Teaching Statistics Do Students Get It Education Essay

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ABSTRACT

This paper outlines a study that evaluates the effectiveness of using stories and pictorial icons in improving learning outcomes for students.

Students have problems learning statistics

New educational theories - contextualisation

How do we teach stats? (Contextualised narrative - PBL approach) encourage students to go further to contextualise theories in ways that are more relevant to them. Contextualise various abstract statistical concepts.

What results do our students get? Why?

Key Words: Statistics education, Problem Based Learning, critical thinking, scenario, stories, pictorial icon, undergraduate economics, Scenario Based Learning Interactive, experiential learning.

INTRODUCTION

Economics and business students are required to enrol in statistics and quantitative-based research methodology courses inside their degree programs. Teaching statistics to economics and business students aims to prepare them to understand and to use statistical data in their field of study, and to apply descriptive statistical concepts in economic and business situations.

The literature related to teaching and learning statistic pedagogical methods widely documents that students have negative perceptions as well as difficulties in mastering fundamental statistical concepts (Cochran 2005, Broers 2008, Garfield 1995, Garfield et al. 2002, Iman 1994, Sherwood and McCredden 2010, Kotz 2010, Lee 2007, Landes 2009, Murtonen and Lehtinen 2003, Prabhakar 2008). Certainly our experience with statistics students at The University of Queensland (UQ), from a range of disciplines including law, engineering, arts, economics, social science, tourism and hospitality, and business; is that they consider statistics more difficult than other domains. Keeping up with the continual cumulative material is difficult for students who, as a result, develop a disliking for the subject, do not develop statistical literacy, and fall behind. MacGillivray and Pereira-Mendoza (2011) argue that "the learning and teaching of statistical thinking require gradual building up of concepts, understanding and skills, in a coherent, consistent and cumulative way that engages students in real contexts and authentic learning experiences."

In this paper we present and reflect on the teaching methods for statistics used at a major Queensland university. This course is widely regarded as challenging by many students. One reason is that the work is totally cumulative. This means that it is exceptionally difficult to catch up if a student gets behind in the work. Concepts covered are deemed an essential part of the analytical tool box for well-trained professionals. Success in the subject depends on keeping up-to-date. With this in mind, each topic is assessed as it is completed via a computer managed quiz.

A common problem documented in the literature is student appreciation of relevance of statistics: perceived usefulness and worth of statistics in personal and professional life (Cashin and Elmore 2005, Hollis 1997, Schau, Stevens, Dauphinee, Del Vecchio 1995, Vanhoof, Kuppens, Sotos, Verschaffel, Onghena 2011). Case studies to provide context and relevance are often perceived as stale and artificial. Using a story-based approach for teaching statistics students has demonstrated positive reactions to the online activities, plus pass rates have increased.

Didactic Teaching - The Previous Pedagogy

Teaching statistics to first year students at UQ has traditionally been delivered by didactic instruction method. This involved a lecturer presenting materials and formula plus setting assignments and exams to a large contingent of students. Classes are typically approximately in the order of 800 students.

Contextual Learning - The Current Pedagogy

Teaching statistics usually occurs in an "arid, context-free landscape" where students "rarely think statistically" (Wild and Pfannkuch,1999: 228). Recently, Dierdorp, Bakker, Eijkelhof, and van Maanen (2011) showed real world contexts and examples are useful in explaining statistical concepts. In other words, learning is related to the way we conceptualise things around us (Ramsden, 2003). This implies learning can come from constructing meaning from previous experiences.

Linking "theory with practice" is difficult for many students (Murtonen and Lehtinen, 2010:183). Dall'Alba (2009) argues that that seeing the overall scheme of things is important to fully grasp key ideas.

In this paper, we present the findings of a study aimed to test the following two hypotheses:

Hypothesis one (H1) - students will improve over the duration of a university undergraduate course. Hypothesis two (H2) -students exposed to subject matter materials before a university undergraduate course, and are thus able to continually reflect on these materials throughout the course, will ultimately perform better than students without such exposure.

What results do we (our students) get?

Quantitative results

Qualitative results

TVAL results

Quantitative results

Qualitative results

What does this mean?

What does this not tell us?

RATIONALE AND AIMS OF THE STUDY

We consider that standard texts only provide graphical representations of statistical concepts. Whereas, we have developed a 'character' (i.e. bird picture) that can be associated with standard text book graphical representations, which has not been done before. We borrow from educational psychology and the role of visual markers as anchor points in adult learning. Statistic content continues to be taught in schools, although its significance and application in the real world has become very low. A clear illustration of this gap between everyday cognition and school based knowledge is, for example, provided by studies undertaken by Carraher et al. (1985) in Brazil, in which children were observed while solving arithmetic tasks in different contexts, namely as street vendors and in the classroom. These findings point to the need to anchor learning processes in more realistic situations. Typical school learning is often decontextualized, while real cognitive activities and learning occur in context. There is a need to anchor learning in real life contexts and transfer cognitive skills, which we do not see in standard statistic textbooks.

Our differentiation is the link between the picture and the standard statistical textbook diagram that has not been done previously. For example, the seagull picture relates the student to the theory of normal distribution. Students can easily relate to the real-world analogy of a seagull catching a single fish from a population. So, the picture forms the link to the appropriate theory, and subsequent equation. Modern learning theories were recognised as far back as 1984 (Alesandrini 1984) suggest that particularly strong associative learning is obtained through analogical pictures that help students to relate to new information to prior knowledge. The seagull picture provides the student with contextual cueing and associative learning.

We have created a scenario based on the story of a fictitious fish farm. We have then incorporated our pictures (as appropriate) throughout the scenario as visual aids to the student. The student takes on the role of an Advisor and is required to use hypothesis testing to test claims by the fish farm owner on average fish lengths, then evaluate their findings, and ascertain if the fish farm is a viable business proposition.

Survey was used (pre-test and a post-test) prior to and after the course.

RESEARCH AIMS

The aim of this study is to evaluate the effectiveness of xxx in improving learning outcomes for students. It is hypothesised that students taught statistic in a contextualised method using story-based pictorial icons will learn more and enjoy the learning experience more than students exposed to traditional didactic statistics lectures.

METHOD

Participants

Students enrolled in an introductory statistics (Quantitative Economic and Business Analysis) course taught by two different instructors at a large university located in south-east Queensland in Australia were invited to participate in the study. A total of XXX undergraduates volunteered to participate in the study. All participants were first year university students. None of the participants had any previous university-level experience with descriptive or inferential statistics. Students were told that their participation was ungraded, anonymous and voluntary. Students were informed that the pre-test would not count toward their grade in the course, and that they should not expect to know the answers at the time of administration, as this pre-test was diagnostic of their level of knowledge prior to having taken the course. They were also told that the pre-test might be useful in providing them with (a) a sampling of the kinds of topics to be covered in the course; and (b) an illustration of the types of questions that would be included on subsequent exams in the course.

Procedure

Participating students completed an online questionnaire to test their understanding of fundamental statistical concepts …

Following the semester instruction students were asked to complete the online questionnaire a second time to test if their statistical literacy has improved.

Forty-five questions were developed for this study, including five questions to determine any prior statistics learning, plus forty Multiple Choice Questions (MCQ). The first five questions determined the extent to which students had previously studied statistics in high school (i.e. before university) to gauge what level of performance would be expected. For example, if the students haven't learnt any of the statistics topics previously, most of the items would have plenty of room to demonstrate improvement after the intervention.

The forty MCQ questions are similar to possible exam style questions that test student understanding of fundamental statistical concepts (without any calculations). Two 4th Year economics/commerce tutors were contracted to initially compile the forty MCQs each with five options to provide a greater ability to notice effect.

The aim was to link to the underlying knowledge and concepts to measure the learning of the concepts, therefore, no mention of the pictures or other learning analogies used in lecturers is made in the MCQs because they are only the strategy to teach the concept, which aim is to measure, the 'learning of the concept.'

These were then reviewed and edited by the statistics lecturer. A cross validation was completed by having three senior statistics lecturers complete the forty MCQs to ensure that the questions were worded well (one would expect perfect performance in the expert group). This demonstrated that students are getting the questions wrong because they did not know the content, not because the questions are poorly worded. As a result of this test, there was only one question that needed rewording for clarity.

On completing the post-test online quiz participants received their scored marks provided immediately. Participant also received the correct answers to all of the quiz questions so that they can evaluate how they are progressing in the course, what they have learned, where they might need to focus their studies for the final exam.

Participants / Student Demographics

Participants are primarily first year undergraduate university students who have not yet studied statistics as part of their university course. They come from law, engineering, arts, economics, social science, tourism and hospitality, and business disciplines and are enrolled in 'Quantitative Economic and Business Analysis' as part of their undergraduate degree, which covers basic statistical concepts and techniques such as descriptive statistics, probability concepts, theoretical distributions, inferential statistics (confidence intervals and hypothesis testing) applied in business and economics.

The course had 843 enrolments.

Data Collection

For this study a set of forty-five pre-course quiz questions were developed by the researchers, and implemented at the beginning of semester one. For the post-course quiz the researchers decided to include an additional three qualitative questions; soliciting the opinion of students on the teaching method they have been exposed to. Details on survey administration are included in the section below.

Pre-Course Quiz (quant.): This quiz quantitatively assessed student's prior basic statistical concepts with five quantitative questions. Forty MCQs in this quiz consisted of four groups of ten questions, each group covering the four topics covered in the course; normal distribution, sampling distribution, confidence intervals, and hypothesis testing.

Post-Course Quiz (quant. and qual.): This Quiz included the cognitive questions that were identically reproduced from the pre-course survey. Three affective questions succeeded the cognitive content questions. The addition of the affective questions did not alter the numbering of the content questions. The affective questions contained five point Likert scale ratings with an optional open-ended response.

Survey Administration

The pre-course survey was administered during the first week of classes for the semester. All students in attendance were provided with an anonymous electronic link to the quiz via Blackboard. By the end of the third week of the semester 148 students (17 per cent of the class) had completed the first quiz. During the semester the course instructor often referred to the quiz emphasising it as a learning tool, as it is useful for students to assess what they have learned during a course and identify areas where they could improve. Students were informed that completing the quiz helps exam preparation, and assists the lecturer prepare a final revision lecture.

Two links were provided to students via Blackboard at the end of semester, two weeks prior to examinations. The first link was for the 148 students who had attempted the quiz previously. The second link was for those students who had not completed the quiz before.

The second quiz contained exactly the same questions as the first quiz except three additional questions were added relating to elicit student opinions on the teaching method they have been exposed to. The quiz was self-administered, however, in keeping with the spirit of the educational purpose students were requested not to refer to lecture notes or textbooks. The purpose was to show students how much they have learned within a six week period, and guide students as to how much study preparation they might need for the final exam. Students were presented with a mark, and the correct answers, immediately on submitting their answers to the second quiz.

No tracking of individual student performance was attempted using these pre- and post-course quiz questions, and the questions did not form any part of the formal class assessment.

Data Set

Initially, 148 students completed the pre-course quiz, while only 123 of these finished the post-course quiz. 143 students who had not done the quiz before attempted the post-course quiz exclusively.

DATA ANALYSIS

Quantitative and qualitative data were collected simultaneously for this mixed methods research study but were analysed according to data type. Quantitative analyses include ANOVA, paired-t tests … descriptive statistics. (Not sure what we are using yet …???)

Qualitative data collected from the second quiz was open-coded with themes relating to course materials, content, statistical application, picture icons, and perspective emerging from the data.

Quantitative Analysis Methods

A one-way ANOVA analysis was performed on the cognitive questions from the pre-course quiz to determine differences between prior knowledge from students' statistical education exposure.

…

Qualitative Analysis Methods

Students were able to elaborate on their ratings in the post-course quiz via an optional open-response section. The open-response data were open-coded to find emerging themes, adhering to qualitative methods (Strauss and Corbin 1998). Each student response was analysed either as phrases or complete sentences. Following the coding process the data were examined for central themes. These were grouped together with similar themes into categories.

RESULTS

This section presents the results of the mixed methods data collection and analysis. Participants are mostly first year university students and have done some statistics education at school, mostly covering the normal distribution and z-scores.

H1: it was expected that students would improve by enrolling in and participating in a course and its assessment tasks, this has been demonstrated. Our analysis shows a significant increase in the correct responses students made in their second questionnaire attempt post-course.

H2: The effects of being exposed to the materials before the course was not as important as hypothesised.

Quizzes

Only on the post-course quiz were students asked to rate the difficulty of the 40 MCQs. Figure 1 indicates the majority of students (66 per cent) felt the quizzes were 'moderately difficult' to 'extremely difficult.' A majority of the students chose a rating on the difficult side of the Likert scale; only three students provided negative comments one experiencing "stress" one questioning the "relevance" and the other "struggling" with the remaining student comments having positive connotations not directly relating to the level of difficult as presented in Figure 1.

Answer

Response

%

Extremely difficult

5

10%

Moderately difficult

27

56%

Slightly difficult

14

29%

Moderately easy

1

2%

Easy

1

2%

Total

48

100%

Figure 1: 'Rate the difficulty of the quizzes'

Answer

Response

%

Definitely, very much so

6

13%

A Lot

24

50%

Somewhat

13

27%

A little

2

4%

Not at all

3

6%

Total

48

100%

Figure 2: 'Did doing the quizzes help you learn the course content?'

When asked "what is the most interesting, useful, or valuable thing that you've learned so far in this class?" #% of students responded ... Seagulls, Pelicans and Freaky Fish were mentioned by 8 students, hypothesis testing was mentioned by 18 students, and real-world application was mentioned by 7 students. The summary of student responses to the most 'interesting, useful, or valuable thing learned' is presented in Table 1.

Theme

Number of Responses

Description/Sample Comments

Hypotheses Testing

18

Hypothesis testing and the ability to test a claim about the entire population using a sample

Hypotheses concept. It is useful to me who is doing Commerce

I found hypothesis testing the most interesting thing so far

Picture analogies

8

The pictures with the seagull/pelican etc. really helped me to learn the different transformations and when to use them

using birds to relate to formulas or theory

The fish and bird analogies

Using pictures in understanding different formulas helps in remembering and determining the appropriate formula for specific questions

Seagulls, Pelicans and Freaky Fish

Pictures that helped you remember the transformation

Awesome animals used for demonstrations linked with the lesson

Application of statistics

How you can base conclusions on whole population from small samples with a fairly high degree of confidence

Application of stats to the marketing of services

The ability to test a claim about the entire population using a sample

Able to find out if something (etc. claims) may be true or not

I found it interesting how for once we found out how maths is used in the real world

That although the some of the concepts of statistics are a little amorphous and hard to grasp that they are very useful in real world business situations.

I have enjoyed the learning style with the Pelicans etc. and can now see how the things we learn in this course could be applied to the real world

Other

Thank you for the extra support through this course. I found this quiz helpful and also really appreciated the extra 'feedback'documents you put up. Whilst the quizzes were good, they were an inconvenience

Nothing useful I'd assume. As it's probably not going to help me as an Accountant... but I have to do it.

Keeping up with the content makes everything easier and therefore more interesting

The ability to predict certain events with a degree of certainty

Table 1: Student responses on "What is the most interesting, useful, or valuable thing that you've learned so far in this class?"

DISCUSSION

These results along with a noticeable increase in the level of attentiveness, enthusiasm and participation seem to indicate a benefit over traditional didactic teaching-centred styles.

Why did students do better on the second go, because…

They were the enthusiastic ones.

Did it first go and printed out - used to revise/look at regularly during the semester, reflect on them during the semester.

Were more familiar with the type of question and what's important in the course.

Could have been discussing Qs with their friends, active learning - responsible on their own learning.

They used an immersion/practice approach to learning course content such as a 'synthetic experience' (Timmerman and Greene Jr. 1989).

Small minority of quiz participation relates to first year student apathy.

Challenges Unique to Statistics Courses

While a number of these challenges are general to teaching any course, two areas of challenges unique to statistics courses have emerged. First, the commutative approach was a challenge for students to keep up with whilst completing assignments. Second, the instructor faced the challenges of instructing students from wide-ranging disciplinary backgrounds with varying degrees of prior mathematical knowledge. Several studies focussing on the relationship between student math skills and course performance suggest that grades in previous courses are more related to initial attitudes toward statistics (Carmona, Martìnez and Sànchez, 2005, Johnson and Kuennen, 2006, Lalonde and Gardner, 1993, Ramsey 1999, Ricketts and Berry 1994).

… Johnson and Kuennen (2006) provide several recommendations that address students in need of help in introductory statistics courses.

Challenges General to Teaching

From the data and results, challenges of teaching first year university statistics have been identified. Not all of these challenges are unique to this course; challenges associated with experience level of the instructor are an example that may be transferable to courses with similar settings - a new faculty member teaching a course. These challenges also pose opportunities for faculty to 'think outside the box' and create novel, or adapt existing, pedagogical strategies for statistics courses.

CONCLUSION

Blurb …

FUTURE RESEARCH QUESTIONS

Contextualisation v's non- contextualisation study

Restructure course

Condense descriptive stats (probability, mean, medium, mode)

Extend hypothesis testing

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