More than calculations? Guiding students to thinking with statistics

I am currently on spring break, and yet … with 4 snow days that have canceled classes this semester, I am keenly thinking about what I need to do to get to the end of the semester. As my university doesn’t make up missed snow days … I  have been thinking about what is the most important “thing” that students should leave an applied statistics class with? My answer is … the foundational knowledge to be able to make use of, interpret, and learn more about applying statistics to answer questions. I am expecting that they go beyond regurgitation of information or following of strict steps on how to answer questions using statistics. In short, I want them to be able to think with statistics as one of their tools!

As these thoughts swim through my mind, I continued reading a book, “What the Best College Teacher’s Do!” by Ken Bains. I got to a section of the book on how the best college teachers help students to develop a deeper level of knowing.  To summarize Bains (2004), there are 4 different levels of knowing student vacillate through in a non-linear manner, some times being at the two different levels at the same time. Using terms coined by the great teachers Bain’s researched, here are the four developmental levels of knowing:

The Banking Level where teachers deposit information into the students’ brains for later withdraw.

Does it Feel Right Level where students start to believe that all knowledge is subjective and as such merely a matter of opinion, thus the best knowledge can pass the “feels right” test.

Procedural Level is the point where students can apply their discipline specific rubrics, schemata, scripts in order to “know” or communicate information. Of course, this is discipline specific, with little or no carry over to other disciplines.

Commitment Knowers are students who reach the “highest” level of knowing. Such students have mastered a level of metacognition, that is awareness of their own thinking and how knowledge came to be in their mind. These students are creative and critical thinkers, and have developed a sense of independent thinking. Thus, students can take this knowledge and synthesize it with knowledge gathered from other disciplines and over time to truly result in more advanced cognitive processes. If I were to name this, I would call is The Thinker Level!

Commitment Knowers can be further classified into two components: the Separate Knowers who are emotionally detached from what knowledge they are seeking, and seem to follow a “falsificaction” process of hypothesis testing  and the Connected Knowers who are really don’t ever want to shoot anyone’s idea down, and instead seek to validate or find support for a hypothesis that has been put forward.

My philosophy of science and the application of statistics for the purpose of answering questions and testing hypotheses is fairly clear in that it is best to approach these situations as the Separate Knower. Thus, it’s not surprising that this is where I am guiding my students.

As I review the assignments students are expected to complete, I can see that I am taking students through these levels.   I am truly trying to move students up (within a single semester) from the “Banking” level of knowing, where students work to memorize terms and symbols, to the level of being a “separate – commitment knowing,”  where students know how to apply statistical concepts when answering questions or testing hypotheses.

In looking at the assignments I use (e.g., Assignments and Exercises for Students) the assignments for each chapter start out at the Banking Level, then move to the Procedural Level. It seems by looking at my assignments I don’t care if students “feel it’s right” this may require some reflection on my part. However, for students to hit the Commitment Level, they have to not only complete the assignments within the chapter of the textbook I use (Kiess and Green, 2010, Statistical Concepts for the Behavioral Science, 4/e), but them most certainly have to complete the Integrating Your Knowledge assignments that occur every two to three chapters in Kiess and Green’s textbook. It is then that students are lead to that highest level.

Yet, as I think of the final exam, I see something a bit different. For the final exam, students are given four scenarios, and they have to select the appropriate statistics (all problems require the calculation of several statistics), calculate it, make a decision regarding the results, and when appropriate draw a conclusion.  Of all the exams I give, it is the most calculation rich exam. Yet, I tell students, it is not the step by step procedures involved in the calculations that are most important, but understanding the concepts of what statistics can tell us, what they can’t, when we can use them, when we shouldn’t, and yes, how do they tell us what they tell us. It is the latter reason why I have students complete hand calculations using definitional formulas, but the rest of it is, as the prior sages have stated, relates to the conceptual and contextual understanding of the application of statistics. It is safe to say, students can’t merely regurgitate out how to complete this exam. Though, it seems possible for students who have only reached the level of “Procedural Knower”  to be able to follow the procedures, select the right statistic, follow the steps to calculations and interpretation … and not yet hit that level of “separate-commitment knowing.”

As such, through reading Ken Bair’s text, and thinking about what I really want students to be able to do, and what they are demonstrating … I want them to be Commitment Knowers, and yet, it is possible for them to be successful in my class while being only at the Procedural Level. So now … I’m four classes down due to snow, AND am in the middle of a quandary … am I taking the students’ far enough?

I welcome comments!

Bains, K. (2004). What the Best College Teachers Do. Cambridge, MA: Harvard Press.

Conceptualizing the “Core” in Applied Statistics

I enjoyed reading the sagely ideas offered by Bonnie and Marty that describe the core or central concepts to be taught in an applied statistics course. For me, it is essential early in the semester to have my statistics students (I teach in business, psychology and sociology programs) demonstrate their understanding of the critical connections between a theoretical distribution, sampling distribution and a sample distribution in the context of hypothesis testing and parameter estimation. Such an interrelated conceptualization opens students’ eyes not only to the language inherent in these two forms of inferential analysis, but also sets the stage for subsequent (and repetitive) use of this framework across various statistical procedures as I apply them to “the real world.”

Related to this discussion, for me, is another core component often unspoken in the halls of our academies and seldom part of an applied statistics course: the theory-research connection. None of us in academe operate in a purely applied world sans theory or theoretical applications, or inductive versus deductive thought. Why else would we run paired sample t tests on those cute and fuzzy rats in a t-maze unless we had some inductive or deductive logic underlying our trial efforts? More to the point: Even areas of curricular assessment, so essential to matters of strategic planning and programmatic and institutional accreditation, fuse the worlds of theory and statistical research. Do we want to measure critical thinking in the classroom, across your program and/or, in the aggregate, at your university? Then we should understand the connections between and among the following: paradigms, theory, concepts, propositions, abstract continuum, operationalization, variables, and hypotheses. (Note: For an interesting graphical approach to this pedagogy, I’d like to offer a PowerPoint presentation I use that’s tied to an earlier publication I had on the subject. It usually takes no more than a class period to cover this lecture – and it even includes a closed-ended model – see Figure 5 – to assess student learning. Here is the link: http://worldofevergreen.com/Theory-Research.pdf.  Though this document is formatted as a .pdf file for my students, you are welcome to the PowerPoint presentation on request.)

If one of our classroom objectives, beyond those typically found in an applied statistics course, is relevance, then such an approach will help students better understand (1) why they are taking a statistics class when nearly all of their other classes are geared toward theory, (2) how the structure of theory via propositions and statistical research via hypotheses run parallel to each other (when, ironically, their prior academic experience has largely ignored this important connection), and (3) how all sciences advance based on probability and outcome models in the decision-sciences through this “mother of all paradigms.” Moreover, if an undergraduate or graduate thesis is around the corner for your students, then an hour’s worth of time on the theory-research connection will be well worth the effort.

One final note, for now. You may wonder if this type of core lecture is better suited for a research methods course (or elsewhere) rather than one in applied statistics. That’s a question only you can answer. Because of the level of specificity I take in my review of the “empirical/observable world,” including non-trivial detail of issues to follow in weeks to come, my approach is best suited for my statistics course. Clearly, you may find such pedagogy useful in a class on theory, research methods, applied statistics or none of the above.

As Craig Ferguson often says when a provocative or controversial idea is raised, “I look forward to your email.”