Making students fail???

By now, anyone reading this blog has probably figured out the only thing I like more than teaching applied statistics is understanding what makes students learn the material better. My goal is not for them to learn the material long enough for the exam, but so they can actually do what the class is intended to do … apply statistics to find the answers to important questions.

My focus on the cognitive science underlying student success is no surprise to people on my campus. As such, I wasn’t the least bit surprised with a science faculty member contacted me to find out the answer to this question. What is better, direct teaching or forcing students to try to figure out something prior to being taught, then teaching them. The specific topic at hand was helping students to understand the application of mathematics in this particular science discipline. The topic came from a teaching listserve.

I have come across a research article addressing this very topic. abstract

Kapur, M. (2014). Productive Failure in Learning Math, Cognitive Science, 38, 1008-1022.

What Kapur found is that though students learn a great deal from direct teaching, that is providing students with background information, showing them how to calculate a math problem, then having them practice, preferably in class, then out of class as homework, direct teaching may not always be the most effective way of having students learn how to solve problems in mathematics.

Instead of direct instruction,  Kapur found that by providing students with the problem and having them figure out how to solve the problem before being instructed yields better long term learning, and also increases a students’ ability to apply that knowledge to other problems. Prior to  instruction, almost every student fails. Yet there seems to be benefit in the attempt despite the failure.

I have used this very technique for years as has my science colleague I spoke of earlier.

I actually begin when I teach the (arithmetic) mean. By the time a student is in college he or she has calculated many means. It is actually a concepts taught to 8 year olds. What the students haven’t been taught is the formula for mean, at least not that my students seem to remember.  Equally true, they haven’t thought about how the mean works. They just plug in numbers into their calculator and it spits out a number.

What I have them do is write  in word the steps involved. Then, I let them ask me questions about symbols. If they can’t figure out they need the symbol for sum of the observations and total number of observation, I will eventual give them to the students. Either way, they have to create the formula for the mean.

After teaching students the conceptual meaning of the Sum of Squared, they determine the formula and process to find it. Then, I define for students variance, and again they generate the format. Obviously, they are asked to generate the definitional formula.  In each case (which by the way covers several days), only about 3 or 4 students in a class of 40 are actually successful. However, most students, who initially won’t even try and respond to my requests with an “I don’t know” eventually start giving it a shot, and most of the time can get a piece of it correct.  More importantly, students start thinking about statistics as a process and the definitional  formulas as a set directions and explanation.  Statistics begins to make sense to students, but it starts with failure.

The same process works with z-test, and all three t-tests (one sample, independent, and related).

There is no doubt that direct teaching will be faster, but forcing students to think about the underling concepts of applied statistics , even if it results in failure, seems to yield deeper and longer understanding, and after all, isn’t that what we are after?

I hope everyone has a great break and wonderful 2015!


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Qualities of a Master Teacher

Psychologists interested in understanding what constitutes a “Master Teacher” have conducted several studies to identify various traits. One resource can be found at the Society for the Teaching of Psychology’s (STP) resource center (OTRP) and is written by Jeffrey Stowell, from Eastern Illinois University, and Eric Landrum, STP President from Boise State University. This article, , contains 73 different clips of professors teaching who are demonstrating Master Teacher Qualities.

In this article, Stowell and Landrum provide a short but detailed summary of the research in identifying what constitutes a master teacher. They focus on 8 of those qualities.

As I read through their qualities I noticed 3 categories.

The stuff a faculty member has to come to class with in order to be a Master Teacher.

  • Knowledgeable  – if you don’t fully know the material, you can’t teach it. Nothing more needs to be said.
  • Enthusiastic about the topic AND teaching – Enthusiasm translates into actions outside of the classroom like attending conferences, reading journals, conducting research, and seeking out time to think and talk about your discipline and teaching.
  • Creative and Interesting – Though this category has more to do with the delivery of information, let’s face it, coming up with a creative method for teaching and keeping your students interested, especially in applied statistics takes time and effort outside of the classroom. Master teachers want to keep their students intellectually engaged, and come to class ready to do just that.

Qualities associated with having high expectations for student success while still referencing the needs of the students.

  • Realistic Expectations – Professors have to keep their expectations high but still within reach of their students. Those of us teaching in the United States, especially at state sponsored universities or community colleges are teaching students who are coming to us woefully ill prepared. It is our goal is to meet the students where they are, not where we wish them to be. With such expectations, it shapes the efforts a professor will entertain to assure student success.
  • Flexible – it is not enough to have high expectations, Master Teachers reference the needs of the student, that means, they have to be flexible, at least at times.

Qualities that help create a welcoming culture of respect within the classroom.

  • Respectful – If you want students to be respectful, you need to model it yourself.
  • Cares for Students – Dr. Jyh-Hann Chang conducts research on compassion and defines compassion as having two components: empathy and action to alleviate their suffering. It’s not just enough to say you care about students, you have to have empathy for them, particularly when something is out of their control like the death of a loved one. With this, however, I also believe, based on the work of Chang, that Master teachers actively try to keep students from suffering.
  • Personable – Who would you rather learn from, a grumpy person or a pleasant person? Most students would select the pleasant student.

What’s great about Stowell and Landrum’s article from STP’s OTRP is it includes links of professors demonstrating these very traits listed above. If you are wondering if you are meeting the standard of being a master teacher I encourage you to watch the video clips.

Until the next time, happy teaching!


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Great Resource for the Teaching of Applied Statistics

Hello All,

The Society for the Teaching of Psychology has an office dedicated to great, peer-reviewed resources for teaching called the Office of Teaching Resources in Psychology.

Two such (free) resources for those of us teaching applied statistics include the free on-line book, Teaching Statistics and Research Methods: Tips from TOPS.

Another such resource, is Statistical Literacy in Psychology: Resources, Activities, and Assessment Methods

The web site housing these two resources is filled with great ideas, all of which have been peer-reviewed. You can find teaching resources including example syllabi as well as article on how to maximize your students’ learning. Even if you are teaching applied statistics in an area outside of psychology, I encourage you to make use of this value set of tools. ( )

Happy Teaching!



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Starting a new semester … engaging students


To aid with the start of the semester…

Originally posted on Statistical Sage Blog:

School has started, which is always exciting.  After all, the new school year is filled with GREAT possibilities.

Yet, lets face it … most of the students in our classes this fall aren’t going to have that level of excitement, especially about having to take statistics. I often contemplate, why aren’t students excited about the possibilities of learning statistics? Though I certainly don’t have all of the answers, and look forward to hearing from the sages, I do have a few hypotheses, each that I will be discussing over the course of the next few weeks.

(1) People don’t trust statistics, and the students have heard these comments, possibly for years. Take this link to a list of quotes on statistics, and see how many of them basically say … you can use statistics to lie. Of course, it probably doesn’t help labor day marks the start of the big push for…

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First Day of Class — starting off right


Ah, the first day of the semester is upon us …

Originally posted on Statistical Sage Blog:

How do students comes to us on the first day of class? Yes, I can just about hear you mumbling …

(1) They wonder why they even have to take this class … after all they are a [non-quantitative] major. Why does [psychology, sociology, business, education, etc] need statistics?

(2) They may have had really bad math experiences in the past leading to (a) math anxiety (b) poor math attitudes including a low self efficacy and/or (c) weak math skills.

(3) They have heard lots and lots of stories as to how hard or useless or manipulative statistics can be. We have all heard the quote … and so have they … “There are lies, … , and statistics!”

But the first thing I want to let you know is … instructors of applied statistics may be over estimating the negative thinking of their students. Mills (2004);col1 found that, in general…

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The Importance of Questions in Data Analysis

“The sexy job in the next ten years will be statisticians” said Google’s Chief Economist back in 2009.  The ability to understand data and pull out valuable insight will become increasingly in demand in business, government, and journalism to name but a few fields.

And one of the most important first steps when analysing data is the questions you ask.

Let’s take journalism as an example.  In years gone by, a researcher would surround himself with the national and regional papers and scour them for hours, searching for one line – a line that begged more questions to be asked.  He’d return to the newsroom from this activity present the line to a journalist, and say “follow this up.”

A brainstorming session would follow.  But these were different from what you and I might think of as a brainstorming session.  It wasn’t sitting around staring at a blank flipchart or whiteboard.  Instead they arrived with the idea.  The goal of the brainstorming session was for numerous people to fire as many questions as they could think of in 10 minutes.  Any more than 10 minutes, and they had probably started naval-gazing.  This was a quick hit to explore as many angles as they could think of.  Then filter them down to the juiciest ones, guided by every journalist’s greatest asset – a nose for a story.

Let’s take a current example.  The European Court of Justice ruled in March 2011 that “taking the gender of the insured individual into account as a risk factor in insurance contracts constitutes discrimination”.  The ruling will come into effect in December 2012.  Insurers have had the time in between to adjust their pricing models.

This ruling poses a number of questions for insurers and the general public.  It also challenges the application of statistics in this context.

Faced with this news, what questions can your class generate?  What if they take on different roles?  What questions might the insurer ask?  How might they adjust their policies to account for the new ruling?  What about a journalist?  What questions might they ask in the public’s interest? What about the perspective of the judge in the ruling?  What might the opposing lawyers have argued?  If you take this ruling further, what implications could there be?  What challenges could you make to the ruling?

The average premium for women in the UK is £425 pa compared with £536 pa for men.  However, what challenges can be made to the use of averages in this instance?  Given the opportunity, how would you dive into the data to gain greater insight?

Some commentary and coverage around this ruling could add additional contextual information and offers the jump-off point for further questions and discussion:

“Currently millions of insurance policies take gender into account. The court ruled that practice as inappropriate since there are myriad other factors that could be considered. Gender, however, is typically easy to check and can point to sound statistical conclusions, the industry says.”  NY Times

Speaking of the case’s advocate general, Julianne Kott, the Wall Street Journal writes:

“Life-insurance discrimination might be permissible under the law, she allows, if women live longer because they are women, if there is something innate and biological about the female sex that causes longevity.”

But, she argues, important causes of longevity are behavioral—eating habits, smoking and drinking, sports, work environments, drug use. That women have, on average, behaved differently than men doesn’t necessarily mean any one woman’s femaleness is the reason why.

Differences in longevity “merely come to light statistically,” Ms. Kokott writes, and sex is thus just shorthand for whatever is causing those differences. And, she says, “the use of a person’s sex as a kind of substitute criterion for other distinguishing features is incompatible with the equal treatment of men and women.””

One suggestion is that insurers might encourage more people to sign up for black box insurance.

Black box insurance – also known as ‘telematics’ or ‘pay as you go car insurance’- aims to offer drivers a cheaper alternative by delivering driver-centred premiums based upon actual driving style rather than statistics.”

Similar in concept to the black boxes in aeroplanes (though presumably not indestructible), these devices track when and where you are driving and measures your speed, acceleration and braking.  Instead of using statistics based on your demographics, it would give a more direct impression of how safe a driver you are.  However, this doesn’t remove statistics completely.  The roads you drive on and the time of night you drive impact how much you have to pay, which presumably is based on the probability of having an accident.

The Guardian discusses other ways insurers might respond to the new ruling:

““It has been suggested some insurers may try to get round the rules by re-classifying the cars typically bought by young men into a higher insurance category, which would in turn push their premiums up. The ABI research paper mentioned an unnamed insurer which said women accounted for 70% of its Mini drivers, but only 30% of its BMW drivers. Alternatively, car insurers may start paying more attention to people’s occupations.”

One suggestion is that insurers might encourage more people to sign up for black box insurance:

Black box insurance – also known as ‘telematics’ or ‘pay as you go car insurance’- aims to offer drivers a cheaper alternative by delivering driver-centred premiums based upon actual driving style rather than statistics.”

As an example exercise, you could divide students into small discussion groups, and assign them roles (e.g. one group could be journalists for national press, another could be journalists of an insurance industry publication, and a third group could be senior managers of an insurance company).

Give them each ten minutes to brainstorm within the group as many different questions as they can.  Then get them to filter down the questions to the most important, and discuss how they might go about answering these questions, and the potential implications of their findings.  Then get each group to report back to the larger group, and invite further questions from the class.

You could then review the whole session and how asking more questions early on has an impact in how you approach statistical analysis, and other contexts in which you could apply this approach.

All of this should hopefully stimulate engaging and lively debate based on a real-world example of applied statistics.

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Populations vs. Samples in Statistics

Hello All,

So, my first love is teaching applied statistics. It has been and probably always will be my favorite thing to do at work. However, for the past two years I served as an interim administrator. So for my next few posts, I am discussing what information needs to be understood by administrators, as many of you very well may be called upon to lead professional development workshops or work, one on one, with an administrator.

If you look down my list that I posted previously regarding what information should be included in a training session with administrators you will see that the first four posts were more broadly based, dealing with issues technically outside of applied statistics but that either provide the foundations for good decision making with data or that are there to help administrators understand why we need to use statistics to make good decisions.

  1. Epistemology, Decision Making, and Statistics
  2. Cognitive Biases; How Statistics can be used to get to the Truth
  3. Detecting Data Integrity Issues
  4. Data Management Protocol
  5. Populations vs. Samples
  6. Observational Errors: Measurement, Experimental, and Sampling
  7. Quality Decisions are Limited by the Quality of Measures
  8. Sampling and Quality Decisions
  9. Statistics and Sampling Error
  10. Parameters and Mathematical Modeling vs. Inferential Statistics (Introduction)
  11. Mathematical Modeling, Parameters, and Assumptions
  12. Statistical Decision Errors: Type I and Type II

However, now we are up to #5, which is simply two terms that can be found at the beginning of every statistics book: Population vs. Sample.

A population is an entire group of something sharing a common characteristic or characteristics. For example, in a memo that I recently received, the GPA for all students from our institution was listed. This number was compared to the GPA for all student athletes from our institution. All students from an institution is one example of a population. All student athletes is another example of a different population. In each of these cases, the GPA is NOT a STATISTIC.

A statistic is a number that capture what is going on with a sample, that is a subset of a population. 

A Parameter is a number that captures what is going on with a population, that is the entire set of something or someone sharing a common characteristic, like being student athletes at a particular institution.

Now before I can explain why this matters, we will have to go through a few most posts for background information. Until then, let’s just say … we don’t use statistics to understand populations, we use parameters.

And we can’t treat a sample like a population, it is a subset, which means it is probably going to be less varied than the total population and there very well may be differences in the people in the sample when compared to the overall population. Take, for example, when  a professor holds an optional study session for the exam. Think about the students who would show up for such a session. How might they differ from the students in the class who didn’t show up?

  • Maybe the students who didn’t show up have to work or take care of a family member, so they didn’t have the time.
  • Maybe the students who showed up are  really motivated to master the material while the ones who didn’t show up are satisfied to just do well enough.
  • The theories of Carol Dweck would predict students with Incremental Views of Intelligence (that belief that with effort they can get smarter) would be more likely to participate than those with Entity Views of Intelligence (those who believe we are either born smart or not).

There are any number of reasons why students in these two groups may differ, but if the goal is the  estimate how well the entire class is prepared by using the sample of those who show up for study group, there is going to be error that will keep you from seeing everything.

Population parameters don’t have that kind of error, because everyone is in the group.

Understanding these two terms is requisite for understanding what is to follows. Certainly professors  teaching applied statistics know and understand this, but often administrators do not, so if you are called to train them or work with them in areas of assessment or the use of data to make decisions, make sure they understand this distinction.

Till next time ….


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