Prepared by the Numeric/Symbolic Reasoning General Education Core Area Committee SUNY Geneseo, October 18, 2021
R/ General Education Committee Members:
 Jeffrey Koch (Chair), Political Science
 Jeffrey Johannes, Mathematics
 Stephen J. Tulowiecki, Geography
This committee assessed Geneseo’s Numeric/Symbolic Reasoning (hereafter R course/requirement) core requirement courses utilizing data from the Spring 2021 semester. The committee contacted instructors of courses in the following academic departments: (Geography, Mathematics, Political Science, Sociology, and Psychology). We asked to receive data from at least one course from a department that taught a R course. For some departments we received data for several courses, thereby enlarging the number of cases available for analysis. Data was attained from 7 courses, 13 classes (one instructor did not provide data), providing more than 500 cases. A deadline of September 30, 2021 was set for submitting data. The submitted data were then analyzed by Professor Jeffrey Koch of Political Science, the chair of the Gen Ed R subcommittee, and subsequently reviewed by committee members Johannes and Tulowiecki.
To assess the effectiveness of the selected courses for attaining the R outcomes instructors were asked to identify three questions on their course’s final exam or an equivalent assignment that measured the two criteria listed below. These two criteria were chosen as they are most strongly related to each of the three R/core learning outcomes.
 Ability to analyze, interpret and reason from quantitative data
 Demonstrated ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments
Instructors were asked to select three questions on the final exam (or, if there was not a final exam, an equivalent exercise) that measured the two criteria. If there were less than three questions instructors could use which instruments or means were available. Instructors were asked to assign one of the following values for each learning outcome area for each student exam: exceeding standards, meeting standards, approaching standards, or not meeting standards.
Instructors returned data to Professor Jeffrey Koch by September 30, 2021. Data from all courses were combined into a simple 1 X 4 crosstab, with frequencies and percentages. The crosstabs for each of the criteria are presented in Table 1.
Table 1
Proportion of students meeting Assessment Criteria
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  46% (246)  31% (168)  13% (70)  10% (54) 
Criteria Two  48% (253)  30% (158)  14% (76)  8% (42) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester. Represented departments include Geography, Mathematics, Political Science, Psychology, Sociology.
The data indicate that the majority of students are either meeting the standards or exceeding at the standards. Seventyseven percent of the students either exceeded or met the standard for criteria 1, and 78% for the 2^{nd} criteria. By this measure we are confident that the desired outcome for the R requirement is attained for most students, albeit not for all. Moreover, only 10% of the students failed to not meet Criteria 1, and 8% did not meet Criteria 2.
One limitation of aggregating the data in this manner is the possibility that one course or set of courses from one department are driving the results. For example, Psychology provided data for all PYCH 250 courses. After combining data from several departments, more than half the cases are from the Psychology Department. It may be the case that the results are driven by the data from Psychology, and that many students in other courses are not meeting the specified criteria.
Except for the Psychology 250 course, the data from each course were analyzed separately. While for each course the number of cases is relatively small, one can determine if a particular course or group of courses with large number of cases are responsible for the patterns evident in Table 1. Examining the data this way we find in all courses a majority of students were either exceeding standards or meeting standards. These data are presented in Tables 2a through 2i.
Table 2a
Geography R/125 (01)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  11% (5)  58% (26)  20% (9)  11% (5) 
Criteria Two  29% (13)  44% (20)  16% (7)  11% (5) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2b
MATH 141 (02)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  40% (4)  40% (4)  20% (2)  0% (0) 
Criteria Two  30% (3)  60% (6)  10% (1)  0% (0) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2c
PLSC 251 (01)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  13% (3)  67% (21)  13% (4)  7% (2) 
Criteria Two  10% (3)  70% (21)  13% (4)  7% (2) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2d
Sociology 211
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  29% (10)  44% (15)  12% (4)  15% (5) 
Criteria Two  24% (8)  59% (20)  9% (3)  9% (3) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2e
MATH 141 (01)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  86% (19)  14% (3)  0% (0)  0% (0) 
Criteria Two  82% (18)  14% (3)  0% (0)  4% (1) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2f
MATH 141 (04)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  77% (17)  23% (5)  0% (0)  0% (0) 
Criteria Two  36% ()  45% ()  18% ()  0% () 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2g
Psychology 250 (all sections)
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  57% (170)  29% (85)  2% (7)  12% (35) 
Criteria Two  52% (154)  23% (69)  16% (48)  9% (26) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2h
MATH 221 01
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  36% (4)  27% (3)  18% (2)  18% (2) 
Criteria Two  27% (3)  36% (4)  9% (1)  27% (3) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Table 2i
MATH 10401
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
 
Criteria One  42% (13)  22% (7)  19% (6)  16% (5) 
Criteria Two  52% (16)  16% (5)  26% (8)  6% (2) 

Note: Ns in parentheses. Criteria one refers to demonstrated ability to analyze, interpret and reason from quantitative data. Criteria two refers to ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments. Data are from the Spring 2021 semester.
Disaggregating the data to the courselevel reaffirms the conclusion reached from the aggregated data. One should not be concerned that one course, or a few courses with many students, contributed to the results in the analysis using the aggregated data. The lowest proportion for a course of students either meeting or exceeding the standard is 63%, and that course included only 11 students—a small number of cases. In sum, in most courses most students are meeting or exceeding the standard. Table 3 contains the minimum, maximum, and mean values for the statistics reported in Tables 2a through 2i.
Table 3
Summary Statics for data in Tables 2a through 2i
 Exceeds Standards  Meets Standards  Approaching Standards  Not Meeting Standards 
Criteria One  
Min  11%  14%  0%  0% 
Mean  43%  36%  12%  9% 
Max  86%  67%  20%  18% 
Criteria Two  
Min  10%  14%  0%  0% 
Mean  38  41  13  8 
Max  82%  70%  26%  27% 

Conclusion
Overall, we find that for the Geneseo courses sampled here that allow students to fulfill the R requirement students meet the specified criteria. Ideally, a 100% of the students who completed the courses sampled in this report would either exceed or meet the standard. Why that outcome is not attained is unclear. We do not know if that results from practices by the instructor, the students, the design of the course, or some other factor. We do know that the courses result in most students being able to analyze, interpret and reason from quantitative data (Criteria One), and most students demonstrating an ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments (Criteria Two).
Appendix A
Email sent to instructors of R courses taught Spring 2021.
I write to you as chair of the Gen Ed committee on Geneseo courses that fulfill the R requirement (Numeric/Symbolic Reasoning). I write to you because you taught a course that fulfills the R requirement during the Spring 2021 semester. Geneseo is required to assess these courses. This is an especially important time for this assessment as the Middle States accreditation visit is approaching.
Two student learning outcomes need to be assessed for Numeric/Symbolic Reasoning:
 Criteria 1: Ability to analyze, interpret and reason from quantitative data
 Criteria 2: Demonstrated ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments
I ask that you select three questions on the final exam that most strongly relates to each of the two R/core learning outcomes. Based on student answers to each question, assign one of the following categories for each learning outcome area: exceeding standards, meeting standards, approaching standards, or not meeting standards. Please let me know if this not possible given the type of final exam you utilized. Perhaps there was another assignment that is more appropriate. Please let me know it that is the case.
Please submit the result so me in a 2 (for each outcome) by 4 (for each category) table with frequencies and relative frequencies. I need the raw data.
I realize this represents a demand on your time, and I appreciate the time you will need to spend to provide these data. I am trying to complete the assessment process in a manner that is least burdensome on you as well provides a reasonable measure for each outcome.
Subsequent to Jeff Koch’s initial email he specified September 30 2021 as the due date.
Appendix B.
Numeric/Symbolic Reasoning Outcome Statement from Geneseo Bulletin. General Education courses in Mathematics emphasize logical reasoning conducted in a numeric or other symbolic language. Such courses will foster the student's ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments; they may, in addition, enhance the student's ability to collect, analyze, interpret, and reason from quantitative data. Courses approved for the requirement emphasize the connection between methods of problemsolving (numerical, formulaic, algorithmic) and the logical and mathematical foundations that justify them.
Summary of Outcomes:
 Ability to analyze, interpret and reason from quantitative data
 Demonstrated ability to reason analytically, solve problems, apply theoretical concepts, and construct sound arguments
Appendix C
Assessed Courses: The courses assessed by each department, along with the catalog description for each taken from the SUNY Geneseo Undergraduate Bulletin, are listed below:
Geography 125 R/Digital Earth. How do sensors on airplanes discover lost ancient cities? How does a GPS know where you are? How does Google Maps determine the fastest route between two locations? This course focuses on quantitative reasoning and problemsolving in geography, including methods associated with current tools and technologies that geographers use to study the earth. Students will first learn about 21stcentury tools including global positioning systems (GPS), geographic information systems (GIS), and remote sensing. Students will also learn specific quantitative methods and skills that geographers use, such as structured query language (SQL), map algebra, and network analysis.
Mathematics 104  R/Mathematical Ideas. Designed for the liberal arts student, this course investigates the meaning and methods of mathematics. By viewing mathematics as a search for patterns, a way of thinking, and a part of our cultural heritage, it emphasizes the various roles of mathematics. Mathematical ideas from geometry, number theory, and algebra are presented that support the proposition that mathematics is much more than just a collection of techniques for obtaining answers with standard problems.
Mathematics MATH 141 R/Mathematical Concepts for Elementary Education II. This course is intended for education majors and is designed to provide a mathematical treatment of the fundamental concepts of probability, statistics, and elementary geometry as they relate to the elementary school mathematics curriculum.
Mathematics – MATH 221 R/Calculus I. Topics studied are limits and continuity; derivatives and antiderivatives of the algebraic, exponential, logarithmic, trigonometric, and inverse functions; the definite integral; and the fundamental theorem of the calculus.
Political Science: PLSC 251 Modern Political Analysis
The purpose of this course is to introduce Political Science majors to the methods of modern political science research. The course will include a presentation of the scientific approach as practiced by Political Scientists, focusing on both theoretical and methodological issues. The purposes of research, measurement problems, and other data management problems in political science research will be discussed. Students will be introduced to basic statistical techniques of data analysis including: dispersion and central tendency, correlation coefficients, hypothesis testing, confidence intervals, ChiSquare tests, student ttests, and simple regression analysis.
Psychology: – PSYC 250 R/IntroBehavioral Statistics. Mathematics Computation, application, and interpretation of the major descriptive and introductory inferential techniques. Topics include measurement, frequency distributions, graphing, central tendency, variability, binomial and normal distributions, standard scores, correlation, regression, hypothesis testing, ztests, onesample ttests, twosample ttests, analysis of variance, and nonparametric significance tests.
Sociology: SOCL 211 R/Statistics for Social Research Data presentation, descriptive statistical analysis, and basic inferential techniques. Theoretical and methodological issues, as well as statistical applications, are studied. Students are trained to develop quantitative analysis skills and an ability to use statistics in social science disciplines and daytoday life.