# 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?