Chapter 5: Analysis of Mathematics Teachers’ Interviews
5.2 Students' Learning Attitudes and Performance
5.2.4 Gender difference
When the teachers were asked about gender differences in mathematics learning, two teachers (B and E) commented that there was no gender difference. However, the other four teachers did observe that there were differences.
a. Students’ behaviour
Two teachers reported that there was gender difference in learning behaviour towards mathematics. The teachers said,
In this level Form 4, Form 5, I can say almost equal. Of course boys will be a little of lazy or a little bit of naughty (Teacher C).
Girls are better. Discipline better, easy to control. They are sort of more hardworking than the boys. Don’t say so loud, later all the male teachers all come here…ha…ha.. (joking) But in terms of maths, my students usually the
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better one are boys. The top one, ranking one. Because some boys they have the mind (Teacher D).
Both teachers perceived that female students paid more attention in their study, while male students were more playful. Nevertheless, Teacher D said male students usually performed better in mathematics. Teacher C said he did not observe any gender difference in mathematics performance. However, the teacher could be making a cautious statement (i.e. for possible gender bias). Both teachers were teaching Additional Mathematics so most probably this subject required strong determination, practice and hard work.
b. Topics learned
Teacher A and Teacher F observed a difference in the topics learned. Teacher A and Teacher F said,
Some topics boys like it more… Like index, transformation, locus. And in certain topics like indices, the boys like it. Where else the girls do not like it…They like more on the normal straightforward question like linear equation, normal one, parameter, polygon. When they come to abstract, locus, geometry construction, they don’t really like (but boys like it) (Teacher A).
If for Form 4, Form 5 mathematics, there is more imagination right? Female students cannot. I am surprise… Boys can get it. They can imagine. For example earth and sphere, you have to imagine the earth, the earth rotates and you have latitude, and you have the longitude. And then one more they have to think of plane and elevation. If you see the object you can imagine. You see the object like this, if you see this object at this side, girls cannot get it (Translated from BM) (Teacher F).
Teacher A and F had noticed that male students had a better imagination ability, and they could understand better on certain topics such as index, transformation, locus, geometry construction, earth, and sphere, plan and elevation. On the other hand, female students preferred topics such as linear equation, parameter, and polygon. Male students were claimed to be better at visualising an abstract object than female students. Two female students also did mention that they were weak in imagination and spatial skills [refer to Section 6.1.3]. Both Teacher A and F were teaching Mathematics and Modern Mathematics so most probably these two subjects required strong spatial abilities.
Males are known to be better than females in spatial ability due to genetic differences (Paul, 2013). The analysed data could suggest that boys have an advantage over girls
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because they could understand better in some particular mathematics topics that require imagination. Nevertheless, looking from a different perspective - mathematics is a subject that not only requires creativity and imagination but also requires much practice and discipline, so girls would have the advantage too.
To improve visualisation skill, females should play more computer games. Computer games could enhance one’s spatial abilities (De Lisi and Wolford, 2002). Females have been urged to play more action games to practise and improve their spatial skills (Paul, 2013). Simulation games are also found to support spatial skills, iconic skills and visual selective attention (Mitchell and Savill-Smith, 2004). Therefore, females who play action and simulation games are expected to have good spatial abilities.
Students’ interviews revealed inconsistent result between games played (i.e. simulation and action) and self-reported spatial abilities [refer to Section 6.1.3 and 6.3.2]. Although no experiment had been conducted, students’ self-reported spatial abilities were used as comparison. In this study, simulation and action games did not seem to have a significant connection with students’ self-reported spatial abilities.
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5.2.5 Summary
Table 5.3: Students’ Learning Attitude s and Performance in Mathematics
Mathematics or Modern Mathematics Additional Mathematics Positive attitude.
Routine problem. LOTS are required.
Negative attitude. Non-routine problem. HOTS are required. Students’ Weak Problem-Solving Skills
Students
Weak in cognitive & metacognitive skills.
Digital native character - random access and want to be fast and easy.
Teachers
Unable to spend sufficient time to teach every individual student.
Student should be patient, read slowly and follow step-by-step predefined routes.
Mathematics Learning Computer Games Lack of motivation.
No confidence - disbelief in self- efficiency.
No interest - no longer stimulated curiosity.
Exam-oriented - performance
achievement learners.
Motivating.
Autonomy - control and grasp of strategies and outcome.
Uncertainties stimulate interest and curiosity.
Satisfaction to overcome challenges -
mastery achievement learners.
Male Female
Good in spatial ability. Less disciplined.
Preferred topics: index,
transformation, locus, earth and sphere, plan and elevation.
Weak in spatial ability. More disciplined.
Preferred topics: linear equations, parameter, and polygon.
5.3 Teaching Approaches
To explore the potential use of gaming pedagogy in mathematics learning, an understanding of the current teaching approach should be sought from the mathematics teachers. Firstly, there was a need to find out the current teaching approach in schools. Secondly, the adoption of computer games in mathematics learning must take into account the teachers’ perceptions of the feasibility and challenges associated with their teaching profession. The teachers were using several teaching approaches: (1) classroom teaching, (2) group work, (3) computers, (4) problem-solving techniques and (5) motivation efforts.
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5.3.1 Classroom teaching
All the teachers had spent most of their time teaching in the classrooms. The conventional classroom instruction was described by Teacher B. He said,
Give the basic first then example; ask them to do some of the examples in front to show their friends. Then drill them through exercise. Give exercise and they can discuss among themselves. Ask the teacher also can (Teacher B).
In brief, the conventional classroom teaching starts with teaching the basic knowledge to the students that is followed by some examples. Students are then asked to do some exercises on the whiteboard in front of the classroom and to show their work to the class. Finally, more exercises are given to drill the students’ problem-solving skills. During this process, they could discuss among themselves or ask for help from the teacher.
In fact, some teachers (e.g. Teacher A and D) still preferred the conventional approach. The teachers said,
I still prefer showing more examples on the board… Yes, traditional way… I still prefer face-to-face teaching with my students. I can see their face, I will know whether they understand or not, their reaction (Teacher A).
If you say mathematics computer games, I think still classroom better (Teacher D).
Teacher A said she preferred to have a personal interaction with students so that she could understand their problems easily. The presence of a good teacher in the classroom should not be underestimated.
Teachers have the most significant influence on students’ motivation to learn mathematics because the support and recognition given by teachers can build up students’ confidence in learning (Marchis, 2011). Looking from a different perspective, the teachers want to control the students’ approaches to learning. They might be guided by a teacher-centred approach.
In computer games, players are self-educating. Players have full control and responsibilities for their learning experience.
The learner is an “insider”, “teacher”, and “producer” able to customise the learning experience and game from the beginning and throughout the experience (Gee, 2007, p.208).
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In games, players customise their game characters to create their own story. They can project what they want their game characters to be (e.g. heroic, aggressive or cooperative) and how to solve problems in games. Self-taught trial and error is the most popular and fundamental way to play a game. Other than that, players can read game tutorial, watch video, find the walkthrough or cheat on the Internet.
5.3.2 Group Work
Group works such as group discussion and project were the most popular and widely used method among the six interviewed teachers. A teacher said,
I always use group discussion. And also students present like teacher, mentor mentee system. Let say, the mentor comes out and presents their answer… They like actively involve them. Students like to hear their own friends presenting… Very effective. I can get them interested in my class. Else they fall asleep (Teacher D).
Most of the teachers (i.e. A, D and E) had a standard approach to group discussion. Students would sit in a group or in pair to discuss a particular mathematics question. After the discussion, a student from each group would be asked to present the solution in front of the class. Though this method seemed to be simple and ordinary, Teacher D, who had 30 years’ teaching experience in mathematics said, this was an effective teaching approach.
By chance, two teachers (i.e. D and F) used statistics as an example of a group project. A teacher said,
They learn statistics using field data. That means they go and find the data in this school… So, I give them a title, types of cars. Then, they go and jot down Toyota, Mazda, Ford. Find in the whole school. They count and then they have to do the statistics. Find the mod, median, mean [Translated from BM] (Teacher F).
This could indicate that not all mathematics topics are suitable for this teaching approach. Some topics are too abstract, so the project-based activity may not be applicable. Statistics would appear to be the easiest topic to relate to daily life activities such as data collection, analysing data and presenting the findings.
There are a few similarities between group discussion and project. In both activities, students are actively involved, playing certain characters (e.g. researcher or mentor) and working as a team. Nevertheless, these activities are not competitive because it is not a competition.
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Similarly, multiplayer computer games do actively involve the players. Every player is role-playing certain games’ character and they work as a team. However, the games are very competitive because they are built on competitions and victory is a pride for the team members. Competition is one of the essential elements in game design (Ebner and Holzinger, 2007) because intrinsic motivation could be influenced by the perceived challenges (Wishart, 1990). People normally engaged in a strong team spirit when they have common opponents (e.g. World War II and World Cup).
Most of the computer games nowadays are also built on group work. For instance, MMORPG is the most popular and addictive genre of computer games (Dickey, 2011) because it is very competitive and built on a strong team spirit and culture where everyone works together to achieve a common goal.
Young people see game playing as almost entirely social, preferring to play in multiplayer settings of one sort or another (Gee, 2007, p.8)
Multiplayer games suit the interest of many young people. The young generation performs best when they are networked (Prensky, 2001a, 2001b) and they can learn from their peers (Beck and Wade, 2006). In games, players can learn how to plan the best strategies to make the best use of the skills and abilities possessed by every team member.
5.3.3 Use of Computers
All teachers interviewed except Teacher B had used a computer to teach mathematics. This was surprising since Teacher B was the youngest teacher among all the teachers participated in this study and would therefore be expected to be the most digital native among all the teachers. Some of the computer technologies used were (a) courseware and (b) mathematics computer games.
a. Courseware
There were two types of courseware used by the teachers. The PPSMI courseware was provided by the MOE, and another courseware was provided by UNESCO. The teachers said,
(PPSMI courseware) Initially they were quite interested when they see it. But, if I used it too frequently, they get bored and they are not pay attention… Because the questions are very slow (Teacher A).
(PPSMI courseware) I just used it to show 3 dimensional objects. How it rotates to form a solid… It is effective for the students who cannot visualize…
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Some of them think that it is boring because the CD is slow [Translated from Mandarin] (Teacher E).
(UNESCO courseware) Let say I teach the quadratic function or equation. I can show them how does the effect of A, how the graph look like (Teacher C).
Here, two points were highlighted – visualisation and interactivity. The courseware was useful in presenting diagrams and helping students to visualise abstract concepts. However, it was passive and boring. Teacher A and F had the same opinion that the PPSMI courseware was quite impressive when it was first introduced to the students. However, students got bored because the flow in the CD was too slow. Teacher A explained further that most of the time, students could not understand what was taught in the courseware because it was not interactive. Teacher A said,
Maybe if they are answering a quiz, this question answer, then it is okay la… They are doing a quiz on the computer, maybe they will be more interesting (Teacher A).
One of the possible reasons contributing to students losing interest in the PPSMI courseware was that students were not actively involved in learning. During the interview, both teachers (i.e. Teacher A and E) indicated that they had stopped using the PPSMI courseware because it was not motivating. The courseware was merely like a slow motion television show in which students were passively consuming the learning content. The courseware was good at visualising abstract concepts, but not interactive (i.e. passive learning).
Computer games, however, help to improve players’ spatial abilities (Feng et al., 2007; Cherney, 2008; De Lisi and Wolford, 2002) as well as engage them in active learning. Interactivity is one of the essential elements in computer games because players are learning by doing. In games, learning is a cyclic process because knowledge is constructed through constant practice. Given a problem in games, players devise a solution, test it, reflect on the feedback, refine the solution, and test it again (Kiili, 2005b). To learn, games have to provide instant feedback on what the players have done. The interactivity in games engages active learning. This is an experiential learning in which knowledge is a combination of grasping experience, and learning by doing (Dieleman and Huisingh, 2006). In games, knowledge is not passively consumed, but it is actively discovered. It eliminates the negative learning experience such as boredom and confusion in understanding.
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b. Mathematics Computer Games
Teacher C had used and was still actively using computer games to teach mathematics. He said,
Only four basic operations just like plus, minus operations. There is a game called Command and Conquer (i.e. he was not sure of the actual name)… Even a student very good, sometimes they not perform very well in that game… Because they need spend their mind, how fast they can get… They will feel fun. After they feel fun, they will build their interest. After they build their interest, they will learn mathematics better (Teacher C).
After the interview with Teacher C, I had the opportunity to look and play the computer game (refer to Section 4.4.2). The game taught ones with basic calculations and shapes. From my observation, the game was more appropriate for primary or lower secondary students because it involved basic mathematics. Nevertheless, it could be used to add little excitement to the classroom learning environment. Although the game was simple, I did have some fun when playing it because it tested my response rate in addition to my mathematical skills. From my point of view, it was the implicit skills required (i.e. fast response rate and concentration) that made the game interesting, not the quality of the questions in the game.
Computer games value not only explicit and verbal knowledge, but also the implicit knowledge that built into their movements, bodies and unconscious ways of thinking (Gee, 2007). Neither explicit nor implicit knowledge alone is sufficient to be a good game player. The need for multiple abilities and intelligences has made the game interesting. Children like to play games because games require different learning skills such as researching, thinking skills, problem-solving and social skills (Prensky, 2001c). A broad coverage of skills and knowledge is taught across different game genres because different genres require different of implicit skills.
5.3.4 Problem-Solving Techniques
Problem-solving is the fundamental activity in the teaching and learning of mathematics. Three teachers shared their problem-solving techniques, and adopted four primary stages - understanding the problem, devising a plan, carrying out the plan and looking back (Polya, 1945). They said,
Understand the problem, do proper sketching; we need to draw a simple diagram to understand yes, they do. Then write down your equation and then solve it and check your answer (Teacher A).
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We ask them to read question at least more than 3 times. And then try to identify what are the information given. Then try to plan out the strategy. What formula to be used. What have to find. Step by step (Teacher D). They have to understand the question, and then they have to identify what is required by the question. I will ask them to underline the important points. Identify the formula and solve it. Finally, check using a calculator [Translated from Mandarin] (Teacher E).
In the first phase of understanding the problem, students are advised to read the question for at least three times. In this stage, students need to understand what is required by the question based on the information given and highlight the important points. During the second phase of devising a plan, students should plan their strategy (e.g. do proper sketching or diagram) and identify the formula to be used. The third phase is to implement the plan. Finally, the fourth stage is looking back, and students are advised to check their answers (e.g. using a calculator).
Problem-solving techniques that are stressed by these teachers include both cognitive and metacognitive skills. For instance, reading is a cognitive skill (Artzt and Armour- Thomas, 1997) while understanding the problem, planning a strategy and checking the answer are metacognitive skills (Artzt and Armour-Thomas, 1997; Yimer and Ellerton, 2006). The process of problem-solving seems to link with Bloom’s Taxonomy – remembering (e.g. recall a formula), understanding (e.g. comprehend the question), applying (e.g. solve the problem), analysing (e.g. draw a diagram), evaluating (e.g. check the validity of the answer) and creating (e.g. planning a strategy). In this section, it is understandable that mathematics problem-solving is taught formally and in a step-by-step manner in schools.
In computer games, however, problem-solving appeared to be informal, natural and flexible. In games, players are not confined to a pre-fixed step-by-step problem- solving approach but free to adopt any strategy that they think will work through trial and error. The players can learn and progress by testing a hypothesis, taking a