There are four tracks to choose from in senior high school in the Philippines: Academic, Technical-Vocational-Livelihood (TVL), Sports, and Arts and Design track. Under the Academic tracks comprises of Science, Technology, Engineering and Mathematics (STEM), Humanities and Social Sciences (HUMSS), Accountancy, Business and Management (ABM), and General Academic Strand (GAS) strand. Only the STEM strand takes the subject Calculus. Basic concepts of calculus include limits, differentiations, and integrals.
When it comes to learning mathematics, students are easily intimidated (Yang, 2014; as cited by Mutawa, 2015). However, the researchers believed that this should not always be the case. Learning mathematics can be achieved through different formats. The researchers will be developing a board game to make the study of mathematics a fun, learning experience. They will focus more on the basic concept of derivatives.
Some concepts of mathematics cannot be solved by algebraic formulas. This is where differential calculus comes in. One importance of differential calculus is that it is used to calculate for the rate of change. It is integrated to calculate the changes from dependent to inter-changing variables in different spaces. Not only in mathematics but differential calculus is also needed in physics, and engineering. It is also used in biology and economics to design the structure of complex systems (Bhakuni, 2018).
The HUMSS students did not take Calculus as one of their subject. Hence, the researchers will be introducing the game to them to test the effectiveness of the developed board game.
Statement of the Problem
The researchers will use pure lecture or the traditional technique of teaching to the Grade 12 HUMSS of Benguet State University and subsequently conduct a pretest. Afterwards, the strategy of the board game will be presented and the post-test will also be conducted to measure the effectiveness of the board game.
• Is there a significant difference between the previous math grades of the HUMSS students on both sexes?
• Is there a significant difference on the performance of HUMSS students before and after playing the board game?
Scope and Delimitation
The focus of this study is to determine the effectiveness of learning derivatives through the aid of board games. The researchers will teach the basic rules of derivatives which involves the product rule, quotient rule, constant rule, power rule, and sum and difference rule. The board game that was developed by the researchers adopted the rules of the educational war game “Game of the Generals”. Every piece will have a corresponding derivative problem.
The aspects to be looked into are if there is a significant difference between previous math grades of the students on both sexes, and if there is a significant difference on their performance during the pretest and the posttest.
Significance of the Study
This study is to help students in improving their academic performance in the Basic Calculus subject. Through this, it will help students develop their critical thinking skills, creativity skills, strategic skills and help to understand the lesson easily compared to using conventional ways.
Also, using board games as a learning tool will serve as the venue of recreational activity for students without spending money. With this, students will not only be educated but will also be entertained.
In addition, this study is also beneficial to the teachers, wherein they can devise strategies that will make their lessons more understandable and enjoyable for the students.
Furthermore, the study will also be beneficial for further researches.
Review of related literature:
History of Calculus
The problem of finding the tangent to a curve has been studied by many mathematicians since Archimedes explored the question in Antiquity. The first method came from Gilles Persone de Roberval during the 1630's and 1640's. Behind his idea is the notion of Instantaneous Motion. From his methods, he was able to find the tangents to numerous other curves including the ellipse and cycloid. Yet, he was not able to generalize it and exists as a precursor to the method of finding tangents using infinitesimals (Wikipedia, 2018).
At nearly the same time, Pierre de Fermat used the notion of maxima and the infinitesimal to find the tangent to a curve (Wikipedia, 2018).
Isaac Newton and Gottfried Leibniz thought of the fundamentals concepts in different way. Leibniz introduced dx and dy as differences between successive values. On the other hand, Newton used the quantities of x' and y', which were finite to determine the tangent. Yet they completed the necessities in the development of Calculus. Through the differentiation and integration, they were the first to explain an algorithm process. Second, they were able to present its usefulness as a general process. Finally, they were able to explicitly pronounce and rigorously prove it (Wikipedia, 2018).
The notation of Leibniz closely resembles to which the modern used and his discoveries about the inverse relationship between the integral and differential. Leibniz discovered the inverse relationship between the area and derivative by utilizing his definition of the differential. Integration is also known as the indefinite integral or anti-derivative due to the inverse relationship found by Leibniz. That is, the derivative of the indefinite integral of a function yields the function itself. . Leibniz also developed a notation for definite integrals, or integrals which produced the area underneath a curve between two bounding values (rather than a symbolic answer). His notation for the definite integral was to supply the lower and upper-bounding x-values (Wikipedia, 2018).
Ultimately over 100 years of achieving the rigorousness of Calculus, Cauchy, Weierstrass, and Riemann reformulated Calculus in terms of limits. The derivative and the integral were formulated in terms of limits. By putting Calculus on a logical footing, mathematicians were better able to understand and extend its results, with some of the subtler aspects of the theory (Wikipedia, 2018).
Math Performance of Both Sexes
There questions on whether there is a difference between men and women when it comes to math and science continues. American Psychological Association (2014) stated that this may be partly because there is a clear difference in the number of males and females in science and math careers, with males outnumbering women. Heidelberg (2015) agreed to this by citing Shane Bench and stating that more men pursue careers in the field of science and engineering.
There have been studies that show results concluding a difference in performance of the two sexes. A review of 111 studies by Elizabeth Spelke, PhD, a psychologist at Harvard University, and colleagues in 2005 showed that a genetic basis was discovered to show that there is a difference in gender when it comes to the cognitive system of both sexes. Janet Shibley Hyde, PhD, a psychologist at the University of Wisconsin and colleagues also found out through a published meta-analysis on a compilation of 100 different studies on math performance in 1990 that during elementary and middle school females displayed slightly better performance in computation, while males were slightly better in problem solving in high school. Additionally, Diane Halpern, PhD, and colleagues including Hyde published a report that showed that although women are most likely to score higher than men on verbal activities, men are slightly better when it comes to visuospatial skills (American, Psychological Association, 2014).
There are many factors that are mentioned to cause the disparity aside from biology. Bench, as cited by Heidelberg (2015) reasoned that the lack of women in the fields of math and engineering may be due to “men’s overestimation of their abilities,” as evident in two studies conducted. This is somehow negated by Steven Spencer and colleagues in a 1999 study tackling the difference of men and women with strong math backgrounds. The study gave men and women a math test. The researchers told half of the women that a previous math test showed gender difference between males and females. The results showed that half of the women who were told that there was a difference in the results between the two genders during a previous test performed worse than the other half who had equal results as the men. A 2014 study by researchers at Boston College also revealed that anxiety may also contribute to gender differences in math performance. Women are more likely to get anxious during math tests which then affects their memory and result to underperformance during the test. It was suggested that there should be more emphasis on the management of stress by girls in order to remove any gaps or difference between both genders. Another factor, as suggested by Halpern and colleagues “conclude that early experience, educational policies and culture also strongly affect success in math and science.” Hyde and colleagues, as cited in the American Psychological Association (2014), mentioned that boys’ slightly better performance in problem solving during high school may be due to them taking more science classes that emphasizes on those skills.
Despite all of these, the point that there is no difference in math performance between male and female when looked into as a whole is dominant. Spelke and colleagues, as cited in the American Psychological Association (2014), suggested that “men and women on the whole possess an equal aptitude for math and science.” There is more evidence that shows little to no difference in the performance of males and females. Hyde and colleagues negated the notion of biological difference through the published meta-analysis. It was found out that there was no significant difference between the performances of males and females in relation to math concepts. In fact, the meta-analysis showed that there is lesser and lesser difference between the sexes as the years progress. This was supported by Hyde and colleagues, as cited by American Psychological Association (2014) that “boys and girls understood math concepts equally well and any gender differences actually narrowed over the years, belying the notion of a fixed or biological differentiating factor.”
Board Games as an educational tool
For this mathematical investigation, the researchers will present a board game strategy to introduce derivative.
According to Treher (2011):
Board games are an important tool to provide hands-on and heads-on skill and knowledge development for people of all ages on all subjects. Not only do well-designed games create an engaging atmosphere, they also provide a nonthreatening, playful, yet competitive environment in which to focus on content and reinforce and apply learning. Mistakes are useful and point out what we need to learn. The board itself provides a visual metaphor to help connect information. Game elements, discussions, and problem solving with fellow team members about the content are vehicles for learning. Subtle redundancy to reinforce learning and insure retention should be incorporated into the game design. Good questions, problems to solve, and situations to consider allow players to think through and apply what they learn.
The idea of using educational games to engage students in active learning is not new. Great number of research shows that the academic performance of students can be improved through innovative teaching strategies and other kinds of innovation (Adunola, 2011; Ayeni, 2011).
According to MacKenty (2006) and Schrand (2008), gaming activities tend to show learning benefits because of the active learning components that are present in each game. Gee (2003) summarized that good learning is also being reflected through games. Johnson (2006) praises games for their ability to help us "find order and meaning in the world and make decisions that create order." Regardless of the format of the game, students can simultaneously build their problem solving skills while having fun throughout the process if an instructional game is well-designed (MacKenty, 2006; Harris, 2009). As stated by Franklin, Peat and Lewis (2003), when students work cooperatively on a gaming activity, “games foster group cooperation and typically create a high level of student involvement that makes them useful tools for effective teaching.” In addition, Squire and Jenkins (2003) also promote games for good learning because they “encourage collaboration among players and thus provide a context for peer-to-peer teaching and for the emergence of learning communities.”
On the other hand, Okan (2003), using games may have negative effect as he stated that “meaningful learning may sometimes be difficult and requires cognitive and emotional effort especially in the light of the fact that post-secondary education is not usually a fun undertaking.” It results to student that depends only in the innovative teaching which is the board game.
Audrey Amrein-Beardsley (2008) stated that, “Methods of gaming tests, result in false test score gains unrelated to true gains in student learning”. She explained that many teachers are simply “teaching to the test” with games and this causes students to “become experts at answering test questions without entirely understanding the concepts justifying their answers”
Kebritchi (2010) poses the concern that games are becoming such innovative learning tools that teachers may conclude that they don’t need to lecture. Instead they may “rely on the game and use it as a teaching replacement and not as a supplement”.
Methodology
In this chapter, the research design, sources of data, instrumentation and data collection, and analysis of data are presented.
Research Design
The researchers used the correlational and experimental method in this study since the purpose of this design is to determine the effectiveness of Board Games in learning derivatives among the respondents. Experimental method was used because it provides a systematic and logical method of discovering information through experimentation. According to Ary et al. (1972), as cited by Aboy (2001), experiment is generally regarded as the most sophisticated research method for testing hypotheses. Also, correlational method was used because it is used to determine the relationship between two or more variables.
Sources of Data
The respondents of this study were Grade 12 students of the Humanities and Social Sciences strand of Benguet State University-Secondary Laboratory School (BSU-SLS). There were a total of 44 respondents, 8 of them were males and 36 were females.
The school is located in Km. 6, Balili, La Trinidad, Benguet.
Instrumentation and Data Collection
The data of the students’ profile were collected from the students’ themselves. The records of students about their General Mathematics grades were taken from their subject teacher.
The researchers used the traditional method of teaching to give a simple introduction about derivatives and specifically about the basic rules of derivatives. At the end of the lesson, a Pre-Test was given. On a separate day, the researchers then introduced the derivatives board game to the respondents at which the respondents played against each other. After the game, a Post-Test was given to test the effectiveness of the board game.
The board game adopted the rules of the educational war game “Game of the Generals.” This was chosen because the respondents have already tackled this game during their Physical Education class and so the game is more familiar to them.
To gather the data on the proficiency level of the respondents in solving derivatives, a Pre-Test was given to the students after using the traditional method of teaching. And, to determine if there is an effect of using a board game in learning derivatives on the level of proficiency of the respondents, they were given a Post-Test after playing the board game.
In order to determine if there was a significant difference on the performance of the students between learning through the traditional method of teaching and playing the board game, the scores were tallied and interpreted by the researchers.
The reliability of the test was 0.8385 which means that the testing instrument is reliable and can be administered to the respondents to achieve considerable data.
Analysis of Data
Data gathered were interpreted and analyzed. In order to determine if there is a significant difference between the previous math grades of both sexes of the HUMSS students and if there is significant difference on the performance of the students before and after playing the board game, T-test was used.
RESULTS AND DISCUSSIONS
This chapter presents and interprets the results on the: (1) significant difference between the sex and previous math grades of the students; and (2) significant difference on the performance of the students before and after playing the board game.
Significant difference between the previous math grades of both sexes
The table below shows the significant difference between previous math grades of the students on both sexes.
Table 1. Previous Math Grades of both sexes
Variables Mean T-stat T-critical Decision Remarks
Males 87.75 0.9858 2.201 Accept Ho There is no significant difference.
Females 89.41
As shown in the table 1, the mean grades of females, 89.41, are higher than that of the males, 87.75. It also shows that t-stat (0.9858) is lower than t-critical (2.201). Therefore, there is no significant difference between the sex of the students and their previous math grades. With this, sex is not a factor on the performances of the students in mathematics.
This is supported by Spelke and colleague’s and Hyde and colleague’s study which stated that there is no difference among the performances of men and women in mathematics. Other studies also share the same conclusion American Psychological Association (2014).
As the results show, sex does not show who is better in mathematics, you can be as good as anyone regardless of what your sex is. Either you are a male or a female, it does not have an effect on your academic performance in mathematics.
Performance of the Students before and after playing the board game
The table shows the significant difference on the performance of the students before and after playing the board game.
Table 2. Performance of the Students before and after playing the board game
Variables Mean T-stat T-critical Decision Remarks
Pretest 5.2273 12.4032 1.6810 Reject Ho There is a significant difference.
Posttest 7.4091
The table shows that the mean score of the students from the pretest to the posttest increased by 2. This means that the students have a higher academic performance as reflected on their posttest. It shows that the performance of the students improved with the use of the board game as educational tool. Additionally, it shows that there is significant difference in the students’ performance before and after the board game.
According to Tate (2009), using board game as an educational tool is an effective strategy in delivering content knowledge. Games can be used to enhance motivation and improve students’ academic skills. With this, it helps students to better understand and remember important information. This goes with the saying by Carl Orff, “Tell me, I forget. Show me, I remember. Involve me, I understand.” Tate stated that teachers see that authentic learning may not take place if students are not involved or participate.
Adunola (2011) and Ayeni (2011) said that a great number of research shows that the academic performance of students can be improved through innovative teaching strategies and other kinds of innovation. Gee (2003) also said that good learning is being reflected through games.
As the result shows, engaging students with the use of board games has a positive effect on the academic performance of the students. Students became more active in participating than in listening to lectures.