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. http://teachpsych.org/ebooks/stats2012/index.php

Another such resource, is Statistical Literacy in Psychology: Resources, Activities, and Assessment Methods.  http://teachpsych.org/Resources/Documents/otrp/resources/statistics/STP_Statistical%20Literacy_Psychology%20Major%20Learning%20Goals_4-2014.pdf

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. ( http://teachpsych.org/ )

Happy Teaching!

Bonnie

 

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A great resource

Hello All!

The Society for the Teaching of Psychology offers so many great resources for the teaching of applied statistics (http://teachpsych.org/index.php). One important resource is Sherry Jackson and Richard Griggs’ edited e-book, “Teaching Statistics and Research Methods: Tips from TOP” The book can be accessed for free by following this link.  

http://teachpsych.org/ebooks/stats2012/index.php

This book includes articles published in the journal, Teaching of Psychology, that cover several areas in the teaching of statistics including: generating data sets, illustrating statistical concepts, teaching strategies, application of technology, and helping students to develop skills in statistics.

Thanks to Jackson and Griggs, it is now easy to have a single source at your finger tips with several articles on the teaching of applied statistics.

Happy teaching!

A review of tips for teaching applied statistics from Statistical Sage

Hello All,

Another semester is about to start. To help people who are new to Statistical Sage or even for those of you who visit here often, I thought it helpful to review some key prior postings on the teaching of applied statistics. I have included tips along with the links to the posts from Statistical Sage.

1. A great class has to start with a great syllabus.  https://statisticalsage.wordpress.com/2011/08/16/backward-design-and-syllabus-formation/
2. Even for those of you who don’t want to teach applied statistics, you can still do a great job and even have fun doing it. https://statisticalsage.wordpress.com/2012/01/09/so-you-dont-want-to-teach-stats/
3. Great ideas can come from anywhere … so keep on the look out. (and please share them with us when you have them). https://statisticalsage.wordpress.com/2012/01/20/great-ideas-can-come-from-anywhere/   https://statisticalsage.wordpress.com/2012/01/27/using-current-research-to-help-students-understand-concpets-in-applied-statistics/ 
4. Don’t forget to apply the concepts of Cognitive Development to the classroom. https://statisticalsage.wordpress.com/2012/02/11/applying-the-science-of-cognitive-development-to-the-classroom/
5. Talk with (or read) others who have experience in teaching applied statistics; they can serve as a wealth of knowledge and help you to minimize errors and maximize learning (both yours and your students). https://statisticalsage.wordpress.com/2011/02/12/bonnie-and-hals-five-tips-to-teaching-statistics/
6. Applied statistics is more than just calculations. It is important that you get students thinking about statistics. https://statisticalsage.wordpress.com/2011/03/08/more-than-calculations-guiding-students-to-thinking-with-statistics/
7. Make sure to start that first class out, right! https://statisticalsage.wordpress.com/2011/01/29/first-day-of-class-starting-off-right/
8. Don’t forget to have fun teaching!!! https://statisticalsage.wordpress.com/2012/02/01/having-fun-teaching-applied-statistics/

I hope that everyone has a very productive fall semester, and that students’ excuses are few and class attendance is high!

Bonnie

Difficult Concept: Teaching Sampling Error and Sampling Distribution of the Means

I am currently teaching sampling distribution of the means and sampling error to my students. They are difficult concepts to convey to students, and unlike much of my teaching, where lecture comprises a fair portion of my teaching time, I find myself “slowing down” the progress at this point by putting more of the activities in the hands of the students, forcing   them to participate in activities during class time, and requiring them to generate ideas in and out of class.

There are three activities that I use to help students learn the concept of the sampling distribution of the means and sampling error.

(1)    Generating hypothesis, then identifying “individual differences in extraneous variables”

• First, I model for them, using the Socratic method (asking them questions as a means of leading them to the answer), how to identify individual differences. I first do this when introducing extraneous variables, during the first week or two of class, and periodically do so throughout the first half of the semester, anytime I speak of Independent, Dependent, or Subject Variables, I have students generate the extraneous variables as well. This task, repeated early on, and especially as we approach sampling error, not only helps students to understand sampling error, but it makes the teaching of confounds easier as well. (Sampling error are random variations in extraneous variables, while confounds are systematic variations in extraneous variables.)
• I assign for homework, that students have to generate a hypothesis (by this point, they have been doing this throughout the semester), then generate a list of 10 individual differences in extraneous variables.
• During class time, they form groups, to discuss and critique each others’ list, then generate another list, as a group, that gets graded as a quiz. Truthfully, I have too many students (and no TA)  to grade all 80 of these assignments, by working in groups of 5, I have little trouble grading the list.

Notice how much time I spend on the concept of individual differences and extraneous variables. But, as a critical concept, it is time well spent. Truthfully, it comprises about 50 minutes, but it typically takes place over the course of weeks, helping build students’ thinking.

(2)    M&E creation of a pseudo empirical distribution of the means.

• I formally model sampling distribution in class with the M&M demonstration.  Though I’ve described this activity before, I’ll describe it again here.
• I get plain M&M’s whose proportion by color is: 24% blue, 14% brown, 16% green, 20% orange, 13% red, and 14% yellow.
• Each color receive a value (e.g., 1 – 6).
• I calculate what the mu would be given the stated proportions.
• I have students randomly sample N=X (that value depends on how many M&M’s I have to share with the students, 10 should be the smallest value).
• Students then calculate the mean for their sample.
• Then I have them report their sample means, I enter them into Excel and do a very quick (and sloppy) empirical sampling distribution, and tell them what mu is.
• We compare our mean of the mean to the mu, and talk about the variability in the rest of the sample means.  
• We talk about how their individual sample means differ from mu and why.
• It seems so obvious to the students, that I can then switch over to other examples, like dog weight or performance on at recall for a list of words. 
• Students generate the extraneous variables that serve as sampling error, just as the colors of the M&M’s can serve as sampling error.

(3)    I end with having students participate in a Mathematica Demonstration, both in and outside of class.  If you haven’t used Mathematica Demonstrations, start with  reviewing this prior blog https://statisticalsage.wordpress.com/2011/01/08/before-the-semester-starts-im-playing-with-pictures/ or this one https://statisticalsage.wordpress.com/2011/05/24/using-mathematica-deomnstrations-to-visualize-statistical-concepts/.

If you have used Mathematica, this demonstration works well in helping students to understanding the sampling distribution of the means

http://demonstrations.wolfram.com/SamplingDistributionOfTheSampleMean/.

This year, I am requiring that student answer a series of questions about each mathematic demonstration to see if focusing them on the activity will increase what they are gaining from it.

For this demonstration the questions are as follows:

1. Try three different sample sizes. Which ones did you select? Draw the sampling distribution of the means by each N. What happens to the shape of the sampling distribution of the mean as N gets larger? Explain why this happens.

2. Using N = 15, change mu. What happens to the shape of the sampling distribution of the means as mu changes? Explain why this happens.  

3. Write the symbol for standard error. Change the standard deviation. What happens to the standard error as sigma gets larger? Explain why this happens.

4. Define Sampling Distribution of the Means. Define sampling error. What value do we calculate to find sampling error. Write down that formula. Why is this such an important part of statistics?

As with all of our difficult concepts. If you have any recommendations, I encourage you to  first work on getting it published in http://www.teachpsychscience.org/ and then let us know about it!

“I’m sexy and I know it … ”

If students don’t believe that learning statistics is a worthwhile adventure, will they try? Yet, we all know students are bombarded with messages that statistics are hard, incomprehensible, mysterious, or just plain wrong. Students are well aware of the inaccurate, though oft stated  comment that you can say whatever you want with statistics. My response is not if you know to use and interpret statistics.

So, how can we counteract the big push against the need for students to learn statistics.

Tell students the truth! Applied statistics is sexy!

I have comprised a few short articles and clips that characterize that statistics jobs are “sexy” and in demand.  

If you have other resources, please let me know, and I’ll add them to the list.

TED Talk by Arthur Benjamin  http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html

For Today’s Graduate Just One Word: Statistics (NY Times)

http://www.nytimes.com/2009/08/06/technology/06stats.html

Why Math and Statistics are Sexy

http://theappslab.com/2012/02/17/why-math-and-statistics-are-sexy/

Hal Varian’s “Sexy Job”

http://www.youtube.com/watch?v=D4FQsYTbLoI

 Now, what we need is a set of graduate students to pull together a video with statistics mocking the song, “I’m sexy and I know it.” It’s only a matter of time until someone creates such a video. When you do (or if you see it), please let me know.

I’m going to end with a TED Talk that I found it both interesting and funny  http://www.youtube.com/watch?v=1Totz8aa2Gg&feature=related  that further demonstrates … we all need to understand statistics and how it can be used, lest someone takes us down some incredible path, far from where we should be going.

Happy calculating!

Applying the Science of Cognitive Development to the Classroom

Applying the science of cognitive development to the classroom may seem like overkill for many, but I suspect not for the individuals reading this blog. We hear and see fellow faculty follow the same approaches to teaching for decades, patting themselves on the back when they so deftly transferred their notes from yellow paper to PowerPoint presentations a decade or two ago. Today, they use those same Powerpoint presentations. Many still follow a two or three test pattern. When students do not master the material, they belittle the students. But, it doesn’t have to be that way. There have been a movement on foot to apply the science of cognitive development to the classroom. This is particularly evident from a day long conference on this topic that was held at Harvard http://chronicle.com/article/Harvard-Seeks-to-Jolt/130683/ . Though many of these issues have been discussed in this blog, over the next few weeks, I am going to bring to you some of my favorite messages from cognitive development and how the lessons learned in the lab can be used in the applied statistics classroom.

Since the benefit of testing was brought up at Harvard’s Conference, work popularized by Henry L. Roediger, III (e.g., http://www.psychologicalscience.org/observer/getArticle.cfm?id=1951) we will begin here.

Here are a few important points to know about self testing.

1. Students benefit from the act of attempting to retrieve information, even if they are unsuccessful.
2.  Free recall yields the best future retrieval, thus, it is important to encourage students to attempt to recall answers WITHOUT looking at their notes or trying to get a cue from something like even a photo in their book
3.  If, after an attempt at free recall retrieval has failed, then, a brief cued recall should be used … but, this should be taken as a sign that more studying is needed.
4. Incredibly … let’s just say there are 10 concepts that students have learned, and you only have time to have them “test” 5 of those concepts … the even if the specific topic was not retrieved during testing, the act of self testing, just in that general area of knowledge, benefits ALL of the concepts. This is critically important, because their just isn’t enough time in the day to get students to test on everything we are covering in class.
5. This shouldn’t surprise most of us … but students do not seem to come up with the right rules of self testing, and instead HAVE TO BE TOLD … when they do their homework, close their notes and book to get the greatest benefit. 
6.  And yes, self testing gains much greater storage of information in a shorter period of time than massive studying.

So, how should this look in your classroom?

1. Though there are many who feel multiple choice questions are the bane of education, there is some benefit to them with regard to just getting students memorize symbols and terms. So, it’s a start, but not an end. There are several ways you can adopt multiple choice testing.

a. This semester I have 5 questions on-line after every class. They cover the material that was for homework that was due in that class period. This is my first semester trying this (based on student responses from last semester’s class). So far, students find this fairly favorable. This is graded. Each quiz is worth 2.5 points, and it will sum to a full test grade. (Yes, I’m dropping the lowest few grades).

b. I also have a symbol’s quiz that students can take as often as they want. I will open it when we have covered all of the major symbols, at about the 7th week of the semester. Though many students never touch this non-graded quiz. Other students complete it weekly to make sure that they keep all of the symbols straight in their heads.

c. I also have a practice final exam. My final exam is (sadly) all multiple choice. I will be adding questions to the practice test, based on areas of weakness from my last semesters class. d. There are other ways to use online multiple choice quizzes, graded or not. Some faculty permit students to keep on repeating quizzes until they achieve a particular benchmark.

2. Back when I was an elementary school teacher, we were taught about the “lesson cycle.” We were instructed to start off each class with a “hook” or “focus” of students attention. This was called, an anticipatory set. Even during my early years as a teacher, I recognized that one of the best ways to get students focused on what was coming, was to have them retrieve the information that would serve as a basis for the newly learned material. Thus, to this day, I start off almost every class with something akin to a “quiz.” It’s not graded; it gets students mentally focused, and it provides students with all of the benefits of self testing. And, unlike multiple choice questions, I can ask more complex questions, like how are the one sample t-test and the z-test similar and how are they different? Here are a few links to examples of a “lesson cycle” http://www.irvingisd.net/staffdev/documents/New%20Teachers/10-11/12%20The%20Lesson%20Cycle%20Explanation.pdf, www.texascollege.edu/eTC/omason/…/The%20Lesson%20Cycle.ppt

3. Probably the most important tool we have for students for self testing is the homework we provide and how we instruct them to complete it. The textbook, Statistical Concepts for the Behavioral Sciences, 4/e, have extensive supplements for students, including advanced (higher cognitive level) questions for each chapter and Exercises and Assignments for Students, a free supplement that includes everything from calculations to practicing terms. Finally, within the body of the textbook, there are three different types of homework problems. Testing Your Knowledge, Chapter Review, and Integrating Your Knowledge. The latter questions force students to integrate information from multiple chapters in order to solve a “real world” problem with statistics. My students know … all of this homework must be completed with their books and notes closed. Then, they get the benefit of self testing. In all cases, the answers are provided to the students for them to self correct.

4. Though this last recommendation is a bit “silly” … it works. I have been encouraging students to create their own quizzes or tests, but they always ask … how do I create the questions? I encourage students to always write down any question I may ask in class. Then use my in class questions as a basis for self testing questions. I wish students just came to us knowing how to learn. Many of my students don’t. So it is incumbent upon us to explicitly teach them how to study. The application of self testing is a tremendous tool too many students haven’t learned to adopt in their study strategies. Hopefully, with encouragement and instruction by us, we can see students who get more out of applied statistics than just the credit hours!

Anyone who has used self testing with applied statistics students is encouraged to tell us, how did it go.

So, you don’t want to teach stats …

Here at Statistical Sage, though we have well over 100 followers from all over the world, most of our viewers seem to arrive to  us through Internet searchers. I always enjoy looking at the different terms people are using, and, in fact, plan on analyzing those terms to gain insight into the challenges people may be having in teaching applied statistics.

However, one search term caught my attention recently … “I don’t want to teach stats.”

I certainly understand about not wanting to teach certain classes we end up getting assigned to teach. I am sure I’m not alone in sighing, at least on occasion, when seeing what classes I will be teaching (or more importantly, what classes I won’t be teaching) for future semesters, but I have to admit, I have never thought “I don’t want to teach stats.”

If I were to talk to an individual who was “stuck” teaching statistics, here are the tips I would provide to them to help them through in teaching this class.

(1)    Never let your students know your lack of desire in teaching this class.

Students will be coming to your class not wanting to take it. You can’t give them additional reason as to why they are right, particularly when applied statistics is so critical for their future professional and graduate student success.

(2)    Don’t reinvent the wheel. Get the a syllabus from someone who has been successful in teaching the course. You can obtain a copy of a syllabus and tips on syllabi formation from a prior posting,

https://statisticalsage.wordpress.com/2011/08/16/backward-design-and-syllabus-formation/.

By the end of 2012, APA’s Division 2 Task Forces on Statistical Literacy will have recommendations for the teaching of applied statistics in psychology. This group will be providing to everyone a list of student learning outcomes, a bibliography of resources, a list of Best Practices in Teaching for each student learning outcome, and a detailed outline of assessment practices.  As this information becomes available, I will post it here.

(3)    Seek out from others who have taught this class the potential pit falls, and be prepared to address problems before they become problems. Understanding issues like the most critical concepts https://statisticalsage.wordpress.com/2010/11/23/core-statistical-concepts/  and activities to help students master them can  help you help your students before real challenges erupt. Though this blog is filled with such information, I recommend you start with Hal and Bonnie’s Five Tips to Teaching Applied Statistics,

https://statisticalsage.wordpress.com/2011/08/14/new-to-the-blog-follow-bonnie-and-hals-five-tips-to-teaching-applied-statistics/.  Or you can learn from others who are successful in  your discipline and apply the process of their success to the process of your success as a teacher of statistics https://statisticalsage.wordpress.com/2011/11/13/learning-from-steve-jobs/ .

(4)    Get a book that students find easy to read and understand that comes with it a set of homework problems (both in and out of the textbook). Of course, my favorite applied statistics book is Kiess and Green (2010) http://www.pearsonhighered.com/product?ISBN=0205626246. In addition to it coming with a detailed instructor’s manual, with specific classroom activities, chapter outline, and student outcomes, it also has about 5 homework assignments per chapter, and several  problems in the textbook for students to use, http://www.pearsonhighered.com/product?ISBN=0205626246#tabbed. A great book will make teaching applied statistics easier.

(5)    You are going to need to give examples in class of studies that use statistics. Have fun with it, and use studies YOU find interesting. If you find it interesting, it will be bound to show to the students, and talk about your own research or areas where statistics have been applied in your life. Given the example will take up about 15 minutes of each and every (50 minute) class, you can be guaranteed of at least part of every class time being interesting to you. If you are interested in the topics you are talking about, your students will be excited about coming to class to listen to what you have to say next, that enthusiasm will rub off on you, the professor, in a nice, circular, and upward lifting manner.

(6)    Chances are you are going to try to get out of having to teach statistics in the future. And let’s face it, you are probably just one new hire away from having your wishes fulfilled. However, I still encourage you to read up on pedagogy, because, after all … the economy is bad, and you may be at the bottom of that seniority pile for longer than you expected, as the senior faculty who should have retired years ago no longer can do so thanks decreases in their retirement funds. If you don’t want to invest a great deal of time in the study of pedagogy, that’s why StatisticalSage is here … for you, as, after all … you may be “stuck” teaching applied statistics, but you still cared enough to google “I don’t want to teach stats,” and you cared enough to read a few entries here. That means, you do care.

There are lots of things I don’t want to do … clean out my refrigerator, go for my annual check up with the doctor, go to the dentist for a teeth cleaning, and yet … I do it. And you can teach stats well, too, and who knows … maybe  you’ll even like it, a little.

Please let me know how your semester turns out!

Looking for an Inexpensive Conference in the Teaching of Statistics???

Is $15 for a conference on the teaching of statistics  inexpensive enough???

As professors in applied statistics, it is important that we attend conferences, but travel time and cost are an issue for most of us. I highly encourage everyone to look at the Consortium for the Advancement of Undergraduate Statistics (CAUSE)’s Electronic Conference on Teaching Statistics (eCOTS).

“The Electronic Conference On Teaching Statistics (eCOTS) will take place from May 14-18, 2012. The conference will be hosted by the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE: www.CAUSEweb.org). Just like the United States Conference On Teaching Statistics (USCOTS), eCOTS has been designed to focus on undergraduate-level statistics education (including AP Statistics), with a target audience of statistics teachers. Whereas USCOTS is held in odd-numbered years, eCOTS will occur during even-numbered years and seeks to provide a virtual meeting space for educators to share ideas, teaching methods, and research results. It is hoped that eCOTS will be a forum where statistics educators from around the world can network and connect as they learn how to incorporate new ideas, methods, and resources into their existing courses or programs. The registration fee for attending eCOTS will be $15.”

Their Call for Proposals ends February 15th, 2012.

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 (http://www.psychologicalscience.org/index.php/news/how-to-keep-your-resolutions-all-year.html). 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 (http://www.psychologicalscience.org/index.php/news/releases/the-first-step-to-change-focusing-on-the-negative.html) ?

Though I can’t attest to the quality of the data, it is reported http://proactivechange.com/resolutions/statistics.htm 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 (http://projects.ict.usc.edu/itw/gel/EricssonDeliberatePracticePR93.pdf, also reviewed in https://statisticalsage.wordpress.com/2011/05/22/evaluating-the-implementation-of-mathematica-demonstrations-next-semester-deliberate-practice/ ), 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!  http://nsse.iub.edu/NSSE_2011_Results/pdf/NSSE_2011_AnnualResults.pdf#page=8. 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 http://chronicle.com/article/Middlebury-College-Invents-a/126088/ , 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!

Khan Academy

Hello All,

As we get ready for the up coming semester, I thought I would provide you with a few short posts highlighting things that may help you prepare for  your upcoming semester.

I’m sure I’m not alone in having students who have conceptual gaps in basic mathematics. I have brought up specific areas in prior blogs, where students conceptual weaknesses interfere with their ability to master statistics. One method that I use for helping students overcome those gaps is to refer students to specific sections on a free educational website called Khan Academy, khanacademy.com.

There are videos and exercises mostly in the area of mathematics and applied mathematics, like statistics. The skill set starts at the elementary school level and continues through the college level. There are almost 60 different videos available on Khan Academy just for statistics, with more becoming available every day.

So … what are the two practice problems and video’s I refer students to the most???? ANOVA, t-test, standard deviation … nope … Order of Operation and Points on a Number Line are the two practice problems and video clips I am most likely to refer my students to.

Sure, I would rather have students come to me with their math skills in tact … but absent of that, I am grateful for Khan Academy, and highly encourage you to refer it to your students.

Happy preparation!