Elaboración, adecuación y pruebas de funcionamiento del bombo de

Introducing and attempting to implement any new teaching approach comes with its own challenges. According to McIntosh and Jarrett (2000), many teachers feel unprepared to take a problem-solving approach in teaching mathematics because few teachers learned mathematics themselves in this way. They further argue that even if they encountered problem solving in their college methods courses, once in the classroom, they often conform to the conventional methods that hold sway in most schools. McIntosh and Jarrett noted that teachers today have failed to be agents of change because teachers are often caught between daily pressure from colleagues, parents, and others to uphold tradition in the classroom, and pressure from policymakers to employ standards-based practices (with the conflicting expectation that students will perform highly on standardized tests that measure basic skills, not performance of standards-based material).

In this section, the study will discuss questions that focused on the negative effects and challenges of implementing a problem-solving approach intervention, as highlighted by the facilitators. To start with, the study established at what level the respondents first encountered a problem-solving approach in their academic ladder. The results in Figure 4.22 show that 87.5%

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of the respondents first encounter problem solving at the college level while 12.5% encountered it at the secondary school level.

0 20 40 60 80 100 secondary college 12.5 87.5 P er ce n tag e

Figure 4.22: Encountering a Problem-solving Approach

With a majority of the facilitators (87.5%) encountering a problem-solving approach at the college level, it leaves many unexplained questions concerning how they learnt mathematics in their earlier levels of education. Nonetheless, the techniques used for teaching at the primary and secondary levels directly impact how one perceives the teaching and learning process. If the procedural/conventional approaches were used, learners get accustomed and it becomes somewhat of a challenge to adapt to different approach like problem solving.

The study went further to established how frequently the respondents used problem solving approach and the results in Figure 4.23 indicate that 87.5% used it at times while 12.5% used a problem-solving approach always. These

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12.5% respondents claim of using a problem-solving always, depend upon their understanding and interpretation of a problem-solving approach.

0 20 40 60 80 100

Never at times always

0 87.5 12.5 P er ce n tag e Figure 4.23: Frequency of Use of a Problem-solving Approach

This signifies that the use of a problem-solving approach has a long way to go to take root in classrooms in a major way because teaching through problem solving is not easy since many of were taught by remembering facts whether or not they were related to each other, whether or not were interested in the subject, and in some instances were taught by rote. In fact, many teachers may say that problem solving in their particular subject area is not possible, not helpful, or only possible in limited parts of the subject matter. For example in a study conducted in Ethiopia, Bishaw (2011) established that teachers have low level beliefs regarding the use of a problem-solving approach and that teachers are employ a traditional (conventional) approach.

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This study established from respondents on what they regarded as negative effects of a problem-solving approach and these included time wasting, only applicable to small class size, pegs high demand on the teacher, require lots of resources and lacking in individual evaluation as shown in Figure 4.24. The study established that 75.0% of the respondents said the approach wastes time, only applicable to small class size and pegs high demand on the teacher respectively, 62.5% indicated that it requires lots of resources to implement and 100% said it lacks individual evaluation.

Figure 4.24: Negative Effects of a Problem-solving Approach

With regard to time, the respondents alluded that a problem-solving approach causes a delay in the completion of the syllabus. They felt that it takes a considerable amount of time to cover the syllabus through a problem-solving approach which spills out of the government stipulated school terms and thus

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they were concerned that parts of the mathematics curriculum will need to be omitted.

Pertaining to class size, the respondents expressed the fear that learners have never met open-ended problems before and with the growing class size the facilitators will not effectively reach all the students to ensure they have constructed their own appropriate conceptual knowledge. It is not surprising that in more open problem-solving situations, some learners will feel insecure. They added that traditionally, some teachers of mathematics have given learners algorithms to practice and copy because of their inability to reach all of them in a class lesson.

Accordingly, in relation to a problem-solving approach placing high demand on the teacher, the respondents noted that this approach comes with lots of new demands on the facilitator that bring about discomfort because it is new to most of the pre-service teachers. Most pre-service teachers currently teaching have not been students in a classroom where a problem-solving approach was part of the mathematics teaching programme. Many of the respondents believed that it is not possible to use this approach to teach without first experiencing the approach as a student.

The other challenge mentioned was that this approach requires a lot of resources to implement. The 62.5% of the respondents who agreed to this challenge noted

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that a problem-solving approach requires the use of different teaching resources to facilitate learning, which are not readily available in the study centres. Some cited that they only have one set of reference materials (a non-activity oriented text book or module) and varying the novel questions will be challenging without multiple sources.

The challenge of lack of individual evaluation was reported from 100% of respondents who noted that when most of the work is done in groups it becomes difficult to quantify individual understanding and performance. They also said that it kills the spirit of competition because learners work harder when they know that when they get correct answers alone they will also do well in summative evaluation and be ranked.

The study went further and investigated the challenges respondents encountered while implementing the problem-solving approach in teaching and learning mathematics. The challenges listed included: lack of time to prepare for the lecture, the teaching module they used was not activity oriented too many learners in a class to manage them in groups, slow method that delays completion of the syllabus, external examination pressure, negative student reception and rejection by fellow respondents (see Figure 4.25).

171 0 10 20 30 40 50 60 70 80 90 100 lacked time to prepare for the lecture teaching module not activity oriented to many learners to manage in groups slow method that delays completion of syllabus external examination pressure negative student reception rejected by colleagues 50 100 75 62.5 62.5 37.5 50 P e r c e n tage

Figure 4.25: Challenges of a Problem-solving Approach in Teaching and Learning of Mathematics

In relation to time, 50% of the respondents said they did not have enough time to prepare for the lecture, citing the complexity involved in finding good problems to use for different concepts.

They also mentioned the teaching modules approved by the institutions. All of the respondents noted that the modules were not designed with activities that promote the use of a problem solving approach. The study could not supply the facilitators with problems as a result of limited time. However, the facilitators were guided during the workshop to write out activity oriented problems from the mathematics modules they have been using to teach mathematics. In

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addition, they were supplied with set of hand-outs containing problems for use during face-to-face meetings.

Class size was also a challenge with 75% of the facilitators mentioning that the classes were too large to be managed effectively in small groups.

Negative reception of a problem-solving approach at minimal with only 37.5% registering this concern, while 50% of the respondents noted rejection of the approach from fellow facilitators. That is, fellow mathematics facilitators in the same study centre they teach with refused to use the approach to teach mathematics, therefore encouraging rote learning.

Finally 62.5% of the facilitators noted that a problem-solving method was a slow method that delays completion of the syllabus and external examination pressure does not allow respondents to implement it to the fullest.

The findings in the results above are in agreement with those obtained by Anderson (2005). For example, Anderson (2005) found that teachers agreed they needed considerable support in the form of time and resources so that they can implement problem-solving approach in the classroom.

173 4.7 Chapter Summary

This chapter has considered results, interpretation and discussions. The study found that a problem-solving approach used in teaching mathematics to pre- service prospective elementary mathematics teachers has the potential of positively affecting their levels of cognitive learning domains and thereby improving their achievement in mathematics. It was also found that the views of the pre-service prospective elementary mathematics teachers before and after the intervention were more of instrumentalist driven than problem-solving driven. Additionally, a problem-solving approach, if fully implemented has the potential of changing the instrumentalist driven view of the pre-service prospective elementary mathematics teacher to a problem-solving view. The study also observed that before the training workshop, the facilitators who teach pre-service prospective elementary mathematics teachers, held divided views of what mathematics teaching and learning consists of. Their views were divided between instrumentalist and problem-solving driven views. However, after being immersed in teaching and learning mathematics through a problem- solving approach during the workshop, their views became more oriented towards a problem-solving driven view than an instrumentalist driven view of teaching and learning mathematics. The facilitators during the implementation stage could not fully put into practice their newly formed perceptions about mathematics teaching and learning as a result of a number of impeding factors.

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CHAPTER FIVE

SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATIONS

5.1 Introduction

Students‟ achievement in mathematics is largely dependent on the instructional approach. Therefore the purpose of this study was to investigate the effect a problem-solving approach had on the UCC-CCE distance learners‟ achievement in mathematics in Ghana. The study was guided by four objectives: (1) to determine the difference a problem-solving approach makes on UCC-CCE DBE DLs achievement scores in mathematics, (2) to establish the change UCC-CCE DBE DLs‟ perceptions about mathematics teaching and learning before and after learning mathematics through a problem-solving approach, (3) to determine the effects of a problem-solving approach on UCC-CCE mathematics facilitators perceptions about mathematics teaching and learning and (4) to determine the challenges faced by facilitators in adoption of a problem-solving approach in teaching mathematics. The data collected were analyzed, presented and discussed based on the above objectives using Microsoft Excel and Statistical Package for Social Sciences (SPSS) package. It also tested and discussed two hypotheses. Therefore, this chapter summarizes the findings of the study, draws conclusions, makes recommendations and suggests areas for further research.