A NÁLISIS LOCAL DE LA TRANSFERENCIA DE CALOR POR CONVECCIÓN

5.3.1 Research question 1

This research question is re-stated in Section 5.2.4 of Section 5.2. In Section 1.9.3 and Section 1.9.4, the researcher provided suitable definitions for what constituted the constructivist-based teaching method (CBTM) and the traditional teaching method (TTM). Hence these definitions provided a suitable context to highlight the key features of differences between the two comparative teaching methods. For instance, in Section 1.9.3 the researcher used Brooks and Brooks (1999) to emphasise the fact that CBTM is more learner-oriented than the TTM, which was explained as largely emphasising the role of the teacher. In TTM, the teacher is considered to be the pourer of knowledge while in the CBTM the self- construction of knowledge by learners is foregrounded. In addition, Section 1.9.2 was used to emphasise a useful link between CBTM and a group learning approach (Section 1.9.9). It was made clear that CBTM is better positioned to embrace elements of group learning approach than TTM, which seems to give a teacher a bigger role during a lesson.

Furthermore, in Table 2.2 of Section 2.3.6, the researcher drew from the existing literature to highlight the distinguishing features between CBTM and TTM (for

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examples, see, Applefield et al., 2001; Brooks & Brooks, 1999). Finally, a description of instructions in the experimental group and control group during the course of this study is documented in Section 3.7.2.2 and Section 4.6. Section 4.6 in particular provided a detail discussion on how CBTM teaching was implemented in the experimental group. This discussion is useful in providing a context of contrasting pedagogical approaches that were meant to expose and provide a suitable treatment for the emerging learners’ errors during a sequence of experimental lessons (investigation). Subsequently, the superiority of CBTM over TTM is confirmed by the results of this study, which are presented in Chapter 4. Given this background it is reasonable to conclude that the first research question was addressed through the literature and observations of instructions in both groups.

5.3.2 Research question 2

This research question is re-stated in Section 5.2.5 of Section 5.2. In simple terms, the second research question of the current study was meant to observe the teacher moves, which were primarily meant to encourage learners to expose or reveal their tendencies to do errors when they solve Grade 11 algebraic tasks. It must be noted that the teachers in the experimental group and the control group used contrasting pedagogical strategies to achieve this. In the experimental group, where CBTM was prominent, the researcher opted to incorporate elements of group learning approach (Section 1.9.9) in which participants continuously engaged in constructive learning dialogues. In Section 1.9.10 these dialogues are fittingly described as exploratory talks (see, page 13 of this dissertation) because during these robust verbal interactions learners argued, critiqued and probed their group members’ points of views.

The process that is described in the preceding paragraph tended to encourage group members (in the CBTM lesson) to be more keen to verbalise their pre- existing algebraic knowledge, which also tended to reveal (expose) their conceptual errors in algebra (see, Section 3.9; see also, Section 4.6). In Section 4.5 several examples of some of the learners’ errors that were identified (exposed) during a CBTM lesson were elaborated. In an attempt to observe the teacher’s moves that facilitated the exposition of learners’ errors in the control

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group where a TTM was implemented, the researcher conducted a series of lesson observations (see, Section 3.7.2.3). Section 4.7 discussed and described how the lesson observation enabled the researcher to ascertain how learners’ errors were exposed and how the teacher treated the errors during instruction.

In comparison with the experimental group, error exposition and treatment were minimal in the control group (see, Section 4.7). Moreover, Table 4.29 and Table 4.30 provided evidence about learners’ errors that were exposed and the effects of both interventions on the frequency of learners’ errors before and after the intervention. It was evident from Table 4.29 that CBTM intervention significantly reduced learners’ errors in all the four conceptual areas in algebra in the experimental group than the TTM intervention in the control group. On the basis of the evidence alluded to, it can reasonably be concluded that the second research question of the current study was adequately answered.

5.3.3 Research question 3

This research question is re-stated in Section 5.2.6 of Section 5.2. Research question 3 focused on the possible treatment of learners’ errors that were anticipated in both comparative learning environments (the CBTM and TTM). In this context, the treatment of learners’ errors would be measured in terms of learners’ successive pre-test and post-test performances during the course of an experiment. Given that this study had initially drawn a link between learners’ errors in algebra and performance in Mathematics (see, Section 1.5 & Section 2.2), the current study was therefore premised on the notion that more errors would result in learners’ poor performance in Mathematics, and vice versa. In an attempt to answer research question 3, the researcher monitored learners’ performance in both learning environments (CBTM and TTM). Hence the performance of learners (participants) in the achievement test at pre- and post- stages of the experiment was considered to be a suitable yardstick to achieve the measurement, namely, the treatment of learners’ errors during each type of instruction.

Descriptive statistics presented in Table 4.2 of Section 4.3 shows a relatively better post-test performance of learners in the experimental group when compared with

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learners in the control group (see comparative mean scores in Table 4.2). In Section 4.3 the researcher concluded that the observed post-test performance, which was observed to show significant gains from the pre-test performance in both groups, suggested “a significant reduction in learners’ errors in algebra” (see, Table 4.30). Most notably, the comparative post-test performances of the experimental group and control group suggested that CBTM is more effective than TTM in terms of producing a treatment of learners’ errors in Grade 11 algebraic classrooms (research question 3).

In fact, Chapter 4 presents several study results that persistently confirm the fact that CBTM is more effective than TTM (for examples, see, Table 4.3; Table 4.4; Table 4.5; Table 4.6; Table 4.8; Table 4.11; Table 4.30). Almost all the information that is contained in the tables that are given as examples in the preceding sentence confirms that CBTM is more effective than TTM. Hence the performance of learners in the CBTM learning environment was superior to that of the learners in the TTM learning environment. Given these observations, it is therefore possible to conclude that the third research question of this study was adequately answered.