Texas A&M University



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Summary

The Automated Mathematics Evaluation System (AMES) is designed to help Physics 218 students identify and overcome the mathematical weaknesses that prevent them from doing well in the course. The system, which is completely self-contained and web-based, is an interactive set of quizzes on problems addressing the core of the prerequisite math skills. This system is used before the beginning of the semester as an evaluation tool, and during the semester as a skill building/rebuilding tool. To use the system, all a professor has to do is pass out the enclosed handout to class (see page 16), and download their students' grades from the web as necessary.

Questions are drawn from a large pool of problems from various mathematical topics essential for 218. These include: symbol manipulation (algebra), vectors (trigonometry), quadratic equations, systems of equations in two variables, translating word problems into mathematical equations and some simple differentiation and integration.

Students are allowed to take as many quizzes as they like, with only the top ten scores counted towards their grade. Each time a student submits a quiz, they receive immediate feedback as the system shows them which questions they answered correctly. Each question answered incorrectly is placed on their next quiz. Those with moderately inadequate mathematical backgrounds thus develop the necessary skills by taking the quiz repeatedly. After attempting the quiz several times, those who cannot achieve a satisfactory grade can be warned by their professor or TA that they are in need of immediate remedial mathematics course(s) while their areas of deficiency are clearly identified to them via the feedback screens.

1. Motivation

The motivation behind developing a web-based, entirely automated, mathematics quiz for Physics 218 students comes from our observation that many 218 students lack basic mathematical skills. For instance, the majority of students express difficulty in solving problems. In their own words, "we've seen it before, but don't know/remember how to do it". They evidently have a hard time translating the words into mathematical equations. If they are successful in writing down the correct equations, they often fail to solve them especially if a problem involves a system of two or more equations. Similarly, nearly all students have trouble with quadratic equations, especially when they are required to solve in terms of symbols. Trigonometry is another common problem area that is addressed by AMES.

There is a high correlation between students who are poor in mathematics and those who eventually fail or drop the course.

While there are other reasons for failing, it seems that nearly all students would benefit from remedial math work before and during taking 218. Even those who have a solid mathematical background will profit from AMES since during lecture/recitation professors and TAs will be able to spend less time explaining trivial mathematical steps and more time teaching physics. AMES is also designed to make students accept a higher standard of basic mathematical skills.

2. Two goals and how they are achieved

A) Weeding out those who will fail at the beginning: Evaluation quiz

The first goal of AMES is to identify early on (first week of semester), students with a severe lack of math skills. It achieves this by giving a quiz after the first class period for evaluation purposes. Those students can then be urged to get immediate help or postpone taking Physics 218 until they have the necessary background. Typically, this quiz would not be counted as part of their grade.

B) Helping those who can succeed: Regular Quiz

Our second goal is to help those students who may have, at one point, had sufficient math skills, but for one reason or another, are now "rusty." AMES is designed to remind them of what once were familiar concepts and make them practice them. AMES allows students to re-take the quiz until they achieve a satisfactory grade. There is no limit to the number of attempts and each attempt has a short time limit. After each attempt, they are given a "feedback" screen where they can see which questions they answered correctly and which not. Each time they ask for a new quiz, they are given one that contains the same questions that they got wrong during their previous attempts and new ones replacing those that they got right. This way, AMES works as a teaching tool.

By forcing repetition in the quiz taking, we aim to familiarize students with heavily used techniques which may be new to them, e.g. solving equations without plugging in numerical values (thus eliminating "symbol fear"), quickly seeing trigonometric relationships etc.

3. The questions:

The quiz interface is user-friendly, with real mathematical symbols (i.e. not "x^2" etc.) and a pleasant layout with color images. The questions are multiple-choice with push-buttons and they follow the arrangement of common computerized tests such as the SAT and the GRE.

Each question has five possible replies that are designed to guide the student towards the correct answer effectively teaching them in the process. The example question shown below is designed to test and teach cancellation of common factors in fractions (a very widespread disability among Physics 218 students)

Note that the "21/7", becomes a "3" in every one of the answers. This serves the purpose of showing one should divide the numerator by the denominator. One may then infer that they must also divide out x and one of the y's since these could stand for any number

The question pool contains approximately 300 questions that fall into seven broad categories shown below.

• Section 1: Simple algebraic expressions with one variable

• Section 2: Systems of equations in two variables

• Section 3: Quadratic equations, quadratic identities

• Section 4: Trigonometry/geometry

• Section 5: Fractions, numbers, exponents, powers of ten etc.

• Section 6: Word problems, proportionalities etc.

• Section 7: Derivatives and integrals

Examples from each section follow:

[pic]

Section 1: Algebraic expressions with one variable

[pic] Section 2: Equations with two variables

[pic]

Section 3 : Quadratic equations

[pic]

Section 4: Trigonometry/geometry

[pic]Section 5: Fractions, Numbers, exponents, powers of ten etc.

[pic]Section 6: Word problems, proportionalities etc.

[pic]

Section 7: Derivatives, integrals, and other mathematical concepts

4. Taking the quiz

Students taking Physics 218 register with the system following the directions presented in the "AMES Handout" (cf. page 15). This begins on the web where students encounter the login screen with directions for setting up a password ().

As soon as the students register with their name, section number, and student ID, they are ready to begin taking quizzes. All information is communicated via a secure connection.

[pic]

Below is a sample quiz-opening screen: Note the timer, clear directions and intuitive interface (push-buttons).

Once students reach the end of the quiz (see figure above) they can submit the quiz for grading or ask for all their answers to be reset. Note that they can change their answers at any time before they hit the "Submit" button.

After students are satisfied with their answers and they hit the "Submit" button, they are shown their score and are given feedback on their performance in the individual questions. If students are unhappy with their score they can simply click on the "Try Again" button and immediately attempt another quiz. The top ten scores for the student are shown at the top of the feedback screen shown below.

[pic]

Note that correct and wrong answers are clearly marked and questions left unanswered are not marked at all. Next time the student takes a quiz the wrong and un-answered questions will reappear.

[pic]

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4. Professor instructions and student handout

5. Conclusions

This tool will supplement the work of professors and TAs and decrease the amount of lecture and recitation time spent explaining trivial mathematical steps. It sets a clearer and higher mathematical standard as the norm for Physics 218. AMES is easy to incorporate into the class syllabus. By using it, problem students can be identified early on in the semester. There is no work-hour overhead for professors and TAs since the quizzes can be taken at any time without the presence of proctors and the grading and feedback are entirely automatic. Our approach is such that students taking the quiz repeatedly will automatically develop those math skills needed for 218, and they will take these with them to Physics 208 and other courses.

6. Acknowledgments

We wish to thank Profs. Kamon, McIntyre, Walther, Webb and Welch for trying AMES in their classes during the Fall 2001 semester, sharing ideas and helping develop the material. Prof. Kenefick was very helpful in TA-ship arrangements. We also wish to thank the Physics Department for its support and the students themselves. Physics 218 students have taken more than thirty five hundred quizzes since September 2001 and provided feedback that has allowed us to remove program and content bugs and fine-tune the system.

7. Relevant web addresses and contact information:

Prof. David Toback has been the driving and coordinating force behind the AMES project since Spring 2001 providing direction and securing funding. Joel Walker has developed the software and Andreas Mershin wrote the problems.

• For more information, comments/suggestions regarding any aspect of AMES please contact Prof. David Toback (toback@physics.tamu.edu)

• For specific information, comments/suggestions etc. regarding the software contact Joel Walker (jwalker@physics.tamu.edu)

• For specific information, comments/suggestions etc. regarding the quiz content or this brochure please contact Andreas Mershin (mershin@physics.tamu.edu)

• To see the entire pool of questions with statistics, login with your physics web userid/pass to:

• To see the entire pool of questions without statistics, login with your physics web userid/pass to:

• To take a sample quiz, first create an AMES userid/pass at: by choosing "sample" instead of section number and then logon to AMES at



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(Example) question #5017

What is the following equal to? [pic]

a [pic]

b [pic]

c [pic]

d [pic]

e [pic]

[pic]

Physics Department

Texas A&M University

A.M.E.S.

Automated Mathematics Evaluation System

PHYSICS 218 'Mechanics'

WEB-BASED MATH QUIZ

A.Mershin, D.Toback, J.Walker

December 2001

HOW TO USE A.M.E.S. IN YOUR CLASS

• Pass out the "AMES directions" handout (see next page) to your students along with your syllabus on the first day of class. You may wish to familiarize yourself with its contents as the students are instructed to take their evaluation quiz after the first class session.

• Check your students' performance and download their grades on the web at URL:



AMES directions for Physics 218 students

The Automated Mathematics Evaluation System (AMES) is designed to improve your math skills. Experience has shown that students with insufficient mathematical background do very poorly in Physics 218. AMES will help you overcome your potential weaknesses in the areas of mathematics you will be using in this course.

AMES is a series of web-based quizzes that you are allowed to take until you are happy with your overall semester average. If you cannot achieve an average better than an 80% during the first week of semester, you should seek immediate help, take remedial math courses, and/or take Physics 218 at a later time when your math skills have been adequately developed.

The questions in the quizzes are meant to remind you of mathematical concepts that should be familiar to you and which are going to be used repeatedly during the course. Very early on in the semester your professor and TA will assume that you are proficient with these types of problems. Your AMES grade will be determined by averaging your ten best attempts. There is no limit to the number of times you can retake the quiz and only your ten highest scores will be recorded.

To start taking quizzes:

• Go to URL and follow the on-screen instructions to set up your AMES account. You should have your Physics 218 section number and student ID number handy (NB: only the last five digits of your ID or SSN will be recorded).

• Once you are registered with the system, you can begin taking quizzes immediately from any campus computer with internet access, just go to: For off-campus computers you must either have a TAMUnet modem connection or have a VPN (Virtual Private Network) client running (e.g. if you have a cable modem or DSL connection). For more information about VPN and TAMUnet, please refer to the CIS support staff (979) 845-8300.

• You can check your scores by referring to the top of the feedback screen of each quiz you take or by going to



If you have any questions regarding AMES you can email Prof. David Toback (toback@physics.tamu.edu). For specific problems regarding registration/lost passwords etc. please email Joel Walker (jwalker@physics.tamu.edu). For questions/comments regarding individual quiz problems contact Andreas Mershin (mershin@physics.tamu.edu) (please cut and paste the entire statement of the quiz question in the email).

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