Mars and Murrie Milk Chocolate Statistics
For a fifth term the MS 150 Statistics course began with a problem solving open data exploration leading to a presentation. The exercise effectively flips the role of the students from that of being students in a class to that of being statisticians reporting on their statistical findings. This shift allows the instructor to begin the second week of class by saying, "I know you already know how to calculate statistics and make charts..." This gives the students an early sense of success and a sense that they can succeed in the course.
For fifteen years the statistics course started with gathering data on body metrics and then launching into a lecture driven course. In 2008 I added statistics projects to the lecture and test mix in an attempt to both increase student engagement with statistics and to integrate more writing into the course. The statistics projects did not result in increased student engagement with statistics.
In 2013 the experiment with projects was replaced with exercises in open data exploration based in part on my becoming aware of the American Statistics Association's Guidelines for Assessment and Instruction in Statistics Education, a set of recommended best practices.
In 2015 the open data explorations were capped off by a single student presentation. In subsequent terms the number of end of term presentations would be increased. The course was still structured around a lecture and test format in the first eleven to twelve weeks of the course, and three to four weeks of open data exploration. In an attempt to integrate a more problem based learning approach to learning in statistics, in fall 2016 the curriculum was redesigned to include open data exploration and presentations from start of the term. The exercise was repeated again in the "low bandwidth Internet" spring of 2017.
As is often the case, the thought first struck me while out on a run in the summer of 2016: "What would happen if I walked into class on the first day and the first thing I said was, 'Presentations are due on Friday.' Any questions?" When I voiced this to my son he said the students would be confused and scared. First day fearfulness has been identified as an issue in assessments done fall 2015 and summer 2016. The data source for the presentation had to be something fun and the statistical aspect had to be accomplished on essentially zero knowledge. In the realm of statistics there is a widely known known statistical exploration exercise based on a product developed by Forrest Mars and Bruce Murrie seventy-six years ago.
With two sections of statistics, there is considerable up front costs in this approach, especially on the remote island of Pohnpei. In a request for funding what can one say that will make sense from a learning perspective? I opted for wording along the lines of "Consumable supplies for problem based learning activity in MS 150 Statistics." I filed the petty cash request a week ahead of the first day of class and obtained approval.
Cases of milk chocolate MMs contain 36 bags. At Yoshie bags of MMs had been a dollar each for the first three terms. With a five cent per bag discount for buying by the case, two cases (72 bags) of MMs were $68.40. In the spring of 2018 MMs had risen to $1.10 a bag. With the five percent discount the two cases were $75.20. Fall 2018 the list price for two cases was $86.40, $1.20 per bag. The two case price was $77.80, roughly a ten percent discount.
The presentations were driven by ten questions:
Fall 2018 I passed out the syllabus along with a new tech guide to the websites and associated apps that would be used in the course.
I handed out the MMs and began explaining the assignment. On the SMART board I displayed the assignment with the questions in Schoology.
The weight of a bag of MMs varies from bag to bag, as does the number of MMs per bag. The number per color would vary even more widely bag to bag. The filling process has a randomness to it which provides a wonderful way to introduce statistical concepts.
Giving each student their own bag of MMs and having the students work in pairs proved critically important: the students immediately discovered that the bags varied in MM total count and the relative frequency of the colors. This led to good discussions in each pair, and between neighboring pairs, over how to tackle the questions posed. The students were engaged in discussing data and statistics.
I asked the students to pick their own partners - I wanted them to have some sense of control over the process. I also knew that in life one often gets to choose partners for projects and I wanted to mirror that as well. I knew too that many would choose someone they knew in the class, which would increase their sense of comfort. One article I had read over the summer of 2017 argued for permitting problem based learning groups to remain stable, to not force groupings nor change groupings. The article noted that there are learning benefits to keeping the teams intact.
Wednesday was left as purely a working day which helped me sort out the churn in the add/drop role, get newly added students paired and started, and to assist students in getting logged into Schoology. I also helped students navigate Google Sheets and how to get charts from Sheets into Google Slides.
On what was effectively a zero knowledge start back on Monday, the Friday presentations went well. Students reported minimum, maximum, sample size, and averages. By identifying the most common color, the groups identified the mode without knowing the statistical name. Each group made a chart, usually a column chart. All of the pairs noted the differences in the number of MMs per bag and the differences in the color counts.
The presentations were marked using a rubric in Schoology.
The rubric included course student learning outcomes, specific student learning outcomes, and presentation metrics that are not student learning outcomes for the course. Schoology permits the mix of outcome based criterion and non-outcome based criterion in a single rubric. The full rubric is included at the end of this article.
The MM presentations provides a solid foundation on which to built the terminology and concepts of basic statistics. The students spent the week engaging with data, making decisions on how to report that data. The students have also had an opportunity to share their findings with their peers. The course remains a mix of presentations built on problem based learning/open data exploration and content delivered in a more traditional format.
The MMs also provide useful data for homework problems during the early weeks of the term.
My thanks to my instructional coordinator and the administration for their ongoing support for the course and for the curricular and methods changes being made as a part of engaging in recommended best practices and continuous improvement of the course. I am especially appreciative of the support for this particular activity. The request for funding for two cases of MMs is unusual. This support allowed the course to start in a new way that was fun for the students. Beginnings are important, and a beginning in which statistics is fun helps set a positive tone for the course ahead.
Students starting work on their MMs
For fifteen years the statistics course started with gathering data on body metrics and then launching into a lecture driven course. In 2008 I added statistics projects to the lecture and test mix in an attempt to both increase student engagement with statistics and to integrate more writing into the course. The statistics projects did not result in increased student engagement with statistics.
In 2013 the experiment with projects was replaced with exercises in open data exploration based in part on my becoming aware of the American Statistics Association's Guidelines for Assessment and Instruction in Statistics Education, a set of recommended best practices.
Two cases of MMs launched the term
In 2015 the open data explorations were capped off by a single student presentation. In subsequent terms the number of end of term presentations would be increased. The course was still structured around a lecture and test format in the first eleven to twelve weeks of the course, and three to four weeks of open data exploration. In an attempt to integrate a more problem based learning approach to learning in statistics, in fall 2016 the curriculum was redesigned to include open data exploration and presentations from start of the term. The exercise was repeated again in the "low bandwidth Internet" spring of 2017.
Students are increasingly arriving tech ready
As is often the case, the thought first struck me while out on a run in the summer of 2016: "What would happen if I walked into class on the first day and the first thing I said was, 'Presentations are due on Friday.' Any questions?" When I voiced this to my son he said the students would be confused and scared. First day fearfulness has been identified as an issue in assessments done fall 2015 and summer 2016. The data source for the presentation had to be something fun and the statistical aspect had to be accomplished on essentially zero knowledge. In the realm of statistics there is a widely known known statistical exploration exercise based on a product developed by Forrest Mars and Bruce Murrie seventy-six years ago.
Cases of milk chocolate MMs contain 36 bags. At Yoshie bags of MMs had been a dollar each for the first three terms. With a five cent per bag discount for buying by the case, two cases (72 bags) of MMs were $68.40. In the spring of 2018 MMs had risen to $1.10 a bag. With the five percent discount the two cases were $75.20. Fall 2018 the list price for two cases was $86.40, $1.20 per bag. The two case price was $77.80, roughly a ten percent discount.
The presentations were driven by ten questions:
- Before opening your bag, determine the weight of each bag.
- Does the weight match the weight printed on the bag?
- How many M&Ms in your bag?
- Is the number of M&Ms the same in each bag?
- What might be the average number of M&Ms in a bag?
- How many colors are there in a bag?
- How many MMs of each color are there?
- Which color is there the most of?
- Make a chart showing the number of MMs of each color in a bag. If you are working with a partner, make a chart for each bag.
- Is the number of MMs of a particular color the same in every bag?
Websites and apps used in MS 150 Statistics
Fall 2018 I passed out the syllabus along with a new tech guide to the websites and associated apps that would be used in the course.
Vinessa presents her analysis: students reporting statistics ahead of instruction
I handed out the MMs and began explaining the assignment. On the SMART board I displayed the assignment with the questions in Schoology.
Giving each student their own bag of MMs and having the students work in pairs proved critically important: the students immediately discovered that the bags varied in MM total count and the relative frequency of the colors. This led to good discussions in each pair, and between neighboring pairs, over how to tackle the questions posed. The students were engaged in discussing data and statistics.
Gregorlyn presents her analysis: she is the statistician
I asked the students to pick their own partners - I wanted them to have some sense of control over the process. I also knew that in life one often gets to choose partners for projects and I wanted to mirror that as well. I knew too that many would choose someone they knew in the class, which would increase their sense of comfort. One article I had read over the summer of 2017 argued for permitting problem based learning groups to remain stable, to not force groupings nor change groupings. The article noted that there are learning benefits to keeping the teams intact.
Wednesday was left as purely a working day which helped me sort out the churn in the add/drop role, get newly added students paired and started, and to assist students in getting logged into Schoology. I also helped students navigate Google Sheets and how to get charts from Sheets into Google Slides.
Arlynn presents
On what was effectively a zero knowledge start back on Monday, the Friday presentations went well. Students reported minimum, maximum, sample size, and averages. By identifying the most common color, the groups identified the mode without knowing the statistical name. Each group made a chart, usually a column chart. All of the pairs noted the differences in the number of MMs per bag and the differences in the color counts.
The presentations were marked using a rubric in Schoology.
The rubric included course student learning outcomes, specific student learning outcomes, and presentation metrics that are not student learning outcomes for the course. Schoology permits the mix of outcome based criterion and non-outcome based criterion in a single rubric. The full rubric is included at the end of this article.
The MM presentations provides a solid foundation on which to built the terminology and concepts of basic statistics. The students spent the week engaging with data, making decisions on how to report that data. The students have also had an opportunity to share their findings with their peers. The course remains a mix of presentations built on problem based learning/open data exploration and content delivered in a more traditional format.
The MMs also provide useful data for homework problems during the early weeks of the term.
My thanks to my instructional coordinator and the administration for their ongoing support for the course and for the curricular and methods changes being made as a part of engaging in recommended best practices and continuous improvement of the course. I am especially appreciative of the support for this particular activity. The request for funding for two cases of MMs is unusual. This support allowed the course to start in a new way that was fun for the students. Beginnings are important, and a beginning in which statistics is fun helps set a positive tone for the course ahead.
| Outcomes | ||||
| 4 | 3 | 2 | 1 | |
| 1.0 Basic statistics Perform basic statistical calculations for a single variable up to and including graphical analysis, confidence intervals, hypothesis testing against an expected value, and testing two samples for a difference of means. |
Exceeds expectations: Correctly reports all relevant statistics | Meets expectations: By and large correctly reports relevant statistics. | Does not meet expectations: Incorrectly reports a limited number of statistics | Severe does not meet expectations: Little to no evidence in support of the outcome |
| 1.1 Measures of middle and spread Calculate basic statistical measures for the middle, spread of data including quartiles and relative standing |
Exceeds expectations: Engages in a fully complete, correct exploration and analysis of the data | Meets expectations: By and large engages in an appropriate exploration of and analysis of the data | Does not meet expectations: A minimal, limited effort exploring the data | Severe does not meet expectations: |
| 3.0 Open data exploration Engage in data exploration and analysis using appropriate statistical techniques including numeric calculations, graphical approaches, and tests. |
Exceeds expectations: Engages in a fully complete, correct exploration and analysis of the data | Meets expectations: By and large engages in an appropriate exploration of and analysis of the data | Does not meet expectations: A minimal, limited effort exploring the data | Little to no evidence in support of the outcome |
| 3.1 Report appropriate statistics Generate appropriate basic statistical measures of the data without specific guidance on which measures should be calculated |
Exceeds expectations: Correctly reports all relevant statistics for the questions asked | Meets expectations: By and large correctly reports relevant statistics for most of the questions asked | Does not meet expectations: Reports confusing and at times irrelevant statistics or incorrectly reports most of the statistics | Little to no evidence in support of the outcome |
| 3.2 Generate appropriate charts Generate appropriate charts and graphs for the data without specific guidance on which charts should be generated |
Exceeds expectations: Correctly done fully appropriate chart | Meets expectations: Appropriate if not optimal chart choice | Does not meet expectations: Inappropriate chart, confusing, or does not correctly display the intended statistics | Little to no evidence in support of the outcome |
| 3.3 Report results of analysis Draw conclusions based on statistical analyses and tests, obtain answers to questions about the data, supported by appropriate statistics |
Exceeds expectations: Obtained correct answers to all of the questions about the data | Meets expectations: Obtained generally correct answers to most of the questions about the data | Does not meet expectations: Incorrect or inappropriate analysis or answered only a limited number of questions | Little to no evidence in support of the outcome |
| Presentation software Original work submitted as presentation software, presentation is appropriate to the material and subject matter, presentation generally follows guidelines for a good presentation. |
4 Excellent presentation that heeds general presentation guidelines, avoids distracting visual extras, and is appropriate to the subject matter. |
3 Good: presentation with only a few areas in which the presentation as a visual aid could be improved. |
2 Satisfactory :presentation with more than a few issues. Transitions distract from the content, timing is inappropriate, or other issues such that the visual aid becomes a distraction. |
1 Needs Improvement: Submission of a spreadsheet or other fundamental fault in the submission. |
| Presentation mechanics Presentor delivered clearly, concisely, demonstrated familiarity with the contents. |
4 Excellent: Well delivered exhibiting preparation and knowledge of the presentation. Spoke clearly and always towards the audience. | 3 Good: Showed evidence of preparation and some familiarity with the content of presentation. Usually faced the audience. |
2 Satisfactory: Presentor read the slides, sometimes with their back to the audience. |
1 Needs Improvement: Little evidence of preparation, unfamiliar with the slide contents, spoke facing the display panel throughout the presentation. |
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