Playing with Numbers: Using Top Trumps as an Ice-Breaker and Introduction to Quantitative Methods

Abstract

Statistics anxiety has been widely documented among both postgraduate and undergraduate social science students and shown to be an obstacle in engaging students in quantitative methods. This article builds on previous studies that have highlighted the utility of fun and games in productive learning and overcoming anxiety. A personalized version of the game Top Trumps was developed for use with a class of postgraduate sociology students in the UK. This game provides an ideal way for students to inductively learn about basic statistical concepts, such as range and dispersion. The game also creates opportunities to engage students in critical discussion of measurement and social categorization. The article suggests that the employment of such hands-on learning exercises, especially when used in the first week of a quantitative methods module, can stimulate student interest, ameliorate statistics anxiety and encourage critical discussion, thereby positively impacting learning goals in the rest of the module. The article ends by briefly outlining how to adapt the game for use within an undergraduate module.

Keywords:

• Quantitative methods
• sociology
• games
• play
• statistics anxiety

Introduction

In this article I describe an adapted game of Top Trumps developed for a postgraduate quantitative methods module in a UK sociology department and since employed in undergraduate teaching. I begin by addressing the issue of statistics anxiety, since it is against this backdrop that any statistics teaching at undergraduate or postgraduate level must occur in sociology (and most social sciences). Following this is a brief discussion of the pedagogic use of classroom games and play in stimulating student interest, ameliorating statistics anxiety and encouraging critical thinking; all of which are especially important in the first week of a module. In the second part of this article I describe Top Trumps (for those unfamiliar with the game), explain how to personalize it for use in a quantitative methods classroom and highlight different ways in which this game can be used to introduce basic statistical concepts while encouraging a critical sociological approach to quantification. In the final section I review student feedback and draw conclusions about the approach.

Undergraduate and postgraduate statistics anxiety

Much has been written about undergraduate students’ ‘statistics anxiety’ (Leming 1979, Blalock 1987, Schacht & Stewart 1990, Fisher-Giorlando 1992, Potter 1995, Paxton 2006). This anxiety is such that “sociology undergraduates tend to want to avoid mathematics in general and some feel incapable of performing even basic mathematical operations” (Paxton 2006, p65). Writing, however, about postgraduate statistics teaching, Timothy Patrick Moran dismisses approaches that focus on fear as concerning themselves with “undergraduate-level issues”; implying that these are irrelevant to postgraduate students (Moran 2005, p263). In contrast, Moran suggests that postgraduate courses should ‘demystify’ statistics by developing a critical historical perspective that focuses on the controversies surrounding the introduction of particular statistical techniques, such as the null hypothesis inference test (Moran 2005, p266–9). His suggestions are useful, and I support giving space to discussion of the political and historical role of statistics in society (in this context I have found that Dorling & Simpson’s (1999) critical and readable collection is a useful starting point). Onwuegbuzie & Wilson (2003), however, provide voluminous evidence that both undergraduates and postgraduate students experience statistics anxiety, with between two-thirds and four-fifths of postgraduate students affected (Onwuegbuzie & Wilson 2003, p195). They show further that statistics anxiety produces negative outcomes, including poorer academic performance (Onwuegbuzie & Wilson 2003, p199–201).

My experience of teaching quantitative methods to sociology students in the UK and US corresponds with Onwuegbuzie & Wilson’s findings. Postgraduate students have greater academic confidence, as exemplified by the decision to pursue a programme of advanced education, but their statistics anxiety can be as severe as that of undergraduates. This was highlighted during a ‘taster’ session before the first postgraduate class I taught (designed to give students an opportunity to find out about the module and ask questions). The session was attended by 11 students, who filled in a mini-survey used within the session illustratively. In responding to the survey four students categorized themselves as ‘terrified’ about the upcoming module, with a further three ‘nervous, but not quite terrified’. Just one claimed to be ‘enthusiastic’. Eight out of 11 had enrolled on the module because it was a requirement.

Students’ terror/anxiety about statistics or quantitative methods is closely correlated to anxiety about maths (Onwuegbuzie & Wilson 2003, p196–97). This is exacerbated by the anti-math selection bias among social science students; with the choice to pursue a social-science education in some cases itself indicative of a disinclination for, or lack of achievement in, science. When they embark on postgraduate study, British sociology students may not have studied maths or statistics for many years: for instance, the majority of students in the taster session stated that it had been over five years. This hopefully is changing, with ESRC/Nuffield/HEFCE funded schemes, including Q-Step (www.nuffieldfoundation.org/q-step), increasing the breadth and depth of undergraduate social science quantitative training; but these schemes will take time to impact postgraduate cohorts substantially. Moreover, since sociology postgraduate training in neither Britain nor the US requires students to possess a sociology first degree, changes to the undergraduate curriculum are unlikely to fully resolve the issue. In contrast to the UK, the standardized aptitude tests required for US university entry (the SAT and GRE), include basic mathematics. Therefore US students are more likely than British students to have studied mathematics shortly before beginning a university sociology course. This may provide some advantages, but as in the UK, few undergraduates or postgraduates begin their degrees with more than a fleeting familiarity with social statistics.

Where incoming postgraduate students differ from undergraduate is that their intellect is perhaps more centrally constitutive of their sense of self. Encounters with a subject in which they feel incompetent is therefore additionally undermining, and the fear of being seen either by instructors or other students as foolish, perhaps more acute than the equivalent fear among undergraduates. In addition, the institutional quantitative–qualitative division in sociology (Tilly 2004) provides discursively able postgraduate students with the toolkit to re-frame fear of statistics, legitimizing fear as an ‘epistemological choice’ to use qualitative methods. This reinforces pre-existing psychological barriers to the comprehension of quantitative methods (a comprehension that paradoxically is the prerequisite for making such an epistemological choice). This means that any instructor wishing to deal with ‘statistics anxiety’ among sociology postgraduate students must counter both student worries about their own incompetence and their legitimization of this incompetence as philosophical stance (Williams et al. 2004). Games and hands-on exercises can introduce levity and encourage playful interactions among class members, and in doing so they establish an environment in which students feel less anxious, are able to ask for help and also feel free to question the epistemological basis of what is being taught.

Class-based games and play

The approach described here builds on analyses that have highlighted the need to develop statistical reasoning and dynamic student–teacher interactions (Bradstreet 1996) as well as on studies that have shown that fun is productive for learning (Lesser & Pearl 2008). The game of Top Trumps described below is designed for the first day of class. As such it is in-line with Macheski et al. (2008) suggestion that in teaching difficult subjects, like statistics,

…constructing a community of learners begins on the very first day. Faculty need to begin constituting their class as a community of people, that is, the first day experience needs to focus more on building relationships rather than course content. Classroom activities need to be interactive, creating an environment that feels emotionally safe to students, and which allows them to get to know each other in a relaxed atmosphere that is nonthreatening, and even fun. (Macheski et al. 2008, p44)

In distinction, however, to these authors’ juxtaposition of fun and relevance, the game described here is interactive and also provides a way to develop students’ statistical thinking (‘course content’) from day one. Given the pressure to fit ‘necessary’ learning within limited teaching hours this combination is critical.

The efficacy of games as learning aids is now widely acknowledged (c.f. Lean et al. 2006, Ellington et al. 2013). Within sociology in-class simulation games, providing experiential understanding of key themes such as stratification, are especially popular (Coghlan & Huggins 2004, Lean et al. 2006, Fisher 2008). There has been less emphasis on simulations and games for social science quantitative methods teaching, notwithstanding a growing wealth of web-based simulation and game resources, ranging from the highly statistical and encyclopaedic (for instance Rice Virtual Lab, http://onlinestatbook.com/rvls.html, which provides excellent simulations), to simpler sites focused on a single game (for instance stayorswitch.com, a site dedicated to playing and learning about the Monty Hall problem). Where games have been used in the classroom they have largely served as a mechanism for stimulating competition and consequently motivation. See, for instance, recent discussion of ‘gamification’, whereby students gain points, prizes or leader-board places for within-game achievement, most often for answering subject-relevant questions correctly (Glover 2013). Yet games provide benefits that go beyond competition. They facilitate student-centred learning (or learning by doing); provide spaces for creative thought; allow the affective learning environment to be altered, including the student–teacher relationship; and of course they may increase student enjoyment and consequently motivation (for more see Ellington et al. 2013, pp6–8). It is these wider benefits of games that are the focus here. Specifically the game described allows students to develop quantitative skills inductively within a critical sociological perspective.

Top Trumps

How to play

Top Trumps is a children's card game, initially popular in the UK in the 1970s and 1980s. It was revived in the UK in 1999 and introduced into the US and elsewhere (see www.toptrumps.com). Each pack of Top Trumps has a different theme (e.g. racing cars, footballers, Buffy the Vampire Slayer, The Simpsons). Each card pictures an item (super-hero/footballer/type of racing car etc.). This item is then scored using a set of measures specific to the pack's theme. For example, the Buffy cards include the attributes: Combat Daytime (rated 1 to 10); Combat Night-Time (1–10); Fright Factor (1–10); Killer Rating (%); and Intelligence (%). In contrast, footballer top trumps include: Height (cm); Career Goals (N); International Caps (N); Trophies (N); Year of Birth (Year).

To play Top Trumps the pack is dealt out to two or more players. Each player's pack is held face down. The player who goes first looks at their topmost card, without seeing anyone else's cards, selects an attribute and states its value (e.g. ‘Career Goals: 34’). All other players then look at their top cards and state their value on the selected attribute. The player who scores highest in the selected attribute wins the round. The winner takes all of the cards played in that round and places them at the bottom of his or her pack. The round winner then looks at their next card and selects an attribute for the next round.

If there is a draw (two people with an equally high attribute value) the cards from the original round are placed on the table and the player who originally selected the attribute selects an attribute from their next card. Whoever wins this round takes both sets of cards. [Note: When playing in class I alter the rules for a draw. Instead of players laying down their cards after a draw and selecting an attribute from a new card, I ask the original player to select a second attribute from their initial card. This slows down the game as only one round of cards will be won at a time.]

The object is to win rounds and thereby cards. When a player has no cards left to play he or she is out. The eventual game winner is the player who holds all of the cards.

Winning depends on attribute selection, since a card may score highly on some attributes and low on others. For example, if playing with a set comprising footballers, a defender card will have a relatively low score for the attribute ‘career goals’ (since defenders tend not to score goals) but potentially a high score for ‘international caps’ or ‘height’. As play progresses players become familiar with what is ‘high’ and ‘low’ for each attribute and are better able to predict whether the scores on a specific card for a particular attribute are high or low. Winning the game relies on this skill: the ability of the player selecting an attribute to predict which attribute score is likely to be strongest in comparison to others’ scores. For instance, it is only when I have a sense of the spread of scores that I can determine whether 34 career goals is likely to be high enough to win a round and, importantly, whether this score on this attribute is more likely to be a winning score than a score on another attribute (say, 21 international caps). Thus success at Top Trumps requires that players inductively assess the distribution of scores across several attributes. This is a valuable introduction to thinking through introductory statistics and relates to the teaching activities described below.

Producing personalized Top Trumps

Before the first seminar of the module I produced a set of personalized Top Trumps cards in which I placed photos of each of the students on the module onto a playing card containing the student's name. Student photos are frequently made available to staff via virtual learning environments (e.g. Moodle) and can be printed out. Where photos are not available instructors may choose to leave the picture space blank, enabling students to ‘draw’ themselves, or might want to insert cartoon images. An example card is shown below with a picture of Karl Marx (who was not in my class). The version that I used had a brightly coloured (rather than grey) border (a template Word document, containing cards that can be adapted to your own class is available from the author by request).

Figure 1 Example of a personalized ‘Top Trump’ card.

As can be seen the attributes chosen are light-hearted: Genius Rating; Laziness; Number of Pets Ever; Number of Jobs Ever; Height and Strength. Some of these attributes (Genius Rating and Strength) are modelled on the types of attributes found on super-hero Top Trumps cards which focus on characters’ ‘powers’. Height is an attribute often found in sporting hero Top Trumps. Others have more sociological roots (Number of Jobs Ever). And both Laziness and Genius Rating turned a non-serious spotlight on students’ academic prowess. What is most important however is that categories should: a) have numeric responses, ideally with a range of between zero and 20 (or that can be scored as a mark out of ten); b) be easily scored by everyone in the class; c) be willingly scored (thus the light-hearted Genius Rating rather than ‘Intelligence’, a category more usually used in Top Trumps but a quality which may demand more serious self-analysis to score, and consequently more self-exposure); d) vary across students; and e) potentially contain interesting or fun information. Also important, as I shall discuss, was the ambiguity of some of the attributes.

In the first seminar meeting, attended by about 25 students, I passed round the cards and told students to take ‘their’ card. I had produced some blank cards (with no name or photo) in case students who were not on my register attended. Students who did not find their card in the pack were instructed to take one of these blanks, write in their name and draw themselves in the space provided – some rather comical stick-figures and lopsided faces resulted. Each student was then instructed to fill in their own scores. This almost immediately turned into a discussion of the meaning of several of the categories. Strength was especially problematic. “What kind of strength to do you mean?” someone asked, “Emotional or physical strength – I don't understand?” I responded that they should answer as they saw fit. More importantly this generated a short discussion that harkened back to the first lecture of the module (given that morning) in which the problems of quantifying social phenomena had been introduced. We talked about which of the categories were more or less problematic to quantify. Height was straightforward (although some confusion emerged with European students using centimetres and UK students, feet and inches). Number of Jobs Ever was easy for those who had had few, but difficult for students who had had over ten. Moreover it was seen as debatable that someone who had held three jobs over a single summer had held three times more jobs than someone who had held the same job for several years, and how to count babysitting generated fairly heated discussion. Similar problems emerged with regard to pets since one student had had a large number of goldfish, which other students were unconvinced ‘counted’ as real pets. Thus in attempting to quantify some simple attributes we were able to enter into a discussion about the meaningfulness of quantification. This addressed students’ lack of conviction that numbers were important by allowing them to see that in this de-contextualized game it was difficult to decide how to count, and that context was necessary for determining what ‘counted’ and what did not. It also highlighted the differently problematic nature of different types of counts (for example that Height was relatively unproblematic).

Playing the game in class

After students had filled out their cards they were put into three groups. Each group collected together the cards of those in their group and placed these in a pile (face down). The different groups then played each other at Top Trumps. This part of the activity had three purposes. First, the game simply served as an ice-breaker. Second, because students were in effect playing using themselves as characters (and as cards changed hands sometimes losing out to the card representing themselves) it became quite common for them to challenge the scores when these were especially high or low, sometimes re-opening discussions about the meaning of different counts. This led to good-humoured banter and allowed students to express themselves freely in my presence, an important precedent to set in the first meeting. The banter also gave students a chance to get rid of some of their maths-anxiety tension, allowing less maths-able students to speak with confidence. Third, as suggested above, the game allowed students to start to get a feel for the spread of scores and to see that they can discover the distribution – high, low and middling scores – for themselves. Midway through the game I initiated a brief discussion of this last aspect of the game, asking students to contribute ideas about average scores for different attributes and discuss how they arrived at the responses that they gave. Having several attributes scored 1 to 10 was useful here as it allowed us to compare the distribution of scores with a formally equivalent range. This discussion nicely set up the next set of Top Trump activities.

Using Top Trumps to introduce statistics

After one team had emerged victorious from the game I collected the pile of cards, divided the class into groups of five and redistributed the cards (giving five to each group). I then delivered a series of short review lectures on averages (mean, median, and mode); dispersion and variability (quartiles and standard deviation); and finally, the normal distribution and z-scores. After covering each topic I stopped and the groups were told to use their cards to calculate the relevant measures (for example work out the mean, median and modal values for their five characters’ Laziness Ratings). This is where it became important that the scores for each category involved relatively low numbers, enabling simple mathematical calculation. Using cards (rather than a list of numbers) for calculations was especially useful when it came to thinking through measures of central tendency: the median could be found by rearranging cards into the ‘right’ order and picking out the middle card and the mode by putting the cards into piles matched by score and selecting the biggest pile. The fact that there were potentially six different categories in which averages could be calculated meant that groups that finished the calculations for one category had plenty of material to keep them occupied while I helped other groups. As each group has a different set of five cards, all with the same six attributes, Top Trumps can also be used to introduce sampling distribution, but this was not a topic addressed within this week one seminar.

Because we were using cards representing their classmates and scores that they had contributed themselves, students found the results they produced relevant and interesting, and we could talk about the substantive meaning of these easily and jokily, discussing average student laziness and standard deviations of genius. As has been noted (Schacht & Stewart 1990, Schacht & Stewart 1992), humour is an excellent tool in teaching statistics and reducing anxiety. Moreover, students asked questions of me and one another, and left the classroom smiling and joking.

The seminar lasted two hours. In this time I got to know the students and they became familiar with me and one another – something that you would expect from any good ice-breaking exercise. We had, however, also covered a considerable amount of key material for an introductory session and I was able to develop a sense of different students’ quantitative and sociological abilities. Critically, while some of the statistical material that we covered was ‘basic’ essentially comprising a refresher, couching this material within a game meant that more statistically able students, who might simply have switched off, remained engaged providing support to less able students; an important precedent.

Evaluation

In evaluation forms completed at the end of the ten week course students were asked to comment about the three ‘practical seminars’, the one described here that involved Top Trumps and two others – one which employed personal ads to introduce sampling, coding, and the construction of contingency tables (Rushing & Winfield 1999) and another in which students produced posters to visually represent published multivariate analyses. A question asked whether these seminars were ‘useful/helpful’ and student responses included: “Yes and they were fun”; “useful and enhanced understanding of stats”; “[I] enjoyed the practical seminars and learned more in them than first anticipated!”; “Useful and good fun”; “These were the most useful ways of operationalizing the concepts we were learning”. Other responses echoed these and no negative reactions were received. Both more and less statistically able students were enthusiastic about the Top Trumps session. Thus students found play and hands-on sessions enjoyable and believed that these had usefully contributed to their understanding of quantitative methods.

Although it is difficult to unpick causality, these sessions also appear to have contributed to a positive response to quantitative methods. For instance, despite their trepidation on entering the module, nearly half of students described either the module or quantitative methods generally as ‘fun’ or ‘enjoyable’ in open-text responses within their module evaluations. Others used words like ‘interesting’ and ‘stimulating’. Several mentioned their loss of statistics anxiety (e.g. “I don't feel scared of quants, and feel positive about them and hopefully will use some simple stuff in [the] future”). More confident students described instances when they had already used, or were planning to use, quantitative methods in their research.

These evaluations cannot of course be entirely attributed to the development of hands-on activities or games, or specifically the use of Top Trumps. Nevertheless, the counterfactual argument – that without activities in which play was encouraged it is highly unlikely that students would have described the module as ‘fun’ – is logically compelling.

The above discussion relates to the use of Top Trumps within a postgraduate module and seminar. I have, however, also worked with two teaching assistants (both PhD students) to incorporate personalized Top Trumps into a required first year undergraduate sociology class. The teaching assistants were responsible for seminar teaching and so they ran a series of sessions in which Top Trumps was employed, basing the seminars on my instructions, as above. Both instructors reported that the game was easy to introduce and enjoyable to play with groups of 15–30 students. The main difference in their experiences with undergraduates in comparison to mine with postgraduates, was that undergraduate students were less vocal in critiquing the meaning of categories and slower to relate discussion over the validity of measurement to broader issues in sociological methodology. Undergraduates were, however, quite able to make such connections once prompted to think about them by their instructors.

Conclusion

Top Trumps is a simple and enjoyable game to play, requiring no prior knowledge to understand the rules. It is also easily customizable: it would, for instance, be possible to create a pack of ‘Sociological Theorists’; ‘Media Conglomerates’; or other sociologically related themes if instructors preferred these. The game and activities described here inductively introduce basic ideas of central tendency and distribution, the essential building blocks of statistical reasoning, but topics which are not always sufficiently understood (Garfield & Ben-Zvi 2007, p386). The game also facilitates discussion of social quantification. Taking up two hours of a course with a ‘game’ may appear frivolous, but is beneficial when it reduces statistics anxiety, encourages student voice, and legitimates a critical approach. As such, play activities can transform a ‘dull’ and ‘scary’ course into one that students find ‘interesting’, ‘useful’ and ‘fun’, and produce material that is enjoyable to teach. Given research showing that positive instructor interactions do a lot to decrease statistics anxiety (Onwuegbuzie & Wilson 2003, pp203–4), this is likely to create additional benefits. Moreover, since a corollary of a module being fun is that students are at ease with one another and with the instructor it may be that the inclusion of games means that at the (inevitable) moments in a quantitative methods module when students feel confused they are less likely to completely disengage and more likely to seek support and regain interest in the subject.

Since the 1999 re-launch of Top Trumps the game's educational benefits have been highlighted in a series of exercises for school teachers collated by TES Connect (see www.tes.co.uk/article.aspx?storyCode=6153662). These exercises are interesting but differ to that suggested here in two ways. First they tend to use Top Trumps like flash-cards, to facilitate students’ retention of the information presented on the cards and do not emphasize the potential of the game to develop an inductive understanding of range and distribution. Second, the school-focused exercises adopt a more positivist relationship to the attributes on the cards, whereas this exercise is designed within a critical sociological perspective, in which questions about social categorization and quantification are welcomed.