjust the exam length so the time in Step 1.d. corresponds with the time in Step 1.e.

2. Give the exam, noting any peculiarities, such as having a fire drill, a power outage, or all students finishing well before the allotted time expires.

3. Grade the first exam.
    a. Give the number of points earned for each answer or part thereof.
    b. While grading, adjust possible points or expected answers.
If students did not know the number of points possible for each question, adjust the possible points for answers that were generally much better or much worse than you should have expected (e.g., student answers show I gave a confusing presentation). If students knew the number of points possible for each question, adjust the answers you accept for questions where answers were generally much better or much worse than you should have expected (e.g., student answers show I gave a confusing presentation).
    c. Regrade questions or test papers where you adjusted the possible points or the expected answers.**

4. Add the points earned by each student and record that number in the grade book (Test 1) (sample grade books). To minimize errors and to permit careful checking of my computer files, I write the grades by hand on a hard copy of my grade book before entering the grades into my computersí grade book spreadsheet. As backups, I make a photocopy of the written grade book and a backup file of the spreadsheet. I keep these in separate secure locations, because I have had my grade book stolen and my office computer used without my permission. I now have a power-up password installed on my computer.

5. Determine the total possible number of points attainable on the exam.

6. Make a graph showing the number of students who earned points within each point range (e.g., for small exams 0-1, 2-3, 4-5, etc.) (e.g., for large exams 0-4, 5-9, 10-14, etc.) Computers can do this (Graph 1), but I just use a piece of lined paper and place an X-mark for each studentís score (Hand drawn Graph 1)

7. Determine the minimum number of points required to achieve each letter grade. These values can be anything you choose based on what the letter grades mean. For example, on an 85 point test, they may be A= 69, B= 59X, C= 50, D= 41. To do this, consider all circumstances for the particular exam plus your concept of what each letter grade represents. (Table 2) For me, my institutionís catalog describes grade meanings well. (Table 3)

8. Create an EXCEL grade conversion table (GCT). Title the first two columns "Letter Grade" and "Number grade". The third column is for "Points." (GCT for Test 1) and "Instructions for creating a grade conversion table")
(Grade Conversion Table Template) (sample GCT tables).

9. Before returning the graded papers to the students, show the students the graph and grade conversion table. Explain the meaning of the grade cut-offs (e.g., 69 points = "90" = "A-", 59 points = "80" = "B-", etc.) and explain that point values between the cut-offs equal grades between the cut-offs. (e.g., 63 points = "84" = "B"; 55 points = "76" = "C"; etc.) The graph shows trends in the student achievement on the exam plus each studentís letter grade and level of achievement relative to all students in the class. The grade conversion table shows you and each student his or her letter grade and numerical grade on the standard A/B/C/D/F and 100/90/80/70/60/0 point scales, respectively. Post the graph and grade conversion table where students can refer to them, such as on bulletin boards or convenient web pages.**
I always have students who misinterpret the bar graph at first because they are accustomed to receiving their grades as percentages out of 100. My students also initially resist looking up their letter and numerical grades on the grade conversion table for the same reason. My solution is to persist by (a) repeating my explanation and (b) using the graph and table patiently and consistently with every student who wants help with knowing and understanding his or her grade.(Go to top of page)

Second exam
1. Make up the second exam. Use the same steps as for the first exam. This exam does not have to be the same length as the first exam; it can be any length and have any point value. (e.g., 77 maximum points possible for a test covering less material than the previous 85 point test)
2. Give the exam, noting any peculiarities (e.g., fire drill, power outage).
3. Grade the second exam**
4. Use the same steps as for the first exam. (e.g., bar graph with 70 points = "90" = "A-"; 61 points = "80" = "B-"; 52 points = "76" = "C-"; 44 points = "60" = "D-").(Hand drawn Graph 2)
5. Create a grade conversion table for the second test (GCT for Test 2) and a grade conversion table for the total of Test 1 + Test 2 (GCT for Test 1+2). Title the first two columns "Letter Grade" and "Number grade". The third column is for "Points." ("Instructions for creating a grade conversion table") (Grade Conversion Table Template)
6. Before returning the graded papers to the students, show the students the bar graph and grade conversion tables, and explain the meaning of the grade cut-offs. Explain that for a student to determine an exact exam grade, use the GCT for Test 2. Explain that for a student to determine an exact exam average, add the studentís scores on the two exams to get the point total. Find that total in the "Points" column on the GCT for Tests 1+2. The corresponding average and letter grades are in the adjacent "Grade" columns. Of course, point totals between those in the table correspond to grades between those in the table (e.g., 89 points = "62.5" = "D-").**
At this point, I always have students who become confused because they are accustomed to determining their course average by adding grades and dividing that sum by the number of tests. My solution is to persist by (a) repeating that the student need only add SCORES, find the sum on the table, and see the letter and numerical GRADES next to that score and (b) going through the procedure with each student who wants help with knowing and understanding his or her grade. After this, students understand and appreciate the systemís simplicity and clarity, and they rarely seek assistance with it.(Go to top of page)

Third exam, etc.
1.
Make up and give the third and subsequent exams. For each exam, use the same steps as for the first exam.**
2. Grade the third and subsequent exams. For each one, use the same steps as for the second exam. Update the grade conversion table to include all exams given. (GCT for Tests 1+2+3+4+5)

Creating and grading make-up exams

1.
Create and give a make-up exam
    a. Use the same steps as for the second exam.
    b. Determine the maximum possible points on the make-up exam (e.g., 103 possible points on the make-up for Test 1.)
2. Grade a make-up exam
    a. If the make-up exam is considered to be equivalent to the original exam Ė
        (1). Determine the percent of the total points possible on the make-up exam that the student actually earned on the make-up exam (e.g., 89 points on a 103-point make-up exam = 86.4%).
         (2). Use that percent to calculate the equivalent number of points on the original exam (e.g., equivalent points on original exam = 85 x 0.864 = 73.44 = 73 points).
3. Record the equivalent points as the points earned for the exam that was being made up.
    a. If the make-up exam is not considered to be equivalent to the original exam Ė
        (1). Use your judgment to determine the studentís equivalent points for the original exam.
         (2). Record the equivalent points as the points earned for the exam that was made up.
        (Go to top of page)

Changing the effect or weight of an exam

To change the effect or weight of any exam on exam averages after the exam has been given and graded (e.g., to decrease the effect of class-wide poor performance on the first exam because there is class-wide improvement in performance on subsequent exams, to increase the effect of an exam because subsequent exams covered less material due to canceled classes.)

1. Decide how much adjustment should be made (e.g., lower the weight of an exam so its maximum possible points are only 57 points = 66.7 percent (i.e., 0.667) of its original weight, increase the weight of an exam so it has 110 points = 127.8 percent (i.e., 1.278) of its original weight). This final weight is "value (4)".
2. Multiply the point value for each grade cut-off and multiply each student points on the test by value (4). Using the EXCEL table for grades eliminates the need for doing the individual calculation for every student. (Test 1 Revised) Many students will not do the arithmetic to calculate their revised points, so I also create and post a table showing the revised points that are equivalent to the original points. Students find their revised points next to their original points. (Changing maximum possible points on Test 1) If you do not use an EXCEL table for grades, you can use this table to find the revised points for each student and enter those revised points for each student into your grade book.
3. Create a revised grade conversion table using these new adjusted point values for the grade cut-offs and grade 100. (GCT for Tests 1+2 Revised)
4. Calculate student exam averages using the revised grade conversion table and revised student points. (GCT for Tests 1+2 Revised) (Test 1+2 Revised)
  (Go to top of page)

Calculating an exam average grade at any point in the semester

1.
Add points earned on exams.
2. Use the grade conversion table to find the grade corresponding to points earned with either the original Test 1 or the revised Test 1. (GCT for Tests 1+2+3+4+5 Original) (GCT for Tests 1+2+3+4+5 Revised) (Tests 1+2+3+4+5 Revised)

Predicting what will be needed on future exams to achieve a certain numerical average for all exams

1.
Calculate the studentís point total.
2. Estimate the final maximum possible points for all exams.
3. Estimate the total number of points needed to achieve the desired exam average on all exams. (Since my courses are similar from semester to semester, I use previous bar graphs and grade conversion tables to do this.)
The difference between the studentís point total and the points needed to achieve the desired exam average is the total points the student must earn on remaining exams.
4. Estimate for each upcoming exam how many points, what percentage of total points possible, or what grade range the student must earn to end up with the total number of points needed. (e.g., after three exams, a student is eight points below the grade B cut-off. If there are two exams remaining and the student wants to end up with a B, the student must earn an average of four points above the grade B cut-offs on each of the two remaining exams.)
(Go to top of page)

Calculating final grades
(e.g., calculating final numerical "average" for exams)

1.
For each student, add points earned on all exams.
2. Use the grade conversion table to find the numerical grade corresponding to points earned with either the original Test 1 or the revised Test 1. (GCT for Tests 1+2+3+4++5+6 Original) (GCT for Tests 1+2+3+4+5+6 Revised) (Tests 1+2+3+4++5+6 Revised)
For point totals that are between whole grade numbers, estimate to the nearest tenth of a grade number (e.g., 293 points = 72.6 = C-). Note you also get the letter grade for exams on an A/B/C/D/F basis. (GCT for Tests 1+2+3+4+5+6 Revised)
3. Use the numerical "average" for exams with any other graded component in the course to determine the final numerical course grade and final letter course grade. (e.g., final grade = 66.67 % from lecture tests + 33.33% for lab tests). I set up my EXCEL grade book with additional columns to do these calculations once I enter the students' numerical grades for each course component.
  (Go to top of page)

Additional strategies using EXCEL spreadsheets
 (e.g., drop lowest grades, find letter grade for each numerical grade), see the following.

"Using Spreadsheets to Keep Track of Students' Grades" by Richard Zach, http://www.ucalgary.ca/~rzach/teaching/grades.html September 2004

Conclusion

In developing, modifying, and using this system of practical methods for addressing diverse issues with exams and other grading, I now believe it has become a coherent, efficient, and effective set of procedures, interactive tables and graphs that are applicable to many courses. It permits me to make justifiable decisions consistently. I follow the steps starting from the first stages in developing exams and other evaluation methods through the last step in determining final grades. The system permits reasonable adjustments and flexibility when unusual or unpredicted circumstances occur during a course. Students quickly find the system to be fair, simple, clear, and useful once they adapt to some of the systemís novel features. Main ones are my using exams of different weights, grading based on points rather than percents, adding points rather than calculation of averages, and using grade conversion tables to find the exact grade that is equivalent to the number of points earned. Improvements to this system could include automating my spreadsheet grade book templates so they create grade distribution graphs and convert the final point totals into final numerical grades and final letter grades. Currently, I do these two procedures by hand. The referenced web site by Richard Zach explains other possible additions and options for the EXCEL spreadsheet grade book.   (Go to top of page)

References

Salisbury University Undergraduate & Graduate Catalog  The 2016-2018 catalog is at
https://www.salisbury.edu/academics/catalog/16-18/Full-Catalog_16-18_sm.pdf. See page 21.

               or

    1. Go to http://www.salisbury.edu.
    2. Search for "Catalog" to go to the "Salisbury University Undergraduate & Graduate Catalog"
    3. Search for "Grading System"

Zach, Richard, "Using Spreadsheets to Keep Track of Students' Grades" (2004) http://www.ucalgary.ca/~rzach/teaching/grades.html
(September 2004), Department of Philosophy, University of Calgary

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Augustine G. DiGiovanna, Salisbury University (November 2004)
agdigiovanna@salisbury.edu

© Copyright 2017, 2004 A.G. DiGiovanna, Salisbury University, Maryland. All rights reserved.