Teachers’ activity in the classroom (Observable indicators) Type of visualization processes after Debes (1969) Rich evidence Medium evidence No evidence Teacher brought to class visual materials Designing visuals Visual materials brought to class are aligned with the subject content Designing visuals Lesson was introduced with the use of visual materials Designing visuals Teacher demonstrates the use of visual elements (lines, shapes, angles and dimensions) Designing visuals Teachers’ activity in the classroom (Observable indicators) Type of visualization processes after Debes (1969) Rich evidence Medium evidence No evidence Teacher used different representation during the lesson. Manipulating visuals Teacher demonstrates proper use of geometric concepts Manipulating visuals Teacher used visuals in a way that allows learners to connect new concepts to what they already know. Manipulating visuals Teacher used visuals in an orderly and logical way to avoid confusing learners. Manipulating visuals Teachers’ activity in the classroom (Observable indicators) Type of visualization processes after Debes (1969) Rich evidence Medium evidence No evidence Teacher used strategies that allow learners to produce visuals Visual language Teacher used visuals in conjunction with his/her verbal explanations. Visual language Teacher responded to questions asked about the visuals by the learners Visual language Teachers used visual language that was consistent with mathematical language and terminologies. Visual language Teachers’ activity in the classroom (Observable indicators) Type of visualization processes after Debes (1969) Rich evidence Medium evidence No evidence Teacher properly identified and evaluated visual materials Interpreting visuals Teacher asked questions that prompted critical thinking and critical reasoning among learners. Interpreting visuals Teacher concluded the lesson using visual materials. Interpreting visuals
Teachers’ activity in the classroom (Observable indicators) Type of visualization processes after Debes (1969) Rich evidence Medium evidence No evidence Teacher communicated to learners using visual materials Analyzing visuals Teacher used visual materials that deconstructed properties of shapes. Analyzing visuals Teacher encouraged learners to work with the visuals in terms of the concepts that were taught. Analyzing visuals The coding of various observable indicators which will form the basis of my analysis is as follows: Rich evidence: Here the teacher demonstrates an abundance and big variety of the specific indicator. For example, under designing visuals, abundance would refer to the teacher bringing to the class four or more visual materials. It would also refer to the teacher engaging deeply with these visuals. Medium evidence: Here the teacher only uses one or two visual materials and engages with them on a relatively superficial level of the specific indicators. No evidence: Here the teacher does not use any visual materials and does not engage with any visual processes. Validity Maxwell (2009) asserts that validation is an important way of ruling out the possibility of misinterpreting the meaning of what participants say and do, and the perspective they have about what is going on. Cohen, Manion and Marrison (2007) state that in qualitative research validity should be addressed through the honesty, depth and scope of the data achieved. In this study I will use triangulation (Gay, Mills & Airasian, 2012) to validate the data collected. For example, I employ audio-video recordings, stimulus recall and focus group interviews. This study will adopt a strategy of member checking to ensure internal validity and credibility. Meriam (2009) states that the process of member checking involves a discussion of preliminary analysis and interpretations with the participant teachers before making any conclusion. Member checking will help me to identify my own biasness and misunderstanding. All the four participating teachers will be involved collectively to share their views and perceptions about the interventions in the context of my stimulus recall and focus group interviews.