At best, students leave Stat 101 able to define and use p-values. They understand sampling variability and the role of the central limit theorem. They can correctly state confidence interval and hypothesis testing conclusion by the end of the course. They can use a calculator and/or spreadsheet and/or statistical software to do tests and can dutifully interpret p-values. For most, a few months later, all they will remember is, p<.05 is “good.”

Thus, Stat 101 students finish their course having learned an increasingly rejected statistical paradigm which will propagate into their science labs, advanced statistic courses in the social sciences and business, into their capstone papers and beyond into who knows what after they graduate. We are placing the vast majority of our students in a “statistical” hole.

So here is my plea for somebody somewhere to do something. Not that people haven’t tried, and failed by their lights. My interpretation of such efforts is that the authors tried for too much – include too much explanation, too much background, too complicated of models, too complex model checking.

Take a look at an elementary statistics textbook such that it is. The explanations are limited. The types of questions/problems are simple and the subsequent analysis can be written in a sentence. This is appropriate for these students. Why not, instead of a p-value conclusion, have a modeling conclusion based on model sampling. Stat 101 students can just as easily be taught to state conclusion properly in modeling language as in p-value language. Since most students treat calculators or statistical software as a black box anyway, using provided p-value results or model sampling results will make no difference to them. The situations are simple – inferring population parameters from a sample, comparing two populations from samples, using normal or binomial distributions. These simple problems cover most of the cases they will confront in their college career.

So my plea – someone, somewhere write a elementary statistics textbook for non-majors using Bayesian models. Get it underwritten by a major publisher. Most of the content will be like the traditional text. The changes will be just in how the problems are worked out using Bayesian capable software and how the conclusions are stated. this would be good start.

Note: No links in this post. It is just my general sense of the field. I am not an expert in the field of statistics. I have avoided teaching elementary statistics for many years now because I disagreed with the content. I could do this because I am department chair and past retirement age.

]]>One: U.S. academics are shaken by the current political situation. They are looking to their research for solace, hope, and/or solutions. Creativity as it relates to wisdom and ethics is now a hot topic. The social-cultural aspects of creativity are being described.

Two: I found many presentations tinged with bravery and sadness. Bravery because many of the presenters were at the beginning of their professional life and putting a significant part of their work out there for critical questioning (Though most people were nice.). And sad because this consuming work was dismissed with a desultory question or two and a polite clapping. Many times I wanted to engage them, as the interesting people they are, in a detailed conversation, really out of curiosity, but I was off to the next section. And anyway, attention from me would not have enhanced their career or research.

]]>- Creativity can be taught.
- Creativity can be measured.
- Creativity is good.
- Creativity is trans-disciplinary.
- Creativity is thinking.
- Creativity produces artifacts.
- Creativity is resisted in college.
- Creativity involves empathy.
- Creativity needs permission.
- Creativity can be embedded in a story.
- Creativity requires overcoming fear.
- Creativity requires discipline.
- Creativity takes time.
- Creativity is hard to transfer.
- Creativity is a process.
- Creativity is domain specific.

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My perception is that that one idea generates many other ideas – one realization generates many other realizations. The implication is that we will run out of resources before we run out of ideas. I notice this in science and math. One research paper generates many possible paths for future research. There is not enough money or people to follow all the leads. Too many paths are not taken and it will only get worse. I say worse because some of those ideas could save the world.

]]>The idea is that the measured underlying behavior could be ideally rated on a continuous scale and that our rubric criteria divides the scale into intervals. Thus, in these figures the underlying behavior is depicted as the blue normal curve and our rubric divides the number line into intervals by establishing cut-points, the black dots.

The histogram thus represents the frequencies in each interval. As can be seen, the rubric assigning D, C, B and A could break up the line unevenly in many different ways. The question becomes, can we recover the parameters of the blue line from the given histogram? The answer will be yes – if we can tolerate some error.

My research scheme was therefore, after setting a normal curve (mean [*mu*] and standard deviation [*sd*]), to define a set of cut-points and generate a histogram. Then use the cut-points to get numerical values representing the categories. Use the R function, *fitdistr()*, to recover *mu* and *sd*. Repeat 10,000 times. Change the cut-points and try again.

Since the scale is arbitrary, I chose it to be the standard deviation of the given normal distribution which fixed to be one. I used a *mu* of 2.5 since I have been addressing a rubric scale of 1, 2, 3 and 4. The problem became: How does varying the cut-points affect the recovery of the mean? The answer was that we can get fairly close.

The key was devising a way to attach numerical values to each category. Let *d1*, *d2* and *d3* be the cut-points. Then the numerical value of the two inner bars was assigned to be *(d1+d2)/2* and (*d2+d3)/2*. Define *le* as the “limit” of the left end bar. In point of fact, the continuum extends infinitely in the left direction but I set it to be *d1-sd*(1.5)*, one and a half standard deviations to the left of *d1*. The value for the leftmost bar became *(le+d1)/2*. Similarly I set *re* to be *d3+sd*(1.5)*, and the value for the rightmost bar to be *(d3+re)/2**.*

Other details. The histogram represents a sample size of 100. I used the R function *fitdistr()* to find a parameters for a normal distribution since I knew where the data came from. For that reason I did not do any normality checks. *fitdistr()* actually gives error bounds but I preferred to just do 10,000 samples.

The following table has the results of the experiments. Note that even with a fairly wide variation of cut-points, we still get close to the underlying mu of 2.5.

From the table, it looks like a reasonable scheme to compute a mean for the underlying distribution on an arbitrary scale could be devised. First devise a set of cut-points using a scale that you want for the standard deviation. Calculate representative numbers for each category. Pass the information to *fitdistr()* and report *mu* with the error. For example here is the result for some data I have been looking at.

The cut-points were calculated assuming the expected results that 70% of our seniors would lie in the two rightmost categories and that 7.5% would be in each of the outermost categories. When simulated this yielded a *mu* of 2.56. In other words the crude method I used to calculate values for the categories yielded a slight plus average. From the table, I think it is fair to say that in cases 4, 6 and 7 our students did not meet our expectations and in case 5 they exceeded our expectations.

In sum, this exploration turned out to be a pleasant diversion from my intention to model rubric data. At best the results offer a way of quantifying the results with one number that has more justification than just taking an average of rubric numbers.

A note on the method. I built my R program to read and write from a CVS file. This allowed me to set the experimental values on a line with comments and get back on the same line the results including the file name of the associated graph.

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The graphics below are my attempt at depicting this reality. Consider each person (point in space) as an amalgam of traits. Each trait is normally distributed among all people. The length of the colored line represents the “accomplishment” for that particular trait, defined by direction and color. The diversity of lengths of expertise is evident.

Now we enclose each person (point) in a bubble with a two standard deviation radius. We can see some trait spikes sticking out. These represent an exceptional measurement, a ninety-fifth percentile of accomplishment.

They say everyone has a story. Also everyone has an exceptionality.

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I worry that my students will embarrass themselves after they graduate and apply for their first job. I worry that they will misspell or mispronounce a word or write incomplete sentences or reason sloppily or be ignorant of a common math concept. Grammar counts when I grade written work.

I worry that I sometimes treat students like they are stupid. They are not stupid. They are just new to the material. I mean to treat them like adults using adult vocabulary and adult reasoning and adult expectations.

In sum, curriculum, standards, respect – of course.

]]>And yet I needed to walk home – a mile uphill into the sun. It hurt to keep my eyes open so I started experimenting. In a few blocks I had my method – close my eyes, walk eight steps, flash the eyes open to see the near terrain, walk eight steps, repeat. I relaxed my face, kept my mind empty. Easy to do without any visual stimuli. I arrived in, seemly, no time. I had “sleep-walked” home.

Of course, I opened my eyes at intersections and upon hearing the approach of a car. I was walking up unbusy residential streets with no sidewalks so no problem.

When I walk to work, I cross an empty parking lot. A game I played was to walk with my eyes closed, taking as many steps as I could before I got scared or veered too far off course. This required alertness to the kinesthetics. “Sleep-walking” eight steps at a time turned out to be unstressful, even relaxing.

]]>**One assignment – Three outcomes**

I am working with a group of faculty (science, writing, math) that is considering this idea. What about assignments that have multiple outcomes? How about, say, a lab report that the science faculty could grade for science correctness, the writing faculty could grade for technical writing proficiency and the math faculty could grade for quantitative reasoning? Such an assignment would have efficiency benefits for the student – one paper for three classes and efficiency benefits for the faculty, if the logistics were not too bad, of just grading in the area of their expertise. I have seen syllabi that prohibit such “two-fer” projects but why not?

**Outside experts – Collaboration among faculty**

I have heard faculty complain that students in their classes cannot do simple quantitative reasoning tasks despite having taken our elementary statistics course (or not). What about having an expert, a math faculty statistician, visit the class, lecture on the issue at hand and even help design the assignment and evaluation instrument. Our librarians visit classes all over campus helping students with information literacy and I am sure there are other pockets of expertise on campus. This type of collaboration needs to be built into the faculty reward structure.

**Time spent grading tests – Or not**

I know of faculty members who carefully annotate tests and papers. And I have seen students place such papers immediately in the trash can. The faculty wasted their time and the student learned nothing further. Why not grade the papers just to determine the students’ grades with wrong or incomplete answers circled and points assigned according to a rubric? Then let the students correct the papers for an additional percentage. The faculty member will have to grade the papers twice but can be much more efficient each time. Other time saver possibilities. Record verbal comments as the paper is being graded to cut down on writing comments. If part of an answer is a Yes or No choice, have students circle the answer rather than write the answer somewhere on their paper – faster to grade.

**Commonalities **

There are commonalities of approach that occur within a discipline and between disciplines. In math for example there is Vedic Math developed (or rediscovered) in the early 1900’s which has 12 or 16 Sutras or common methods. Here is an example. http://www.vedicmaths.org/vertically-and-crosswise The general scientific method would be common in biology, chemistry, and physics. Data analysis would be common to economics, political science, sociology, etc. I taught an efficient combined linear algebra and differential equations course – efficient because the topics had significant overlap – bases, linear combinations, independence and the like. The Common Core is designed with scaffolding that cycles upward through repeating basic concepts. If such commonalities were taught in a consistent manner, the faculty would have it easier and so would the students.

**Variations – Common structure**

This is a little bit in the math weeds, but often we teach how to approach a problem by working from simple to complex and then often give up on the complex. If we taught the logic of the problem with all the ramifications at the beginning, we would get more bang for the buck. Since I am currently teaching them, I am thinking about word, motion, and mixture problems.

**Variations – Levels of learning**

Again in the math weeds. The examples one works in class can be chosen so that we can talk to students of differing proficiencies at the same time. The basic algorithm that solves the type of problem would be what the average student needs. The variations of the problems would have lessons that the above average student can use and appreciate. This is a bit hard to articulate. I think I mean that the average student is most interested in mastering the method and the more proficient student can, with the aid of the instructor, get more context and nuance at the same time.

**In conclusion**

The ideas above are examples of collaboration outside of our disciplines, leveraging of expertise throughout the campus, consideration of the student learning value of a teacher’s time expenditures and leveraging commonalities. Some could be encouraged with an appropriate reward structure.

“The past, the present, and the future walked into a bar.

It was tense.”

I reposted

“.2, .3, and .4 walked into a bar.

They were tenths.”

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