### Authentic assessment in statistics

The shift in statistics education to an emphasis on data exploration and analysis coupled with a drive in collegiate education for authentic assessment of skills has led to my trimming statistics content to provide space for students to engage in open data exploration and then presentation of their analysis to the class.

Presenting findings

In February 2016 a draft document of the American Statistical Association  (ASA) updated the Guidelines for Assessment and Instruction in Statistics  Education (GAISE) at the college level. The original GAISE document has guided the slow evolution of MS 150 Statistics at the college.

This presentation demonstrated general adherence to good presentation guidelines

The draft has slightly modified the original recommendations:
1. Teach statistical thinking.
• Teach statistics as an investigative process of problem-solving and decision-making.
• Give students experience with multivariable thinking.
2. Focus on conceptual understanding.
3. Integrate real data with a context and purpose.
4. Foster active learning.
5. Use technology to explore concepts and analyze data.
6. Use assessments to improve and evaluate student learning.

Demonstrating the ability to integrate spreadsheet charts into presentations

The images are of students presenting their findings and conclusions based on data provided to them along with open ended questions about the data. The students are not told what statistics to use in their exploration of the data. They have only the raw data and the knowledge from a brief twelve weeks of statistics.

Appropriate use of signaling colors, reduced title font size, dark background, and less than six elements on the slide being demonstrated

Making curricular space for these explorations and presentations required removing material from the course. GAISE has provided some guidance in this regard. Areas that can be omitted are:

• Probability theory. In MS 150 Statistics this topic is now greatly reduced.
• Constructing plots by hand. Since taking over the course in 2000, the course has never constructed plots by hand.
• Basic statistics. This recommendation is based on the inclusion of statistical concepts in newer mathematics texts in the elementary and high schools. These texts are not in broad use in Micronesia and basic statistical skills are not necessarily being taught. I have students who are not familiar with basic measures of the middle, let alone variation, histograms, and other basic concepts. This area cannot be omitted at present.
• Drills with z-, t-, χ 2 , and F-tables. Since statistical software produces a p-value as part of performing a hypothesis test, a shift from finding p-values to interpreting p-values in context is appropriate. Since 2001 the course has not used tables, shifting instead to the use of software to generate values. The course is also now guided by the 2016 American Statistical Association (ASA) statement on statistical significance and P-Values.

A student demonstrating the integration of a graph into her presentation

The February 2016 ASA GAISE draft does not recommend specific topic areas. The course still covers topics from basic statistics up through confidence intervals and t-tests for a difference of sample means. This section of the course is roughly twelve weeks at present, with the three open data exploration analysis and presentations spanning the final three weeks of the course.

Reading from the slide rather than facing the audience and speaking may be a sign of a lack of familiarity with the presentation

The goal of providing the content a student might need as a foundation for more advanced or subject specific courses remains a curricular challenge in the light of the current guidance from the ASA on the goals for an introductory course:
1. Students should become critical readers of statistically-based results reported in popular media, recognizing whether reported results reasonably follow from the study and analysis conducted.
2. Students should understand the investigative process through which statistics works to answer questions.
3. Students should be able to produce graphical displays and interpret what graphs do and do not reveal.
4. Students should recognize and be able to explain the central role of variability in statistical tendencies and associations.
5. Students should recognize and be able to explain the central role of randomness in designing studies and drawing conclusions.
6. Students should gain experience with how mathematical models, including multivariable models, are used in statistics.
7. Students should demonstrate an understanding of, and ability to use, basic ideas of statistical inference, both hypothesis tests and interval estimation, in a variety of settings.
8. Students should be able to interpret and draw conclusions from standard output from statistics software.
9. Students should display an awareness of ethical issues associated with sound  statistical practice.
The course is making some progress on goals two, three, seven, and eight. While students can calculate variation and have some idea of the definition, achieving a deeper recognition of the central role of variability remains elusive. The students accept spread as a feature of data, but often hold a weltanschauung that sees their world as unfolding according to an immutable plan in which randomness does not play a role. The students can calculate variation but do not necessarily accept the implications of randomness and how that plays out in the design of studies.

Multivariate models are also under-represented in the course. Gaining basic skills in single and two-variable statistics remains central to the course.

The course has also not chosen to use statistical software. At present the rising force of R would make R the logical choice. The guidelines do also suggest the use of on line tools. Bandwidth, while improved, remains an issue for the college, especially at the remote sites. Post-graduation the students may or may not have the necessary Internet access to use those tools, hence the focus on "over-the-counter" spreadsheets. At present the course uses LibreOffice.org and Microsoft Excel, which share a common library of functions and capabilities. An on line tool which uses R is used currently to generate box and whisker plots.

The course will continue to be guided by current best practices provided by the American Statistical Association and the Guidelines  for  Assessment  and Instruction  in  Statistics  Education.

Demonstration of the integration of table into a presentation

Having the students present their findings to the other students is a critical component of the authenticity of this activity as an assessment tool. In their fields of work the students are not likely to face "a test on this Friday" but rather "a presentation on the data this Friday."

The solution arrived at by the student might be a fully appropriate analysis of the data with conclusions supported by the appropriate statistics, or the solution might be inappropriate and unsupported. The key is that across all presentations, the students are confronted with the different solutions and during questions and answers the validity of a particular approach may be questioned.

Relationship analysis in progress during the presentation

The presentations then form a major part of the course grade for the students, a portion of the grade which has increased with each passing term. Note that the students were marked on statistical content, appropriate use of presentation software, and, for the second two presentations, their presentation skills.

The course has evolved from being a collection of formulas and methods applied in isolation to decontextualized data towards teaching statistics more as an investigative process of problem-solving and decision-making.

The balance is complex. Problem-solving and decision-making cannot occur in a content-free vacuum. Students will little to no prior introduction to statistics do not permit simply launching into raw data and asking them what might be done with the data.

The structure of a three hour a week three credit introductory course also does not necessarily lend itself well to larger data gathering projects. The course did experiment with data gathering projects between 2008 and 2011, the assessments did not show a learning benefit to those projects. Both term long and smaller mini-projects did not lead to increased engagement with statistics and statistical thinking, and never led to more complex analyses involving inferences. The typical project was a reporting of the mean and standard deviation for the number of dishes washed each night after sakau.

The presentations done by the students also meet the following institutional learning outcomes here at the college:

1. Effective oral communication: capacity to deliver prepared, purposeful presentations designed to increase knowledge, to foster understanding, or to promote change in the listeners’ attitudes, values, beliefs, or behaviors.

2. Effective written communication: development and expression of ideas in writing through work in many genres and styles, utilizing different writing technologies, and mixing texts, data, and images through iterative experiences across the curriculum.

Although the presentation is an oral presentation, the software is a written expression and requires integration of data and graphs (images) which are submitted along with the oral presentation.

4. Problem solving: capacity to design, evaluate, and implement a strategy to answer an open-ended question or achieve a desired goal.

The open data exploration exercises are framed by open-ended questions. The students must then design, evaluate, and implement a statistically appropriate strategy to those questions.

8. Quantitative Reasoning: ability to reason and solve quantitative problems from a wide array of authentic contexts and everyday life situations; comprehends and can create sophisticated arguments supported by quantitative evidence and can clearly communicate those arguments in a variety of formats.

The core subject is statistics and numerical reasoning, thus this institutional learning outcome is also met.

The open data exploration and presentations also meet fully or partially the following general education course learning outcomes.

1.1 Write a clear, well-organized paper using documentation and quantitative tools when appropriate.
1.2 Make a clear, well-organized verbal presentation.
2.1 Demonstrate the ability for independent thought and expression.
2.2 Demonstrate understanding of the modes of inquiry by identifying an appropriate method of accessing credible information and data resources; applying mathematical concepts; and organizing results.
3.1 Demonstrate understanding and apply mathematical concepts in problem solving and in day-to-day activities.
3.2 Present and interpret numeric information in graphic forms.
3.3 Communicate thoughts and ideas effectively using proper mathematical terms.
5.2 Demonstrate professionalism, interpersonal skills, teamwork, and leadership and decision-making skills.

The use of presentations is also made possible by recent installation of an LCD panel SMART board, which replaced a projection based system that was too dim to be used. Technology and technical capacity are critical to providing such a learning experience.

The MS 150 Statistics course will continue to seek to improve and deploy best practices in statistics education and learning.