Afari, Aldridge, & Fraser

ERNEST AFARI, JILL M. ALDRIDGE and BARRY J. FRASER

EFFECTIVENESS OF USING GAMES IN TERTIARY-LEVELMATHEMATICS CLASSROOMS

Received: 22 August 2011; Accepted: 8 March 2012

ABSTRACT. The primary focus of this study was to investigate the effectiveness ofgames when used in tertiary-level mathematics classes in the United Arab Emirates. Ourstudy incorporated a mixed-method approach that involved surveys (to assess students’perceptions of the learning environment and attitudes towards mathematics), interviews,observations of classes and narrative stories. A sample of 90 students from 3 tertiary-levelinstitutions in Abu Dhabi participated in the study. In-depth qualitative data providedinformation about the introduction and use of games in mathematics. A narrative, basedon classroom observations of students playing Jeopardy!-type mathematics games,provided insights into games in action in the classrooms. The data were analysed toexamine students’ interactions during the games and to triangulate, clarify and explainstudents’ responses to the learning environment and attitude questionnaires. To examinepre–post differences in students perceptions of the learning environment and theirattitudes, 2 questionnaires were administered to students before and after the introductionof games. Pre–post differences for 3 of the 6 learning environment scales (TeacherSupport, Involvement, Personal Relevance) and both attitude scales (Enjoyment ofMathematics Lessons and Academic Efficacy scales) were statistically significant.Information obtained from interviews with students and teachers were used to explainthe pre–post differences.

KEY WORDS: academic efficacy, attitudes, mathematics games, narrative, United ArabEmirates, What Is Happening In this Class? (WIHIC)

INTRODUCTION

The United Arab Emirates is located at the southern tip of the ArabianGulf and has a total area of 83,600 km2. The country forms a border withSaudi Arabia, Qatar and Sultanate of Oman. The United Arab Emirates isa federation of seven independent states, namely Abu Dhabi, Dubai,Sharjah, Ajman, Umm al-Quwain, Ras al-Khaimah and Fujairah. It hasbeen noted with concern that, within the United Arab Emirateseducational system, poor-quality instruction and learning exist in sometertiary-level institutions and that, on the whole, teaching methods are

Electronic supplementary material The online version of this article (doi:10.1007/s10763-012-9340-5)contains supplementary material, which is available to authorized users.

International Journal of Science and Mathematics Education (2012) 10: 1369Y1392# National Science Council, Taiwan 2012

based on rote memorization (Gaad, Arif & Scott, 2006; Shaw, Badri, &Hukul, 1995). Innovation on the part of teachers is often viewed asdifficult because of the demands of complying with a centralisedcurriculum and evaluation system enforced by administrators and schoolinspectors. Explanation and discussion are the most common teachingmethods, with little use of small-group, individualized, lecturing,experimental, laboratory or role-playing methods.

To overcome this, the Ministry of Education in the United Arab Emirateshas adopted Education 2020, a series of 5-year plans, up to the year 2020,designed to introduce advanced education techniques, improve the innova-tive skills of teachers and enhance the self-learning ability of students.Research indicates that improving classroom environment has the potentialto improve student outcomes (Dorman & Fraser, 2009; Fraser, 2012). It isagainst this backdrop, and with the hope that the uses of games would fit intoAbu Dhabi’s new Education 2020, this study of the effectiveness ofintroducing mathematics games at the tertiary level was undertaken.

BACKGROUND

Mathematics Games

Students often lack motivation when it comes to learning mathematics, andthis, in turn, can affect their achievement. The results of past studies suggestthat the introduction of games in mathematics can improve students’attitudes (Bragg, 2007; Massey, Brown & Johnston, 2005), but this has notbeen systematically verified in the United Arab Emirates at the tertiary level.Past research has indicated that when teachers design, develop andimplement innovative teaching methods in their classrooms, they are likelyto capture students’ interests and optimise their learning outcomes (Chandra& Fisher, 2009). Past research indicates that games have the potential todraw students into the learning process and to encourage them to participatethrough a more interactive environment (Gosen & Washbush, 2004;Proserpio & Gioia, 2007; Zantow, Knowlton & Sharp, 2005).

United Arab Emirates citizens, after completing high school, haveaccess to higher education at a variety of government and privateinstitutions. In all of these tertiary institutions, students are required toundergo a compulsory 1-year foundation programme that includesmathematics. The foundation programmes are designed to bridge thegap between the secondary and college-level education.

There is a significant body of research to support the potential of usinggames as an educational tool (Annetta, Cheng & Holmes, 2010;

ERNEST AFARI ET AL.1370

Paraskeva, Mysirlaki & Papagianni, 2010) and to complement traditionallectures for enhancing students’ learning (Kiili, 2005; Tan, 2007; Tan,Tse & Chung, 2010). As an educational tool, games have the capacity toengage and motivate students (Paraskeva et al., 2010; Prensky, 2001), andtherefore, the learning from games is more likely to be retained (Annettaet al., 2010). The aim of our study was to evaluate the effectiveness ofgame activities in mathematics instruction at tertiary institutions in theUnited Arab Emirates in terms of changes in students’ learningenvironment and attitudes towards mathematics.

Learning Environment

Because students spend up to 20,000 h at educational institutions by thetime they finish university (Fraser 2001), their reactions to theireducational experiences—specifically their learning environments—areof significance. The term learning environment refers to the social,physical, psychological and pedagogical context in which learning occursand which affects student achievement and attitudes (Fraser, 2007, 2012).Results of studies conducted over the past 40 years have providedconvincing evidence that the quality of the classroom environment inschools is a significant determinant of student learning (Fraser, 2007,2012). Students learn better when their perceived classroom environmentis more positive (Dorman & Fraser, 2009).

In 1936, Lewin’s (1936) field theory acknowledged that the environ-ment and its interaction with an individual’s personal characteristics arestrong determinants of behaviour. His formula, B = f(P, E), depicts humanbehaviour (B) as a function (f) of the person (P) and the environment (E).

Although Murray (1938), like Lewin, was also attracted to the internaldeterminants of behaviour, he asserted that Lewin was interested only in theexternal determinants of behaviour and had overlooked developing a theoryof drive or need. To this end, Murray’s needs-press model corrected theomission by including the situational variables found in the environment andwhich account for a degree of behavioural difference. Murray made adistinction between ‘needs’ and ‘press’, defining needs as ‘…a force …which organizes perception, apperception, intellection, conation, and actionin such a way as to transform… an existing, unsatisfying situation’ (Murray,1938, p. 124) and press as an external influence on motivation. Murray alsomade a distinction between alpha press (the environment as observed by anexternal observer) and beta press (the environment as perceived by peoplethemselves). In this way, Murray’s needs-press model complementedLewin’s formula by depicting personality characteristics as goal oriented

EFFECTIVENESS OF USING GAMES 1371

and environmental characteristics as external (either positive or negative) tothe personality needs of an individual. Lewin and Murray are widelyaccredited with having established the groundwork for research onclassroom learning environments. Later, Murray’s beta press were furtheredrefined by Stern, Stein & Bloom (1956) as being either private beta press (anindividual’s view of his or her environment) or consensual beta press (thecollective view of a group as a whole).

The first learning environment questionnaires appeared in the late1960s. The Learning Environment Inventory was developed by Walberg(1968) as part of the research and evaluation activities of Harvard ProjectPhysics (Anderson & Walberg, 1968). Walberg’s research demonstratedthat classroom climate could be reliably and economically measured withthe use of high-inference measures (Anderson & Walberg, 1974). TheClassroom Environment Scale (CES) was independently developed ataround the same time, at Stanford University, by Moos & Trickett (1974).The CES was based on research involving perceptual measures of avariety of human environments, such as psychiatric hospitals, correctionalfacilities, university residences and work milieus (Moos, 1974, 1979).

Since this time, researchers have developed numerous questionnairesdesigned to assess students’ perceptions of a range of dimensionspertinent to the learning environment (Fraser, 2007, 2012). Our studydrew on past evaluations of educational innovations (Maor & Fraser,1996; Wolf & Fraser, 2008; Nix, Fraser & Ledbetter, 2005; Martin-Dunlop & Fraser, 2008) from the field of learning environments ininvestigating the effectiveness of games in the mathematics classrooms.

Students’ Attitudes

Learning clearly has an affective component, and according to Kind,Jones & Barmby (2007), developing positive attitudes is important forstudents’ achievement. One definition that is commonly used to describeattitudes includes the three components of cognition, affect and behaviour(Kind et al., 2007; Rajecki, 1990). These three components are defined byReid (2006, p. 4) as knowledge about the object, or the beliefs and ideascomponent (cognitive); a feeling about the object, or the like or dislikecomponent (affective) and a tendency towards action, or the objectivecomponent (behavioural).

Although some researchers have defined attitudes solely in terms of theaffective component (George, 2000; Germann, 1988), Fishbein & Ajzen(1975) viewed attitudes as being formed spontaneously and, inevitably,involving the attributes of an object. Attitudes or the affective component


of attitudes, therefore, are linked to the beliefs that a person holds (Kindet al., 2007). It is with this in mind that the definition for attitude, used forour study, was the feelings that a person has about an object, based ontheir beliefs about that object. Our study aimed to determine whether ornot the introduction of Jeopardy!-type games can help to improvestudents’ enjoyment of mathematics lessons (as well as the quality ofthe classroom learning environment).

Jeopardy-Type Games

Jeopardy! is an American quiz show that features topics such as history,literature, the arts, pop culture, science and sports. The show has a uniquequestion-and-answer format in which contestants are presented with cluesin the form of answers and must phrase their responses in question form.

Based on the television quiz show, Story (2007), a mathematics professorat Akron University, USA, recognised the potential of using games in theclassroom and developed a mathematics games that is based on the popularAmerican television game show Jeopardy! In our study, these Jeopardy-typegames were modified to involve teams of students (usually two) within theclass. A computerised jeopardy game board is used with up to fourmathematical concepts, each with a series of point values underneath. Ingeneral, the higher the point value, the more difficult the question orproblem. When a point value is selected by a team of students, a secondscreen appears with the associated problem or question. Once the question isrevealed, themembers of the teamwork together to answer it. If the answer iscorrect, they earn the point value of that question, and if the answer isincorrect, the point value is subtracted from the total. A group that gets thecorrect answer is then expected to present the solution to the class.

METHODS

Participants

The sample for our study involved a total of eight classes containing 90students, 38 of whom were females and 52 were males, attending threetertiary-level public institutions located in Abu Dhabi, the capital andlargest emirate (by area) of the United Arab Emirates. The sample wasrandomly selected from the colleges in Abu Dhabi.

All of the participants were in the foundation programmes of theirrespective university, preparing for careers in primary school teaching,engineering and business. The participants of the three institutions


differed in terms of the mathematical abilities of the students. Thosestudents attending the primary school teaching college, for the most part,had majored in Arts in high school and were considered to have anintermediate level of mastery in mathematics. However, the participantsin the engineering college had majored in science at high school and wereconsidered to have a strong background in mathematics. The participantsin the business college were all mature age students who had left schoolprior to completion, and therefore, they were considered to have a lowlevel of mathematics ability.

Approximately 95 % of the students were United Arab Emiratesnationals, and the remaining 5 % was made up of other Arab nationals.The students’ ages ranged between 18 and 35 years. The selection of theclasses was based on the willingness of the teachers to trial the use ofJeopardy!-type games. Overall providing a sample of 90 students whowere attending classes that used these games (from the three tertiary-levelpublic institutions) made up the sample.

Observations

The study was largely qualitative in nature, involving the gathering ofdata using a range of methods during the implementation of theJeopardy!-type games, including observations, interviews with studentsand teachers, and narratives. Observations of classrooms were used toassess how appropriate the introduction of games was to the learning ofmathematics in the college context in the United Arab Emirates. Thisinformation helped us to detect learning problems as they arose during thegames activities and to examine the students’ approaches to the use ofgames. The observations added to the richness of the data base as awhole. All eight of the classes that were exposed to mathematics gameswere observed three times during the 6-week period (once at thebeginning, once in the middle and once at the end). The observationsfocussed on the students’ and teachers’ reactions to the games and howthese reactions influenced the learning environment and students’attitudes. Also observations were made of the interactions betweenstudents and how they worked together as they played the Jeopardy!-typegames. Observations were video-recorded and a narrative was written toprovide insights into games in action in the classrooms.

Interviews with Students and Teachers

Twenty students (seven females and 13 males), who were exposed tomathematics games, volunteered to be interviewed. The interviews took


place once at the end of the 6 weeks and involved a semi-structuredformat, with a fixed set of questions that helped to guide us and toprovide a degree of consistency across all interviews, whilst ensuring adegree of flexibility (Creswell, 2009). These interviews included ques-tions, based on the observations of the classrooms, to help us to betterunderstand the students’ comprehension of, and interaction with, thematerials.

In-depth interviews were conducted with the teachers who used themathematics games in their classes. These interviews sought teachers’views of the games, and like the student interviews, teacher interviewswere semi-structured and focussed on the successes and problems thatwere encountered during their implementation.

Narratives

A narrative, based on the classroom observations, was written to providethe reader with insights into the classrooms that were exposed to theJeopardy!-type games. Clandinin & Connelly (2000) defined narrative asthe study of the ways in which humans experience the world. Carter(1993) asserts that the attractiveness of story in contemporary research onteaching is that it is grounded in the notion that story represents a way ofknowing and thinking that is particularly suited for explicating issues. Tocapture the essence of classroom life in the classes that were observed,narratives were written (as recommended by Clandinin & Connelly,2000). Following the narratives, a commentary was used to interpret thenarratives and to help to make sense of data from interviews andobservation, as recommended by Polkinghorne (1995).

During the writing, the authors were aware of the need to representresearch participants in a socially honest manner in written text.According to Stacey (1988), there is a major difficulty with representingthe experiences of others. She argues that, despite the desire to ‘engage inegalitarian research’, there is a contradiction in the power relationshipbetween the researcher and the subject that always poses a risk of betrayaland manipulation. Lincoln & Denzin’s (1994) description of the ‘fifthmoment’ in qualitative research encompasses issues associated withrepresentation and legitimisation, which we addressed in two ways. First,we ensured that any quotations included in our narrative were in factspoken by the people portrayed. Second, the first author placed himselfwithin the texts. In doing so, he acknowledged that this narrative andsubsequent commentary was, in fact, his interpretations of situations,experiences and interviews. We attempted to address the important issue


of legitimisation in the writing of the texts in three ways. First, wetriangulated data from different sources, following Denzin & Lincoln’s(1994, p. 2) advice that ‘… the use of multiple methods, or triangulation,reflects an attempt to secure an in-depth understanding of the phenomenon inquestion. Objective reality can never be captured. Triangulation is not a toolor a strategy of validation, but an alternative to validation.’ Second, we askedmembers of the group involved to read the stories to verify its authenticity.Third, we attempted to represent those whomwe studied and their classroomenvironment using verisimilitude (i.e. to resemble truth or reality).

The present study involved a pre–post design in which the initialcollection of the data was carried out before Jeopardy!-type games wereintroduced to all of the 90 students over a 6-week period. At the end ofthe 6 weeks, the questionnaires were readministered to the students toassess whether there were changes in students’ perceptions of the learningenvironment and their attitudes towards mathematics.

Instruments

The What Is Happening In this Class? (WIHIC; Aldridge, Fraser &Huang, 1999) questionnaire was used to assess students’ perceptions ofthe learning environment. The WIHIC incorporates the best features ofexisting instruments, adapting their salient scales and combining themwith particular aspects of constructivism and other relevant factorsoperating in contemporary classrooms to bring parsimony to the field oflearning environments research (Aldridge et al., 1999; Dorman, 2008).For the present study, the WIHIC was modified by omitting two of theoriginal scales (Investigation and Task Orientation), as these were notconsidered to be pertinent to the context of the study and adding one scale(Personal Relevance) as this aspect was considered to be important.Table 1 provides a description and sample item for the scales used in thepresent study. The reliability and validity of the WIHIC have beensupported for samples in Taiwan and Australia (Aldridge et al., 1999), theUSA (Ogbuehi & Fraser, 2007; Wolf & Fraser, 2008), Indonesia andAustralia (Fraser, Aldridge & Adolphe, 2010), Singapore (Chionh &Fraser, 2009; Khoo & Fraser, 2008), Korea (Kim, Fisher & Fraser, 2000)and United Arab Emirates (Afari, Aldridge, Fraser & Khine, in press).

Two scales were used to assess students’ attitudes, namely Enjoymentof Mathematics Lessons and Academic Efficacy. The Enjoyment ofMathematics Lessons scale, consisting of eight items, was adapted fromone scale in the Test of Science-Related Attitudes (Fraser 1981) bySpinner & Fraser (2005). The second eight-item Academic Efficacy scale


was based on Jinks & Morgan’s (1999) Student Efficacy Scale. A scaledescription and a sample item for the WIHIC, Enjoyment of MathematicsLessons and Academic Efficacy scales can be found in the Table 1.

RESULTS

Our results are based on the triangulation of quantitative data andqualitative information. First, a narrative, based on observations in all ofthe classes that were exposed to the games, is used to provide anunderstanding of the games in action. Using a pre–post design,

TABLE 1

Scale description and sample item for each scale in the modified What Is Happening Inthis Class? questionnaire and attitude scales

Scale Description Sample item

LearningEnvironment

The extent to which …

Student Cohesiveness … students are friendly andsupportive of each other.

I make friends amongstudents in this class.

Teacher Support … the teacher helps, befriendsand is interested in students.

The teacher helps me whenI have trouble with the work.

Involvement … students have attentiveinterest, participate indiscussions and enjoy the class.

I explain my ideasto other students.

Cooperation … students cooperate witheach other during activities.

When I work in groups inthis class, there is teamwork.

Equity … the teacher treats studentsequally, including distributingpraise, questions andopportunities to be includedin discussions.

The teacher gives as muchattention to my questions asto other students’ questions.

Personal Relevance … there is a link betweenwhat is taught and students’out-of-school experiences.

This class is relevant to mylife outside college.

AttitudesEnjoyment ofMathematics Lessons

… students enjoy theirmathematics lessons.

Lessons in mathematicsare fun.

Academic Efficacy … students have confidence intheir academic competence.

I find it easy to get goodgrades in mathematics.

All items used the response alternatives of Almost Always, Often, Sometimes, Seldom and AlmostNever


questionnaires were administered before and after the introduction ofmathematics games. Pre–post changes on learning environment andattitude scales were used as an index of effectiveness. Finally, interviewswith students who participated in the games activities were conducted tohelp to explain the quantitative data.

The following narrative is based on a number of visits to differentclasses in which the games had been introduced. For each of the teachers,we created a Jeopardy!-type game (a PDF interactive, based on the topicfor the week) and worked with teachers to ensure that they were confidentabout using the game with their students. Because the conditions andobservations in these classrooms bore a great deal of similarity, thisnarrative reports a typical lesson involving Jeopardy!-type games. Thenarrative is provided below and then interpreted with a commentaryimmediately after, following the approach recommended and used inother learning environment studies (Aldridge et al., 1999; Aldridge,Fraser & Ntuli, 2009).

I met Fatima, the teacher of the class that I was visiting, at the college’s staff room. As wewere already known to each other, the atmosphere was relaxed. As we walked to theclassroom, Fatima, an experienced mathematics teacher of 12 years, told me that she iskeen to try new teaching methods but does not do so because of time constraints.Although Fatima had read of different methods of teaching, she had not tried them for fearthat her students’ grades might be jeopardised.When we arrived at the class, it was about 10 minutes before the start of the lesson. Thestudents were aware that I was coming and most of them were already seated when we gotthere. This was to be the first lesson involving jeopardy games to which they had beenexposed. The classroom, as with all of the college classrooms in the UAE, was wellequipped with an interactive white board, an LCD projector and a desktop computer forthe teacher’s use. The 12 students were all male UAE nationals, dressed in the traditionalwhite ‘kandoura’ (robe) and ‘ghutrah’ (head cloth) with a black ‘aqal’ (rope) around theghutrah. The students were aged between 19 and 23 years and were studying mathematicsas part of their engineering program. When Fatima introduced me, they shouted thecustomary ‘Welcome to our class’.In readiness for today’s lesson, Fatima had assigned the students to two groups that wererelatively similar in terms of the number of low and high achievers. At this point, shereminded the students about the groups to which they had been allocated, and instructedthem to arrange the tables so that they were facing each other. During the shuffle of desksand chairs, there was a great deal of excitement and noise. This was something new, astraditionally in UAE settings, desks are arranged so that students face the front of theclass.Once the students were settled, Fatima explained the rules of the game. She told them thattoday’s game was based on trigonometric identities, a topic that they had studied in theprevious lesson. Fatima started the session with some revision and ‘warmed’ up thestudents with problems similar to the ones that they would encounter during the game.The revision session was fast, lasting less than 10 minutes, and the students listened


intently, apparently keen to give their team an advantage. Fatima then proceeded tointroduce the Jeopardy!-type game.The game board was projected onto the whiteboard and Fatima carefully explained therules. She explained that the game included questions related to trigonometric identitiesand involved four categories of (1) Fundamental Identities, (2) Using FundamentalIdentities, (3) Verifying Identities and (4) Applying the Cosine and Sine difference toVoltage. As she read each one out, she pointed to the column that included questions forthat category. She then indicated the four blocks beneath each category, and explained thatthe numbers on each were the point value for each of the questions. The higher the pointvalue, the more difficult the question was likely to be. She went on to explain that eachgroup would take turns in selecting a category and a question and that, once the group hadselected a category, she would click on the cell and the corresponding question wouldbecome visible.Once Fatima was satisfied that the rules of the games had been understood, she flipped acoin to help to decide which of the two groups (Group 1 or Group 2) would make the firstselection. When the toss indicated that Group 2 had won, students cheered loudly. Thehush from the members of Group 1 made their disappointment clear. Fatima’s quickreassurance, that the first selection did not have any bearing on who would win the game,helped them to overcome their disappointment.The second group was instructed to select a category and a block. Students wereclearly hesitant and, after considerable deliberation, they decided to select thefundamental identities category (which included questions related to expressing onefunction in terms of another) and the cell with the lowest value of points—clearly‘testing the water’.Fatima clicked on the selected block and read out the question: ‘Express cos x in terms oftan x’. The group began to talk excitedly to each other but, after a couple of minutes whenit became clear that students were confused about how to answer the question, Fatimastepped in to give them a clue—because sec x is related to both cos x and tan x byidentities, they should start with 1 + tan2x = sec2x. With this clue, the members of thegroup proceeded to try to solve the problem individually. Fatima encouraged the othergroup also to try solving the problem. The members of Group 2 began to compare theiranswers and, as some of the answers were different, students started to explain to eachother how they had calculated their answer. It was clear from the discussion generatedwithin the group that students were forced to negotiate their answers and, if convinced thatthey were correct, justify and persuade the other group members that theirs was the one tochoose. Once the group members had agreed on an answer, they shared it with Fatima. Itwas correct and the group jumped and shouted boisterously. The value for that questionwas given to the team and Fatima went on to ask one of the team members to solve theproblem on the board for the benefit of all of the students.It was now Group 1’s turn to make a selection. Fatima also provided this group with a hintwhen students appeared to be struggling. After several minutes of sharing and discussingideas, they agreed on an answer, which was correct. Again there was much shouting andhugging.Both teams had to answer eight questions. As the game progressed, students became moreconfident. After all of the questions have been answered, the game was declared a tie.Each of the teams promised to win the next time that they play the game. The studentsexpressed how much they had enjoyed playing the game and asked Fatima to let themplay games after every lesson.


The narrative describes how the members of the group worked togetherto solve problems. The amount of talking and excited hand gestures, asstudents tried to decide which answer was correct, suggested a high levelof engagement among the students. According to Park (2005) and Finn &Voelkl (1993), one of the most persistent issues in improving studentlearning in mathematics is the lack of student engagement. A studyconducted by Park (2005) indicated that higher levels of studentengagement had positive effects on student academic growth inmathematics.

In addition to being engaged, students exhibited excitement, suggestingthat the games made the students more motivated. All of the teachers whowere interviewed felt that games had made their students more motivatedto learn and to be involved. One teacher stated: ‘I have enjoyed playinggames with my students because the students became more motivated.’Another teacher commented: ‘I think playing games affects the studentsin a very positive way. When using traditional methods of teaching, someof the students think that mathematics is dry and uninteresting but, withthe games, they realise that math can be fun.’ A third teacher commentedthat ‘the advantage of using the games is that it makes my students moremotivated’.

The narrative suggests that the use of games provided opportunities forstudents to interact with each other. Research indicates that studentinteraction through classroom discussion and other forms of interactiveparticipation is foundational to deep understanding and is related tostudent achievement (Bruce, 2007). In a study of mathematics classroomactivity, student interaction was one of the essential characteristics ofeffective mathematics teaching (Ross, McDougall, Hogaboan-Gray &LeSage, 2003).

According to the narrative, students shared ideas and helped oneanother, and if the answer was correct, the teacher would ask one of themembers of the group to present the solution to the rest of the class.Alternatively, if the answer was incorrect, the teacher explained thesolution to the whole class. According to Bruce (2007), encouragingproductive argumentation and justification in class discussions leads togreater student understanding in mathematics. As students played theJeopardy!-type games in class, they continuously argued and justifiedtheir solutions before agreeing on an answer.

The teachers who introduced the games in their classes commented ontheir 6-week experience with the Jeopardy!-type games. Like mostteachers, these teachers faced many challenges related to the complexitiesof teaching mathematics in ways that they had not experienced


themselves when they were students. These teachers lacked any sustainedprofessional development opportunities in addition to a lack of time,especially in the face of curricular demands. The interview data suggestthat the introduction of games changed the teachers’ perceptions. Whenasked to briefly describe whether they enjoyed playing mathematicsJeopardy!-type games with their students, one of the teachers commented:‘I enjoyed it a lot and I think my students enjoyed it too. I think thereason that they enjoyed it is that they were all able to participate andreally had fun experiencing something other than classroom lecturing andlistening.’ Another stated: ‘I enjoyed it very much. It is good to see thestudents involved in team work with each other and the designatedspeaker to get the final answer.’

All of the teachers felt that the mathematics games were beneficial butthat they had not used them because of time constraints and the pressuresassociated with having to complete the syllabus. When asked to relaywhat they considered to be the benefits and pitfalls of using Jeopardy!-typegames in the classroom, one teacher stated that ‘I see lots of benefits becauseI think that the students find it different, and it makes them more active asactive learners. The pitfall will be the timing.When you are tight with timing,it is difficult to play many games with them.’ Another disadvantageperceived by a teacher was that ‘the class sometimes becomes too noisyduring the game playing. The students often seem to be aggravated and shoutout the answers—not fighting, but raising their voices at each other. It’s just amatter of noisy classroom, that’s all.’

According to the narrative, the teacher gave the students support duringthe game, by providing hints and ideas to help them to solve the problems. Itwas clear from observing this class that the game promoted studentmotivation. The students enjoyed playing the Jeopardy!-type game andurged their teacher to play mathematics games with them more often.

Pre–Post Differences in Learning Environment and Attitude Scores

The jeopardy games were introduced to 90 students in eight classes over a6-week period. Before the introduction of the games and at the end of the6 weeks, the WIHIC and attitude scales (see Table 1) were administeredto all students. To provide a measure of the effectiveness of themathematics games, differences between students’ pretest and posttestscores on the WIHIC, Enjoyment of Mathematics Lessons and AcademicEfficacy scales were used. Pre–post differences were explored using aone-way multivariate analysis of variance (MANOVA) with repeatedmeasures (using the student as the unit of analysis). The set of six


learning environment scales and the two attitude scales constituted thedependent variables, and the testing occasion (pretest/posttest) constitutedthe independent variable. Table 2 reports the average item mean, averageitem standard deviation, effect size and MANOVA results for pre–postdifferences for each of the WIHIC and attitude scales. The average itemmeans indicate that, for all six WIHIC scales, students’ scores increasedsomewhat during the use of games.

Because the multivariate test (Wilks’ lambda) revealed significantpretest–posttest differences overall, the ANOVA with repeated measureswas interpreted for each individual WIHIC and attitude scale (seeTable 2). Statistically significant pre–post differences (p G 0.05) emergedfor three of the six WIHIC scales (namely Teacher Support, Involvementand Personal Relevance) and for both the Enjoyment of MathematicsLessons scale (p G 0.01) and the Academic Efficacy scale (p G 0.01).

To examine the magnitudes of these pretest–posttest differences, aswell as their statistical significance, effect sizes were calculated in termsof the differences in means divided by the pooled standard deviation (asrecommended by Thompson, 1998, 2001). The effect sizes, for those

TABLE 2

Average item mean, average item standard deviation and difference (effect size andMANOVA with repeated measures) between pretest and posttest scores on each modified

What Is Happening In this Class? and attitude scale

Scale

Averagemean item

Average itemstandarddeviation Difference

Pretest Posttest Pretest PosttestEffectsize F

Learning EnvironmentStudent Cohesiveness 4.20 4.23 0.66 0.68 0.02 0.46Teacher Support 4.00 4.19 0.78 0.73 0.12 2.51*Involvement 3.73 3.93 0.67 0.66 0.15 2.88**Cooperation 3.97 4.04 0.78 0.75 0.05 0.82Equity 4.28 4.35 0.62 0.66 0.05 1.07Personal Relevance 3.59 3.86 0.78 0.70 0.18 2.68**AttitudesEnjoyment of MathematicsLessons

3.60 3.86 0.99 1.00 0.13 2.87**

Academic Efficacy 3.74 3.97 0.89 0.88 0.13 2.81**

N = 90 student in eight classes present for both the pretest and posttest*p G 0.05; **p G 0.01


scales for which pretest differences were statistically significant, rangedbetween 0.12 and 0.18 standard deviations, which are considered to be‘small’ according to Cohen’s (1992) criteria. According to the quantita-tive data, the use of games in the mathematics classroom facilitated asomewhat more positive learning environment (in terms of more TeacherSupport, Involvement and Personal Relevance) and also somewhat greaterEnjoyment of Mathematics Lessons and Academic Efficacy.

Explaining Pre–Post Differences

Analyses of the information collected during interviews and observationshelped to explain the statistically significant pre–post differences forTeacher Support, Involvement, Personal Relevance, Enjoyment ofMathematics Lessons and Academic Efficacy. The effectiveness of themathematics games—particularly in terms of the pre–post changes—areexamined below in light of literature related to effective learning inmathematics.

Teacher Support. The Teacher Support scale assesses the extent to whichthe teacher helps, relates to, trusts and is interested in students. Theteacher’s relationship with his or her students is an important aspect ofany learning environment, and it can lead the student to love or hate asubject and to be inspired or turned away from learning. Thesupportiveness of a teacher helps to give students the courage andconfidence needed to tackle new problems, take risks in their learning,and work on and complete challenging tasks. If students consider ateacher to be approachable and interested in them, then they are morelikely to seek the teacher’s help if there is a problem with their work. Theteacher’s relationship with his or her students, in many ways, is integral toa student’s success and to creating a cooperative learning environment(Hijzen, Boekaerts &Vedder, 2007).

The students who were interviewed generally agreed that they felt thattheir teachers were more approachable after the use of games and thatthey were more comfortable about seeking help from the teacher if therewas a problem with their work. To this end, one student commented: ‘If Ihave trouble with my work, I ask my teacher for help and she works withme to solve the problem. My teacher gives me strategies, ideas andinformation to solve the problem.’ The students who were interviewedperceived their teachers to be more supportive and approachable after theuse of games. These students also generally agreed that the teacherseemed to be more interested in their learning.


Involvement. The Involvement scale assesses the extent to whichstudents feel that they have opportunities to participate in discussionsand have attentive interest in what is happening in the classroom. TheInvolvement scale assumes that language plays an important part inhelping students to understand what they are learning (Taylor &Campbell-Williams, 1993) and that giving students the opportunity toparticipate in classroom discussions and to negotiate ideas and under-standings with peers, rather than listening passively, is an importantaspect of the learning process. Classroom observations indicated thatstudents were actively involved when they were playing the Jeopardy!-type game, were engaged in discussions with their team mates and oftenwere forced to negotiate their ideas. An interesting point made by one ofthe students was that, ‘when we play the game, it gives us a chance tochallenge the information that we have in our mind’.

When the students were asked to comment on the level of involvement,they all agreed that there were more opportunities to discuss their ideasduring lessons with games than during their regular mathematics classes.The students who were interviewed generally felt that their commentswere respected by their fellow students and that the games enabledstudents to be more involved in the learning process. One studentcommented: ‘We gather all of the ideas and we decide on the best one.We respect each student’s ideas.’ Another student remarked: ‘Discussingideas in class was very important. We needed to understand what eachstudent was talking about so that we could answer correctly.’ Researchsupports the notion that if students are actively involved in learningactivities such as this, then it is likely that learning will be moremeaningful to students (Kangas, 2010; Kember, Ho & Hong, 2010).

Personal Relevance. To ensure that students engage in their learning, itis necessary for teachers to make mathematical content relevant tostudents’ lives outside school (Nicol, 2002; Taylor, Fraser, & Fisher,1997). The Personal Relevance scale assesses the connectedness of asubject with students’ out-of-school experiences. Interviews with studentsdid not make clear how the mathematics games led to increased students’scores on the Personal Relevance scale. However, students agreed thatmathematics in general was relevant to their lives. One studentcommented that ‘mathematics is not only in our studies, but we usemathematics everywhere, even in our lives’. Another commented:‘Mathematics is very important because we can use it in our lives. Inmy life, I use maths every day. If I buy or sell something, I use maths.’Another student commented that often teachers did not identify


applications of a mathematics topic to real life and suggested that, ‘whenwe start a new lesson, maths teachers should tell us how the lesson isrelated to real life because sometimes we take lessons and we don’t knowhow we can use it’.

Enjoyment of Mathematics Lessons. The Enjoyment of Mathematicsscale assesses the extent to which students enjoy their mathematicslessons. Because the present study aimed to determine whether or not theintroduction of Jeopardy!-type games can help to improve students’enjoyment of mathematics lessons, we were interested in finding out howstudents regarded their mathematics class. Students were asked abouttheir enjoyment of mathematics both before and after the use of games intheir classroom. The students who were interviewed generally felt thatthey did enjoy mathematics more when the games were included. Onestudent commented:

In my opinion, having games in mathematics makes the lesson interesting. Gameshelp me to understand the topic more easily than when the teacher is on the boardexplaining. With games, we did not feel bored, it was fun and I had a betterunderstanding of mathematics.

According to another student: ‘Without using the games, mathematicslessons are not interesting. When we use games, the information sticks inour memories.’ Another stated: ‘Games make mathematics fun. They alsohelp students to understand more.’ The students who were interviewedgenerally agreed that the introduction of games in their mathematics classimproved their enjoyment of mathematics lessons.

All of the teachers who were involved agreed that the introduction ofmathematics games increased their students’ enjoyment of mathematicslessons. One teacher commented: ‘When games are used, the students cansee that mathematics can be fun. They enjoyed playing games together.’Another stated: ‘Playing games has a big impact on the students,especially those who are bored with worksheets and textbooks.’

Academic Efficacy. A student’s self-efficacy positively affects engage-ment and effort and is important to learning (Aldridge & Fraser, 2008;Bandura, 1989; Velayutham, Aldridge & Fraser, 2011; Zimmerman,Bandura & Martinez-Pons, 1992). Many of the students who wereinterviewed commented about how the use of mathematics games hadmade them feel that they were performing well in mathematics. Onestudent commented: ‘Before we started using games, I thought mathe-matics was complicated, but now I realise that, if I try, I can solve it.’


Many of the students felt that the use of games helped them tounderstand and remember concepts. Various students commented:

The games helped me to understand more.In general, people think that mathematics is very difficult, but sometimes I find it easywhen we play games.The games make the mathematics lesson easier and more interesting. With games, I don’tfeel bored and the concepts I learn stick in my mind more.Actually it makes the ideas stick in my mind. In the test, I actually remembered onequestion that we played in the class; so it is kind of fun and important.

Some students felt that the competitive aspect of the game encouragedstudents to work harder than they would have otherwise. Studentscommented:

When we are put in groups and have to compete, we work harder.The games affected all the students in the class not just me because, when you play gamesin mathematics, it is a challenge for us to answer the questions before my friends or theother team answers the question. This gives me a proof of how I am doing in mathematicsand also prove to my friends that I am clever.

Of the 20 students who were interviewed, one of the students did not feelthat games made a difference to the way in which he felt about his ability.This student commented that ‘the games did not really affect my feelingsabout how well I will do, but I find games better than doing homeworkfrom the book’.

Finally, some of the students who were interviewed felt that the use ofmathematics games positively affected their outcomes. One studentcommented that ‘I am doing well because I like mathematics withgames’. Another stated: ‘The games were very good. After the lessons,students are prepared to answer each question correctly. Some of thequestions that we have seen in the games might be in the finalexamination. In a funny way, the games have helped us.’

It would appear that the 6 weeks of including Jeopardy!-type gamesimpacted on both the teachers and students. All of the teachers stated thatthey were planning to incorporate games into their lessons in the future,and the students whom we interviewed were keen for them to do so.

DISCUSSION AND IMPLICATIONS

In our study, we used a mixed-method approach involving surveys,interviews and observations of classes in investigating the impact ofmathematics games. The results suggested that the games impacted


positively on students’ attitudes towards the learning of mathematics andtheir perceptions of some important aspects of classroom environment. Ourfindings suggest that, during exposure to games, students experienced someimprovement in Teacher Support, Involvement, Personal Relevance,Enjoyment and Academic Efficacy.

A narrative of students playing mathematics games suggests that, withthe introduction of games in the classroom, students were given theopportunity to interact with each other and to explain and compare theirsolutions with those of their team mates. In a typical mathematicsclassroom in the United Arab Emirates, students are taught to listenpassively and are not given the opportunity to participate in class. Ourresearch indicated that the use of games can enhance students’participation and engagement in class.

Analysis of the interviews suggested that the students generallyenjoyed mathematics more when games were included in their lessons.Students’ comments about their academic self-efficacy revealed how theuse of mathematics games had affected their feelings about how well theywere performing in mathematics.

Also, the information obtained from interviews with students andteachers helped to explain pre–post differences for those scales whoseresults were statistically significant (Teacher Support, Involvement,Personal Relevance, Enjoyment of Mathematics Lessons and AcademicEfficacy scales). Students’ interviews revealed that teachers were moresupportive and approachable and seemed to be more interested in theirstudents’ learning after the use of games.

In the United Arab Emirates, there is a push for teachers to shift in theirfocus from more traditional education and delivery methods to contem-porary approaches (Nicks-McCaleb, 2005). The results of our studysuggest that it could be useful for mathematics teachers to use morecreative pedagogical practices such as games in order to improve theclassroom environment and students’ attitudes towards mathematics.

Our findings provide a starting point from which practical attempts,involving the use of mathematics games, can be used to enhance students’learning environments and attitudes towards mathematics. In manymathematics classrooms in the United Arab Emirates, teachers’ willing-ness to incorporate games or different pedagogies in their lessons couldbe a key to success in improving classroom environments and students’attitudes. Because our study involved only teachers and students in AbuDhabi, United Arab Emirates, the generalisability of the findings could belimited. It is therefore unclear whether our findings would apply to othertertiary-level institutions in the United Arab Emirates. It is recommended,


therefore, that future studies involving larger samples with studentsoutside of Abu Dhabi be carried out.

The limited sample size also limited the power of statistical analyses. Alarger sample would have permitted pre–post differences in perceptions oflearning environment and attitudes to be identified more clearly. To tryand overcome this limitation, however, rich, in-depth, qualitative datawere gathered to complement findings from the quantitative data. Becausestudents were exposed to the mathematics games for only 6 weeks, alonger period of exposure might have provided more insights into theeffect of games activities on students’ attitudes and the learningenvironment. It is recommended, therefore, that further similar researchbe carried out using larger samples drawn from other countries toinvestigate the benefits of using mathematics games at the collegelevel in terms of the learning environment and a variety of studentoutcomes.

The results of our study provide information about the effectiveness ofJeopardy!-type games in terms of the classroom learning environment andstudents’ attitudes towards mathematics. Because teachers are oftenreluctant to use games in their mathematics classrooms, our study issignificant as its results have the potential to encourage mathematicsteachers to incorporate the use of games in their classrooms as a viablealternative pedagogical approach. In particular, this study will providevaluable information that could help teachers in the United Arab Emiratesto improve their pedagogical practices. The results of this study have thepotential to influence educators and curriculum developers to incorporatethe use of mathematical games in the curriculum as a practical way toimprove classroom environments and students’ attitudes.

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Afari, Aldridge, & Fraser