The Quality Teaching Dimensions: Outcomes focus Quality teaching is focused on valued outcomes and facilitates high standards for diverse learners. Ava and Moana’s initial focus At the outset of the intervention, Ava was confused about the outcomes she intended to focus on. She wanted her students to learn the rules and procedures of mathematics and, in light of her previous professional learning, she also wanted them to be able to articulate, within their groups, the mathematical strategies they were using. However, she did not set out to create a mathematical discourse community (that is, a classroom community of novice mathematicians whose learning includes understanding and using the specialised language of mathematics). As each student spoke, the other students sat silently. Initially, Moana was focused on a limited set of low-level outcomes. She ascribed her students’ low achievement levels to their lack of prior experiences at home, their lack of interest and engagement in mathematics, and their passive approach to learning. She later reflected, “I thought I had high expectations … I have realised I [had] low expectations.” Ava and Moana’s shift in focus Both teachers developed a comprehensive new approach that focused on valued outcomes. They set out to develop in their students the communication and participatory skills needed to advance their thinking and extend their mathematical knowledge through active participation in the classroom mathematical discourse community. The teachers aimed to develop their students’ abilities to explain mathematical concepts, justify their arguments, and make generalisations. They expected the students to use mathematical language and definitions and also to use generalisations and inscriptions8 to support their explanations and to clarify their understandings of others’ explanations. The teachers did not form these new expectations overnight. Rather, as the teachers participated in the iterative professional learning process and the changes began to be embedded, they saw how their students extended their mathematical proficiency through the new teaching and learning approach. Both teachers began to develop their students’ identities as mathematicians and members of a learning community in which each person had high expectations for their own outcomes. The teachers became adept at identifying and addressing barriers to progress and keeping the focus on the outcomes. Teacher knowledge and inquiry Teachers work smarter, not harder, through the use of evidence for continuous improvement. Teacher knowledge and inquiry at the outset of the study: Ava Ava explained that she had initially liked teaching mathematics but had lost confidence in her mathematics teaching expertise after participating in the NDP. The NDP professional development had created dissonance between her prior view of mathematics teaching as focused on rules, procedures, and routines and the new focus on students developing their mathematical thinking. Observations revealed that Ava had tried to implement what she had learned from the NDP. But in practice, she had done what many teachers do when confronted with new curricula designed to change the nature of teaching. She had transformed the NDP lessons to fit with her old way of doing things. Her students listened to each other in silence and answered the teacher’s questions, but there was no process to build a mathematical learning community amongst students. Teacher knowledge and inquiry at the outset of the study: Moana Moana had always disliked mathematics. Her memory of her own schooling was negative: “I didn’t have the ideas that other kids had so I just never said anything. I thought they were all brighter than me.” Before the intervention, Moana was using a learning styles approach. She saw her Māori and Pasifika learners as kinaesthetic learners needing practical activities. (This approach has been found to have little benefit for student achievement and has even had negative effects on Māori and Pasifika student achievement.) In her mathematics lessons, Moana did most of the talking because she saw her role as instructing students in how to use mathematical procedures. She explained that she had adapted the NDP’s knowledge and strategy activities so that they were always at a concrete and manipulative level. She focused on students ‘learning by doing’, because she believed that they found explaining difficult. Teacher inquiry through the study The professional development was delivered through a mix of whole-staff meetings and eight meetings of a teacher study group. The professional learning activities included examining research, considering how other teachers had changed the forms of mathematical talk towards inquiry and argumentation, and reading about mathematical practices used by students in inquiry environments. The researcher used a DVD from an international research study to stimulate examination of inquiry practices. The teachers re-examined the materials in the NDP and discussed which learning tasks best supported their goals, which involved changing the classroom discourse patterns. The TLRI project funded the necessary teacher relief time. This amounted to at least six days for each participating teacher. Initially, the researcher was in the school for two mornings a week and worked collaboratively with the teachers to provide support both in and out of class. Data gathering in the classrooms commenced from term 2 and included the researcher making video recordings of lessons, which were later transcribed. The study group used these recordings extensively. They viewed them repeatedly, collaboratively examining and identifying critical incidents and the antecedents and consequences of these incidents. The teachers recorded their lesson intentions and drew on excerpts from the transcripts to trace how their actions had influenced what students actually said and did. The researcher perceived that the classroom videos were key to the professional learning, especially at the start, because they illustrated “the power of who asks what in the classroom.” It was also important to provide the teachers with a small number of research articles in a timely way that addressed a specific need. The DVD had helped motivate the teachers by “pushing their vision of possibilities”. The collaboration between the researcher and teachers persisted beyond the study when some teachers co-presented their findings with the researcher in conference workshops. The teachers became members of a local mathematical professional group. Smart tool The researcher developed, and then worked with the teachers to refine, a tool they called the Mathematics Communication and Participation Framework (see Appendix 1 on page 15 of this case). This framework provided an outline of both communicative and participatory actions, along with examples. Teachers could use it to scaffold students’ learning about how to participate in communities of mathematical inquiry. Teacher inquiry Teacher inquiry: Ava After reading relevant research and taking part in discussion, Ava was convinced of the value of the new approach and decided to take immediate action to change her teaching practices, using the Mathematics Communication and Participation Framework. Her initial focus was on students’ participation in mathematical explanations. Within a month, she decided to stop the use of ability-group streaming. Teacher inquiry: Moana Moana was quiet when the study group discussed the framework. She believed strongly in certain theories about teaching and learning, and at first she did not believe that the students would learn more through a learning community. She was focused on students getting the right answers. However, the videos stimulated Moana to build on what she had learned about how other teachers were changing their classroom practices. She decided to start by developing students’ ability to construct and present mathematical explanations. When she saw the initial changes in her students, she was convinced of the value of the new approach and whole-heartedly engaged with the change process.
Posted on: Sat, 18 Oct 2014 09:31:53 +0000
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