Category Archives: Maximizing Cognitive Development

A Statistics Professor’s New Year’s Resolution – 2012

Happy 2012! It is time for us to set goals for the new year.

There is good reason for us all to make New Year’s Resolutions as applied statistics professor (and students)  as in doing so, it  increase the likelihood of us making a change ( The first step in making a change is to focus on the negative … what’s going on in your classroom that you would like to change or that needs improvement ( ?

Though I can’t attest to the quality of the data, it is reported that 40 – 45% of all people make New Year’s Resolutions … with weight loss and exercise topping that list, followed by quitting a bad habit like smoking, and managing money better. Setting a New Year’s Resolution actually does increase the likelihood of a person achieving that goal. But that shouldn’t be surprising … Yogi Berra is reported to say, “If you don’t know where you are going, you’ll end up some place else.” Specifically, a New Year’s Resolution is a goal for a person to achieve.

My professional goal for 2012 is two fold … (1) I reverted back to a cumulative final exam for this past semester, and noticed that there were a few areas where most students had challenges. My first New Year’s Resolution is to help students master these more challenging areas of applied statistics.  (2) I want more students to behave in a manner that will assure their success … you know, the basic things like coming to class, completing homework, and so forth.

However, simply hoping that my goals come true will not maximize the likelihood of them being reached. Borrowing from research on Deliberate Practice (, also reviewed in ), it helps to achieve ones goals is we:

  1. Clearly state what we are interesting in achieving, and a plan of how to achieve it.
  2. Make sure the goal is attainable, and that it takes us to a higher level of achievement.
  3. Establish a way of assessing our progress toward the goals.
  4. Practice, Practice, Practice, and revise, revise revise along the way, recognizing that there will be times that we won’t be successful, but that even in failure, we can learn, and try again.

I want to focus on increasing student learning, by looking at student weaknesses on the final exam. That is fairly specific. To do this I will:

  •  Identify the SLO by examining item analysis on the cumulative final exam.
  • Add additional homework assignments in these areas.
  • Add additional quizzes for students.
  • Notify my student tutor of the areas of weakness, and have her come up with special study sessions for these difficult areas, and make announcements to students … using the carrot of high grades on the final exam,
  • See if the in class activities/lectures are helping students master the material.

It will be easy to assess … homework & quiz performance, feedback from the student tutor, and ultimately student performance on the final exam will all provide evidence of whether my approach improves students’ performance. Throughout the spring semester, I will chronicle what those areas are and share with you additional homework and class activities. And my student tutor, Amy Lebkeucher, has agreed to talk about her experiences in helping students master this material, as well.

As for helping students adopt the kind of behavior we all want to see in our students … I haven’t found the right words to tell students to make them behave. I explicitly tell students what they need to do to be successful in class.  It is printed in the syllabus; I have other students tell them. I remind them on a regular basis, and yet, every semester I have students who fail my class because they simply didn’t buy the book … “Aren’t you one of those great teachers, where I don’t need to buy the book to be successful?” Students come to me at the end of the semester asking what they can do since they missed so many classes and homework … sigh. I know I’m not alone as the most recent report from the National Survey of Student Engagement (NSSE) has the typical college student is studying less than 15 hours a week … that’s one hour of studying per credit hour, which simply isn’t enough time. About a 1/3 of all students do NOT even review notes after taking them, and close to 1 out of 3 students who need help do not seek help from the professor! In short, the NSSE reveals what many of us are seeing … our students aren’t behaving in a manner that will maximize their success.

So, I’m adopting a “Marketing Campaign” that helps students to understand (1) attend class (2) study at least 2 hrs./ week/ credit hour (3) read all assigned reading at least thrice (4) establish a study plan and (5) implement self testing into their study plan. We I will assess this marketing campaign with surveys of student reported behavior, class attendance, and homework checks. However, I would be lying if I said I know what I need to do to help maximize students’ behavior. I’m thinking of trying something like , but … if this was an easy task, I would have had it fixed by now. This may not reach Deliberate Practice’s step of Attainable … but it’s worth trying.

Of course, during 2012, I will let  you know what works and what doesn’t … and if anyone has any ideas, please let us know.

May 2012 be a year of great professional growth, health, and peace for us all!


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Statistics Professor’s New Years Resolution — a Review from 2011

As we come to the end of a year, we often take stock. At StatisticalSage, we have seen a tremendous increase in viewers as we approach 6000 views just for 2011! That’s a big change from our first year, when on our best days we only had a couple of views. Currently we have over 100 people following this blog. Some of the people reading this blog have gotten new jobs, been promoted, and have made real growth in the quality of their teaching (and we would love to hear about it). Of course, another group of students have been exposed to the usefulness of statistics as a tool to answer important questions in health, business, science, and education, and hopefully, many of them have learned something lasting along the way.

As we enter wrap up 2011, I wanted to briefly review progress in my 2011 New Year’s Resolution ( ). Just a brief review, my resolution stated: “I will be applying Mathematica demonstrations to my teaching! My goal for the spring semester is to identify and use at least 5 Mathematica demonstrations and make them available to students electronically via Desire 2 Learn (ESU’s course delivery system du jour). I also hope to make them available to everyone at Statistical Sage as well. For Fall 2011, it is my goal to identify Mathematica demonstrations for all of the concepts I teach.”

Establishing this goal resulted in me making far greater advances in technology that I thought.  Students who used Mathematica did report greater understanding, but far too many students are still not making use of the Mathematica demonstrations outside of class.  My attempts have been documented in two prior blogs (  For Spring 2012, I will add an on-line quizzes that I am hoping will “motivate” students to make use of the Mathematica demonstrations. As I continue to find the best way of implementing Mathematica, I will continue to let you know.

I invite all of you to tell us about your advances in 2011 … it’s always nice to hear good news.

I wish everyone good health, happiness, and peace for you and your family!

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Bain’s (2004) Approach to What Makes a Great Statistics Professor

We continue with talking about what makes a great statistics professor, I would be remiss if I didn’t talk about THE book on great teaching: “What the Best College Teachers Do” by Ken Bain (2004).  I have previously written about Bains approach to teaching, when talking about how to help students master the concepts of statistics Now, I would like to briefly review Bain’s points on what makes a great teacher, though I highly encourage you to add this book to your own personal collection. Chance are your school’s Center for Excellence in Teaching and Learning has a copy for you to borrow. Reading this book might be a great way to “refresh” between semesters.

Under each of  Bain’s points, I am including links to prior blogs that review each of these components. Briefly,according to Bain the best teachers:

1. Know their stuff … they know the material that they are teaching, and they know it well … plus, they know about teaching and how students learn.

2. Actively and intentionally prepare to teach.

I suppose this entire blog is dedicated to getting applied statistics professors to think about teaching, and to help them prepare. Everything from designing a syllabus (e.g., to identifying areas where students are more likely to have challenges (e.g., or Ultimately, great teachers approach teaching with the same gusto they approach scholarship.

3. Expect more of their students.

Professors who expect more from students, have students who simply learn more Sure, there are times when we all want to nash our teeth and clench our fists, as we wonder … what is going on in their heads … but in the end, students are more likely to be successful when teachers hold high expectation, and communicate it explicitly and implicitly.

4. Create a creative and critical learning environment.

This is covered well by Bain, and reviewed in this blog  Of course, focusing on the concepts of statistics and the application of them goes a long way at creating a creative and critical learning environment:

5. Trust that students want to learn, and treat students with decency.

One of the most read blogs on Statistic Sage addresses the idea of simply being decent with students:

6. Assess student learning continuously, and are continually conducting self evaluation.

This can be done directly   AND indirectly

Though no one is perfect, striving towards excellence in teaching is always time well spent.

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Evaluating the implementation of Mathematica Demonstrations … next semester, deliberate practice

Before the spring semester started, I promised to try Mathematica demonstrations with my applied statistics class with the intention of helping them better understand the concepts of statistics. You can access that blog at this link:

Well, I did what I had intended, but not in the manner in which I had hoped. You see, we ended up with my students missing almost a week and half of the semester due to school being closed. So, I had my students “explore” the Mathematica Demonstrations that I outlined in my prior blog. I felt pretty good, as I thought my students wouldn’t fall too far behind in their course work, and their exploration could be even more beneficial than being in class … right? Wrong …

Students logged on and looked at the demonstration. Most reported (cut this in half?) working with each demonstration for less then 6 minutes (ouch). They all said favorable things about Mathematica, but I saw no carry over to questions in class or on exams.

I suppose as I look at the practice of using technology in teaching applied statistics, simply providing students with the tools does not assure cognitive development — and yes, I knew that, and was planning on integrating it during class time, but snow days got in the way. In a few days, I have asked a guest blogger, Livie Carducci, who is experienced in using Mathematic demonstrations in teaching statistics to talk about some techniques to maximize student engagement.

Not surprising, what I noticed this semester is that some students will naturally explore, but others will put forth the minumum effort. I became motivated to figure out a way to assure students will be intellectually engaged in thi assignment. I thought of the new pedagogical practice of Deliberate Practice. Thus, for this summer, I plan on working on developing assignments around each of the Mathematica Demonstrations that increases the likelihood of students engaging in deliberate practice through the application of Deliberate Practice.

So, let me review this for you … first of all, as a pedagogical tool, Deliberate Practice is in its infancy. It is based off of the cognitive developmental research of Ericcson on expertise. Briefly, in the early 1990’s Ericcson and others noticed that people who truly became experts in an area, often devoted a tremendous amount of time and effort over the course of at least a decade before they hit a level of expertise. Ericcson hypothesized that we were born to excel, but through deliberate practice could become experts in areas of music, thinking, physical activity and the like.

Not all practice is deliberate. For practice to be considered deliberate it seems that it requires the following.

(1) We must first not only establish our desired outcome, but establish a means of reaching that outcome, thus we must specify the process.

So, I have a goal: I want to master the pedagogical practice of increasing my students participate in Deliberate Practice when interacting with the Mathematca Demonstrations, but in order to do that I must (a) study about deliberate practice, which will mean reading about it and talking to others who have tried it (b) specify the components of deliberate practice that I need to have my students accomplish (c) look at each Mathematica Demonstration I have selected for my students, and come up with an activity that will increase students’ deliberate practice (d) as I am going to have to assess my students implementation of Deliberate Practice, I should design a quick survey. (e) Immediately, my mind ponders about whether or not I should set this up as a research study … and I say, if I will, I’ll make that a new goal. (f) After looking at the students’ responses to the survey in the fall semester, see about making revisions to improve these assignments.

(2) The established goal must take us to a higher level of attainment.

Let’s face it, we can’t just stay right were we all … deliberate practice is all about hitting a higher level of expertise.  In my example, I’m clearly going outside of my prior experiences, but not too far to make this an unattainable goal.

(3) Now, as you implement your plan, you have to be formally and informally evaluating your progress.

Often this will require the use of an expert to provide you with feedback. Of course, you also have to have a keen sense of your own metacognition and progress. Though I haven’t read this in the literature, yet, I would suspect that individuals with weakened self esteems might have a tough time implementing Deliberate Practice, as you must have clear (and honest) insight into what you are doing, why you are doing it, and how you can do it better. We simply have to be cautious of our own bias to see everything as great. In hypothesis testing, this is called validation testing … where you look for signs that you are right! Instead, people who make strides in increasing their expertise through Deliberate Practice should make use of a practice more akin to “falsification hypothesis testing” where you look for how  you are wrong, and what you must do to get better.

My plan for preparing to implement deliberate practice as a way of maximizing the use of the Mathematica demonstrations will involve a self designed survey, specifically geared to look for how my practice is weak and what I can do to make it better. Of course, I’m also putting my efforts out in this blog, where I invite other statistics professors to comment.

(4) Then, you must … practice, practice, practice … but notice, that practice, alone isn’t enough … you must have a detailed and well thought out plan that takes you to a higher level, and  be critically evaluated by both yourself and an expert.

I would love to say … provide students with the Mathematica Demonstrations and the students will naturally enter into Deliberate Practice, but my experience this semester has been that most will not. So, I will establish an assignment that puts students on the right path. As I work on that over this summer, I will update my prior Mathematica Blog with a new one including the activities that go along with the demonstrations.

As always, I welcome your expertise on this topic! I also encourge you to look at Livie’s post on how she uses Mathematica to get students to master concepts of statistics.


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Unplugging students … We know we need to do it, but is it even possible?

It’s funny, Hal and I have been working together now for a few years, and more times than I can count, as a thought is beating around in my head, Hal will say … “I’ve been thinking … ”

His post of this past week, is yet another example. You see, I just finished the semester, and while correcting exams, I find my mind wandering over … what could I have done better? This semester, the number of times I found students texting in class or checking out their cell phone did increase, in all of my classes, and given that next fall, I will be teaching a develop class to four times as many students, I wonder … it is even possible to unplug them during class?

Yet the problem of students using technology to pull them away from class is a real one. An article in the Chronicle of Higher Ed,, highlights this problem from a different perspective … that of the student who is not texting or facebooking, or searching the internet, but distracted by the actions of those around him. Thus, I have more motivation going into this summer to come up with policies or practices that could minimize these distraction.

I have already taking a multifaceted approach to this problem.

  1.  I am on facebook. It’s an account just for students (and the few friends of mine who like seeing what college students are up to these days.) I can see what students are thinking, feeling, and doing … yes, much to my surprise students will actually complain to every body on Facebook about struggling in classes I’m teaching. Why do I do this? Students are more likely to listen to my concerns about facebook when they know I’m on it, myself. This isn’t a black and white issue … good vs. evil … it’s a moderation issue, and by me being on facebook, I can model that moderation.
  • However, for those of you thinking of trying this yourself, particularly the sages among you … even I was shocked at the personal details and language students use on this forum, to the point that I won’t let my mother “friend” me as I think the comments and language would send this otherwise open minded senior into cardiac arrest.
  • I actually post comments on facebook once or twice a week. They are short, sweet, and often involve links to articles that are summarizing research. Much of this research I will bring into the classroom for discussion and example purposes in statistics.  A couple examples include an MSNBC article on how children multitasking with cell phones. social networking sites, etc. could increase ADD . This link gets students to a free tutorial on math and statistics, or from an article from the Chronicle, students text … a lot during class … and also feel guilty about it, but not enough to stop texting: Of course, there are others … like the study from Psychological Science that demonstrates that students ability to learn decreases with their facebook account simply being open and “running’ in the back ground.

2. Just like the articles I post on facebook, I try to talk to students about these concepts and how to maximize their academic success. But I have to admit, I don’t know if it matters.

3. What seems to have mattered is a practice I started this semester. While I am teaching, out of the blue … I randomly announce in class to “put that away” or “don’t text in my class.”  Typically, one or two students will sheepishly put away their cell phones. Sure, I didn’t see them in the first place, but when I interviewed one of my classes as to how often they felt I was just saying this, they stated they thought I had always seen someone texting. They also stated that it decreased the likelihood of them pulling out their cell phones during class.

4. Of course, there are good ways to use technology. Drew Ziner, one of our “sages” posted about his use of the website “Broken Pencils” Drew has students post questions, and he answers them. He blog on how he used “Broken Pencils” can be found here…broken-pencils/

But I must admit. Thinking back to the days when I threw a college party or two, where we would have everyone put their keys into a bucket to control, let’s say … bad decision making … I’ve been toying with the idea, what if I just had students place their cell phones into a big bucket before class?  Oh, do I reminisce of the days when I taught elementary school where all I had to do was hold out my hand and say, “give it to me, you’ll get it back Friday afternoon!”

Regardless of what method we use, keeping students intellectually engaged results in better short and long term learning. However, now, instead of just having to compete with whatever students have roaming around in their minds to serve as a distraction, we must also attend to the electronic distractions students bring with them to class or beckon them as they study.

In the end, as I used to say about “classroom management” techniques for elementary school teachers … the best method for managing a class effectively, is a well designed and delivered lesson.  For now, I’ll use in class texting as a measure of how engaged (or not engaged) students are, and will use it as motivation to improve the quality of my teaching.

All tips are welcomed.



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Helping Students with Study Skills

I know that many of you are fortunate to be teaching at schools where students have long ago mastered the ability to study efficiently. However, many of you are teaching at schools where students really do not know the best ways of studying. As such, early on in the semester, it may help to talk to students about optimizing their studying.

I use several strategies to aid students in improving their study skills and behaviors.  At the beginning of the semester I often use research on study skills or metacognition for examples of statistical concepts, thus while covering examples of how a correlation might be used or how hypothesis testing work (in a fundamental fashion) I may use a study similar to the ones I have listed here.

Cassaday, H. J., Bloomfield, R. E., & Hayward, N. (2002). Relaxed conditions can provide memory cues in both undergraduate and primary school children. British Journal of Educational Psychology, 72, 531-547.
Gurung, G. A. R. (2005). How do students really study (and does it matter)? Teaching of Psychology, 32, 239-241.

Roediger, H. L., & Karpicke, J. D. (2006). Test-enhanced learning: Taking memory tests improves long-term retention. Psychological Science, 17, 249-255.

Roediger, H. L., & Karpicke, J. D. (2006). The power of testing memory: Basic research and implications for educational practice. Perspectives on Psychological Science, 1, 181-210

Zaromb, F. M., Karpicke, J. D., & Roediger, H. L. (2010). Comprehension as a basis for metacognitive judgments: Effects of effort after meaning on recall and metacognition. Journal of Experimental Psychology: Learning, Memory, and Cognition, 36, 552-557

I also survey students regarding their study skills. (  This does three things. One, it gives me data on what the students are thinking and how they are behaving. If their expectations are off from mine, I can further remind them of what my expectations are, plus the act of taking a survey often sharpens a person’s attention on the topic for which they are being surveyed, thus making them more receptive to information that will follow. Third, I can use some of this data for in class calculations or for exam questions.
This survey includes three components: students’ Implicit View of Intelligence, Students Attitude regarding Mathematics, and Students’ Study Behavior.

I have been asked to speak with students about study skills and metacognition. I am including my most recent PowerPoint presentation.  Learning to Study by bg I find this takes about 20 – 30 minutes to review. Feel free to revise it at you see fit. Though I don’t present this during class time, this presentation does cover important points students often need to know to optimize their studying behavior.

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Webinar on February 10th noon EST

Pearson is proud to announce an instructional webinar on Teaching Statistics with a special focus on teaching at community colleges.

From the comfort of your home or office, join our live webinar hosted by Bonnie A. Green and Harold O. Kiess. Bonnie and Hal, both statistics teachers and authors of Statistical Concepts for the Behavioral Sciences, 4th edition, will talk about best practices for teaching Statistics.

The webinar will take place on Thursday, February 10, 2011 from 12:00 noon – 1 PM EST. There is no registration fee; all you need is a computer and an internet connection. Registration is required; please email to register!

Nicole Kunzmann
Marketing Manager, Psychology

Learn about Pearson’s Psychology list at


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Avoiding Misunderstandings in the teaching of Null Hypothesis Testing

There are so many places were issues can arise for students when they are learning about Null Hypothesis testing. I believe that the best professors highly rely upon the technique of scaffolding (see a prior post for more detail). Briefly, scaffolding is a Vygotskian concept where the professor constrains the situation for the students so they can learn the component parts of a larger, more complex concept. Certainly, as Null Hypothesis testing is complex, scaffolding is in order.

Many of the statistics classes I teach have student learning outcomes that expect students to be able to calculate and interpret statistics like the z-test, t-test, F-test, and correlation coefficients, (i.e., Null Hypothesis testing). Here are the component pieces, in my opinion, that often deserve a full class period ( at least 50 mins.) and homework that requires students to master the pieces before putting it all together. I find in breaking apart the teaching of these concepts, that students not only end up in the same place as when a professor doesn’t break down these pieces and just goes full steam ahead, but that students have a far greater understanding of the underlying concepts, thus minimizing the likelihood of them carrying with them misconceptions. So, though it may seem like it takes more time to teach this way, my experiences has been that it doesn’t, while resulting in greater student understanding.

(1) Though my focus is concepts not mathematics/calculations, I find that students will never fully understand statistics without having do complete repeated hand calculations of small data sets using definitional formulas. Thus, it is critical that students learn how to calculate the Sum of the Squared Deviations (SS). They can then learn how to use the SS for calculating the variance and standard deviation. (See prior post for details on how I use a kinesthetic activity for the teaching of SS which maximizes student comprehension of the Sum of Squares).

(2) I actively teach concepts on the Normal Distribution and z-score, which typically take more than one class period.

(3) I feel it is critical that students fully understand sampling error, standard error, and how to estimate standard error. Again, please see a prior post for a tactile activity I use in the teaching the concepts of sampling error/standard error.

(4) Understanding that we begin by assuming the null hypothesis is true, then we establish a point of rejecting that ones hypothesis is wrong (a line in the sand), and what the consequences are if you hold onto a hypothesis that isn’t true or reject one that is true. This is such a critical component of this entire process, and helps lay out students understanding of the assumptions underlying NHT, what Alpha and Beta are (along with their corresponding errors) and even helps lay the ground work for understanding when to avoid parametric statistics in place of non-parametric statistics.

(5) Students need to understand the purposes, strengths, limitations, and assumptions required for each NHT statistic.

(6) By this point, if all is spelled out, especially if students can calculate the means, SS, and standard error, learning how to calculate and interpret the z-test, t-test, F-test, or correlation coefficient becomes easy. The calculation and interpretation become students’ favorite part of the class, as it all makes sense to them.

(7) However, even though we’ve discussed this previously, we cover yet again, detailed issues of type I and type II error, the requirement that NHT does not work absent of a theory that is predicting a specific outcome, and that though we have estimated sampling error, that estimate still contains sampling error, measurement error, and experimenter error.

(8) We calculate effect size statistics and confidence intervals. The latter so students get begin to get an idea of the size of an effect, the latter is to aid in general understanding of what the point estimate of the sample mean is really telling us. Confidence Intervals are truly easier for students to “get.”

Students don’t leave my class, or at least I hope they don’t, thinking that if their Observed t falls in the rejection region that there is proof that their independent variable caused the change of the dependent variable ; they don’t leave thinking the p-value and effect size are one in the same; they don’t leave believing that any research design (in general) or any experiment (in particular) is equally helped by using a specific statistic,… but they do leave recognizing that this one test is providing evidence, and that to be sure, more needs to be done.

I liken the types of conceptual mistakes individuals have about how and when to use NHT and what it can tell us to when my children were young and they thought … to get money, you just had to go to the cash machine. Yes, I get money from the cash machine, but obviously not without first putting it in. And yes, a significant statistics test can tell us something, but not outside of the context of us first understanding all that went into that study for the statistic to come out, and just like the amount of money available to me from the cash machine … there are significant limitations for which we must always be aware, lest we look like fools.

I believed if taught well, students “get” this.

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Engaging Learners by Focusing on Three Learning Styles ???

This weekend I had a chance to spend time with a former middle school principal. Like others she began talking about the importance of “learning styles”. Many of you may remember having someone talk to you about “learning style” whether you are an auditory, visual. kinesthetic, or tactile learner. However, this movement in K-12 education was never grounded in either sound logic or empirical support going beyond anecdotal evidence. Thus, not surprisingly, a Pashler, McDoniel, Rohrer, and Bjork concluded, after examining extensive research that is reviewed in that there is no real support for the “visual” vs. “auditory learner.” Nonetheless, all students learn better if we, as teachers, include all “modalities” of learning when we teach, if for no other reason than it engaged students. Visual illustration can help students in understanding concepts like the difference between discrete variables and continuous variables. We know, as an example, that coupling arm movements with verbal explanation aids students learning. However, though visual forms of teaching are often coupled with auditory forms of presenting information, professors are much less likely to use kinetic or tactile activities during teaching. Here I will describe an example of each type of activity and encourage those of you reading this to post activities you use involving kinesthetic and tactile activities. The two toughest, and in my opinion, most important concepts to teach well is sum of squares and sample distribution of the means. It will be these two topics I will provide examples for. Kinesthetic activity for understanding the concept for sum of squares: I start by talking to students about the concept of variability, that is how spread out the data are. I have students who live on campus stand up, so we can see the differences between students living on and off campus (typically the latter are commuter students), then the standing students pair up with someone sitting. They are to get a measure, in miles of how “spread out they are” in pairs. We take that number and find the average “spread outedness.” Then we do it again, this time people who live off campus stand representing the county in which they live. They pair up with someone for the same county and all on-campus students pair with each other. Again, they obtain their distance from each other in miles and we find the average “spread outedness”. Always, for my students, this number is smaller, so I conclude they live close together now. The students laugh, and we discuss how to better do this…the students conclude we need a stable location (campus). From this, I begin to explain what the sum of squares is, and how it works. By having them physically move and pair up (kinesthetic) they are better able to comprehend the concept of the sum of squares, that is that the individual observation is “paired up with” the “centralized” mean. Of course, the Sum of Squares becomes the basis of the variance, sd, Z test, t test, correlation. The act of moving in this one activity transfers conceptual understanding for all that follow. An example tactile activity is helping students to understand sampling distribution of the means and the concept of sample error. Most of us are already doing an activity like this one, with chips or pieces of paper. You make a “population” and have students draw a sample to try to figure out the population. Such activities really help students in understanding the sampling distribution of the mean and sampling error. In my class, I have a bit of a “twist.” I use plain M&M’s, as we know the proportion of red, blue, and other color M&M’s. Thus, I assign a value to each M&M, everyone in the class gets a sample of size 20, and they find the individual sample means. We then find the mean of the means for the entire class, using excel to graph those means and the students get a real sense, through this tactile activity, of what is sampling error and what is the sampling distribution of the means. So, is there any support for some students learning better with one style over another? No. Yet, there is still good reason to look at the four “learn styles” (verbal, visual, kinesthetic, and tactile) to see how you can better address certain concepts by not simply relying upon the sample lecture.

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