6.6 Teaching strategies used by the mathematics teachers when teaching functions
6.6.1 Findings from face to face interviews
The data obtained from face to face interviews revealed that when teaching functions the mathematics teachers used the strategies outlined in Table 6.2.
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Table 6.2: Summary of the findings from face to face interviews on the teaching strategies used by the mathematics teachers when teaching functions. (n=25)
Strategy used by the mathematics teachers Frequency Percentage
Peer group discussions 25 100%
Individual work 25 100%
Projects 15 60%
Guided discovery 11 44%
Demonstration and illustration 25 100%
Interactive e-learning and ICT 3 12%
Inquiry 2 8%
Peer group discussions
Data obtained from the mathematics teachers during face to face interviews revealed that all (100%) the mathematics teachers who participated in this study used both individual and group activities when teaching functions. The researcher found that twenty (80%) of the participating teachers reported that they allowed their students to work in pairs while five (20%) said they allow them to work in groups of three. When asked to explain how he used group work when teaching functions, one of the mathematics teachers gave the following response:
“I use both group work and individual work. When I use group work, I give them tasks to perform in groups of three. I always keep the groups small so that each member of the group gets a chance to participate. If the groups are too large some of the students become passive. I give individual tasks after group discussions as a way of checking if the students would have understood the concept taught.” (Ms BT1, pers. comm.).
The researcher asked Ms BT1 to comment on the effectiveness of using group work when teaching functions. She had the following to say:
“When students work in groups, they get an opportunity to discuss on what they consider solutions to given problems unlike in situations where they learn
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as individuals or as a whole class. In groups, they learn to interact, communicate and express themselves to their peers. Some of the students like to lead in the discussions. However, I normally do not use group work due to shortage of time. Discussions need enough time which may not be available.
Thirty five minutes allocated to a mathematics lesson is not enough for me to use group work effectively. The time is not enough for me to allow them to discuss and then get feedback from them. I propose that the lessons be allocated enough time, even up to an hour per lesson. Imagine students who want to make a table of values for the function f(x) = 3x +5, draw the graph to a given scale and then give feedback to the class. It cannot be done in thirty five minutes.”(Ms BT1, pers.comm.).
Projects
The mathematics teachers also reported that they sometimes used projects as learning tasks.
Fifteen (60%) teachers claimed that they gave their students tasks to collect data and then use the data to draw graphs. Another group of mathematics teachers indicated that they gave tasks in the form of projects in the early stages when they introduced concepts on functions.
The following statements were said by two of the mathematics teachers:
“I sometimes give assignments or projects to my students which they do over a period of one or two days. For instance, last time I assigned them to collect information on daily temperatures in the month of June. I further instructed them to use the data they collected to draw a line graph on graph paper. They also drew a line that showed the general trend of the temperature on the graph.
They went further to find the equation of the trend line.” (Mr FT1, pers.
comm.).
“Normally I teach concepts on sets before I teach functions. My understanding is that functions depend on sets of values. It is during this period that I give students some projects to do.”(Mr ET2, pers.comm.).
Guided discovery
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Eleven (44%) of the mathematics teachers indicated that they used the guided discovery method when they teach functions. Those teachers reported that they guided their students to discover patterns and trends in the concepts they teach. One of the teachers gave the following explanation:
“I believe that one of my role as a mathematics teacher is to lead the students to make logical mathematical conclusions. They should find patterns that arise from using particular formula. When they learn about functions, they can find the patterns created by the functions. For example, they can find the relationship between the coefficient of x2 in a quadratic function, ax2+bx+c, and the shape of the graph produced by the function. I mean the fact that when the coefficient is negative the graph faces downwards and when it is positive it faces upwards. The concept sticks well in their minds if they discover these patterns and relationships on their own.”(Mr FT1, pers.comm.).
Demonstration and illustrations
All (100%) the mathematics teachers who participated in this study indicated that they used demonstrations in their lessons on functions. According to the teachers, demonstrations were done by either the mathematics teachers themselves or by other students. One of the teachers had the following comment on the use of demonstrations in mathematics teaching:
“Demonstrations normally help in giving my students direction. I normally demonstrate on the chalkboard while explaining to them how calculations are done or how graphs are drawn. Even my students sometimes demonstrate to their peers.”(Mr AT2, pers. comm.).
Interactive e-learning and information and communication technology systems (ICT) Three (12%) of the mathematics teachers claimed that they used electronic learning systems as well as information and communication technology when teaching functions. Those teachers said that they used video tapes, audio tapes and computer software to teach their students concepts on functions. They reported that they got some of the video and audio tapes from the internet. One of the three teachers said:
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“Another effective strategy is using electronic systems. These can be in the form of videos which are obtainable on the internet. On the internet we get videos that demonstrate on quite a number of concepts on functions. For example, there are videos that demonstrate how to draw graphs of given functions. Each time I use these videos, I find my students quite eager to learn.
Excel and other computer software can also be used to teach students how to draw graphs of functions.”(Mr GT1, pers. comm.).
The researcher probed the other teachers who did not mention ICT as one of the strategies they used when teaching functions. This was done in order to establish the teachers’ reasons for failing to use ICT system. Table 6.3 summaries the reasons that were given by the teachers.
Table 6.3: The teachers’ reasons for not using ICT as a teaching strategy. (n=25)
Reason for not using ICT Frequency Percentage
Shortage of time 5 20%
The teacher not computer literate 17 68%
Shortage of required equipment 19 76%
Lack of training on the use of ICT 13 52%
Supply of electricity not constant 5 20%
School authorities or leadership not supportive 2 8%
Teacher having negative attitude towards use of ICT 2 8%
The data obtained from the mathematics teachers revealed that the most common reason for not using ICT in teaching functions was shortage of ICT equipment in schools. At three (30%) of the schools that were selected for this study, the teachers reported that they did not have computers and other information and communication technology equipment at their schools. The researcher also found that computer illiteracy, on the part of the teachers, was also a major cause for the teachers’ failure to use computers or other information and communication technology systems. The following were some of the statements that were mentioned by some of the teachers concerning the use of ICT:
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“I need to learn to use a computer. My students are far ahead of me in terms of technology. How can I try to use ICT in my lessons when my students know better than me? I will end up embarrassing myself.”(Mr DT1, pers. comm.).
“Computers in this area are not very common. We do not have even a single computer set at this school.”(Ms HT1, pers.comm.)
The researcher observed that some of the mathematics teachers had negative attitude towards the use of computers in teaching mathematics. Two of the mathematics teachers interviewed frowned before responding when they were asked about the use of computers in mathematics teaching. The other teachers blamed the school authorities for not being supportive in sourcing computers for them. Two of the teachers were quoted as follows:
“mmmmm information and communication technology systems do not really work with the students I teach. I do not consider them effective.”(Mr ET1, pers.comm.).
“We have been requesting for laptops to use in the department for a long time now. Nothing has been done for years. We are tired of making the same requests again and again.”(Mr FT1, pers.comm.).
Inquiry learning
Two of the three teachers who claimed that they used ICT when teaching functions reported that they used ICT when they used the inquiry method of teaching. According to those teachers, inquiry method meant that the teacher gives a mathematics problem to the students and ask them to seek solutions through investigation and online researching. The students could make use of online sites or social media for inquiry purposes. The teachers said that the students could connect with people in the outside community for possible solutions. The teacher’s role in this case was that of facilitating the inquiry process. Mr GT1 explained the strategy as follows:
“At times I ask my students to make use of social media or sites that are online to find solutions to given problems. All I do as their teacher is to give them tasks. In most cases I give each student a different task. The students look for
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possible solutions from different sources even from distant people. They use the
‘anytime-anywhere’ mode of learning. This method is very effective as it ensures that the student looks for his or her own possible solutions to problems. It means the student becomes an active learner.”(Mr GT1, pers.comm.).