BASELINE ASSESSMENT OF MATH 1050 AND STAT 1040 Department of Mathematics and Statistics & Office of Analysis, Assessment, and Accreditation Utah State University January 2006 INTRODUCTION An important part of USU s assessment program involves evaluation of courses used to meet the university s general education requirements. During Spring Semester, 2005, an assessment of student performance in relation to course learning objectives was conducted for the two largest freshman courses of the Department of Mathematics and Statistics--College Algebra (Math 1050) and Introduction to Statistics (Stat 1040). This is a continuous assessment of Math 1050 and Stat 1040 that began in Spring, 2004. Math 1050 is taught every semester in multiple sections of size 40. Typically, there are 15-18 sections in each of the fall and spring semesters, and 3-4 in the summer semester. Thus, about 1500 students take Math 1050 on-campus each year. (More than 400 additional students take the course each year via USU Extension services or through high school concurrent enrollment, but the current assessment effort involves only the oncampus sections). Math 1050 meets the university s general education requirement for quantitative literacy and is a terminal course for a few majors, but for most students who take the class it serves as the primary pre-requisite for calculus courses required of Science, Business, and Engineering majors. It is also required for several majors in the Colleges of Natural Resources and Agriculture. Stat 1040 is taught every semester in multiple sections of size 50. Typically, there are 12-14 sections in each of the fall and spring semesters, and two during the summer session. Thus, about 1450 students take the course each year. Most students take Stat 1040 to meet the quantitative literacy requirement, but 30-40% need the course as a prerequisite for either Psychology or Sociology statistics or research methods courses. This study was undertaken to provide a baseline assessment of these two courses. For Math 1050, the process involved randomly selecting three sections from the Spring, 2005 class list. All students in Math 1050 take the same final examination. To assure consistency in scoring, the exam for each student in the four selected sections was regraded by a single instructor familiar with the course. Most of the questions on the test were multiple-choice, so each student received either full or no credit. Some questions were problems requiring work to be shown. For these questions, the grader used a common partial credit scheme for all the re-graded finals.
A similar approach was used for Stat 1040 which also has a common final exam. Four Spring Semester, 2005 courses were randomly selected and the final examinations were re-graded. Because the Stat 1040 test consisted of word-problems requiring written solutions and stated conclusions, a common partial-credit scheme was used by the grader to score all examinations. The objective of the study was to identify which topics and learning objectives in Math 1050 and Stat 1040 the students seemed to have mastered and those that may require more time or a different pedagogical approach. In both courses, more than one question on the final examination may have related to a specific main topic or learning objective associated with the course. In such situations, each student s total score was computed for all the questions related to that topic or learning objective. MATH 1050 RESULTS The Spring, 2005 Math 1050 final examination had 20 multiple choice questions worth seven points each if answered correctly and zero otherwise. The test also had five problems requiring work to be shown, each worth from 0 to 12 points, depending on the student s response. A total of 92 students took the Math 1050 final examination in the three sections. The mean score for all students was 61.2%. The percentage of total students in the sample who correctly answered each multiple-choice question along with the topic each question was designed to address is shown below. Where more than one question related to the same topic, the percentage is the average for all of the related questions.
Topic Maximum Quadratic Function (1)(10) 11.2/14 4.2 80% Complex Number (2) 4.1/7 3.5 59% Rational Inequality (3) 3.5/7 3.5 50% Rational Equation (4) 5.5/7 2.8 79% Radical Equation (5) 2.9/7 3.5 41% Function Domain (6) 2.9/7 3.5 41% Function Graph (7) 5.6/7 2.8 80% Function Inverse (8) 3.7/7 3.5 54% Function Composition (9) 5.6/7 2.8 80% Rational Function (11) 3.2/7 3.5 46% Circle Equation (12) 5.6/7 3.0 80% Polynomial Function (13)(14) 6.4/14 4.8 46% Log Function (15) 1.3/7 2.8 19% Log/Exp Equations (16)(17)(18) 13.3/21 6.7 63% Combination/Permutation (19) 4.6/7 3.3 66% Partial Fraction (20) 4.3/7 3.5 61% Total Multiple-Choice 83.4/140 23.9 60% Taken as a total group, the students in the sample exhibited considerable variation in their scores on the topics covered by multiple-choice questions. Eighty percent correctly answered the questions on quadratic function(s), graphing functions and equation of a circle, but only nineteen percent got the logarithm question correct. The standard adopted by the Department of Mathematics and Statistics for Math 1050 was that successful instruction in the course required that at least 60% of the students be able to answer the questions related to a topic. Using this criteria, student outcomes met the standard for only six of the fourteen topics. The overall average of 60% on the multiplechoice questions was right on the 60% criteria.
The last five questions on the exam were problems. The topic of each question and the mean score for all students are shown below. Topic Maximum System of Nonlinear Eqns (21) 6.8/12 4.3 57% Exponential Function (22) 9.6/12 3.3 80% System of Linear Eqns (23) 9.2/12 4.0 77% Graph of Inequalities (24) 6.5/12 3.9 54% Quadratic Function (25) 6.9/12 4.4 58% Total Show-Work 39/60 14.0 65% Total Score 122.3/200 33.7 61.2% Students did better on the word problems than on the multiple choice questions. The mean score was 65%, compared to just 60% for the multiple-choice items. The performances on the problems about exponential function and system of linear equations were far above the 60% standard, and the performances on the other problems were slightly below the 60% criterion. STAT 1040 RESULTS The Spring, 2005 Stat 1040 final examination had nine problems with possible scores ranging from nine to fourteen points. A total of 138 students took the Stat 1040 final examination in the four sections. The mean score for all students was 71.13 over 100, with the standard deviation 17.23. The topic of each question and the mean score for all students are shown below Topic Maximum Chance Error in Sampling (Q1) 6.5/10 2.2 65% Probability (Q2) 6.7/9 2.6 74% Confidence Interval (Q3) 7.4/10 2.6 74% Normal Approximation (Q4) 6.0/10 3.0 60% Two Sample Z-Test (Q5) 6.6/12 3.9 55% Experimental Designs (Q6) 9.1/11 1.9 83% Regression (Q7) 12/14 2.6 86% Chi Square Test (Q8) 9.1/12 3.7 76% T-Test (Q9) 7.7/12 3.7 64% Total 71.1/100 17 71%
The standard adopted by the Department of Mathematics and Statistics for Stat 1040 was that successful instruction in the course required that at least 70% of students be able to answer the questions related to a topic. Using this criterion, student outcomes met the standard for five of the nine topics, and the overall average of 71% was above the 70% criterion.