A review of problem- and team-based methods for teaching statistics in Higher Education
aa r X i v : . [ s t a t . O T ] S e p A review of problem- and team-based methodsfor teaching statistics in Higher Education
Elinor Jones and Tom Palmer Department of Statistical Science, UCL, London, UK Department of Mathematics and Statistics, Lancaster University,Lancaster, UK MRC Integrative Epidemiology Unit and Population HealthSciences, Bristol Medical School, University of Bristol, Bristol, UK17th September 2020
Abstract
The teaching of statistics in higher education in the UK is still largelylecture-based. This is despite recommendations such as those given bythe American Statistical Association’s GAISE report that more emphasisshould be placed on active learning strategies where students take moreresponsibility for their own learning. One possible model is that of collab-orative learning , where students learn in groups through carefully crafted‘problems’, which has long been suggested as a strategy for teaching statis-tics.In this article, we review two specific approaches that fall under thecollaborative learning model: problem- and team-based learning. We con-sider the evidence for changing to this model of teaching in statistics, aswell as give practical suggestions on how this could be implemented intypical statistics classes in Higher Education.
University courses in statistics have traditionally been given in the instructionalstyle, in which a lecturer transcribes a set of notes for students over a courseof lectures. In this process students are passive recipients of information. Thismethod of delivery can be scaled up to cope with ever increasing class sizes,a crucial factor in determining which teaching methods could realistically beimplemented, but the quality of the resulting education is questionable.The American Statistical Association, however, specifically endorses a more ac-tive approach to teaching with students taking responsibility for their own learn-1ng (Carver et al., 2016). Going further, the idea that statistics education shouldresemble statistics practice - in terms of presenting legitimate and relevant sta-tistical research questions as part of the learning process (Rumsey, 2002), andrelying on cooperation, communication, and team-work (Roseth et al., 2008) -is clearly advantageous but does not a always happen in higher education.Collaborative learning, where students learn in groups through carefully crafted‘problems’, has long been suggested as a strategy for teaching statistics (Garfield,1993; Carver et al., 2016; Roseth et al., 2008). Despite recommendations, statis-tics education in higher education in the UK is still largely lecture-based, thoughthe tide is slowly turning.In this article, we review two approaches that fall under the collaborative learn-ing model: problem- and team-based learning (PBL and TBL). We focus onPBL and TBL for two reasons. Firstly, they provide a strategy for fundamen-tally changing the nature of how statistics is taught throughout a course ormodule, rather than possibly one-off activities to promote effective learning.Secondly these learning models have been used extensively in other disciplinesto good effect, with a considerable body of evidence documenting their advan-tages. Though the review has in mind introductory undergraduate statistics,we hope that the ideas discussed here may also be useful to those teaching moreadvanced courses.The paper is organised as follows. In Section 2 we describe both PBL andTBL, and consider the evidence for using these strategies - both specifically forstatistics and also more generally - in Section 3. In Section 4 we consider thepracticalities of using these methods for the teaching of statistics and offer tipsfor effective implementation.
PBL and TBL have made their mark in a number of disciplines, includingmedicine and allied health professions, business, and engineering. Both ap-proaches fall under the umbrella of ‘active learning’, loosely defined as engagingstudents in activity, which have been advocated for STEM disciplines includingMathematics (Braun et al., 2017). In this case, the activity consists of studentslearning through a sequence of carefully crafted problems in small groups orteams.The set-up, and therefore the nature of how students learn, is different. In PBL,the problem posed becomes the source of learning: students become independentseekers of information in order to provide a solution, but under the guidance ofa facilitator. For TBL, however, students learn first by using resources madeavailable by the instructor and class time is then dedicated to applying this2nowledge to solve the problem in teams.In this section we review the ‘classic’ implementation of both PBL and TBL.Examples of possible variations on these are given later in Sections 3 and 4.
Problem based learning has been used in medical schools and law schools asearly as the 1960s, for example by McMaster Medical School, and with increas-ing uptake since the 1980s (Knight and Yorke, 2003; Boud and Feletti, 1997;Schwarz et al., 2001). The traditional instructional approach to medical ed-ucation, consisting of an intensive pre-clinical period of basic science lecturesfollowed by a clinical teaching programme, has been criticised for failing to equipdoctors with all the skills they needed and for not providing students with thecontext of how their knowledge should be applied (Lancaster Medical School,2016).In the UK the General Medical Council set the requirements for how medi-cal students should be trained. They advocate PBL for the following reasons(Lancaster Medical School, 2016; Savery, 2006): • students must have responsibility for their own learning, since learning ismost effective when it is active; • problem scenarios facing students should be complex, since real-worldmedical problems are rarely straightforward; • learning should be integrated from a wide range of disciplines and subjectareas; • learning should integrate collaboration, since clinical practice demandsthat doctors share information and work constructively with others; • students should share with their work groups what they have learned andhow that contributes to the solution of the problem; • a summary analysis of what has been learned should be undertaken be-cause reflection and evaluation are critical; • self and peer assessment should be regularly undertaken.PBL aims to teach students to identify problems and then to design a set ofobjectives, the accomplishment of which will lead to the development of thesolution (Schmidt, 1983). Medicine isn’t the only area to widely use PBL: lawis the other main area which has adopted this strategy at scale. Schwarz et al.(2001) points out that the challenges faced by a law school have similaritesand differences with those faced by a medical school. It is not unreasonableto assume that the same is true in statistics training: many of the aspectslisted above apply directly to applied or practical statistics education, with theothers requiring only minor modifications in language. Though the focus here3s on the teaching and learning of applied, or practical, statistics, there is alsoevidence that PBL can be used in teaching and learning the more theoreticalaspects of scientific disciplines, including in mathematics (Dahl, 2018). There iscertainly scope, therefore, to do similarly with teaching more theoretical aspectsof statistics. In contrast to traditional lecture courses common in Higher Education, studentsare randomly assigned to small groups (typically between 6 and 10 students,though groups are changed every few weeks) to work on an open-ended problem,often called scenarios.Within a PBL group there are specific roles. Each member of the group isexpected to peform each role at least once per term. The roles are as follows: • Chair – to move the group through the stages of PBL in a timely man-ner, to ensure coverage of a topic, and to encourage all of the group toparticipate. • Scribe – listens and records information (often on a whiteboard), writesup the agreed objectives, and contributes to discussions. • Other group members – contribute to discussions, articulate knowledge,identify strengths and weaknesses in the group’s knowledge.
The groups meet to discuss the problem, along with a tutor who acts as a facil-itator by asking questions and prompts to guide discussion toward the learningoutcomes. With each new scenario the students rotate through the differentroles (chair person, scribe, group member), which gives them the chance todevelop new skills.During the first group meeting, students identify what parts of their knowledgeare lacking in tackling the problem. They then set their own goals in termsof what information they require in order to solve the problem in hand. Eachmember of the group researches the required information. The group thenreconvenes to discuss what they learnt from their self-study, and apply theirnew knowledge to the problem in hand. There will typically be several daysbetween the first session and the second session.
Each PBL session is evaluated through surveys in which the students reflecton their learning experiences. The facilitator guides students through this self-4ssessment of outcomes relative to the goals they set at the start, to show themthe extent of their learning. Final assessment can take any form, and need notbe reliant on the group-work during PBL.
Similarly to PBL, the fundamental idea of TBL is that students work on pro-fessionally relevant problems. That is, problems that are similar to what theymight encounter in the workplace (Michaelsen et al., 2004). The learning dif-fers from that of PBL, however. Teams are formed of between five and sevenstudents, but are not randomly allocated. Instead, the instructor carefully cre-ates groups to ensure that they are heterogeneous, for example, in terms ofpreparation or previous experience. Students do not change groups during thecourse. TBL is now popular in Nursing and Medical schools (Liu and Beaujean,2017), and though in these settings the focus tends to be on developing appliedknowledge, there are examples of its use in teaching more theoretical aspects ofmathematics (Parappilly et al., 2019) and physics (Parappilly et al., 2015).
Prior to the teams meeting to discuss the allocated prob-lem, each student must prepare for the group work by studying the providedmaterials. This could be in the form of reading, watching videos, or any otheractivity that prepares students sufficiently for the task ahead.
During the session – readiness assurance
The Readiness Assurance Pro-cess (RAP) aims to ensure that all students have the pre-requiste knowledgeof the course material self-studied, in order to take part in the later problemsolving exercise.Each student completes an individual test (individual Readiness Assurance Test,or iRAT), designed to highlight any deficiencies in the student’s understanding ofthe pre-class material. These tests are typically quick-fire multiple choice tests,done using electronic voting equipment so that they are marked instantaneously.Once completed, students re-take the test, but this time in their allocated groups(team Readiness Assurance Test, or tRAT). Discussion of the questions amongteam members is encouraged, so that the tRAT itself becomes a learning toolwhere students learn from each other.Results are available immediately after the tRAT, allowing students to assesstheir understanding, but also to contest the questions and/or answers. Teamsprovide written justification as to why they think they deserve a higher mark,5ith evidence, e.g. from course material, for the instructor to consider. If theinstructor finds in favour of the team, additional marks are awarded. However,only teams who contest will be eligible for additional marks, even if the problemdetected was common for all groups. This encourages students to question thematerial, and also helps with team cohesion.
During the session – lecture
Finally, a lecture component directed at allgroups gives the instructor opportunity to clarify misunderstandings and com-mon conceptual errors which were picked up during the iRAT and tRAT.
During the session – working on a problem
The remaining time is spenton solving a problem using the material learnt. The problems are aimed attesting students’ deeper understanding of the course material, while the RAPprocess tests base knowledge (Liu and Beaujean, 2017). Such problems gener-ally satisfy four criteria (commonly known as the “4S”): • the problem must be Significant; • the teams have a Specific set of possible answers from which they chooseone; • each team works on the Same problem; • teams must Simultaneously report their final answer.Importantly, the problem must not be easily segmented into smaller parts thatdifferent team members can tackle: the idea is that the group works togetheron the whole problem. Assessment for the course is generally a combination of individual tests (iRATscores and final exam mark), and groupwork mark (tRAT scores, scores fromthe problem and peer evaluations). Further summative assessment can take anyformat.
Among their recommendations, the GAISE College Report suggests that mod-ern statistics education should teach statistical thinking as an investigative pro-cess of problem solving and decision making, should integrate real data with acontext and purpose, and foster active learning (Carver et al., 2016). All theseattributes are fundamental to both problem- and team- based learning. TheGAISE College Report also calls for using technology to explore concepts and6nalyse data. While in medicine, for example, hands-on patient-based activitiesmay not be possible in a classroom setting, we can incorporate practical dataanalysis into problem- or team-based learning in statistics.The general approach of group-based learning aligns with the constructivistphilosophy of learning, where students actively construct their own knowledgerather than passively receiving it (Garfield, 1993). Not only do students learnthe subject matter in this way, but they develop softer skills in problem solvingthat captures some of the non-formal learning that happens in the workplace(Eraut, 2000).Group-based learning is posited as a largely positive strategy for teaching non-specialist students. Though we found no published literature on the effective-ness of such strategies in teaching statistics to specialist students (i.e. thosepursuing degrees in the mathematical sciences), group-based learning has beensuccessfully implemented for mathematics students in discrete mathematics(Paterson and Sneddon, 2011).Though there are numerous approaches to measuring effectiveness in teaching,the evidence relating to group-based learning tend to fall into three categories: • performance on end-of-module assessments or similar; • long-term retention of information; • student enjoyment or engagement with the material.We discuss the findings of other studies in implementing variants of TBL or PBLin each of these categories. Evidence of impact on staff is considered separatelyin Section 4. Kalaian and Kasim (2014)’s meta-analysis of the effectiveness of group-basedlearning in statistics, in comparison to lecture-based instruction, revealed thattheir effectiveness is dependent on the type of group-based learning imple-mented. In particular, cooperative or collaborative learning (for example TBL)was found to be effective while no evidence of improved academic achievementwas found for inquiry-based methods (such as PBL).Though the meta-analysis did not point to an overall benefit to using PBL incomparison to lecture-based instruction, there are examples of superior studentperformance on statistics assessments after a PBL-type course rather than alecture course (Karpiak, 2011). However, it is not clear whether this is gen-uinely due to better understanding of the course material or some other factors(Gijbels et al., 2005; Karpiak, 2011). For non-statistics major courses in partic-ular, the use of PBL may be helpful because it generates a constant use for thestatistical methodology, and hence provides students with a motivation to learn(Jaki and Autin, 2009). Better performance on module assessments could also7e a consequence of students engaged in active learning as opposed to learn-ing passively, rather than the effect of the PBL itself, or unwittingly increasingthe amount of guidance from PBL tutors to students especially since studentsbenefit from guidance in very small groups (Bud´e et al., 2009).Improved grades on end-of-module tests was also observed for TBL for service-type courses mathematics (Nanes, 2014) and specifically in statistics (Liu and Beaujean,2017; Haidet et al., 2014).
While there is a growing body of evidence to suggest various group-based learn-ing methods improve end-of-module assessments, far fewer studies have lookedat the long-term impact of these strategies on knowledge retention.We found no studies looking at long-term retention of knowledge and skillsin statistics, and only one in teaching medical students (Emke et al., 2016).In this study, which looked at short- and long-term retention of knowledgeand compared a cohort of students taught via TBL with a cohort that wastraditionally taught, there was some evidence that the TBL group performedbetter on assessments in the short-term but no evidence that they retained moreknowledge longer term.
A large body of evidence in the literature points to group-based learning asbeing a positive experience for students. That this is an aspect that receivesmost attention is not surprising given the difficulties in comparing understandingof course material between cohorts.Students are generally positive about TBL in mathematics (Nanes, 2014; Krogstie et al.,2018) and in statistics (St. Clair and Chihara, 2012). In particular, some re-ported students finding mathematical ideas more accessible when the materialwas taught as a TBL class as opposed to traditional lectures (Paterson et al.,2013). Balancing this overwhelming positivity are some interesting student in-sights from other studies. Naturally, not all students will enjoy an active group-learning environment (Haidet et al., 2014), but more specifically a group envi-ronment can encourage some students to ‘coast’ in TBL maths classes, relying ontheir team-mates for back-up (Paterson et al., 2013). Others - perhaps weakerstudents - may find the team environment intimidating (St. Clair and Chihara,2012). In the latter case however, team-working and communication is an essen-tial skill which should be developed alongside mathematical or statistical skills(Nanes, 2014; Tinungki, 2015).Though most of the research we found on student engagement was based onTBL, aspects of problem-based learning for large cohorts have been consid-8red. Klegeris and Hurren (2011) found that PBL sessions for a pharmaceuticalcourse increased attendance in comparison to traditional lectures. This was tri-alled with and without student additional marks for attendance. They foundthat offering such a reward for attendance did not significantly affect atten-dance rates. For large statistics classes in particular, Bud´e et al. (2009) foundthat more guidance from tutors/facilitators during the session resulted in bet-ter student perception of the course. They warn that increasing the amountof guidance from tutors in a PBL setting could inadvertently lead students tobecome passive about their learning and less motivated, though they did notfind evidence of this in their study.While the evidence on balance suggests improved student engagement throughthe use of TBL and PBL, it is not clear whether these approaches to teachingwill suit all students. Making learning inclusive, for example to those withadditional educational needs, may mean that adaptations to PBL and TBL arenecessary though to our knowledge there are no published papers exploring thisparticular aspect.
Statistics is perhaps an obvious candidate for group-based learning, rich withopportunities in tackling ‘real’ problems and can easily be framed as a believableand relevant problem for either team- or problem-based learning strategies. Itis therefore not surprising that PBL for example has been used in statisticscourses for over 20 years (Hillmer, 1996; Boyle, 1999).The nature of statistics means it is rather dependent on the order that thematerial is introduced. Its highly structured and sometimes abstract naturemakes teaching statistics via group-based learning a challenge: deficiencies inunderstanding of basic concepts may cause difficulties in understanding morecomplex procedures (Bland, 2004; Bud´e et al., 2009). Students can’t front-loada large amount of information so adaptations may be necessary. Nanes (2014)for example, in teaching a course on linear algebra via TBL, suggests increasingthe amount of testing and making the real world problems shorter though caremust be taken not to ‘teach to the test’. It is not unreasonable to assume thatthe same issue could arise in teaching statistics in this manner.Implementing group-based learning in statistics therefore needs careful consid-eration, and in some cases modifications may be necessary. In this section wereview the major components of group-based learning and give advice on prac-tical solutions to potential issues. 9 .1 The real-world problems
Problems for group-based learning can take any format, though will be differentin nature for PBL and TBL. In TBL, students are required to complete a setof learning activities for the session - such as pre-reading, watching videos, orcompleting other tasks - when technical information can be conveyed whichis relevant in solving the problem. In this way, common procedures such ashypothesis testing and statistical modelling can be taught. Contrast this withPBL: it is probably unrealistic to expect students to tackle data-driven problemssolely through PBL (Bland, 2004). For example, expecting students to cometo the conclusion that a t -test is appropriate without some prior knowledge isunreasonable, though introducing these concepts in other ways is possible. Herewe discuss alternatives to data-driven real-world problems, and their suitabilityfor both TBL and PBL.Real-world problems that don’t require directly handling data may be easier toimplement in class, especially if computing power is not required. These canstill provide a rich learning experience, and indeed may enhance a student’sbroad understanding of the subject while alleviating some of the difficulties inobtaining real, relevant, and well structured data for teaching purposes.Alternatives to data driven problems could be of the form of a research paperor similar (Bland, 2004). Asking students to read, digest and report back onfindings from a research paper - especially if it is of direct interest to the students- would broaden the scope of statistics education, taking the emphasis away frommechanical details to interpretation of results, and also motivating students tosee the power of statistics in their own discipline. This strategy in particularis suitable for both PBL and TBL. In PBL, the task could be phrased aroundunderstanding the statistical methods employed in a paper and why they wereused. In TBL, students could critically appraise the use of techniques in contextand suggest alternative ways of addressing the paper’s research questions and/orput forward a different analysis plan for the data collected.In the same vein, students could be asked to provide advice on a consultancybasis either on the design of an experiment or on the analysis of previously-collected data. For the latter, carrying out the data analysis could be set as atask outside the class (in the case of PBL, for example, before the next groupmeeting), or even as pre-work in TBL before the next session. Results of whichcould then be used as a springboard for the following workshop either in termsof discussing output or applying the results to a connected problem.These are relatively easy ideas to implement in introductory or even intermedi-ate courses in statistics. Teaching more advanced mathematical statistics in thesame vein requires more thought. Embedding the topic of interest into a real-world problem may require a little flexibility in what we think of as ‘real-world’as has been done in more advanced mathematics courses (Nanes, 2014), thoughthis is not always the case (for example, it is not difficult to think of many10pplications of the central limit theorem). With PBL we have the advantage ofa dedicated facilitator who can help to guide students through possibly abstractideas, and in TBL the course material students read before the group sessioncan provide the necessary theory before tackling the problem. In teaching moreabstract concepts like this, teachers may need to provide students with moreguidance on how to tackle the problem, especially in the context of TBL, forexample in explicitly asking for students to think about designing simulationsin order to reach a solution.Whatever the format of a real-world problem, Garfield (1993) emphasises thatthe hallmarks of good group activities include that all students contribute tothe task in hand, and suggest that this could be done by simply emphasisingthis. Both PBL and TBL benefit from having problems to solve that cannot besplit into smaller sub-problems to be tackled individually.In Appendices A and B we provide an outline of a PBL and TBL session,respectively. The PBL session frames a general question about mental healthand requires the students to identify the gaps in their knowledge and, somewhatindependently, fill those gaps in order to complete the task. The TBL session isbased on the more technical area of probability. Here, the pre-session materialthat students are required to work on ensure that they have the necessary basicunderstanding of probability which can then be applied to a problem concerningthe sensitivity and specificity of medical tests. Any form of group-based learning benefits from suitable classroom-like teach-ing space where students can comfortably work in groups. Traditionally forPBL, this requires sourcing a suitable room for each group and having accessto learning spaces conducive to group work has been found to improve ses-sion outcomes (Schwarz et al., 2001; Jones, 1988). This is often too complex tomanage, especially with ever increasing class sizes in statistics, with the onlyviable alternative to host sessions in large lecture theatres (Nicholl and Lou,2012; Klegeris and Hurren, 2011; Roberts et al., 2005). With some organisa-tion, however, running PBL in these spaces is not insurmountable.TBL, by its very nature, isn’t hampered by such space constraints and is de-signed to work in lecture theatres. Not all lecture theatres are created equal,however: single level lecture theatres will make it far easier for students to inter-act within their team in comparison to the usual sloping tiered theatre. It is notsurprising that Espey (2008) found that student attitudes toward team-basedlearning improved with when students perceived the environment they were into be a comfortable space in which to work in their teams.Nicholl and Lou (2012) suggests using a classroom that is larger than you needfor your group size, to create a more comfortable environment for students andto allow the instructor easy access to each group. Of course, computer labs may11e required for problems requiring a data-driven solution. Computer rooms areoften easier to set up for groups to work together in the sense that they allowsome flexibility in rearranging seating easily to suit each team. It may be betterfor group cohesion if students are not allocated a PC each; one PC per teamgoes some way to ensure that the students in a group interact with one anotherrather than each student ‘doing their own thing’.
Traditional PBL is staff-intensive, requiring a tutor or facilitator for each group.This is unlikely to be an option for many courses, especially as classes in statis-tics are rapidly increasing in size. Though TBL may seem more practical as itdoes not require a facilitator for each group, some institutions have been suc-cessful in running PBL sessions with only one facilitator for the entire class. Re-searchers found that running PBL alongside traditional lectures in biochemistryand physiology, without having a dedicated tutor for each group, was successfulin terms of improving problem solving skills as well as student satisfaction andmotivation (Klegeris and Hurren, 2011). Nicholl and Lou (2012) suggest usingon-line platforms such as Poll Everywhere or Twitter so that students can sendquestions to the lone instructor, who in turn can either project answers for thewhole class to see or initiate a class discussion. Without a tutor for each group,however, students need to have some background knowledge of the topic underconsideration (Nicholl and Lou, 2012).In contrast, Roberts et al. (2005) compares traditional PBL for undergraduatemedics with a modification where students tackle PBL-like tasks without a ded-icated group tutor. They conclude that the modification is a useful alternativewhen insufficient staff resources are available. They do find, however, that stu-dents with a dedicated facilitator are more likely to perceive the learning activityas being superior though no difference was detected between the two groups interms of achievement.
Teaching in the mathematical sciences is often in traditional lectures with indi-vidual assignments and assessments. This is at odds with the nature of mathe-matics at research level: a fundamentally collaborative endeavour. In statistics,courses with group-work components have been common for quite some time,as reported by Garfield (1993), Hillmer (1996), Boyle (1999), and Jaki (2009).However, students’ experience of this way of working needs to be taken intoaccount at the start of any course using group-based learning.Like any new intervention, it may take time for students to get used to the ideaof working in groups. Students may engage more with the process once they get12sed to it, so doing this every now and again might not show the real potentialof team-based learning.In the first instance, explaining the structure of each session, making clear howgroups are expected to work together, what is expected from students, how toaccess help, the role of any facilitators, and general code of conduct, shouldbe the first priority; this is especially so for implementations in large classes(Roberts et al., 2005). In particular, students who have little or no experiencewith small-group learning strategies like PBL or TBL will need more support,and all sources of help need to be highlighted. All groups need to feel thatthey understand the task in hand, feel confident that they can speak to a tutorwhen they need guidance, and that they have sufficient resources. For the latterin particular, this may mean suitable written and/or videoed material. It hasbeen suggested that recording any lecture components of courses - which occurin both PBL and TBL - benefits students (Jaki, 2009; Jaki and Autin, 2009).Course leaders must be prepared for initial student resistance, especially if stu-dents’ other courses are taught traditionally. Some students may see group-based learning as a glorified version of self-study (in which case, why pay foran education?) while others may worry that their marks will be unfavourablyinfluenced if having to rely on teammates. Responses to such criticisms and con-cerns could for example include the pedagogical reasons for teaching statisticsin a group-based learning environment, or the benefit in terms of developmentof soft skills valued by employers. Students worried that their grades will be un-favourably influenced may be placated if they are reassured of the procedures inplace to ensure that marks are allocated fairly. Even the strongest students ben-efit from group-based learning: strong students in groups that work well (e.g.where students are invested in the group’s achievement), could benefit fromthinking about concepts at a deeper level in order to explain them to weakermembers of the group. There are also opportunities for students to assess eachother. Strategies such as group members having to assess and provide feedbackto each other can help students feel that contribution is rewarded while coastingin the group has negative consequences (Freeman and Mckenzie, 2002).How groups are formed can influence the success of a group-based learningcourse: these learning strategies work only when students engage, and if stu-dents are inexperienced in group working then this needs to be monitored andmanaged carefully (Hansen, 2006). In their original format, both PBL andTBL groups are chosen by the course leader and these groups remain togetherfor more than one session to encourage cohesion and ensure diversity of groups.Groups that remain together over a period of time instead of changing on a regu-lar basis tend to display a more positive group dynamic (Sweet and Michaelsen,2007). What is more, better student engagement within groups has been notedwhen groups not only stay together but also work together on a regular basis(Theobald et al., 2017).Once groups are formed, internal dynamics can influence student performance.Factors that have been found to lower student achievement include being in a13roup where one student dominates, and/or feeling uncomfortable in the group;these tends to be more prominent factors when the group-work involves high-stakes assessment (Theobald et al., 2017).Strategies to facilitate positive group working methods and thus increase en-gagement may be useful, especially if students are not used to group-basedworking. One approach that has been suggested to increase students’ comfortin groups is to establish group ‘norms’ (Theobald et al., 2017). For example,groups could be required to write and submit their own contract for code ofconduct, goals, and methods of working, which could help in establishing trustthrough clarifying commitments to each other (Hunsaker et al., 2011). Thesecontracts could also be helpful in giving groups a way of dealing with dominantstudents. If group-work leads to a summative assessment, a contract could inaddition allow the group to negotiate mark allocation, for example in how marksare distributed between group- and individual- components, or how individualstudents will be assessed if peer-assessment is to be used.It may be tempting to allow students to choose their own groups for a numberof reasons, including making students feel more comfortable (Theobald et al.,2017), potentially decreasing student resistance, and ease of administration. Inaddition, allowing for changing teams in each session may also be tempting. Thisis especially so if students are not required to attend lecture sessions makingsteady teams difficult to manage, though this has been shown not to be aseffective as groups repeatedly working together (Sweet and Michaelsen, 2007).Allowing students to choose may also compromise the heterogeneity withingroups. Moreover, those who don’t have an immediate friendship group in classmay be severely disadvantaged when students are permitted to choose theirown group: though no published work could be found looking at the effects ofthis, the authors’ own experience is that students joining a group of studentswho already know each other may result in problems with group attachment,while creating extra groups consisting of these students may lead to feelings ofresentment.A half-way house is to involve students in the formation of groups in the sensethat they decide on how the groups are chosen even though, ultimately, thegroups are chosen by the course leader. For example, involving students indecisions around the composition of groups: should they be randomly assigned,how long should groups work together for, should groups be mixed in terms ofachievement in previous courses, should groups be balanced in terms of academicbackground of students, should groups be balanced in terms of gender or anyother characteristic? Students who feel that they have some say over how theireducation is managed are more likely to engage in the first place (Bovill, 2019).14 .5 Staff reaction
There is evidence to suggest that lecturers find the use of group-based learninga satisfying experience (Jones, 1988), and it is reasonable to think that thisis because the process is a more interactive experience than didactic teaching.Through this interaction the course leader may naturally find that they have abetter understanding of a student’s strengths and weaknesses, enabling them toaddress these issues directly.When making the transition to group-based learning Boud and Feletti (1997)and Schwarz et al. (2001) found that introducing students and faculty membersinto the new curriculum, as opposed to simply starting it without introductorysessions, helped in its successful adoption.
The importance of quality of teaching in the UK Higher Education sector is em-phasised by the introduction of the Teaching Excellence and Student OutcomesFramework (TEF, Office for Students (2018)) to sit alongside the Research Ex-cellence Framework (REF). The first TEF awards were assigned in 2018, andwere evaluated for each University as a whole. The second round of TEF awards,planned for 2021, will include subject/departmental specific assessment. Uni-versities are encouraging teaching staff to modernise their teaching, with focuson the TEF but also the National Student Survey results (Richardson, 2013).There is mounting evidence that traditional lecture courses are not as effective as‘active’-type learning strategies in Science, Technology, Engineering, and Math-ematics (STEM) subjects (Freeman et al., 2014), and indeed specific evidencethat PBL and TBL - as active learning methods - are effective. Bland (2004)goes as far as saying that not using such methods (PBL in this specific case)for statistics and research methods training is detrimental to students, whileTinungki (2015) highlights the importance of communication in learning math-ematics which is well addressed in group-based learning. Indeed, both PBL andTBL are ideally placed to meet the needs of employers, who have often identifiedpoor team working skills, poor written communication skills, and poor oral pre-sentation skills in graduates (Knight and Yorke, 2003). This is also identified inthe guidelines for undergraduate programmes in the closely allied discipline ofdata science, which recommend that ‘projects involving group analysis and pre-sentation should be common throughout the curriculum’ (Veaux et al., 2017).Though PBL or TBL are not the only methods for implementing this, similargroup based methods are becoming popular in data science education, see forexample C¸ etinkaya-Rundel and Ellison (2020); Saltz and Heckman (2016).There has been an explosion of technological advances since Gelman and Nolan(2002) outlined approaches for teaching statistics. In the modern teaching envi-15onment both teachers and students are surrounded by resources which weren’tpreviously available. From a student’s perspective getting information has neverbeen so easy, speeding up tasks such as the research component in PBL. Froma teacher’s perspective, numerous platforms (listed in Appendix C) make learn-ing and interaction with a class more manageable, whilst student monitoringbecomes ever easier with tracking via virtual learning environments or auto-mated marking of online quizzes. These factors contribute to the success ofgroup-based learning strategies.However, while for statistics modules where there is an applied or practicalcomponent there is clear scope to apply group-based learning for the whole orat least part of the module, it is not clear how, or even whether, such learningstrategies are suitable for statistics modules which are of a more mathematicalnature. In the first instance, the technical nature may make it difficult tocreate a truly ‘real-world’ problem, and this was also noted by Nanes (2014).Secondly, highly mathematical modules generally rely more heavily on students’prior knowledge. For students whose prior knowledge isn’t strong, personalityand motivation is likely to play a large part in their success on the module: agroup-based learning module could be intimidating, or the group environmentmay be the key to success.Paterson et al. (2013) note that few mathematics lecturers use a group-basedlearning approach to their teaching. One possible reason for this is that rewrit-ing existing courses to entirely group-based learning modules in one fell swoopmay not be practical. It needn’t be all-or-nothing, however. Introducing stu-dents to group-based learning slowly may be beneficial (Boud and Feletti, 1997;Schwarz et al., 2001). Elements of group-based learning could be weaved throughmodules, for example particular topics within a module could be taught in agroup-based setting, or even just particular sessions. Care needs to be taken,however, in ensuring that students know why you are doing this, and how itbenefits them, otherwise the risk is that students won’t engage.Using group-based learning needn’t mean using only PBL, or only TBL, how-ever. Some educators have experimented with combining parts of PBL andTBL to maximise the benefits to students. For example, combining the peerfeedback (TBL) with an initial group discussion before the pre-reading assign-ments (PBL), are possibly positive enhancements to any group learning strate-gies (Dolmans et al., 2015). Online variants of PBL have also been trialledsuccessfully (de Jong et al., 2013). That modifications to the traditional PBLand TBL methods have been successful shows that these strategies are ripe forshaping to fit both the practical constraints of the course, as well as the coursecontent.We have shown that implementation of PBL, TBL, or a variant thereof, is possi-ble in the teaching of applied statistics. However group-based learning is imple-mented, the emphasis on a more rounded student education is clear. Of course,these are not the only active learning strategies. Which is the most effective isthe subject of its own debate, and students with different learning styles may16refer different teaching methods (Bloom et al., 1956), but this review showsthat there is scope for group-based learning in statistics.
Acknowledgements
TP would like to thank Simon Allan and Dr Anne-Marie Houghton from Lan-caster University’s Postgraduate Certificate in Academic Practice programmefor helpful advice. TP was supported by the Integrative Epidemiology Unit,which receives funding from the UK Medical Research Council and the Univer-sity of Bristol (MC UU 00011/1 and MC UU 00011/3).The authors would like to thank the two anonymous referees for their detailedand constructive comments which improved the paper.
Author biographies
Elinor Jones is Senior Teaching Fellow in the Department of Statistical Scienceat University College London. She was awarded a PhD in Statistics and Prob-ability from The University of Manchester in 2009. She is interested in how toengage students in the learning of statistics, particularly through active learningstrategies.Tom Palmer is a Senior Lecturer in Biostatistics in the MRC Integrative Epi-demiology Unit, in Bristol Medical School. He was awarded a PhD in MedicalStatistics and Genetic Epidemiology from the University of Leicester in 2009.He is interested in different teaching methods and how to apply these to teachingstatistics.
Author contact details
Elinor Jones, Department of Statistical Science, University College London,Gower Street, London, WC1E 6BT. Email: [email protected] Palmer, MRC Integrative Epidemiology Unit, University of Bristol, Oak-field House, Oakfield Grove, Bristol, BS8 2BN. Email: [email protected] of this paper was prepared whilst TP was employed in the Department ofMathematics and Statistics, Lancaster University, Lancaster, LA1 4YW.17 eferences
J. M. Bland. Teaching statistics to medical students using problem-basedlearning: the Australian experience.
BMC Medical Education , 4:31, 2004.doi: 10.1186/1472-6920-4-31.B. Bloom, M. D. Engelhart, E. J. Furst, W. H. Hill, and D. R. Krathwohl.
Taxonomy of educational objectives: Handbook I: Cognitive domain . DavidMcKay Company, New York, US, 1956.D. Boud and G. Feletti.
The challenge of problem-based learning . Kogan Page,London, UK, 1997.C. Bovill. Co-creation in learning and teaching: the case for a whole-classapproach in higher education.
Higher Education , 79(6):1023–1037, 2019.doi: 10.1007/s10734-019-00453-w.C. R. Boyle. A problem-based learning approach to teaching biostatistics.
Journal of Statistics Education , 7(1), 1999. URL http://jse.amstat.org/secure/v7n1/boyle.cfm .B. Braun, P. Bremser, A. M. Duval, E. Lockwood, and D. White. What doesactive learning mean for mathematicians?
Notices of the AMS , 64(2):124–129, 2017. doi: 10.1090/noti1472.L. Bud´e, T. Imbos, M. W. J. v. d. Wiel, N. J. Broers, and M. P. F. Berger.The effect of directive tutor guidance in problem-based learning of statisticson students’ perceptions and achievement.
Higher Education , 57(1):23–36,2009. doi: 10.1007/s10734-008-9130-8.R. Carver, M. Everson, J. Gabrosek, N. Horton, R. Lock, M. Mocko,A. Rossman, G. H. Rowell, P. Velleman, J. Witmer, and B. Wood.Guidelines for Assessment and Instruction in Statistics Education (GAISE)College Report. Technical report, American Statistical Association, 2016.URL .Accessed 2019-08-12.M. C¸ etinkaya-Rundel and V. Ellison. A fresh look at introductory datascience.
Journal of Statistics Education , 2020. doi:10.1080/10691898.2020.1804497. Published online: 14 Sep 2020.B. Dahl. What is the problem in problem-based learning in higher educationmathematics.
European Journal of Engineering Education , 43(1):112–125,2018. doi: 10.1080/03043797.2017.1320354.N. de Jong, D. M. L. Verstegen, F. E. S. Tan, and S. J. O’Connor. Acomparison of classroom and online asynchronous problem-based learningfor students undertaking statistics training as part of a public health18asters degree.
Advances in Health Sciences Education , 18:245–264, 2013.doi: 10.1007/s10459-012-9368-x.D. Dolmans, L. Michaelsen, J. van Merri¨enboer, and C. van der Vleuten.Should we choose between problem-based learning and team-based learning?No, combine the best of both worlds!
Medical Teacher , 37(4):354–359, 2015.doi: 10.3109/0142159X.2014.948828.A. R. Emke, A. C. Butler, and D. P. Larsen. Effects of team-based learning onshort-term and long-term retention of factual knowledge.
Medical Teacher ,38(3):306–311, 2016. doi: 10.3109/0142159X.2015.1034663.M. Eraut. Non-formal learning and tacit knowledge in professional work.
British Journal of Educational Psychology , 70:113–136, 2000. doi:10.1348/000709900158001.M. Espey. Does Space Matter? Classroom Design and Team-Based Learning.
Applied Economic Perspectives and Policy , 30(4):764–775, 2008. doi:10.1111/j.1467-9353.2008.00445.x.M. Freeman and J. Mckenzie. SPARK, a confidential web–based template forself and peer assessment of student teamwork: benefits of evaluating acrossdifferent subjects.
British Journal of Educational Technology , 33(5):551–569,2002. doi: 10.1111/1467-8535.00291.S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt,and M. P. Wenderoth. Active learning increases student performance inscience, engineering, and mathematics.
PNAS Proceedings of the NationalAcademy of Sciences of the United States of America , 111(23):8410–8415,2014. doi: 10.1073/pnas.1319030111.J. Garfield. Teaching statistics using small-group cooperative learning.
Journalof Statistics Education , 1(1), 1993. doi: 10.1080/10691898.1993.11910455.A. Gelman and D. Nolan.
Teaching Statistics: A bag of tricks . OxfordUniversity Press, New York, US, 2002.D. Gijbels, F. Dochy, P. V. den Bossche, and M. Segers. Effects ofproblem-based learning: A meta-analysis from the angle of assessment.
Review of Educational Research , 75(1):27–61, 2005. doi:10.3102/00346543075001027.P. Haidet, K. Kubitz, and W. McCormack. Analysis of the Team-BasedLearning Literature: TBL Comes of Age.
Journal on Excellence in CollegeTeaching , 25:303–333, 2014.R. S. Hansen. Benefits and problems with student teams: Suggestions forimproving team projects.
Journal of Education for Business , 82(1):11–19,2006. doi: 10.3200/joeb.82.1.11-19. 19. C. Hillmer. A problem-solving approach to teaching business statistics.
TheAmerican Statistician , 50:249–256, 1996. doi: 10.2307/2684667.P. Hunsaker, C. Pavett, and J. Hunsaker. Increasing student-learning teameffectiveness with team charters.
Journal of Education for Business , 86(3):127–139, 2011. doi: 10.1080/08832323.2010.489588.T. Jaki. Recording lectures as a service in a service course.
Journal ofStatistics Education , 17(3):1–13, 2009. doi:10.1080/10691898.2009.11889534.T. Jaki and M. Autin. Using a problem-based approach to teach statistics topostgraduate science students: A case study.
MSOR Connections , 9(2):40–47, 2009.K. Jones.
Interactive learning: A guide for facilitators . Kogan Page, London,1988.S. A. Kalaian and R. M. Kasim. A meta-analytic review of studies of theeffectiveness of small-group learning methods on statistics achievement.
Journal of Statistics Education , 22(1), 2014. doi:10.1080/10691898.2014.11889691.C. P. Karpiak. Assessment of Problem-Based Learning in the UndergraduateStatistics Course.
Teaching of Psychology , 38(4):251–254, 2011. doi:10.1177/0098628311421322.A. Klegeris and H. Hurren. Impact of problem-based learning in a largeclassroom setting: student perception and problem-solving skills.
Advancesin Physiology Education , 35(4):408–415, 2011. doi:10.1152/advan.00046.2011.P. T. Knight and M. Yorke.
Assessment, Learning and Employability . OpenUniversity Press, Maidenhead, UK, 2003.B. Krogstie, K. Berntsen, and A. Wr˚alsen. Adapting team-based learning in amathematics course for computer engineering students.
Proceedings from theannual NOKOBIT conference held at Svalbard the 18th–20th of September2018 , 26(1), 2018.Lancaster Medical School. Problem-Based Learning Handbook Study Guide:Tutor Version. Lancaster University Medical School Study Guide, 2016.S. Liu and A. Beaujean. The effectiveness of team-based learning on academicoutcomes: A meta-analysis.
Scholarship of Teaching and Learning inPsychology , 3(1):1–14, 2017. doi: 10.1037/stl0000075.T. Mann. Law student becomes sixth to ‘commit suicide’ in Bristol this year,May 2017. URL https://bit.ly/2mq2VqI . Accessed 2019-09-19.20. K. Michaelsen, A. B. Knight, and L. D. Fink.
Team-based Learning: Atransformative use of small groups in college teaching . Stylus Publishing,2004.K. M. Nanes. A modified approach to team-based learning in linear algebracourses.
International Journal of Mathematical Education in Science andTechnology , 45(8):1208–1219, 2014. doi: 10.1080/0020739X.2014.920558.T. A. Nicholl and K. Lou. A model for small-group problem-based learning ina large class facilitated by one instructor.
American Journal ofPharmaceutical Education , 76(6):117, 2012. doi: 10.5688/ajpe766117.Office for Students. What is the TEF?, 2018. URL .Accessed 2019-08-12.M. Parappilly, L. Schmidt, and S. D. Ritter. Ready to learn physics: ateam-based learning model for first year university.
European Journal ofPhysics , 36(5):055052, 2015. doi: 10.1088/0143-0807/36/5/055052.M. Parappilly, R. J. Woodman, and S. Randhawa. Feasibility and effectivenessof different models of team-based learning approaches in stemm-baseddisciplines.
Research in Science Education , 2019. doi:10.1007/s11165-019-09888-8.J. Paterson and J. Sneddon. Conversations about curriculum change:mathematical thinking and team-based learning in a discrete mathematicscourse.
International Journal of Mathematical Education in Science andTechnology , 42(7):879–889, 2011. doi: 10.1080/0020739X.2011.613487.J. Paterson, L. Sheryn, and J. Sneddon. Student responses to team-basedlearning in tertiary mathematics courses.
Proceedings of 15th AnnualConference on Research in Undergraduate Mathematics Education , 2:619–626, 2013.J. T. E. Richardson. The national student survey and its impact on uk highereducation. In M. Shah and C. S. Nair, editors,
Enhancing student feedbackand improvement systems in tertiary education , number 5 in CAA QualitySeries, pages 76–84. Commission for Academic Accreditation, UAE, AbuDhabi, June 2013. URL http://oro.open.ac.uk/37730/ . ISSN 2227-4960.C. Roberts, M. Lawson, D. Newble, A. Self, and P. Chan. The introduction oflarge class problem-based learning into an undergraduate medicalcurriculum: an evaluation.
Medical Teacher , 27(6):527–533, 2005. doi:10.1080/01421590500136352.C. J. Roseth, J. B. Garfield, and D. Ben-Zvi. Collaboration in learning andteaching statistics.
Journal of Statistics Education , 16(1), 2008. doi:10.1080/10691898.2008.11889557. 21. J. Rumsey. Statistical literacy as a goal for introductory statistics courses.
Journal of Statistics Education , 10(3), 2002. doi:10.1080/10691898.2002.11910678.J. Saltz and R. Heckman. Big data science education: A case study of aproject-focused introductory course.
Themes in Science and TechnologyEducation , 8(2):85–94, 2016. URL .R. J. Savery. Overview of problem-based learning: definitions and distinctions.
Interdisciplinary Journal of Problem-Based Learning , 1(1):9–20, 2006. doi:10.7771/1541-5015.1002.B. Schloerke, J. Allaire, and B. Borges. learnr: Interactive Tutorials for R ,2018. URL https://CRAN.R-project.org/package=learnr . R packageversion 0.9.2.1.H. Schmidt. Problem based learning: rationale and description.
MedicalEducation , 17(1):11–16, 1983. doi: 10.1111/j.1365-2923.1983.tb01086.x.P. Schwarz, S. Mennin, and G. Webb, editors.
Problem-based learning: casestudies, experience and practice . Routledge, London, UK, 2001.K. St. Clair and L. Chihara. Team-based learning in a statistical literacy class.
Journal of Statistics Education , 20(1), 2012. doi:10.1080/10691898.2012.11889633.M. Sweet and L. K. Michaelsen. How group dynamics research can inform thetheory and practice of postsecondary small group learning.
EducationalPsychology Review , 19(1):31–47, 2007. doi: 10.1007/s10648-006-9035-y.E. J. Theobald, S. L. Eddy, D. Z. Grunspan, B. L. Wiggins, and A. J. Crowe.Student perception of group dynamics predicts individual performance:Comfort and equity matter.
PLoS One , 12(7), 2017. doi:10.1371/journal.pone.0181336.G. M. Tinungki. The role of cooperative learning type team assistedindividualization to improve the students’ mathematics communicationability in the subject of probability theory.
Journal of Education andPractice , 6(32):27–31, 2015.R. D. D. Veaux, M. Agarwal, M. Averett, B. S. Baumer, A. Bray, T. C.Bressoud, L. Bryant, L. Z. Cheng, A. Francis, R. Gould, A. Y. Kim,M. Kretchmar, Q. Lu, A. Moskol, D. Nolan, R. Pelayo, S. Raleigh, R. J.Sethi, M. Sondjaja, N. Tiruviluamala, P. X. Uhlig, T. M. Washington, C. L.Wesley, D. White, and P. Ye. Curriculum guidelines for undergraduateprograms in data science.
Annual Review of Statistics and Its Application , 4(1):15–30, Mar. 2017. doi: 10.1146/annurev-statistics-060116-053930.22
Example statistics PBL session: Student men-tal health – is there a crisis?
A.1 Scenario
Consider the scenario in which you are working as a statistician in the civilservice in the Department for Education. Recently there have been several casesof students committing suicide. For example, six students committed suicide inthe 2016/2017 academic year in Bristol (Mann, 2017).Ministers want to know if there really is a crisis in terms of the number of stu-dents suffering from mental health problems. You are tasked with investigatingthis issue.One minister has read some epidemiological research and is curious as to whetherthis year’s cases are reflective of a truly increasing trend in mental health casesor whether this increase is an anomalous spike in the data.You are tasked with preparing a short structured report (no more than 5 pages)and presentation on this question.One issue to consider is that there is limited extra government funding for youranalysis: you are not be able to carry out a new study to investigate the issue.Therefore, you should address how you can overcome this limitation.
A.2 Indicative learning objectives
Statistical methods: • research how to estimate different measures of association; • investigate time series methods.Applied statistics: • research epidemiological concepts such as incidence and prevalence; • understand the differences between different absolute and relative mea-sures of association such as the risk difference and the risk ratio. Considerwhich measures might be more informative for public health policy mak-ers.Statistical programming: • demonstrate how to access publicly available datasets and prepare thesefor analysis using a software of your choice; • show how to present complex longitudinal analyses graphically.23 .3 For lecturers This session is designed as a PBL exercise to be run over a week. It is aimed atpostgraduate students.A plan for the sessions could be as follows: • Monday: read and digest problem sheet with brain storming session toidentify what issues they will need to research. • Tuesday: Students perform research. • Wednesday: Catch up session - the students assess their progress in theirPBL groups, and discuss what extra topics they need to research. • Thursday: Students finish research and prepare their presentation for Fri-day. • Friday: Students present their findings (as a group) to the whole cohortof PBL groups.
B Example statistics TBL session: conditionalprobability and diagnostic tests
B.1 Learning objectives
By the end of this section, students should be able to: • Explain the difference between the union of two (or more) events and theirintersection. • Calculate the probability of the union of two (or more) events and theintersection of two (or more) events. • Distinguish between independent and dependent events. • Explain intuitively the idea behind conditional probability. • Use tables and tree diagrams to compute conditional probabilities. • Explain the rationale behind Bayes’ theorem, and use it to compute con-ditional probabilities. • Compute probabilities in a range of settings.
B.2 Before the session
Students work through a directed set of materials, which may include reading,watching instructional videos, quizzes, exercises, among other things.24 .3 During the session: multiple choice quiz
Students complete a short multiple choice quiz individually, answering a rangeof questions on probability which might include both theoretical questions suchas asking students to apply their judgement on whether two events are indepen-dent, through to computing probabilities.Once the test is complete and submitted, students join their team and answerthe same multiple choice quiz. This time each question can be discussed withinthe team and the group must decide on their joint final answer for each questionfor submission. Results are available immediately after the team multiple choicequiz, and students can argue their case with the course leader if they think theydeserve a higher mark than the one they received. In statistics, this may bebecause questions or the choice of answers were poorly worded and thus causedconfusion.As the results of the test are available immediately, the course leader can identifyany common misconceptions or errors. A very brief lecture follows to clarifythese.
B.4 During the session: working on the problem
An example problem in this case could be the following.
Down’s syndrome is a genetic condition resulting in some level of learning dis-ability, with around one in every 1,000 babies born having the condition. Expec-tant mothers can opt to take a serum screening test to assess the risk of havinga baby with Down’s syndrome. The test outcome is either ‘positive’ or ‘negative’for Down’s syndrome.As with the majority of medical tests, the test isn’t 100% accurate. From ex-tensive research, it is known that the test is able to detect Down’s syndrome,when the baby has Down’s syndrome, in about 85% of cases. Conversely, whenthe baby doesn’t have Down’s syndrome the test identifies this in about 96% ofcases.A pregnant woman receives a positive test for Down’s syndrome, and asks youfor advice on how likely the test is to be correct. What are the chances that herbaby has Down’s syndrome?
Possible answers: about 85.00%, about 2.08%, about 0.10%, about 0.089%
Correct answer: about 2.08%This problem requires students to identify the required probability from a textdescription, translate the given information into appropriate probabilities, andmanipulate the (indirectly) given probabilities in a non-trivial manner to com-pute the final probability. The work involved means that it is very difficult to25hink of a way of splitting the work between group members: each step abovedepends on information from the previous step.The three incorrect answers are deliberately given as ‘common misconceptions’:85% is the usual prosecutor’s fallacy, 0.1% is the prevalence of Down’s syndromewithout accounting for the additional information from a positive test, and0.089% represents the situation where the calculation of the probability that atest is positive is incorrect (computed without taking the complement of thespecificity). It is useful that all answers have a basis in the numbers given here;if not then students won’t arrive at that particular answer and so unless theyare merely guessing it is of no use.
C Helpful apps, websites, and technologies
This section lists some resources which can be used by both lecturers and stu-dents to make sessions more interactive. • General advice: – Collaboration of TBL practitioners (the Team Based Learning Col-laborative) which makes example teaching material available online( ). • Online polls and quizzes: Students in groups could use these resourcesto aid each other’s learning. For example, in PBL the note taker of thegroup could maintain the notes of the session in an interactive Padlet pageinstead of taking notes on a whiteboard. – Sli.do : website to create audience polls; – Kahoot https://kahoot.it : website to create and run online quizzes; – Turning Point: audience response system and polling software ; – Mentimeter : App and website to cre-ate interactive presentations; – Wooclap : create and run online quizzes,real-time discussion boards suitable for classroom use; – Padlet https://en-gb.padlet.com/ : Interactive web pages with awide range of templates including note pinboards and word clouds. • R packages: – There is a task view on CRAN listing R packages helpful for teachingStatistics, https://CRAN.R-project.org/view=TeachingStatistics .26
The Bayesian task view also has a section devoted explicitly to teach-ing Bayesian Statistics. https://CRAN.R-project.org/view=Bayesian – The learnr package https://rstudio.github.io/learnr/ createsR tutorials and quizzes (Schloerke et al., 2018). – The exams package allows a user to cre-ate quizzes from an R script. The quizzes can be exported in variousformats, such as the xml format for a moodle quiz which can beembedded into a moodle page. – The Shiny runtime ( https://shiny.rstudio.com/ ) produces webapplications running R code. • Notebook formats:The notebook formats are valuable to students because they can containa mix of writing (using either markdown or L A TEX syntax), code, and theoutput of the code. These documents can be worked on by a group in acollaborative environment providing say RStudio server. – R Markdown Notebooks: RStudio ( https://rstudio.com ) providethe .nb.html format in which the cells are active within an RStudiosession. These files can also be viewed in a web browser, at whichpoint the cells are no longer active but can still be viewed. – Jupyter (formerly Ipython) notebooks, https://jupyter.org/ : Thesenotebooks allow users to distribute html documents in which the cellsof the notebook execute analyses if the user has the appropriate ker-nel installed. If the kernel is not installed the cells cannot be executedbut the documents can still be viewed in a browser. • Presentation and document formats:Tools for creating attractive slides or documents are useful for course lec-turers, but also for students if their tasks include submitting or presentingwork. – ioslides - creates html slides with interactive content, e.g. graphics.These can be produced from RMarkdown files. – Prezi https://prezi.com - creates attractive presentations whichdon’t follow the traditional slide format. – Microsoft Sway: An application to produce interactive reports andpresentations. https://sway.office.com/my – L A TEX Beamer (the German for overhead projector). A popular mod-ern Beamer theme is the Metropolis theme https://github.com/matze/mtheme .27