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do not give such problems to my students. However, with the newly introduced curriculum, there is no way out. I have to find time for my students to solve non routine problems.”(Mr BT1, pers.comm.).
Using logic or mathematical reasoning
Although use of activities that prompted students to use logic in making conclusions was not common in the lesson plans that were analysed, the researcher found that in five of the lessons taught by the teachers, students were exposed to mathematical reasoning. The following example was obtained from exercise books for students taught by Mr CT2. The teacher was teaching sets as a prerequisite for functions.
Consider ℳ= , ℵ= and ⅅ=
.Given that ℳ=ⅅ ℵ and ⅅ ℵ , what conclusion can you make about snakes?
Solving project-like problems
Data obtained from the students’ exercise books showed that students taught by the mathematics teachers who participated in this study were sometimes given project-like problems. The students were given real life situations in which they were expected to research, for them to get workable solutions to given problems. The following task was given to students by Mr HT1.
Record sales made by a vegetable vendor at any vegetable stall for a full week.
Draw a graph to show the sales against the days of the week. Draw a trend line on the graph. Find the equation of the trend line. Use the line to decide if the vendor’s business was improving or not.
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Visual teaching aids
Data obtained from the teachers’ lesson plans and from face to face interviews revealed that the mathematics teachers used visual teaching aids when they taught functions. The visual teaching aids that were used by the teachers included charts, question strips and chalkboard.
As stated in the teachers’ lesson plans, the charts used had some diagrams or graphs of functions. Question strips had questions on the concepts learnt. The chalkboard was used for demonstrations. It was also indicated in the lesson plans that the chalkboard was also used for writing instructions and exercises for the students Visual teaching aids were used in ninety- one (72.22%) of the one hundred and twenty- six lesson plans that were analysed by the researcher. The researcher noted that visual teaching aids were the most common type of teaching aids used by the mathematics teachers that participated in this study.
When asked to comment on the type and effectiveness of the teaching aids that he used when teaching functions, one of the teachers said:
“Teaching aids like charts and illustrations on the chalkboard are easy to prepare. I prefer using them because they can easily be found in our locality.
Although I know that there is need for a variety of teaching aids, the administration at this school does not provide for them, hence we use what is available to us.”(Mr JT1, pers.comm.).
Although sixteen ( 64%) of the mathematics teachers thought that visual teaching aids were very effective when used in teaching functions, five (20%) of the teachers reported that they used visual teaching aids simply because of their availability.
Audio teaching aids
Only two of the teachers indicated that they sometimes used audio teaching aids. When the researcher asked them to give examples of the audio teaching aids they used when teaching functions, the teachers mentioned audio tapes and radio. The teachers said they made use of audio tapes that they got from the internet. They also said they sometimes instructed their students to listen to radio lessons broadcasted over the radio. One of the teachers said:
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“At times my students learn from some tapes that I play for them. I get the tapes from the internet. This form of learning is effective in the sense that my students can learn in my absence. Apart from the tapes, I sometimes make use of radio lessons that are broadcasted between 0900 and 1000 every Wednesday on our national radio station.”(Mrs IT1, pers.comm.).
However, some inconsistencies over the use of audio teaching aids were noted between the data obtained through face to face interviews and the data obtained through document analysis. Data obtained from the mathematics teachers’ lesson plans did not show evidence of the use of audio teaching aids. None of the mathematics teachers had planned to use audio teaching aids even though they claimed during face to face interviews that they sometimes used audio teaching aids.
Tactile teaching aids
Tactile teaching aids refer to teaching aids that teachers or their students can touch and manipulate. These teaching aids include mathematical instruments like rulers, pairs of compass and protractors. The mathematics teachers reported during interviews that they used tactile teaching aids mostly when drawing graphs of functions. Data obtained from the teachers’ lesson plans showed that the teachers had planned to use tactile teaching aids in one hundred and seven (84.92%) lessons. One of the teachers had the following to say on the use of tactile teaching aids:
“When drawing diagrams, students mostly use mathematical instruments. They have no choice in most of the cases. They have to use the instruments whether they like it or not. However, most of the students enjoy using drawing instruments as using them does not demand too much reasoning on their part.
Drawing makes them active in the learning process.” (Mr CT2, pers.comm.).
Information and communication technology (ICT) systems
The researcher found that use of information and communication technology systems in teaching mathematics was generally not common among the teachers who took part in this part of the study. The only electronic gadget that was commonly used by students as shown by the teachers’ plan of instructions was a scientific calculator. As mentioned before in this
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report, only three (12%) of the mathematics teachers claimed that they sometimes used ICT when teaching functions. One of these teachers shared the following statement:
“My students enjoy learning through use of computers. I sometimes ask them to use excel to draw graphs. For instance, if you check on the exercise that I gave them on Monday, I asked them to draw bar graphs showing marks they obtained in this month’s tests. Each student had to show his or her marks on a bar graph.”(Mr TC3, pers.comm.).
The researcher observed that in some of the lessons planned by the mathematics teachers, the teachers did not indicate any intension to use teaching aids during their lessons. No teaching aids were indicated in seventeen (13.49%) lesson plans prepared by the teachers who participated in this study.
6.8 How the mathematics teachers assessed their students’ progress during lessons on