| Abstract |
This study challenges a commonly held view that teachers tend to adopt a more traditional teaching method when teaching in classes of lower achieving students. The study comprises two case studies, each of a teacher who teaches the same syllabus in two classes of different levels. Quantitative and qualitative analyses of observed teaching practices and classroom interactions in 46 lessons suggest that one teacher adopts the “transmission of knowledge” approach in both her classes, emphasizing basic skills and rote learning; whereas the other teacher emphasizes more thinking, understanding and problem solving. Surprisingly, both teaching profiles were enhanced in the lower level class of each teacher. The findings suggest that in her own way, each teacher aimed to help more the students who encountered more difficulties – the lower achieving students – and she did it by using the resources available to her. Theoretical and practical implications will be discussed. |
| Summary |
Aim: Current literature suggests that teachers tend to pose challenging problems that require higher order thinking to high-achieving students, and adopt the “transmission of knowledge” approach, emphasizing basic skills and rote learning of facts and procedures, in classes of low-achieving students. However, these findings are based mainly on teachers’ self reports and not on examination of classroom practice. Also, it is not clear whether the reported differences are related to differences between the teachers teaching in the respective classes as research shows that usually the more competent teachers teach classrooms of high-achieving students whereas less competent teachers teach low-achieving. This study addresses this shortcoming of current research and examines actual practices of teaching mathematics and classroom interactions in classes of different levels taught by the same teacher. Methodology: Four classes in the same school participate in the study: two classes of 3-unit level; the other two of 4-unit level (3 being the lowest). All four classes studied the same probability syllabus. Two classes (one 3-unit and one 4-unit level) were taught by one teacher; the other two (one 3-unit and one 4-unit level) – by another teacher. This research design enables us to examine teaching characteristics of each teacher, and to compare practices of teaching mathematics and classroom interactions between (1) different level classes of the same teacher, and also (2) same level classes of different teachers. Main data source is observation of all probability lessons in each class during one school year. The 46 lesson observations were audio-taped and field-notes were taken. After all observations were completed an individual semi-structured interview was conducted with each teacher, focusing on the teachers’ views of teaching probability in different level classes, and whether they thought there were differences between their ways of teaching in the two classes. Two units of analysis were used: utterance and activity. Using utterance as the unit of analysis, we examined students’ opportunities to participate in the class discourse, comparing the relative share of talk between teachers and students and the nature of the talk. We employed, to a large extent, the coding system developed in the comprehensive TIMSS-Video Study with some modification. Statistical analysis was performed on two types of measurements: quantitative measurements using non-negative discrete numbers, and percentages of some totals. In addition, qualitative and quantitative analyses were also conducted, using activity as the unit of analysis. We examined students’ opportunities to make decisions regarding ways of solving problems. We scrutinized various aspects of the nature of talk during whole group work, such as, how problems are solved, what solutions are presented to the whole class, and how they are chosen for presentation. Findings: Quantitative and qualitative analyses of observed teaching practices and classroom interactions suggest that one teacher adopts the “transmission of knowledge” approach in both her classes, emphasizing basic skills and rote learning. The pattern of interaction characterized mostly her classes is the Funnel Pattern (Wood, 1994) where the teacher’s questions aim at directing students to a solution procedure preferred by the teacher. This teacher’s students had very little opportunities to have a significant role in class discourse. The teacher rarely asked students to explain their methods of solution and, instead, focused only on getting a correct final answer. She did not let her students decide about ways of solving problems – instead she asked them to memorize and follow rules in order to get correct final answers. Just on rare occasions did the teacher allow students to present their work to the whole class, and, only if it was correct and done in the way she desired. Compared with this teacher, the other teacher emphasizes more thinking, understanding and problem solving. The pattern of interaction characterized mostly her classes is the Focusing Pattern (Wood, 1994) where the teacher’s questions aim at helping students focus on the important aspects of the mathematics problem but leave the actual solution of the problem to the students. This teacher aimed at understanding students’ methods of solution, encouraged students to propose and justify alternative solutions, and to present and discuss their work with the whole class. Surprisingly, both teaching profiles were enhanced in the lower level class of each teacher. The first teacher became more transmitter of knowledge, expecting her students to be passive retrievers of knowledge, and she tended more to “spoon feed” students with bits and pieces of knowledge, presenting mathematics as a rule-following domain. The other teacher emphasized higher order thinking more in her lower level class, and encouraged more her low-achieving students to propose, present and discuss alternative solutions to problems. A possible explanation for this finding is that both teachers are considered skilled and caring teachers in their school. Both display real desire to help their students. Thus, it may not be surprising that each teaching profile is enhanced in the lower level class. The analysis suggests that in her own way, each teacher aimed to help more the students who encountered more difficulties – the lower achieving students – and she did it by using the resources available to her. For one teacher it means to give them formulas and clear-cut tools, so that they know what to do in each case. For the other teacher it means to be attentive to the students, to understand their thinking, not to give formulas and rules, but instead focus on explanations and understanding. Significance: The unique research design produces reliable results that challenge the commonly held view that teachers tend to adopt a more traditional teaching method when teaching in classes of lower achieving students. The results imply also that it might be beneficial to assign to low-achieving classes teachers whose teaching profile is characterized by emphasis on thinking, understanding and problem solving. Additionally, teacher education should focus explicitly on productive and appropriate ways of teaching in low-achieving classes. |
