Math/Physics Competency Test as a Diagnostic Tool in Undergraduate Mechanical Engineering Curriculum C. Shih and N. Chandra* Department of Mechanical Engineering FAMU-FSU College of Engineering Florida A&M University and Florida State University 2006 ASEE Annual Conference, Chicago, June * Lead faculty, soon will be the Associate Dean, CoE, U. Nebraska, Lincoln

Outline  Historical Background  Transition, Math/Science Preparation  ME Integrated Curriculum  Introduction to ME & ME Tools  Competency Test  Format and Implementation Strategy  Diagnostic Analysis  Summary

Math/Physics Preparation-Historical Background  Levels of Preparation are not uniform among Students  Unique two-institution affiliation + transfer students  Some students do not retain necessary Math/Physics concepts  They cannot formulate word problems in math form  Significant time wasted in repeating the same concepts in a number of sophomore and even higher level classes  Early intervention is necessary so we can identify deficiencies early in order to help students to gain the required knowledge.  Collect enough data and frequently revisit the subject with the ME faculty to decide on the future course of action - involving math/physics faculty and other engineering faculty.  Recent curriculum reform further highlights these deficiencies

Integrated ME Curriculum  Initiate the curriculum change in 1997  Begin professional preparation/higher-level skills early in the curriculum  ME Tools: introduce all relevant ME tools/skills including communication, Mathematical/programming tools, machine shop experience, CAD, and fundamentals of thermodynamics (Stirling Engine)  Introduction to ME: introduce engineering profession, ethics, design process/tools, and engineering mechanics  Streamline related classes into a class sequence to emphasize connectivity between topics, design considerations, project work, team work, etc..  Ex: Combine Thermodynamics + Heat Transfer + Fluid Mechanics  Thermal/Fluids I & II with lab/workshop components  Increase technical electives to four  Culminating into a two-semester senior capstone design project (presented in session 2125)  Integrated curriculum diagramIntegrated curriculum diagram

Integrated Curriculum

Introduction to Mechanical Engineering  The first ME class students take after formally be admitted into the engineering school (sophomore-level)  Passed engineering pre-requisites (Calculus I & II, Physics I, and Chemistry I with C or better in all four)  Outlines: introduce ME as a profession, ethics, design process/tools, and concepts of mechanics (mostly Statics)  Consider one of the gatekeeper courses for ME  About 25% of students received either “D” or “F”  Perfect time to exam students’ proficiency in pre-required knowledge in math and physics  Early warning and intervention tool

Math and Physics Requirements  Calculus I and II and Physics I as pre-requisites  Math covers functions (exponential, logarithmic, trigonometric), calculus (derivatives, integral, ODE), matrices, word problem formulations.  Physics: static/dynamic equilibrium, Newton’s law of motion, friction, and free-body diagrams.  The test is based on these pre-requisite Math and Physics courses using the specific text books (equivalent to high school AP Calculus/Physics).  To establish the baseline competency for students to take more advanced mechanical engineering courses.

Test Format  A large data base of multiple choice questions in math and physics extracted or developed directly from the text books.  The test (35 from math+15 from physics) is given during the second week of Intro to ME course.  A score of 80% gives the student a full 10 (15) points out of the course maximum of 100 points.  Students who fail the first time can retake the test in the eighth week and get a reduced score should they pass with 70% or higher; zero is given to those who did not score 70% or higher.  Remedial classes conducted between the first and second tests.

Test Evolution  Problem quality control  Statistical data taken from each test is used to weed out inappropriate questions (either too easy/difficult or ill-posed)  A question could be reviewed for modification or deletion should the percentage of students answer correctly fall outside an acceptable value (60- 80%)  good reference for remedial lectures  Grading scheme  Grade bias correction: Instead of awarding full 10% credit, the actual test grade will be prorated based on the percentage of questions answered correctly  To emphasize the importance of the Math/Physics preparation, the test percentage has been increased from 10 to 15% in recent semesters.  Add an on-line practice test that exactly simulates the format (and timing) of the test, available starting Fall 2003.

Online Practice Test on Blackboard  The online practice test (through Blackboard) is identical to the in class test, with the same number of questions: 35 math and 15 physics.  The online practice test has questions selected from a database with over 150 questions on each subject. This allowed the students to take the practice test as many times as they choose; they get a different test online each time..  Exam is graded right away with the right answers indicated.  There is an excellent correlation between the online test scores (automatically recorded for reference purpose) and the actual test scores.

Snapshot of the Online Test (graded)

Student Data, Fall 2002 to Spring 2006  A total of 378 students over a period of eight semesters had taken the exam. Competency scores recorded along with their SAT/ACT, pre- requisite GPA, post ME GPA  In general, data indicates a useful tool for both diagnosis and future performance prediction  49% passed the first time and 75% passed for the second time  For those who received a “F” course grade, more than 75% of them did not pass the test  Correlate math/physics skills to readiness for mastering engineering subjects  >80% of those who did not pass the test received either “D” or “F” course grade  The test serves effectively as a gatekeeper (drop one letter grade if not passed)  The test percentage has been increased to 15% in recent semesters

Diagnostic Tool: Test Score vs. SAT & ACT High ACT seems to correlate very well with high test score Significantly more scatter for SAT correlation Math test score only shows similar correlation

Test Score verse the Pre-requisite GPA 70% Pre-Req GPA 2.5

How Good the Test as a Predictor? GPA is calculated based on Mechanics & Materials I, Mechanics & Materials II, Thermal/Fluids I, Thermal/Fluids II, Mechanical Systems I, Mechanical Systems II, Dynamic Systems I and Dynamic Systems II. Good preparation alone may not guarantee good GPA However, in order to have good engineering grade you have to have good preparation

Test Score vs. Final ME GPA

Summary  The test can be used effectively as a diagnostic and prognostic tool  Also supported by anecdotal information from senior exit interviews as well as informal conversations with students/faculty  More systematic analysis on its effectiveness is needed to improve the test  Inform students early on (during freshman year), and allow students to take practice tests prior to taking Intro to ME course.  Coordinated effort in early intervention and remedial assistance is needed.  Will share the data with FAMU and FSU Math/Physics Departments.