Pre–Service Teachers’ Knowledge of Integrating Soccer and Geometry: The Case of University of Education, Winneba

Teacher educators play vital roles in ensuring that positive transfer of knowledge across subject areas occur. This study examined pre-service teachers’ knowledge of integrating physical education and mathematics with particular focus on soccer and geometry. Using a semi-structured questionnaire, views of 145 pre-service teachers from the Department of Basic Education, University of Education, Winneba, were examined. Using descriptive statistics and One-way ANOVA, results indicated that the pre-service teachers have substantial operational but limited conceptual knowledge concerning modelling of basic geometric concepts on the field of play (soccer). The One-way ANOVA result indicated a non-statistically significant difference among the respondents’ knowledge to subject preference [F (2, 136) = 0.943, p = 0.392, η 2 = 0.014]. Among others the study recommended that tutors/lecturers expose pre-service teachers to modeling geometric concepts operationally and conceptually to facilitate their transfer of learning and their future classroom practices. committed by a team and player, time calculations, record analysis, optimal angle for a throw (goal keeper), diagonal system of control, players have to decide the angle in which they have to kick the ball, distance ran by a player in a match, width of the wall and distance of the wall from the goal post while free kick is being kicked and a host of others. knowledge level in applying basic geometric concepts to soccer or not. The mean scores on the various subject preference reported by the pre-service teachers were very high; mathematics ( M = 42.3, SD = 3.6, n = 67), physical education ( M = 43.3, SD = 3.3, n = 32) and other subjects ( M = 42.5, SD = 3.0, n = 40). On the face value, an examination of the mean scores presented indicates that some amount of difference exists. It indicated that pre-service teachers with preference for physical education had the highest mean score. To establish if the differences were statistically significant, a One-Way ANOVA test was conducted. The test of homogeneity was not significant, Levene test - F (2, 136) = 0.943, p = 0.392, for pre-service teachers’ knowledge level scale. The analysis indicated that the homogeneity of variance

competition among many colleges using highly constrained linear programming (Van Voorhis, 2002).
Several factors have been taken into account when designing the mathematics curriculum. These are: mathematical concepts and skills, terminology and vocabulary used, and the level of proficiency of English among teachers and pupils. It is hoped that with the knowledge and skills acquired in Mathematics, pupils will discover, adapt, modify and be innovative in facing changes and future challenges. The learning of mathematics at all levels involves more than just the basic acquisition of concepts and skills. It involves most importantly, an understanding of the underlying mathematical thinking, general strategies of problem solving, communicating mathematically and inculcating positive attitudes towards an appreciation of mathematics as an important and powerful tool in everyday life.

Objectives of the Study
In other to succeed in conducting this research and appreciate the fact that the subjects we study in our educational sectors are linked to each other, the researcher sets out these objectives of the study: 1. To explore pre-service teachers' success of connecting basic geometric concepts applied in soccer. 2. To identify pre-service teachers' knowledge level in applying geometric concepts in the teaching and learning of soccer.

Research Questions
The study was guided by the following research questions: 1. What are the successful connections of basic geometric concepts in soccer by pre-service teachers? 2. What level of knowledge do pre-service teachers have in applying geometric concepts in the teaching and learning of soccer?

Hypothesis H0
Pre-service teachers' knowledge of integrating soccer and basic geometric concept will not differ significantly with respect to their subject preference.

Methodology
The study employed a descriptive survey research design in order to collect valid and reliable data. From a target population of three hundred and ninety-four (394) level 300 pre-service teachers of the Department of Basic Education, University of Education, Winneba, one hundred and forty-five (145) were actually involved in the study. This study considered only the level 300 pre-service teachers in the 2017/2018 academic year because they are the ones who have been imbued with content and theory in both physical education and mathematics which they would be teaching after completion of B.ed Basic Education programme, hence the need to check for their knowledge in integrating them. Even though the level 400 students have also been imbued with content in both physical education and mathematics, they were excluded from the study because they were out for their internship programme.
Purposive and simple random sampling techniques were used to select the sample. A self-constructed semistructured questionnaire was used as a tool for collecting data. The open-ended part of the questionnaire provided the participants with examples of basic geometric concepts and their task was to exemplify as many of such concepts on the soccer field of play as possible. The close-ended section gave an opportunity to the participants to indicate their agreement or disagreement with some items in relation to integrating soccer and geometry as areas of study. The questionnaire was pre-tested to check its reliability and validity. The face validation was ensured by giving the questionnaire to colleague faculty members to check for any typographical errors with the various statements while that of content validation was done by giving the instrument to a Professor of Physical Education and a Senior Lecturer of Mathematics which is consistent with Borg and Gall (2003) position in achieving content validity of an instrument through expert judgement. The reliability of the instrument was approached as the internal consistencies of the various items in the questionnaire was assessed using Cronbach Alfa. The overall instrument yielded a Cronbach Alfa coefficient of 0.86, being indicative of internal consistency as explained by Mcmillan and Schumacher (2010), that a Cronbach Alfa coefficient of at least 0.70 or higher.

Data Collection Procedure and Data Analysis
The respondents were given ample time, during one of the physical education lectures time to respond to the open-ended part first, after which the close-ended part was administered to them. This was to prevent them from transferring information from one section to the other. Summative content analysis, descriptive statistics such as simple frequency and percentages and inferential statistics such as the One-way ANOVA were used to examine the responses received from the respondents. Classifications and codifications from the open-ended section were done by the two researchers (physical education tutor and mathematics tutor). The strength of the agreement between the coders was calculated using the kappa coefficient. The analysis showed that the strength of agreement between the two raters was substantially strong [κ = .785 (95% CI, .300 to .886), p< .000)] .

Source: Field Data (2018)
The data in Table 1 has revealed that out of the 145 participants who took part in the study, 92 (63.4%) were males whereas 53 (36.6%) were females. The results of the pre-service teachers' background characteristics show that their ages ranged from below 18 to 34 and above. However, majority (n = 80, 55.2%) of the participants were between the ages of 24-27 years. The results further show that 70 (48.3%) of the respondents' favorite subject was mathematics, 34 (23.4%) of them asserted physical education was their favorite subject while the rest (n = 41, 28.3%) indicated that they preferred other subjects to the two main subjects under consideration. The respondents also had the chance to indicate their preferred sporting activity and the analysis reveals that 76 (52.4%) liked soccer, 45 (31.0%) like athletics and 24 (16.6%) liked other sporting activities.

Research Question 1
What are the successful connections of basic geometric concepts in soccer by pre-service teachers?
The first research question focused on pre-service teachers' successful connection of basic geometric concepts (point, arc/semi-circle, line segment, angles, triangle, square rectangle and circle) with self-identified examples from the field of play (soccer). Findings with respect to this research question are presented on Table 2.
The respondents were able to operationalize the various geometric concepts in a number of ways. However, some of the examples given by the respondents were not relevant and as such were not included. Others were related to each other and therefore, were amalgamated into a single model. From Table 1 for example, the concept of point was exemplified in about 15 different ways by the respondents and was condensed into 7 models, the concept of arc/semi-circle was exemplified in 13 ways and condensed into 4 models; line segment 15 way and subsumed into 5 models; angles 64 were condensed into 4 models; triangle 36 condensed into 3; square 36 condensed into 2 models; rectangle 64 condensed into 5 models and the concept circle, exemplified by the respondents in 10 different ways and it was condensed into 2 models.  Table 2, the data show examples given by the respondents in relation to the concept of point on the field of play in soccer were: the penalty kick spot (frequency [f] = 68), the corner spot (f = 67), the center of the field (f = 41), the free kick spot (f = 18), the goal kick spot (f = 7), the throw-in spot (f = 4) and the off-side kick spot (f = 4). Some of the misrepresentation of the concept stated by the participants during the study were "indirect point", "goal post", "18-yard box", 16-yard box point" among others. Models representing arc/semicircle were given by the participants and they ranged from, half of the center circle (f = 58) to arc on the 18-yard box (penalty arc) (f = 40) to corner arc (f = 26) and finally to arc of a flying ball (f = 6).
An examination of findings related to line segment indicated that examples such as center line (f = 51), goal line (f = 38), throw line or side line (f = 34), the 18 and 6-yard lines and the liner motion kicks by player (f = 13). When the angle models were examined as presented in Table 2, it could be observed that the pre-service teachers indicated corner kick region (f = 75), the various angles in the 18 and the 6-yard box (f = 25), the various angles found in the goal post structure (f = 25), and center circle/center arc (f = 17) as examples of angles found on the field of play. With regards to the triangle models, pre-service teachers were asked to exemplify the geometric concept on the field of play. They indicated player positioning (f = 46), corner region of the field (f = 16) and dividing the field diagonally (f = 4). A participant however, expressed the idea of not being able to model the concept of triangle by stating "none".
As seen in Table 2, the respondents illustrated the term square, rectangle and circle in various models. The concept square was modeled in the form of player formation (f = 21) and square passing (f = 15) whilst that of rectangle was modeled in the form of the 18 and 6-yards boxes (f = 77), the shape of the field of play (f = 56), the goal post (f = 21), player positions (f = 2) and referees' caution cards (f = 2). And the circle was also modeled in the form of center circle (f = 128) and Circular formation for prayers before start and restart of the game (f = 1). In the case of the circle, some of the misrepresentation of the concept stated by the participants during the study were, "Football or the ball" (sphere), "The nature of how spectators sit around the field" (oval) and "Athletics tracks around the field of play" (oval).

Research Question 2
What level of knowledge do pre-service teachers have in applying geometric concepts in the teaching and learning of soccer?
The pre-service teachers were given the opportunity to indicate their level of agreement or disagreement on 12 items on the application of some basic geometric concepts to soccer. This was to help describe their knowledge level in applying geometric concepts in a hypothetical teaching and learning of soccer situation. Descriptive statistics (mean and standard deviation) were used to analyze the data. Mean rating of 1.0-2.4 represents below average knowledge, 2.5 represents average knowledge and 2.6-4.0 represents above average knowledge. This criterion of mean analysis was used by Shamsid-Deen and Smith (2006). The result of the analysis is presented in Table 3. Points are used in the construction of a soccer field 3.67 0.5 4 The concept of angles is explored in soccer 3.65 0.5 5 There are geometrical shapes on the field of play 3.63 0.6 6 Pythagoras theorem is employed in construction of angles on the field 3.37 0.7 7 Player movement during play create different geometrical figures 3.54 0.6 8 The concept of polygon is sometimes used in the manufacturing of soccer balls 3.19 0.9 9 The concept of angles is explored by goalkeepers in preventing goals from being scored 3.50 0.7 10 Players take kicks from specific spots/points toward intended angles and directions 3.68 0.6 11 Lines and points are used by referees in calling for offside during play 3.69 0.5 12 The concept matching is utilized during play 3.48 0.5

Source: Field Data (2018); Key: M = Mean and SD = Standard Deviation
An examination of Table 3 indicates that most of the respondents' knowledge level on the application of the identified basic geometric concepts to soccer was above average. This observation was made because the mean scores on all the items were far above the average knowledge score (M = 2.5). For example, results as presented in Table 3 reveal that from all the items, pre-service teacher rated "Lines are used in the construction of a soccer field" highest (M = 3.77, SD = 0.4) while "The concept of polygon is sometimes used in the manufacturing of soccer balls" was rated the lowest (M = 3.19, SD = 0.9). This result from the analysis suggests that the preservice teachers who took part in this study have adequate knowledge on the application of the explored basic geometric concepts to soccer to teach their future learners. They have, therefore, adequate knowledge and competence to teach and integrate these two bodies of learning.

Testing of Hypothesis H0
Pre-service teachers' knowledge of integrating soccer and basic geometric concept will not differ significantly with respect to subject preference. A One-Way ANOVA test was conducted on the data with the aim of evaluating if subject preference was a significant differentiator of pre-services teachers' knowledge level in applying basic geometric concepts to soccer or not. The mean scores on the various subject preference reported by the pre-service teachers were very high; mathematics (M = 42.3, SD = 3.6, n = 67), physical education (M = 43.3, SD = 3.3, n = 32) and other subjects (M = 42.5, SD = 3.0, n = 40). On the face value, an examination of the mean scores presented indicates that some amount of difference exists. It indicated that pre-service teachers with preference for physical education had the highest mean score. To establish if the differences were statistically significant, a One-Way ANOVA test was conducted. The test of homogeneity was not significant, Levene test -F (2, 136) = 0.943, p = 0.392, for pre-service teachers' knowledge level scale. The analysis indicated that the homogeneity of variance assumption underlying the application of ANOVA was tenable on the data. The result of the ANOVA test is presented in Table 4.  Table 4 indicates that the ANOVA result was not significant [F (2, 136) = 0.943, p = 0.392]. Another analysis of importance which was considered by the researchers was the effect size, in this case the eta squared (η 2 ). The effect size statistics provide an indication of the magnitude of the differences among groups. There are a number of different effect size statistics. The one used here is the Eta squared (η 2 ). It is important to note that Eta squared range from 0-1 (Cohen, 1988). For the current study, the findings did not show a statistically significant result, and the difference in the mean scores of the groups was very small (42.3, 43.3and 42.5). This is evident in the small effect size obtained (η 2 = 0.014).

Discussion
The findings of the study revealed that the pre-service teachers had substantial knowledge about integrating soccer and basic geometry. The results obtained do not support the assertion that pre-service teachers are deficient in integrating geometry and soccer. For example, the result obtained does not support the idea of a deficiency in pre-service teachers' content knowledge of geometry and pedagogy in integrating soccer and geometry as suggested by Pirasa, (2016). Ginsburg (2008), examined high school mathematics teachers' abilities of connecting mathematics with daily life, also does not lend support to this finding. In Gainsburg's view, although a large number of the teachers' real life examples can be counted, it has been determined that the connections done through these examples were minimal and summarized, and that there was not an ability to motivate and canalize the students to think. The results were however, related to Phillips and Marttinen (2013), Finn and McInnis (2014) and Kokko, Eronen and Sormunen (2015) who found that cross-curricular integration is successful in an array of disciplines. And again confirms, Eli (2009) (as cited by Pirasa, 2016) assertion that the knowledge of pre-service mathematics teachers for geometry instruction was at a low level and that the mathematical connection carried out was a lot more operational rather than being conceptual.

Conclusion and Recommendations
The love for Physical Education and Mathematics or otherwise are instilled at school and as such what teachers do as well as how they do it, is considered absolutely critical to the future of inter-disciplinary teaching. In conclusion, the findings reveal the importance of pre-service teachers possessing the adequate knowledge of integrating Physical Education (soccer) and Mathematics (geometry); however, some of the models exemplified by the respondents were inaccurate. In this research, most pre-service teachers were able to operationally demonstrate the ability of integrating basic geometric concepts such as point, line segment, square, rectangle, triangle among others to models on the soccer (field of play) rather than conceptually. It is also noteworthy to state that when Table 2 is examined, we can see that the participants were able to establish multiple (more than one) connections between the basic geometric concepts and soccer field play. Participants' ability to establish different connections and to eliminate the gap between school mathematics and real life is depending on how much they could transfer their classroom mathematical knowledge to the real life. For that reason, teachers of pre-service teacher have great responsibility.
Based on the findings of this study it is recommended that tutors expose pre-service teachers to modeling geometric concepts operationally and conceptually to facilitate their transfer of learning and their future classroom practices. Again, teacher training institutions should establish and develop teachers' confidence, knowledge and skills to deliver these connections effectively and apply pedagogical principles that underpin practice for both subjects. They should also ensure that adequate teaching and learning resources be made available to move away from abstract thinking to a real life practical experience. Resource centers, therefore, should be developed with charts showing mathematical concepts applied in physical education together with other teaching aids in schools.