Why statistics and what will you learn?
In the third week of MS 150 Statistics 75 students were asked to respond in writing to the following three questions:
1. Why are you taking this particular course?
2. How does this course fit into your academic plan?
3. Do you understand what the course learning outcomes are?
Although the student learning outcomes for the course had been emailed to all students prior to the start of the course and were on the course syllabus, no in class exercises directly engaged the students in learning the student learning outcomes.
The 75 students sometimes put more than one answer to a question, in these instances both answers were recorded. The survey that asked the questions was done anonymously, students were instructed not to put their names on their papers.
Responses to the first question, "Why are you taking this particular course?" fell into seven categories.
The seven categories were then grouped into three larger categories. The three larger categories were students who took the course as a requirement, students for whom learning a particular skill set was at the center of their motivation, and students for whom an innate interest was at the center of their motivation.
Course enrollment is driven predominantly by the course being a program requirement.
The second question, "How does this course fit into your academic plan?", saw a broader range of answers that fell into roughly 15 different categories.
Based on some of the answers there appears to have been different interpretations of what is an "academic plan." The 75 students who were surveyed are almost all using English as an L2 language, different interpretations of words is not unusual and is potentially one factor in the variety of answers. Even those students who did hold the same interpretation as the question writer might not know what an "academic plan" is.
The 15 categories were grouped into seven areas. Some students responded with words to the effect that the course was simply a major, degree, or program requirement. The largest group were those who simply said words to the effect, "Yes, the course fits into my academic plan." Some left the question blank or wrote "I do not know." Some students said, "spreadsheets are useful to me/my major" while others noted that "statistics are useful to me/my major". Another 16% responded more generically that numbers, data, or graphs were useful. There were six responses that were left separate.
In response to the third question, "Do you understand what the course learning outcomes are?" 68% of the students responded with a single word "yes" or "no". Four percent went with "maybe" while two percent left the question blank. There were a few other more specific answers which can be seen in the table below.
Whether the 33 positive responses indicate that those students actually know the student learning outcomes is not knowable from the survey. The questionnaire did not explore whether the students knew or could recognize specific student learning outcomes in the course. That 31 students indicated that learning spreadsheets, statistics, or numbers was useful to their academic plan suggests that about this number of students is aware of the core intents of the course.
Performance against the student learning outcomes is in part being reported this term in the statistics course via the use of an on line grade book with student log in and student learning outcome tracking capabilities, Engrade.
The actual course and specific student learning outcomes are listed below. Although the course is a college level course, there are Common Core standards to which the student learning outcomes can be mapped. The Common Core standards are provided in square brackets.
1. Students will be able to perform basic statistical calculations
1.1 Identify levels of measurement and appropriate statistical measures for a given level of measurement.
1.2 Determine frequencies and relative frequencies, create boxplots, histograms and identify their shape visually. [CCSS.Math.Content.HSS.ID.A.1, CCSS.Math.Content.HSS.ID.A.3]
1.3 Calculate basic statistical measures of the middle, spread, quartiles, IQR, and relative standing. [CCSS.Math.Content.HSS.ID.A.2]
1.4 Calculate simple probabilities for equally likely outcomes.
1.5 Determine the mean of a distribution.
2. Students will be able to obtain results using t-distributions
2.1 Calculate probabilities using the normal distribution [Common core CCSS.Math.Content.HSS.ID.A.4]
2.2 Calculate the standard error of the mean
2.3 Find confidence intervals for the mean [CCSS.Math.Content.HSS.IC.B.4 Includes CCSS.Math.Content.HSS.IC.A.1]
2.4 Perform hypothesis tests against a known population mean using both confidence intervals and formal hypothesis testing
2.5 Perform t-tests for paired and independent samples using both confidence intervals and p-values [CCSS.Math.Content.HSS.IC.B.5]
3. Students will be able to perform linear regressions [Includes CCSS.Math.Content.HSS.ID.B.6]
3.1 Calculate the linear slope and intercept for a set of data [CCSS.Math.Content.HSS.ID.C.7]
3.2 Calculate the correlation coefficient r [CCSS.Math.Content.HSS.ID.C.8, Includes CCSS.Math.Content.HSS.ID.C.9]
3.3 Generate predicted values based on the regression
The students were also asked to project their expected grade. The following chart shows in the inner ring the expected grade of the student. The outer ring shows the grade distribution fall term 2012.
Students are clearly overly optimistic against historic performance metrics.
When the 75 students were surveyed as to how hard they expected to have to work only four students responded that they would not have to work hard, that the course seemed easy. The remainder of the students expressed the opinion that the class would be hard, very hard, require more effort and work than other classes. Nine students responded with the locally popular, "I'll try my very best." One student remarked, "Even though I failed the first quiz, there's always a chance to make that to an A." [sic].
Dr. Allain Bourgoin wrote up results of the same survey in his courses and obtained similar results, although his students appeared to be less optimistic about their grade. Professor Rafael Pulmano engaged in activities to promote learning of the learng outcomes and has also run the survey in his class, reporting on those results in his blog.
1. Why are you taking this particular course?
2. How does this course fit into your academic plan?
3. Do you understand what the course learning outcomes are?
Although the student learning outcomes for the course had been emailed to all students prior to the start of the course and were on the course syllabus, no in class exercises directly engaged the students in learning the student learning outcomes.
The 75 students sometimes put more than one answer to a question, in these instances both answers were recorded. The survey that asked the questions was done anonymously, students were instructed not to put their names on their papers.
Responses to the first question, "Why are you taking this particular course?" fell into seven categories.
| Major/degree requirement | 54 |
| To learn statistics | 14 |
| To learn to use spreadsheets | 4 |
| To learn to solve math problems with computer | 3 |
| Course is interesting/important to me | 4 |
| I love mathematics/numbers | 2 |
| I want to improve my knowledge of math | 1 |
The seven categories were then grouped into three larger categories. The three larger categories were students who took the course as a requirement, students for whom learning a particular skill set was at the center of their motivation, and students for whom an innate interest was at the center of their motivation.
Course enrollment is driven predominantly by the course being a program requirement.
The second question, "How does this course fit into your academic plan?", saw a broader range of answers that fell into roughly 15 different categories.
| Requirement | 8 |
| Part of academic plan | 8 |
| Fits sometimes/well/perfectly | 8 |
| Do not know | 6 |
| Blank | 3 |
| Learning spreadsheets is useful to me/my major | 14 |
| Learning statistics is useful to me/my major | 10 |
| Course will help me deal with numbers and measures | 7 |
| Course has to do with numbers | 5 |
| Course is useful to my future career | 1 |
| Course is important as a foundation before moving on to higher math | 1 |
| Improves my academic mathematically | 1 |
| Math is a part of everyday life | 1 |
| I need to know the pop. of each state that needs to take the immunization shot | 1 |
| I will be able to teach my students mathematics | 1 |
Based on some of the answers there appears to have been different interpretations of what is an "academic plan." The 75 students who were surveyed are almost all using English as an L2 language, different interpretations of words is not unusual and is potentially one factor in the variety of answers. Even those students who did hold the same interpretation as the question writer might not know what an "academic plan" is.
The 15 categories were grouped into seven areas. Some students responded with words to the effect that the course was simply a major, degree, or program requirement. The largest group were those who simply said words to the effect, "Yes, the course fits into my academic plan." Some left the question blank or wrote "I do not know." Some students said, "spreadsheets are useful to me/my major" while others noted that "statistics are useful to me/my major". Another 16% responded more generically that numbers, data, or graphs were useful. There were six responses that were left separate.
In response to the third question, "Do you understand what the course learning outcomes are?" 68% of the students responded with a single word "yes" or "no". Four percent went with "maybe" while two percent left the question blank. There were a few other more specific answers which can be seen in the table below.
| Yes | 33 |
| No | 17 |
| Sort of | 3 |
| Blank | 2 |
| what a student needs to know | 4 |
| to be able to perform statistics calculations | 5 |
| learn to use spreadsheets | 1 |
| learn to use data | 1 |
| student will make graphs, other measurements | 1 |
| I understand SLOs and will meet requirements | 1 |
| I know only some of the main SLOs. | 1 |
| to achieve good grades | 1 |
| to organize and arrange numbers, data, values | 1 |
| once the instructor lectures, then I understand | 1 |
| I would if I read them | 1 |
Whether the 33 positive responses indicate that those students actually know the student learning outcomes is not knowable from the survey. The questionnaire did not explore whether the students knew or could recognize specific student learning outcomes in the course. That 31 students indicated that learning spreadsheets, statistics, or numbers was useful to their academic plan suggests that about this number of students is aware of the core intents of the course.
Performance against the student learning outcomes is in part being reported this term in the statistics course via the use of an on line grade book with student log in and student learning outcome tracking capabilities, Engrade.
The actual course and specific student learning outcomes are listed below. Although the course is a college level course, there are Common Core standards to which the student learning outcomes can be mapped. The Common Core standards are provided in square brackets.
1. Students will be able to perform basic statistical calculations
1.1 Identify levels of measurement and appropriate statistical measures for a given level of measurement.
1.2 Determine frequencies and relative frequencies, create boxplots, histograms and identify their shape visually. [CCSS.Math.Content.HSS.ID.A.1, CCSS.Math.Content.HSS.ID.A.3]
1.3 Calculate basic statistical measures of the middle, spread, quartiles, IQR, and relative standing. [CCSS.Math.Content.HSS.ID.A.2]
1.4 Calculate simple probabilities for equally likely outcomes.
1.5 Determine the mean of a distribution.
2. Students will be able to obtain results using t-distributions
2.1 Calculate probabilities using the normal distribution [Common core CCSS.Math.Content.HSS.ID.A.4]
2.2 Calculate the standard error of the mean
2.3 Find confidence intervals for the mean [CCSS.Math.Content.HSS.IC.B.4 Includes CCSS.Math.Content.HSS.IC.A.1]
2.4 Perform hypothesis tests against a known population mean using both confidence intervals and formal hypothesis testing
2.5 Perform t-tests for paired and independent samples using both confidence intervals and p-values [CCSS.Math.Content.HSS.IC.B.5]
3. Students will be able to perform linear regressions [Includes CCSS.Math.Content.HSS.ID.B.6]
3.1 Calculate the linear slope and intercept for a set of data [CCSS.Math.Content.HSS.ID.C.7]
3.2 Calculate the correlation coefficient r [CCSS.Math.Content.HSS.ID.C.8, Includes CCSS.Math.Content.HSS.ID.C.9]
3.3 Generate predicted values based on the regression
The students were also asked to project their expected grade. The following chart shows in the inner ring the expected grade of the student. The outer ring shows the grade distribution fall term 2012.
Students are clearly overly optimistic against historic performance metrics.
When the 75 students were surveyed as to how hard they expected to have to work only four students responded that they would not have to work hard, that the course seemed easy. The remainder of the students expressed the opinion that the class would be hard, very hard, require more effort and work than other classes. Nine students responded with the locally popular, "I'll try my very best." One student remarked, "Even though I failed the first quiz, there's always a chance to make that to an A." [sic].
Dr. Allain Bourgoin wrote up results of the same survey in his courses and obtained similar results, although his students appeared to be less optimistic about their grade. Professor Rafael Pulmano engaged in activities to promote learning of the learng outcomes and has also run the survey in his class, reporting on those results in his blog.
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