BETH CHANCE

 

Context: My answers pertain to an introductory statistics course for nonmajors, intermediate algebra pre-requisite. Most recently I've tended to teach psychology and other social science and liberal arts majors in a general education course. Class sizes are capped at 48 and I have probably 2-3 sections of such a course each quarter.

Usually I start by thinking about which topics I want to cover. I have given students a detailed review sheet and I use that as a guide of topics to choose from. I also spend some time looking through test banks and previous exams. I'm always searching for interesting, current contexts and continue to use genuine data as much as possible. Once I have the context/scenario, I continually refine the statistical content that I want to assess. I try to make sure the points given to a problem are proportionate to the amount of time it should take them to complete. I hope at least half the points are conceptual over mechanical. I also try to make sure that even when there are multiple parts to a question, later parts can still be answered even if earlier ones cannot. I hope this reduces the number of distinct contexts students need to read through to help with the time constraints.

GEORGE COBB

 

Context: My comments refer to Mount Holyoke's Stat240: Intro to Design and Analysis of Experiments, which for many students serves as an alternative introductory statistics course. (I teach this regularly, but have taught the "standard" intro course only once in 20 years; in fact that course has existed in our department for only the last four years.)

Real data. I always use real data, and I never use data sets that are in the book, or that I've used in class as examples, or that I've ever used on an exam previously. I want every data set to be both real and new to the student. Imposing these constraints on myself means that I spend quite a bit of time, during the weeks leading up to the exam, looking for suitable data sets.

Point values. Questions are grouped by data set. A typical exam might involve 3 or 4 different data sets. Some data sets may be rich enough to support several questions. Others may lend themselves to just one. To help students plan their allocation of effort, I try to create a set of main questions that count equally. (The number varies from exam to exam, but is usually between 6 and 12 main questions.) Some questions may have several parts, but here, also, I try to create divisions into parts that count equally.

Conceptual vs. ritual. For the most part, I rely on HW and weekly quizzes to check for computational ritual. I want the mid-term exam to deal with conceptual understanding. Here I have in mind two main kinds of understanding: interpreting results (going from the abstract numbers or plots to their concrete meaning in relation to the applied context), and recognizing abstract structures (going from the concrete applied scenario to the relevant abstract models or methods). Although that's my main goal, I try to start the exam with a first problem that I hope all prepared students will find straightforward. This one tends to be somewhat more mechanical. Also, unavoidably, most problems have a somewhat more mechanical element to them, and this strikes me as perfectly OK.

JOAN GARFIELD

 

Context: An introductory statistics class taught in a college of education but serving beginning graduate students in many departments across the university who have never before studied statistics. Typically about 25-30 students in a class.

I usually think of an idea or skill to assess, and then look for good items or data sets to use. I don't always use real data sets, but I try to provide contexts for any phony data sets. I try to have each piece of information worth a point. A question with many parts and answers is worth more points.

JOHN HOLCOMB

 

Context: The introductory statistics course in the mathematics department at Cleveland State University (CSU) that I teach generally runs 2-3 sections of 30-45 students in each section with one section offered during the summer. The course prerequisite is a college intermediate algebra course or a suitable score on our mathematics placement exam, although I do not believe that prerequisites are actually checked on our campus. The course is a fifteen week semester with an additional exam week. Cleveland State comes from a legacy of years of teaching on a ten week quarter system, and although we are now on semesters, each course is 4.0 credit hours. The introductory statistics course is generally offered for 65 minutes per class on M-W-F.

Cleveland State University is a comprehensive metropolitan university located in downtown Cleveland. There is only one dormitory on campus, so almost all the students are commuters. In addition, CSU is an open-enrollment institution that accepts every applicant with a high school diploma. The mathematics department where I teach offers a masters degree in mathematics. The general teaching load for each instructor is 8.0 credit hours per semester provided the faculty is active in research in some way.

For in-class exams, I try to use real data from questions that I generally find in statistics texts other than the one I am using in class. I try to have every question reflect real data or at least realistic data. For the take-home exams, the data is definitely real. It comes from my research with scientists in a variety of disciplines. I, however, adapt the questions for the exams to be appropriate for introductory statistics. So the questions might not be the actual questions asked in the research paper, but they are definitely realistic questions. I do not think the distinction between real and realistic data/questions is important. I DO think it is important to use data in the correct context. There are paper now in the literature that use random number generators to generate "real data" so that students have individual data sets, but I do not like that approach because it is devoid of context and context is very important. I generally have questions valued according to how long I think it will take the student to complete the question. Questions taking more time, have higher point values. I like to have each in-class exam total 100 points. I think right now, my exams are about 40% calculation and mechanics and 60% conceptual and interpretation. I think I have been good at asking interpretation questions, but only recently have I tried to construct conceptual questions.

CARL LEE

 

Context: The type of course: Introductory statistics. Covers contents typical to an introductory statistics course. The majority of students are business majors (75%). The rest are from a variety of departments other than Science & Technology. Most students are junior, age ranging from 20 to 25. They are full time students, but many of them have some part time job. For each semester, we have about 400 to 500 students. Their background is usually weak. Less than 10 percent of students had pre-calculus.

The exam questions usually start with a real world problem. Questions are designed to cover a sequence of concepts. The solution of a question is designed by trying to prevent the use of the solutions from previous questions, but use the concepts from previous questions within the same real world problem. True/False questions are also common in the exam. They usually test a specific concept and the relation between concepts. Usually three points for each question. An exam usually consists of 35 questions before final. Final usually consists of 52 questions. Over 905 of the questions are conceptual knowledge/interpretation and reasoning questions.

TONY ONWUEGBUZIE

TONY ONWUEGBUZIE

 

Context: The 3-hour statistics classes that I teach involve graduate students (i.e., master's and doctoral students). My comments below, in boldface type, reflect statistics courses taught at the introductory, intermediate, and advanced levels. I have taught graduate-level statistics at the University of Central Arkansas (previously a master's-granting institution), Valdosta State University (a doctoral-granting institution), Howard University (a Research I, Research Intensive institution), and the University of South Florida (a Research Intensive Institution). My courses almost always are required. My average class size is 20.

 

When constructing examinations, I always use real data. Also, I allocate points for each item based on how important I believe the topic it represents to be and how much time was spent covering it in class and/or in the readings. Much more weight is given for conceptual knowledge/interpretation items than for calculation/mechanics items.

ROXY PECK

 

Context: The comments I gave are based on Stat 130 and stat 217. These are courses primarily for students majoring in liberal arts fields (Stat 130) or social sciences (Stat 217). Class size is usually 45 - 48.  Stat 130 is a general education course in statistical literacy, whereas Stat 217 is more of a methods course for students who will continue on to a research methods course in their own discipline.

When writing an exam, I think it is important that each question have a context, since without a context, it seems that interpretation is not very meaningful. However, I do start with content. I usually make a list of the type of questions I want to include, and then try to write questions with a reasonable context to fit the content questions that I want to ask. I am a real advocate of real data in texts, homework, and especially in any kind of data analysis type project work, but for exams I usually settle for realistic because it usually doesn't take as much in the way of explanation to set them up. I don't want to have students to have to spend an inordinate amount of time reading background information in a timed exam, but I do want them to have a context so that I can see if they can provide conclusions in context. I would take a completely different approach if I were making up a take-home exam.

I would guess that about 30-40% of my exam points are calculation/mechanics, and 60-70% on interpretation and conceptual understanding.

ALLAN ROSSMAN

 

Context: My comments apply to a "Stat 101" algebra-based service course for students in humanities and social science majors. I have in mind the Math 121 course at Dickinson and courses such as Stat 130 and Stat 217 at Cal Poly.

I strive to use real data, as opposed to hypothetical or realistic data, in exam questions. I can't honestly say that I start with a real problem, though. I usually start with the concept or technique or issue that I want to ask about, and then I find real data that can be used to assess students' knowledge of that issue.

I try to assign points to questions based on how many different components comprise the question. My aim is for at least 50% of the points to be based on conceptual understanding and interpretations as opposed to calculations and mechanics.

DEB RUMSEY

 

Context: The course would be the 1st course, audience pretty much anyone.

I always set up a series of learning objectives first, and then design my questions to test those learning objectives. I always provide some sort of real/relevant scenario for every exam question, because I believe you should never ask a student to do something without a good reason (for example: calculate the mean, median, etc. without a reason). I don't care so much if the data are "real" in the sense that it was an actual data set. I just care mostly that it is a relevant scenario for the students, always. My exams are probably 75% conceptual, and 25% computational (always embedding the computations within the concept questions, always within a relevant scenario). On a 100 pt exam, I typically have 6-7 questions with 4-5 parts each, and each part is usually worth around 4-5 pts. Sometimes larger problems are worth 10 points, but not very often. They are usually broken into smaller parts that build up. I like to have bigger problem solving opportunities, without scaffolding, but I don't typically use exam time for that.

CANDACE SCHAU

 

Context:  I taught introductory statistics to graduate students in a College of Education for over 20 years. My classes contained 15 to 30 students and met twice a week for 1.25 hours per session. Most of the students in my classes were working toward Masters degrees in Education (although some were working toward Ph.D. degrees), most were in the course because it was required, and almost all did not want to be in the course. Most of the students held jobs, had significant others, and considered receiving their degrees (with a grade point of 4.0) as essential but usually third in importance (with loved ones first and jobs second). Because so many already were established in jobs (and in their lives) and felt as though they performed them well without ever reading research or understanding the statistics found in every day life, they viewed my introductory statistics course as the most difficult educational hurdle they faced and not very relevant to them. When I first started teaching, I really had hoped that my one introductory course would convince them that statistics is important in their lives. Given my students and their situations, however, that was a dream born from my ignorance (and, I'm sorry to say, my arrogance). For the last several years that I taught, I really hoped to accomplish a few more realistic (for my students) goals. By the end of my course, I wanted my students to: Develop a foundational understanding of important introductory statistical concepts and their uses.

Learn that they could understand a discipline that involved numbers, if they worked hard.

I also hoped that a few students would really like statistics and recognize its value to them and so decide to take additional statistics courses that were not required. My course assessments, however, were designed to assess the first goal.

I did not use "real" data sets during my exams. There wasn't enough time during a class period to use data sets as the basis for assessment items.

I tried to use "real" variables from educational news media and relevant educational research as the basis for my items. At least 75% of my items required conceptual understanding for successful completion. I tried to construct distractor options (the wrong answers) to my multiple-choice and matching items to reflect common misunderstandings held by students who incorrectly answered the items. This process allowed me to identify and to try to remediate common misunderstandings.