I recently taught a day-long statistics class.  That should be enough to make anyone shudder, but please feel free to keep reading . . .

As part of the semester teaching assignment I have at Western Connecticut State University, the course has an extended Saturday class – 7.5 hours!  Clearly planning for that length of instruction with adult learners was a challenge.  When I began thinking about such an experience, I was really careful to ensure that the day got broken up into parts and that the learners would have a chance for some experiential, tangible learning.  I also had the opportunity to bridge from their other course:  Learning and Cognition. 

When I was originally hired to teach the course, I spoke with the program director, who was also teaching the second course the students were taking.  We discussed the extended day, and I said that it would be really great (cool) if we could connect the two courses together in some meaningful way.  The Learning class has the students observe a teacher (or video tape themselves) and analyze the instruction using an instrument called the CPR (Classroom Practices Record).  The CPR examines incidents of higher order thinkingquestioning in both students and teachers.  Since students had to observe both pre and post, I thought this would be an excellent opportunity to analyze data.

Therefore, the topic of the day was chi square, a nonparametric statistical procedure that has many benefits in educational research, and direct application to the CPR data that was collected.  I did a standard, direct instruction introduction to discuss the overarching concepts:

Following the instruction, I had the students participate in a hands-on activity using M&Ms to determine if the package (observed) contained what the company said would be present (expected).  The students appeared to aggressively engage in the activity. 

For me, one of the most facinating parts of the lesson was the inputing of a live data sheet.  I had established a spreadsheet on my Google Docs account and embedded the link in the PowerPoint.  When we got to that section, students entered their data, and on the projector we could actually watch in real time as data appeared.  It almost looked like watching live election returns.  Talk about a classic example of reconfiguring!  New information was being provided to the class (and actually the world at large) in real time.  There was no waiting, students could acquire and use their classmates information as it actually came into existence.  Can you imagine learning based on class data without any lag time?

After data entry, analysis on the M&Ms took place and students were relatively able to work at their own paces.  I think I was able to provide some one-on-one attention, although I’m not sure if everyone got entirely what they needed.  Nonetheless, I think most (if not all) students walked away with a clear understanding of the chi square statistic, and certainly had a major portion of their CPR project completed.

I would be remiss to also add that I also brought in three guest speakers to discuss their research interests and how statistics helped them bring meaning and understanding to their passions.

Adults have different expectations in learning than children do.  Androgogy, the teaching of adults, contains the following important components and tenets:

·         Adult learning is voluntary and learner-oriented. 

·         Education brings freedom to the learners as they assimilate learning with life experiences.

·         Androgogy encourages divergent thinking and active learning. 

·         Often the roles of the learner and the teacher are blurred in the process. 

·         Often there is an uncertainty about the outcome of learning, regardless of the curriculum content. 

I currently have the pleasure of working with many expert teachers in the quantitative statistics course I am teaching for WestConn.  Interestingly, though, the course I am teaching puts many of these expert students in an uncomfortable novice position. 

Research demonstrates that there is a difference in learning between novice professionals and expert professionals.  Three main aspects of performance change in novice to expert learners: 

·         The novice professional’s work paradigm focuses on abstract principles while the expert uses concrete past experiences

·         The novice often views situations discretely where the expert sees situations as part of a whole.

·         The novice is often a detached observer where the expert is an involved performer (Daley, 1999). 

A striking difference when considering novices and experts is that novices are often hindered by specifics of the job, where experts are often hindered by the system.  Novices prefer, and best learn formally, where experts learn best informally, often in conjunction with their peers.  Novice professionals prefer learning strategies like memory and therefore accumulate information, while the expert professional uses dialogue to create a knowledge base (Daley, 1999).    When I consider my students, clearly from an andragonolical standpoint, they behave as experts. 

            Throughout the course, I have assigned work for the students to learn and master statistical techniques that may be useful for them as they begin to research their educational passions.  The assessments have been designed to be formative in nature.  As such, many submit assignments, wait for meaningful feedback, make necessary changes and resubmit.  I am very glad that many feel very comfortable presenting work, knowing that it may require revision. After all, much learning takes place when there is dialogue (in this case, electronic dialogue).  Mistakes are just as valuable as successes. In an adult learning environment, where students are motivated to learn, we can take advantage of the formative process.

            In just a short while, they will begin to work on dissertations, and that is a totally formative process.  Glad we can enjoy it now!

I taught a statistics class last Wednesday evening on correlation, and left feeling very depressed. I could see the level of frustration in some students’ eyes. They were working extremely hard, focusing, and were struggling immensely. These are no ordinary students: they are clearly some of the top educators in the region, all pursing a doctorate in instructional leadership.

I had lost some students along the way, and I my reflection on the process leads me to believe that I didn’t stress the “big idea,” strong enough. What may have happened is that the students got caught in the idiosyncrasies of the mechanics of correlation. Certainly the content was extremely rigorous for some of the students. There was a high level of math concept connected to technical use of the computer to analyze data. In other words, we went from conceptual learning to learning about facts in isolation – always a bad way to go.

What was the big idea in laymen’s terms? Is there a mathematical pattern or trend between two variables? The pattern or trend we were searching for was a linear relationship. So, if a set of points for one measure is compared to the set of points for another, do they plot out to produce an image that looks like a line? Once this line is ascertained, how accurate is it? In other words, do the points that were used to plot it have statistical significance?

I can certainly discuss the concept more, but what I want to focus on is concept acquisition, specifically as it relates to teaching and subsequent learning. When considering learning, Fischer, B.B. & Fischer L. (1979). (Styles in teaching and learning. Educational Leadership, 36, 4, 245) suggest that the environment generated by the teacher can be teaching centered, learning centered, or student centered. (There are actually several others, but I will limit for the purpose of this discussion.)

When designing the class, I tried to design learning activities that would allow for some concept acquisition, followed by skill building activities to learn the techniques necessary for computer calculation of correlation. The activities were intended to be compartmentalized and chunked –learn a concept then apply it practically. I think I had planned my class as a learning-centered teacher, but as the class progressed, I think I transitioned more to a subject-centered teacher. I had allowed the content that I was obligated to cover, take over the responsibilities for the class, and mercilessly plowed along, to the dismay of some of the students. I think I would be remiss to mention that some students were with me without fail the whole time. I am struggling with the balance for all of the students.

The challenge for me is to meet the curricular requirements of the class while allowing students to grow to be autonomous quantitative educational researchers. It’s hard enough to be a teacher, let alone a teacher of teachers.

Probably the ironic part of the whole story is as I sit and beat myself up over my work, there are probably students doing the same thing to themselves. We’ll all grow together.

There have been several requests to make one of the assignments a collaborative group effort.  I believe in the situated, socially constructing knowledge approach, so I am open to the suggestion.  My question to the group is, “What does a statistical collaborative assignment look like?”  I ask, from a very serious perspective, because the purpose of the assignments are to build the requisite skills for conducting individually-determined quantitative skills necessary for conducting an inquiry study (a.ka. a quantitative dissertation).  I have thus far designed the assignments, to (hopefully) build upon the experience in class so an individual student can then apply the skills and knowledge, to hopefully gain a positive disposition to and clear understanding of the statistical process. 

A group assignment would have to take a different form, and I am open to suggestions to think about ways to implement this.  Your feedback is appreciated.

Remember . . . 40% of the course grade are these assignments and these discussions . . .

I will make a post regarding last night’s class by the end of the week

Last week I taught a statistics class on converting data to different forms: z scores, percentile rank, NCE scores, and the like.  The challenge with teaching these concepts, besides the obvious mathematical concerns, is the relevance of doing it.  The basic meaning behind converting scores is to put numbers in common terms so sets of data can be related to one another.  For example if one instrument had potential scores of 1-42, and another had a range from 200-800 (like the old math SAT ranges), its hard to put that interval-level data into common terms.  That’s the ultimate purpose of the z-score:  to base a set of data (e.g., a sample of students with normal distribution with a specific standard deviation), in common terms, regardless of the raw score format.  Remember that z-scores are based on a SET OF DATA that is inter-related.

The majority (~96%) of z-score data will be between the values of -2 and 2, with a mean of 0.  Uggg . . . now all numbers are on the same scale, but still have relatively little meaning to a non-stats person.  So the percentile rank comes in.  Put the scores in percentiles relative to one another.  This comes at a cost:  the data is now ordinal.  But the benefits are enormous:  they have meaning to practitioners. 

Now for an affective comment.  I went home with a sore throat.  Hmmm . . .  I must have been talking too much.  I wonder, for a two-hour class session, if there was too much direct instruction.  Were there enough opportunities for the students to apply their knowledge? 

I pondered this on the drive home, and even more so on Friday, when I had the opportunity to meet with a master World Language teacher for whom I am serving as a dissertation major advisor.  Since my primary role is a science teacher, I wanted to expose myself to the instructional experiences of a high school Spanish teacher.  For me, this was a wonderful and enlightening experience. 

I had never seen a computer-driven language lab and the power of allowing students to demonstrate their technical speaking, reading, and listening skills.  The process was so fluid and dynamic, and the transitions from learning activity to learning activity were masterfully administered.  No doubt, this was due to an extraordinary master teacher.  Easily five different learning activities took place in each class I observed.  Each learning activity was targeted to a specific skill or knowledge and was seamlessly transitioned to the next.  Just amazing to watch, and I know I do it no justice in words.

My learning helps to remind me that students need a variety of instructional strategies to address their varied learning styles.   Also it reinforces my general strategy to vary instruction, especially in an extended-class setting.   

I gave a statistics assignment over the past week to my students which challenged them to assimilate most of the course content and explain it in an applied assignment requiring both visual and written interpretation.  Basically, they took their data set that they had generated in a previous assignment, and analyzed it descriptively:  means, medians, modes, standard deviations, interquartiles, box-and-whiskers, and the like.

But this post isn’t about what the students had to do, it’s about my impression of how they did it.  I received many emails from students expressing how they worked hard, collaboratively.  Together they were able to figure out how to complete the assignment.  They repeatedly told me about the groups that met up together at the University lab, to work, share frustrations, successes and, struggles, and ultimately create tangible products, based on authentic data.

I can’t think of a better example of situated cognition in action.  They were socially constructing knowledge together.  It was in their social interactions that learning took place.  What is interesting, is that they chose to learn this way. 

They were using the authentic tools of the practicing educational researcher:  student achievement data, SPSS software.  Of course, to most, they are new (neophytes) to the field of educational research so they are on a peripheral trajectory to the community of practice. 

Seeing this type of learning in practice makes me think that I must continue to strive to provide cognitive apprenticeship opportunities for the students, both in class, and in the ”homework” opportunities to make the experiences as authentic as possible.  I think these homework assignments should represent the most meaningful learning that takes place for the course.  Kind of interesting to consider the role of an “in class test” in a situated learning model.  Doesn’t really fit so well.  But, as most know, a doctoral class in statistics, complete with objective in-class assessments is a right of passage towards the letters that are earned after your name. 

So how do I reconcile the the two? 

• Make the assessment as authentic as possible. 
• Use the tools of the community of practice. 
• Allow students to have the necessary resources to solve problems. 
• Evaluate on concepts, not isolated facts. 

Any other suggestions?

I have been struggling with trying to describe my last statistics class (central tendency, normal distribution) in a holistic way. The content was certainly more demanding than previous classes, yet I felt the students stayed with me well. I gave an assignment to allow the students to process the information and see if they really understood it. Although the assignment barely took up half a page, I felt that it would probably take a good chunk of time to complete.

I have received many comments from students quantifying the time they spent on the assignment. Ironically the time frame “4 hours” seems to be quite common. I think this is reasonable as the rule of thumb suggests that for every hour you spend in class, you are expected to spend at least two hours working on the course materials. So four hours seems about right to me. I hope that it is not perceived as too much, as I make no qualms that statistics is a very demanding and rigorous course. I feel the experience of the assignment necessitates an extended period of time where students work through the problems and come to a true understanding of the concepts.

That being said, I did not give explicit instructions for all computer tasks necessary to complete the assignment. There was some sorting and sifting – in essence – some inductive reasoning – that had to be accomplished for successful completion of the assignment.

When I think of inquiry as an approach to learning (which is certainly the approach I hope to use when I teach), I realize that there is no one way to solve a problem. However, students often look for the step-by-step, one-size-fits-all method to approach problems. While there are some straight-forward techniques and patterns in statistical analysis, I think it is the willingness of the individual to approach the problem solving from a creative avenue, that ultimately makes them successful.

High-achieving students not only want to learn concepts well, they sometimes also want to complete assignments the way they perceive that the teacher wants it. This has always been an area of contention for some of my students, because I want them to complete their work so they demonstrate meaningful understanding, whether it’s in the format I want or not. You see, I do not perceive my way as the only way. I love to look at solutions that I had not previously conceived. To me, it’s exciting and interesting. To some, it can be very disconcerting. I do not buy into the concept of the right answer. I more readily appreciate the best answer. I don’t define best; that is the ultimate goal for the student.

I recently received an email from a student asking two questions to help decide how to represent data. This data was generated and/or collected by the student, and probably has some personal meaning to the student. The student certainly has a far better understanding of the sample and of the data set that demonstrates some characteristics of the sample than I do. So, although I may have a better understanding of types of analysis, I would venture that the student has a much better understanding of the meaning and relevance of the data.

Thanks for your great effort to learn the stats and SPSS.

Both of your questions are interesting to me as a teacher because I always try to empower my student to make the decision on what is important to show. You have great judgment since you know the data best, so try to select information which “tells the best story.” I guess your questions answers are “it depends,” because there are really no right or wrong answers. The decisions you make for data display will be appropriate in either scenario you present. I’ve personally been struggling with what to write about on my blog this week, but I think your question helps me focus my ideas. Thank you for that.

This past Wednesday I taught my second class in statistics. The focus was to explain types of data and examine visually appropriate ways to represent data. This took the form of making an appropriate APA table as well as constructing several graphs. I think that most of the students recognized the actual attributes of the representations, and some walked away with an understanding of the differences that they might not have known before.

Although I was not surprised, what was most striking to me was how the differences in abilities, mainly related to computer expertise (not content understanding/knowledge). The students are very open, unassuming, and metacognitive when it comes to their level of experience using technology. I value that, because I don’t have to guess what’s happening. They just let me know. Therefore, I can adjust to the needs of the students. Also wonderful, is watching those with more experience and expertise lean over and provide the support and help that some need themselves.

This has all of the feels of differentiation. However, the interesting part is that all students have to end in the same place, in the same 15 weeks of the instructional experience. I guess what makes me fret most is that we meet for a very limited time: two hours per week, only once a week. That’s not a great deal of contact time to meet the individual needs of each student, especially in a fairly large class.

I consider the initial topics of the first two weeks fairly easy.  When the content becomes more demanding, I think my challenges will increase.  It is important for me to continue with my inquiry-oriented constructivist approach (I really hope I’m doing this . . . ) to prepare these students for authentic quantitative studies.

I taught my first graduate class in statistics today. As I said to my students, I think I was far more nervous than they were. I found that I was sweating – probably a combination of nerves and movement while teaching the class. But, nonetheless, I wanted to share my personal philosophy of the discipline. As I have stated before, I view statistics as a tool to help us understand the things that MATTER TO US. Certainly there are those that study statistics for its pure value, however I don’t see it that way. If statistics are to be practical, then there must be value for the user.

I’ve encouraged my students to collect data that is meaningful to them. If they can learn something about their teaching and, in the process, learn something about a sophisticated method to evaluate its effectives, I think we bring such greater meaning. This doesn’t stray far from my dissertation where I purport that learning takes place in a situated environment, where constituents become members of the community of practice (see Brill). Work needs to be authentic, not sort-of-maybe-on-Tuesday-authentic. I cringe every time I hear the saying, “like real life,” in some instructional setting. Why can’t it just be real life?

I think this is an incredibly hard concept for educators to grasp. I gave an assignment for the teachers to collect some data that had meaning to them for further evaluation in our class. I was not completely convinced that everyone bought into the value of this. Some students certainly won’t have access to good or usable information for the assignment, but I think some that might will complete the assignment with arbitrary or fictitious data. This is totally fine and acceptable within the context of the learning. However, I guess my own personal biases in education really want me to have students completing real work. Ultimately what’s most important is that students learn well. That can happen with or without authenticity. As the saying goes, I shouldn’t impose my values on others.

Now for a bad transition. The purpose of the class was to talk about p. p being probability. I wanted students to have a very firm grasp of what p was, since it is the real foundation to statistics. When they see the p, or the Sig. notations, I want them to quickly think about how sensitive that value is compared to other decisions we make that have far higher risk (i.e., a higher p value). We played Black Jack to illustrate this. Students were interested in taking a card with a p value of ~.50 – the 50/50 odds. Yet in education, we wouldn’t dare say anything was statistically significant (make a choice to take a card) unless we were at least 95% sure that it was different (p<.05).

I hope I effectively communicated my big idea of p. So much can make sense with just a simple, yet clear understanding of p values.

Tomorrow, I will begin to teach a doctoral course in statistics. I am excited about the prospect of working with highly motivated, engaged teachers. What concerns me most is the “fright factor” that some have. To me, statistics has always been a tool to help explain whether or not a phenomenon, a teaching strategy, or perhaps student learning changes due to influencing factors.

That said, I think of statistics as an applied tool. Statistics don’t exist in isolation. They exist IN CONTEXT. The challenge for me will be to translate some technical mumbo-jumbo into meaningful concepts that these teachers can realistically apply to their research or even to their understandings of their own students.

When I learned statistics, I was working in a bacterial genetics laboratory examining DNA restriction fragments of human chromosome 6, locus HLA-C (major histocompatibility complex of the immune system). I needed to determine the significance of different fragment lengths to see if our human genome project mapping strategy was working. Now, realistically, I know that most won’t even understand the nature of this genetics project, and that doesn’t matter. The fact was, that I needed to use statistics to explain what I had done experimentally. My data was IN CONTEXT for me. That being said, statistics for educators need to be in context for them. It’s not just good enough to examine fictitious educational data, we also need to consider meaningful data to the student-constituents.

My colleague and good friend, Krista Ritchie sent me some interesting literature recently and one
paper caught my eye:

Singer, J. D., & Willett, J. B. (1990). Improving the teaching of applied statistics: Putting the data back into data analysis. The American Statistician, 44(3), 223-230. (Argues against artificial data sets for learning statistics – that false data makes statistics seem dry and dull. Argues for learning statistics through authentic research).

I had the opportunity to present to this group of students earlier this summer, talking about 21st-century skills and their application in the classroom. I guess now it’s my turn to put up and show that authentic teaching and learning can be a reality. I will attempt to use this blog as a point of reflexivity for both me and my students, I’ve established a collaborative wiki for us to share ideas, and I will attempt to get an online survey working as well. I thought this would be done before writing, but alas, I am having technical difficulties with the limesurvey freeware. If I can’t get it to work by tomorrow’s class, I will resort to paper (maybe bubblesheets from Apperson?). I think the online survey will be valuable to my students, not only as an expository activity, but as a potential tool for their dissertations.

Challenges await for both the students and me. As Marcy says, “I take no prisoners.”