MOVIMIENTO DE TIERRAS .1 ÁMBITO DE APLICACIÓN

Preparation of the questions to be used with the focus groups considered the content, quantity and language used in them. The questions were based on the outcomes from the 57 questions in the MRBQ survey questionnaire used in the first phase of the study. A total of 5 questions from each of the factors were included making a total of 20 questions in all. The questions were designed to probe beyond the questions asked in the MRBQ scale. The focus group

interviews took place within a single class period of duration forty-minutes during the school day. This was considered to be a reasonable time period for students aged 13-14 years of age to engage in discussions.

A number of the questions from the MRBQ questionnaire were combined to make a single question in the interviews. An example of this is:

The language used in some of the questions was altered to aid students’ understanding of the question. An example of this is Q. 42 of the survey instrument that states ‘I think it is important to learn different strategies for solving the same problem?’ The language in the question was changed to ‘Do you think that it is important to learn different approaches for solving the same problem?

The format adopted for use in the groups and individual interviews was designed to make students consider each individual question one at a time. Stimulating discussion was addressed by prompts ‘Why/Why not?’ This did not include the questions on teacher’s perception, as the participants would not

know why the teacher had done or not done something. Also, included were requests to students to ‘give an example’ in order to illustrate and allow them to expand upon their answers. An open question at the end of the interviews was also included to encourage students to give any other views they might wish to include in the discussion. In the beginning of each of the focus group interviews the participants were reminded about the purpose of the study and the

confidentiality of the group’s discussions. The group was advised that their discussion would be recorded in audio. The participants did not appear to have a problem with this. The participants were thanked and advised that each of their contributions was welcomed. The students were then asked to say exactly what they thought in answer to the questions on the role of the teacher in the classroom.

The focus groups had not been a part of the original pilot study (discussed earlier in this chapter) that had taken place in the previous academic year. A focus group pilot study was carried out to test the suitability of the questions and the language used in them. Feasibility is a concern in many studies (Hatch, 2002:51). The interview was audio recorded in the mathematics classroom. This provided a familiar and quiet environment and enabled the discussions to be audio recorded satisfactorily.

The following instructions were given to the group who had volunteered to take part in the pilot. ‘Read the questions one at a time and say what you believe is true. If you are not sure what the question is about you can ask me to explain it to you’. All of the focus group interviews, including the pilot, were transcribed on the same evening that they had taken place (Appendix B). The majority of the questions appeared to have been understood by the participants. A small number of changes were made to the wording of the original questions. An example of this is:

The role of the moderator is a crucial one in determining the success or

stifle discussions or individuals may led to biased findings (Hatch, 2002:132). The goal was to make the students feel responsible for managing the

discussions themselves and hence produce data for this study (Morgan, 1996:49). Reliance was placed on the interaction within the groups based on the questions provided (Morgan, 1996:2). The questions were given to the groups and a request was made for one student to volunteer to read out loud the first set of questions to be discussed. As moderator, the aim was to ensure that every individual was given the same chance to give their personal view on the questions and each participant was also encouraged to generate discussion concentrated on the questions asked (Hatch, 2002:132).

Following the completion of the pilot focus group and subsequent changes to the questions two groups were invited to take part in discussions. They consisted of a group of four boys and a group of four girls (Appendix B). The classes had been divided into small groups for the purposes of collaborative work solving problems in the classroom. These two groups were invited to take part, as they appeared to be a reasonable representation of the intervention class. Ethical considerations were as described earlier in this chapter. 3.8 The Intervention (Phase 2)

Andrews et al. (2000:259) recommended teachers should use classroom interventions with a view to enhancing performance. Much research has been carried out into mathematical instruction on what might help students’

understanding of concepts. Methods such as direct teacher explanations, strategy instruction are but two found to be successful in improving

mathematics skills in students (Bottge, 2001:102). Bottge’s (2001:104) key model of problem solving was adapted for use with the classroom intervention in this study (Figure 2). The literature review (Chapter 2) of this study defined the characteristics of the learning environment that should be employed in the classroom. The characteristics were:

1. Active Learning Methodologies

2. Explicit instruction in problem-solving skills

3. Students gradually take responsibility for their own learning 4. Use of routine and non-routine problems

5. Small group work introduced

7. A focus on effort in the classroom  

INSTRUCTION RESULTING IN OUTCOME

Appropriate activities challenging students to solve tasks themselves

Engagement Explicit Instruction in basic problem- solving skills The provision of necessary tools to enable problems to be solved Informal: Classroom culture promoting growth in students’ knowledge through connecting new information with previously learned knowledge Appropriate Scaffolding Situational : Context and learning are inseparable Transfer of skills to routine and non-routine problems

Social: Small Group Work- encouraging students to

communicate what they are learning.

Teacher gets a more accurate measure of students’ understanding of concepts. Students develop new understandings (Bottge, 2001:108) Teacher Specific: Teacher expectation influences performances (Bottge, 2001:109)

All students are

expected to put in their best effort to learn.

Adapted from Key Model of Problem Solving (Bottge, 2001:104) Figure 2

1. In this study, Active Learning Methodologies were promoted by the use of appropriate activities, matched to syllabus content, that required students to understand and generate meaning about concepts (Zweck, 2006:5). The aim was to develop a community of learners whose members learned together and from each other. The role of teacher helped students make sense of the mathematics by asking questions that prompted them to clarify, elaborate, justify and critique their conjectures and solutions (Goos et al., 2004:105).

Success was measured by students’ understanding, engagement and achievement.

2. The focus is on teaching mathematics via problem-solving by engaging students in doing mathematics, creating, conjecturing, exploring, testing and verifying (Project Maths, 2011). Effective questioning supported students in the monitoring of their understanding. Questions used with students in the classroom when solving problems included:

‘What do I know? What do I want?

What do the words mean? Can I draw a diagram? Can I find an example? Will it always work?

How is it similar or different to what I have done before?’

(Johnston- Wilder et al., 2003:252)

3. Making students responsible for their own learning was a challenge for a number of reasons. The learning environment as described above had been one where transmission learning has been paramount geared to the external examination system. Assessment for Learning (AFL) was used as a tool to improve students’ learning and involved them directly in the learning process. The characteristics of AFL that the practitioner attempted to include in the intervention were:

a. Sharing learning goals with students

b. Helping students to recognise the standards they are aiming for c. Involving students in assessing their own learning

d. Providing feedback, which helps students to recognise what they must do to close any gaps in their knowledge or understanding e. Communicating confidence that every student can improve f. Adjusting teaching to take account of the results of assessment

4. The aim was to provide the students with rich tasks. Rich tasks are tasks that: a. Offer different levels of challenges making them accessible to a

wide range of learners

b. Encourage collaboration and discussion

c. Have the potential to reveal underlying principles and connections with other areas of mathematics

d. Encourage learners to be confident, independent and critical thinkers (NRich, 2008)

An example of an activity used with students is in Appendix B.

5. Small group work: there is general agreement in the literature that small group work has positive effects on learning but that it can be challenging to implement in the classroom (Swan, 2005:8). The aim in this study was to develop genuine collaboration amongst the groups working together. Mercer et al., (2008:31) emphasize the task design. Tasks that were considered to be too simple or indeed too complex were rejected in favour of open-ended, challenging tasks with clear task structure. The quality of relationships in the groups would seem to be important too (Mercer et al., 2008:31). Participants within groups in this study were encouraged to relate in positive ways by being given roles to play in their group. They were given four particular roles with the intention of making individual students responsible for active

participation in solving the task (Cohen, 1994:17). These roles were:

a. Facilitator: who makes sure everybody is listened to, contributes and that everybody agrees and understands the solution.

b. Captain: Keeps the group on task with the work to be completed c. Reporter: writes down the group answers agreed by all and checks

it is written down correctly

d. Resource: Alerts the group to the possible strategies available for solving the problems (CPM, 2009:11).

Participants were given ground rules for working in groups. These rules were reinforced regularly and also at times when they appeared to be necessary. Using group work with the students in the classroom was new to the practitioner.

This provided an additional challenge when implementing the new learning environment.

6. Students to be made aware of their beliefs about mathematics and its teaching and learning: Moscucci’s (2005:301) 5-step meta-beliefs systems activity (mBSA) was not carried out formally in the classroom due to the time constraints but a number of the steps were used and helped to inform the creation of the learning environment.

a. Step 1 of the mBSA activity advised a logbook be kept on the quality of every learner’s beliefs systems. With 28 students in the classroom this was not considered to be feasible.

b. Step 2 involved the carrying out of class conversations to discover learners’ interests and their expectations without referring to

mathematical interests. This step was adapted for use in this study by students being encouraged to express their opinions on all aspects of the teaching and learning in the classroom. During whole class discussions, students’ advice and opinions on the value of the activity being used, the teaching approach, the type of scaffolding that would help the understanding of the concept being taught was sought. A diary was kept recording information on students’ contributions (Appendix B).

c. In Step 3 of the mBSA (Moscucci, 2005:302) a learning

environment is created wherein questions about belief categories arise spontaneously. To help students’ gain awareness of their beliefs about their relationship with mathematics whole class discussions were encouraged at specific appropriate times.

Questions of particular interest included Is there an inborn aptitude to mathematics? and Do you have to be intelligent to be good at mathematics?. This was linked to the belief that persistent effort to learn mathematics is what matters when seeking success.

d. Steps 4 and 5 were not considered for implementation in this study. An analysis of the role of problem solving in constructing

7. As the practitioner, the author placed an emphasis on the effort to learn, to enjoy and to understand mathematics. Participants were encouraged to persist in their efforts to learn mathematics and were reminded that this would bring success over time. Each month participants were rewarded for their effort with a small nominal prize.

Phase 3 - On Monday May 2nd 2011 the survey questionnaire was distributed