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2004-05 Curriculum Survey - Summary

Sean Simpson
NYSMATYC Curriculum Chair
Assistant Professor Mathematics, Westchester Community College

Summary of Main Results

In considering all of the data collected, there are certain similarities throughout the courses that become obvious. For instance, all campuses report that they utilize technology of some kind, but the type of technology varies significantly. The statistics courses seem to be based for the general student and not for a specific curriculum. Additionally, the number of schools offering online versions of their statistics courses is increasing. In terms of the material taught, 31 of the 34 responses (91.2%) indicate that hypothesis testing of some kind is taught in their statistics courses. Similarly, only 2 of the 34 campuses (5.9%) do not teach confidence intervals at all and only 3 of the 34 campuses (8.8%) do not teach basic regression in their statistics courses. All 34 campuses report that tutoring is available at their school, and 31 of 34 (91.2%) report that are not staffing problems at the moment for their statistics courses.

Types of courses

Of the 34 responses received, 26 of them (76.5%) report that the basic statistics course taught at their school is a three credit course. The remaining 8 responses report that their school has a four credit basic statistics course. The majority of hours spent in these classes are in the form of lectures. Only 7 of the 34 campuses (20.6%) report that they have at least one hour of lab work each week, with an additional 2 reporting that they have occasional or optional lab hours. All of these 9 campuses report that they use Excel or Minitab, which makes sense if you are going to have run a statistics lab. The remaining 25 campuses (73.5%) report that they do not have regular lab hours. An interesting point of debate can center on whether statistics courses should have lab hours, and, if so, what lab hours should do for the students.

Textbooks

There does not seem to be a consensus with regards to a textbook. Within 34 responses, a total of 17 different textbooks were mentioned. The most popular authors named were Triola (at a total of 9 campuses with multiple texts), Brase (at 5 campuses), Larson (at 4 campuses) and Sullivan (at 3 campuses). This indicates that there is a tremendous amount of disagreement over what a statistics text should look like and no individual style has necessarily cornered the market. Other authors mentioned were: Moore, McClave/Sincich, Johnson Kirby, Aliaga, Bluman, Peck/Olsen/Devore, Hayter, Bennett/Briggs and DeSanto. Considering that there are numerous other quality texts available, it seems that there will not be any sense of consensus for quite some time, if ever. Since there are so many different texts (and authors), one should ask why this has occurred? What features exist in these texts that make them so appealing to some, but not others? Does any text have all the features we are looking for? While complete consolidation of texts will probably never happen, with so many texts, it is natural to try and make comparisons between different courses. However, it can quite hard to make comparisons between different courses based on different texts, especially given the great amount of variety that exists.

Pre-Requisites

Most schools report a pre-requisite for the statistics course within the same general framework. 10 of the 34 campuses (29.4%) report that Intermediate Algebra is the pre-requisite in order to enroll in the statistics class. An additional 11 campuses (32.4%) report Elementary Algebra as the pre-requisite and 1 campus reports Math A (New York Regents course) as the pre-requisite. In total, this encompasses 22 of the 34 campuses (64.7%). This gives the impression that the required level of mathematical sophistication required to enroll in these courses is rather low. Additionally, it seems that the statistics courses are not really algebra based, since the student is not required to have a tremendous amount of background in algebra. An additional 5 campuses (14.7%) report College Algebra as the pre-requisite for entering the statistics course. Since there is some disagreement over what is considered "Intermediate", "Elementary" and "College", one could almost group together these courses as a general pre-requisite. Most of the remaining responses fit closely into an area related to the already mentioned categories; 3 campuses report Developmental Math as the pre-requisite (comparable to at least Elementary Algebra if not Intermediate Algebra), one campus requires knowledge of functions (comparable to the College Algebra level) and one campus requires PreCalculus as the pre-requisite. Only one school requires calculus as a pre-requisite for their statistics course.

Appropriate Curriculum

The statistics courses being discussed at the 34 campuses seem to be suited for a variety of students and not designed for one particular field or discipline. For instance, 32 of the 34 campuses (94.1%) report that their statistics course is appropriate for a student in the liberal arts curriculum. 16 of the campuses (47.1%) report that students in the science curriculum take their statistics course. 19 of the campuses (55.9%) report that students in the social science curriculum take their statistics course. Since there is tremendous overlap within these schools, the statistics course cannot focus on one particular curriculum. The campuses also report that other general curricula take their statistics course. The Business, Engineering Science/Math, Nursing, GenEd, and Technology curricula are specifically mentioned by multiple campuses. It is clear that our statistics courses appear to be geared for the general student.

Technology

It has become unquestionably clear that technology needs to be included in any statistics course. The calculations made in a statistics class can be extremely laborious, if done by hand, and the introduction of technology has aided in simplifying that. It is also the belief of the curriculum chair that technology has helped increase the material that can be covered in a standard statistics course because less class time is needed to discuss repetitive and (potentially) dull calculations. Additionally, it has made the course much more vibrant for the student, which should help increase interest in class. Technology has also allowed statistics teachers the option of having more of a focus on statistical interpretation instead of only number crunching. Having said that, there is a lot of variation over the exact piece of technology being used; there are several popular products which are used by a number of different schools. Among the campuses that responded to this survey, the most popular piece of technology being used is Minitab; 18 campuses (52.9%) either require or recommend Minitab. 4 campuses (11.8%) either require or recommend Microsoft Excel. It should be noted that this results in 20 total campuses with overlaps. Within these campuses, many have included lab hours, partly to be able to incorporate this technology. As was mentioned earlier, all of the campuses who have at least one lab hour per week either require Excel or Minitab. This could be something for the other campuses that utilize Minitab or Excel to consider. There are 14 campuses (41.2%) that either require or recommend the TI-83/83 Plus/83 Silver/84 Plus calculator. It is interesting to note that only one of these 14 campuses reported having lab hours, making clear that the TI products can be incorporated into a standard lecture instead of necessarily being reserved for a lab setting. A less popular option is the scientific calculator; 5 campuses (14.7%) of campuses report using these. 4 campuses (11.8%) require a calculator of some kind. Finally, SPSS is used by one campus, Maple is recommended by one campus, Statdisk is used in some section on one campus and the TI-85/86/89 is used by one campus.

Online Courses

Online learning has exploded over the past several years with the majority of all NYSMATYC member campuses offering at least some math courses online. Statistics seems to be one of the more popular math courses that is offered online. As of this writing, 20 campuses (58.8%) report offering a current online version of statistics. The majority of these offerings, 11 in total, are through the SUNY Learning Network (SLN). 3 campuses report offering an online statistics course through WebCT, 3 campuses report offering an online course through BlackBoard, 2 through ANGEL and one through another avenue. From the data collected, it is clear that offering statistics as an online course has gained ground in recent years. At least 3 campuses report they have offered their online statistics course for at least 5 years. Another 6 campuses report having offered their online statistics course for at least 3 years, and 6 campuses report that their online statistics course has been in existence for 2 years or less. This data indicates that online statistics has been a growing area with potential for more. In general, the online courses are small. 2 campuses report online classes of less than 15 students, while 12 campuses report online classes between 15 and 25 students. 3 campuses report having between 25 and 40 students while 3 campuses report having over 40 students (spread over multiple sections). This is particularly noteworthy, considering the sizes of standard campus courses, which (on at least one report) can be as large 40 students. The online classes appear to be, in general, a bit smaller than the traditional campuses based class.

Course Curriculum

The topics covered in these statistics courses seem to have some common themes, but are still rather diverse. This is due to a variety of reasons. Among them: the number of hours the class meets (mostly with the 3 credit versus 4 credit difference), lab requirements (or lack thereof), the use of technology and the natural differences between campuses and faculty. All of these reasons play a role in deciding what is (and is not) taught in a class. The Central Limit Theorem seems to be the one topic that virtually all campuses agree on - 32 campuses (94.1%) report that most (1) or all (31) of their sections of statistics cover the topic. In a similar fashion, 30 campuses (88.2%) report that all of their statistics courses cover confidence intervals as a topic. Basic regression analysis is covered in all (or most) sections of statistics at 26 campuses (76.5%), with another 5 campuses reporting that basic regression covered in some of their sections. The only other topic that seems to be covered by a very significant number of campuses is hypothesis testing, but there is a split in the overall topic. 28 campuses (82.4%) report that all (or most) of their statistics classes cover the topic of hypothesis testing using the traditional method. The traditional method requires finding a test statistic and comparing it to a critical value(s) to make a determination whether to reject the null hypothesis. 27 campuses (79.4%) report that all (or most) of their statistics classes cover the topic of hypothesis testing using the P-value method. In the P-value method, you take the test statistic and turn it into a probability value which is compared to the level of significance, ?. It is interesting to note that every school that requires (or recommends) the use of the TI-83/84 calculator cover the P-value method. This makes sense because P-values are given immediately on the screen after the calculator performs the calculations for the hypothesis test. Additionally, only 2 of the 16 campuses that require or recommend Minitab do not cover the P-value method; the remaining 14 campuses cover the topic in at some, if not all, sections. Since the P-value appears immediately, it seems to make sense to talk about it. There is certainly a lot of overlap within these two different hypothesis testing groups. Only 3 campuses (8.8%) report that they do not cover hypothesis testing at all; the remaining 31 use at least one of the two methods mentioned above. However, hypothesis testing seems to be mostly contained to the one sample case. 12 of the 34 campuses (35.3%) report that all (or most) of their sections cover two sample hypothesis testing with 5 campuses reporting that some of their sections cover two sample hypothesis testing. Only 3 campuses (8.8%) report that they cover ANOVA in all sections with 4 campuses (11.8%) reporting that ANOVA is covered in some sections. Multinomial experiments are covered in all sections of statistics at 4 campuses (11.8%) and in some sections of 5 campuses (14.7%). The remaining topics are not nearly as popular in a global sense; individual campuses seemed to have preferences for one topic over another. Only 2 campuses (5.9%) report that all classes cover nonparametric statistics, while an additional 3 campuses (8.8%) report that some classes cover nonparametric statistics. No campus reports covering multiple regression in all (or most or some) of their sections. Instead, the topic of multiple regression is covered infrequently by 5 campuses and not covered at all by 26 campuses (there were 3 campuses that did not respond). Discrete distributions do not play a large role in our statistics classes either. Only 3 campuses (8.8%) report that all (or most) of their classes cover the Poisson distribution while another 3 report that some of their classes cover the Poisson. Other discrete distributions (omitting the binomial) are covered in all (or most) classes at 9 campuses (26.5%) while another 4 report that some of their classes cover other discrete distributions. The most likely explanation for this has to deal with the natural tendency to discuss the normal distribution (since it appears in the Central Limit Theorem, confidence intervals and hypothesis testing) within the basic statistics class. Since the normal distribution can be used as an approximation for the binomial, it would seem appropriate for a basic statistics class to discuss the binomial. While one can also use the Poisson to approximate the binomial, the topic is not covered nearly as often. The curriculum chair attributes part of this to the fact that the Poisson fits very specific questions and is not as useful in general whereas the normal is an easier distribution to discuss and is more easily adaptable to a variety of situations. In a similar fashion, other discrete distributions tend to apply to only a limited number of situations.

Tutoring

All 34 campuses report that tutoring is available for their students. However, some campuses report that there are some problems with the tutoring resources. 23 of the 34 campuses (67.6%) report that there is always or usually enough tutoring resources available. 9 of the remaining 11 campuses report that there are enough resources sometimes and 1 campus reports that there are not enough resources (1 campus did not report an answer). Upon first examination of the number, the curriculum chair presumed that the major reason why there are not enough resources would be financial. In these very difficult budgetary times, there never seems to be enough money to go around. However, only 3 of the 34 campuses (8.8%) report that there is not enough money available for tutoring resources. The much bigger problem, reported by 12 campuses, is the lack of skilled workers. It might be (relatively) easy to find a college algebra or calculus tutor, but it is far more difficult to find statistics tutors. Based on some comments found in the "Odds and Ends" section, it is clear that this problem will continue, and needs to be addressed. Outside of one campus reporting that their only worker is unpaid, no other tutoring related problems are reported by the different campuses.

Other courses

While the primary purpose of this survey was to collect information about the basic statistics course available at the NYSMATYC member campuses, the survey also asked if the campuses offered different versions of their statistics course. 10 campuses (29.4%) report that there is more than one basic statistics offering at their school. Like the standard statistics class, there does not appear to be a common theme throughout these second courses. 2 of the campuses report that the second statistics course is designed for business students. One campus reports that they offer a calculus based statistics course; another reports an algebra based course (note: the campus that reported this used a calculus based course as the basis for their survey results). One campus offers a course designed for liberal arts majors, another offers a course on just descriptive statistics and one offers a course for psychology and sociology majors.

Odds and Ends

One of the motivations behind this choice in topic in the first place was a perception of the curriculum chair: namely, there is an increase in the popularity of statistics classes. The campuses were asked whether there has been growth in enrollment in their statistics classes within the last few years. 15 of the 34 campuses (44.1%) report that there has been an increase in the number of students taking statistics recently. A couple of campuses also made note that the increases in statistics enrollment are higher than the enrollment increases throughout the entire department. Despite the fact that there is an increase of students taking statistics at those campuses, only 2 of the campuses (and 3 total) report that there either have been (or will be) problems staffing the statistics courses properly. As the number of students taking statistics continues to increase, the campuses must at least consider the potential staffing problem that could arise. Of the remaining campuses, only 1 reported that there has been a decrease in statistics enrollment. However, the curriculum chair is not prepared to state that this is a single case; other campuses may have just responded that there was not an increase.