# Assessing Quantitative Reasoning in GE (Owens, Ladwig, and Mills)

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2 Process 1. Planning the Process a. Develop a list of Area A4 GE student learning outcomes. In the late 1990s, a CSU-sponsored project solicited input from three campuses, CSU, Chico, CSU, Sacramento, and San Francisco State University, in developing a comprehensive set of student learning outcomes in mathematical reasoning (Mills, et al., Learning Outcomes for Mathematical Reasoning for the Baccalaureate Degree, Learning Outcomes Project Final Report, California State University, January 15, 1999). That study identified nineteen different student learning outcomes deemed desirable for graduates of the CSU. (See appendix.) These nineteen learning outcomes provided a valuable starting point for this study. Recognizing that nineteen outcomes were too many to target initially, input was solicited from current GE mathematics faculty at CSU, Chico to help rank these outcomes by relevance and suitability for assessment. Ultimately, a total of six student learning outcomes were identified as most significant and pertinent to this assessment project (Table 1, with highlighted goals corresponding to the indicated outcome). The first three outcomes are suitable for assessment by indirect means, i.e., by way of a student response survey. The last three are suitable for direct and embedded assessment. (See the appendix of Learning Outcomes for Mathematical Reasoning for the Baccalaureate Degree for a full description of the significance of each learning outcome.) These student learning outcomes were particularly appropriate to this study because they are strongly correlated with goals of the GE program, as expressed in EM These goals fall into three different categories: GE program goals, GE Core skills, and GE Mathematics (Sub-Area A4) goals. Goals relating specifically to quantitative reasoning, either directly or indirectly, are summarized in Table 2.

3 Table 1: Selected Student Learning Outcomes GE Program GE Core GE Math Student Learning Outcomes in Quantitative Reasoning Goals Skills Goals Baccalaureate graduates of CSU, Chico will be able to: Outcomes 1-3 are suitable for indirect assessment, e.g., a student response survey. 1. view mathematics with heightened interest, increased confidence, and less anxiety as a result of their educational experiences. 2. regard mathematics as a way to think, reason and conceptualize, not simply as a set of techniques. 3. understand and appreciate the connections between mathematics and a variety of quantitative and non-quantitative disciplines. Outcomes 4-6 are suitable for direct assessment, e.g., student performance on a problem. 4. develop and apply measurement techniques to data collection, and evaluate potential sources of error, including variability and bias. 5. interpret, make appropriate judgments, and draw reasonable conclusions based on numerical, graphical and symbolic information. 6. critically evaluate quantitative information, and identify deceptive or erroneous reasoning.

4 Each of the selected student learning outcomes is associated with one or more of the GE goals (Table 1). For example, Outcome #2, Regard mathematics as a way to think, etc., is associated both with GE Program Goal #2 and with GE Core Skill #2. It is noteworthy that all six learning outcomes together encompass all of the GE goals, i.e., assessment of all six student learning outcomes would concurrently evaluate all mathematics-related aspects of the GE program. Much of the prior assessment of mathematics in general education has focused on indirect measures applied to individual MATH courses. In the current study, the focus was to be on direct and embedded means of assessing student performance. That is, students in a course would be evaluated by their ability to perform a task relevant to that course, where the task would also be associated with one or more overarching student learning outcomes. Table 2: GE Goals Relevant to Quantitative Reasoning (EM 99-05) Relevant GE Program Goals are: 1. to improve mathematical reasoning, analysis and problem solving, and the ability to access, evaluate, and apply information. 2. to enhance general knowledge and attitudes 3. to provide coherence, connectedness, and commonality within broad areas of undergraduate education. Relevant GE Core (Area A) Skills The principal charge to this area is to provide students opportunities to learn and demonstrate: 1. effective mathematical reasoning. 2. fundamental links between thinking and mathematical reasoning. GE Mathematics (Sub-Area A4) Goals Students must demonstrate: 1. understanding of one or more mathematical fields 2. understanding of more than computational skills; they must also demonstrate understanding of basic mathematical concepts and apply these concepts to complex real world activities. b. Determine which SLOs will be assessed, and identify course locations, tasks, and rubrics for assessment of the SLOs. With the list of SLOs reduced to six items, the Task Force planned to seek broad input from faculty across campus to determine campus SLO priorities and possible locations for measuring the SLOs. With the goal of identifying locations for embedded assessment of the SLOs, the Task Force initially targeted non-mathematics courses likely to involve quantitative reasoning, focusing on upper-division general education courses, but also including service courses for technical majors. However, several events caused the Task Force to modify this plan.

8 Chi-square = 1.11, p-value = Chi-square = 1.62, p-value = confident not confident attitude + attitude - right % % % % wrong % % % % totals % % % % Chi-square = 0, p-value = 1 Chi-square = 5.574, p-value = The data indicate some statistically significant differences in populations: Females were more likely than males to have the right answer for the right reason. Students who reported having taken a developmental mathematics course did not score as well as those who did not require developmental mathematics. Students who reported a positive attitude toward mathematics (determined by responses to the prompt I have a good attitude about math. ) scored better than those with a negative attitude. Students in MATH 105 scored better than either MATH 101 students (p = , chi-square test) or MATH 107 students (p = , chi-square test). Students in CIVL 302 also scored better than students in MATH 101 or MATH 107, but the difference was somewhat less significant. (E.g., for CIVL 302 versus MATH 107, p = , chi-square test). There were no significant differences in performance between freshmen and other students. Students mathematical confidence (determined by responses to the prompt I can use math correctly. ) had no statistical relation to their performance on the task. The difference in performance between students in MATH 101 and MATH 107 was not statistically significant. While there were some differences in performance between students in different colleges, these differences were probably a reflection of the courses the students took. For example, 75.82% of the 91 students from the College of Behavioral and Social Sciences answered both questions correctly versus 64.14% of the 145 students from the College of Business; however, almost all students from the College of Business were enrolled in MATH 107, while students from the College of Behavioral and Social Sciences were more likely to be enrolled in MATH 105. About the chi-square test: The chi-square test is used to measure the degree of confidence that the difference in characteristics of the samples can be generalized to differences in the population, and are not due to random error. The p-value is the probability if a chi-square value at least as large as the given value. The smaller the p- value, the greater is the statistical significance of the difference in characteristics of the samples. b. The Calculus Task Table 5 displays some of the data collected from the calculus problem and student survey. In the displayed data, there were no statistically different levels of performance

9 in the groups examined. While males performed slightly better than females (mean 2.92 versus 2.52, respectively), the difference was not significant. Similarly, students who reported that they would be taking additional mathematics courses in the future did somewhat better than students in their terminal mathematics class (mean 2.91 versus 2.5, respectively), but again the difference was not significant. There was little difference between the freshman and non-freshmen groups. Attitude did not appear to be related to performance on the problem. Table 5: Calculus Problem Data score male female attitude + attitude % 9 33% 39 51% 11 48% 3 3 4% 4 15% 7 9% 0 0% % 7 26% 15 19% 8 35% % 6 22% 13 17% 1 4% 0 5 7% 1 4% 3 4% 3 13% totals % % % % mean = 2.92, σ = 1.36 mean = 2.52, σ = 1.28 mean = 2.86, σ = 1.32 mean =2.65, σ = 1.47 t-test, p = t-test, p = score no more math yes more math freshmen not freshmen % 40 53% 21 43% 29 57% 3 1 4% 6 8% 5 10% 2 4% % 17 22% 13 27% 10 20% % 9 12% 7 14% 7 14% 0 2 8% 4 5% 3 6% 3 6% totals % % % % mean = 2.50, σ = 1.44 mean =2.91, σ = 1.31 mean = 2.69, σ = 1.33 mean = 2.92, σ = 1.37 t-test, p = t-test, p = There was moderate correlation between a student s score on the calculus problem and the student s grade in the class; illustrating that assessment is different from grading. The bubble graph in Figure 1 illustrates frequencies of pairs of problem scores and course grades. The second graph in Figure 1 illustrates the pairs without frequencies, but includes the regression line for the entire data set. It is important to recall that only students who completed the survey and took the final exam were included in the sample, resulting in a sample containing few D or F course grades. Figure 1: Calculus Problem Score versus Course Grade

10 MATH 120 course grade problem score 5.00 MATH 120 y = 0.309x R 2 = course grade problem score c. Survey Results Figure 2 provides a summary of additional information collected in the student survey. Observations: Since most of the students surveyed were freshmen, student perceptions about the use of mathematics in other classes are necessarily somewhat uninformed. In particular, students may think of low-level arithmetic as an example of use of mathematics. Student perceptions confirm what faculty had suggested: mathematics plays at best a minor role in other general education courses. Excluding the MATH 120 students, most students in the sample experienced no previous college-level mathematics coursework. While many MATH 107 and MATH 120 students will take at least one more mathematics class, most other students are in their terminal mathematics class. Figure 2: Survey Data

11 Class Level Freq uency Current Entering Fre shman Sophomore Junior S enior P ost-baccalaureate Use of Math in Other Classes Frequency Use of math in GE classes Use of math in major classes Never Seldom Occasionally Frequently Don't Know

12 Prior College Math Classes 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% None Remedial Business Math Statistics Trigonometry Precalculus Calculus Other GE Math MATH 120 Students Other Students All Students Surveyed Anticipated Number of Future Math Classes Frequency None One Two Three Four or More MATH 107 and MATH 120 Students Other Students A. Conclusions and Recommendations for Strengthening QR in GE Establish benchmarks for quantitative reasoning expectations. This is a campus-wide task. What are the campus expectations for quantitative reasoning and at which stages should we assess student progress? Embed quantitative reasoning in courses across the curriculum. Are we happy with the results? If not, faculty outside of math must take on their share of the responsibility. We do students a disservice when we avoid QR simply because students find it difficult. Like writing skills, quantitative reasoning skills need to be reinforced and developed over time and in a variety of settings, both in the majors and in GE. Provide and support professional development opportunities in quantitative reasoning across the disciplines, including GE. Develop a collection of resources for faculty wishing to incorporate significant QR into their courses. Provide workshops in which faculty can work together to develop such interdisciplinary resources, including appropriate assessment instruments.

13 B. Future Steps What is the mathematics enrollment history of a typical student? (Analyze a sample of student transcripts?) Begin a campus conversation about the results of this study. Help the campus understand that this study is only a first step is assessing quantitative reasoning and that quantitative reasoning cannot be assessed solely in mathematics courses. We don t know if our students leave college better able to reason quantitatively than when they entered. Do we wish to measure value added? How would we measure this?

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