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Course Level Date Clip# Line Interlocutor Content
Talkbank - - 6 115 T can you talk together?
Talkbank - - 6 116 UNK %xRES:this problem is the only one in this lesson where students are explicitly given a choice of solution methods. That is, they are told that there are multiple ways to solve the problem, and they can decide which method they want to use (see 8:56). When the results are presented, several alternative solution methods are shown, and they are explored at length. In one-quarter of the Australian lessons, students had a choice of solution methods (Video Report, table 5.2). Similarly, in one-quarter of the Australian lessons, alternative solution methods were publicly presented (Video Report, table 5.1). Examining these solution methods in detail was seen only in eight percent of the Australian lessons (Video Report, table 5.3). This problem is mathematically related to the earlier problems in the lesson; more specifically, it is an extension of the mathematical ideas and operations involved in the previous problems. Mathematically related problems accounted for 13% of the problems per lesson, on average, in the Australian data set (Video Report, figure 4.6). More common were repetitions, or problems that required essentially the same operations in order to be solved. Repetitions accounted for 76% of the problems per lesson, on average, in the Australian data set (Video Report, figure 4.6). This problem is also considered to be at a high level of procedural complexity due to the fact that it requires more than four steps and has several embedded sub-problems. High procedural complexity problems were not very common in Australian lessons. On average, only eight percent of the problems per lesson were coded as high procedural complexity (Video Report, figure 4.1). The problem is stated in such a way that students are asked to conjecture and reason about the minimum pieces of information needed to determine if two triangles are congruent. This is considered a "making connections" problem statement. In Australian lessons, on average, 15% of the problems in each lesson asked students to make connections (Video Report, figure 5.8). After students work on the problem, the teacher goes over the results. Because she focuses on the answers and identifying the corresponding rules, without making explicit the mathematical reasoning behind these rules, the problem is considered to have a "stating concepts" implementation. In Australian lessons, on average, 23% of the problems stated as making connections were implemented as stating concepts (Video Report, figure 5.12).
Talkbank - - 6 117 SN where did you want us to move?
Talkbank - - 6 118 T um, yes.
Talkbank - - 6 119 T yeah, one of you move down there one so you've got a group of three and one of you can <move> work with one of these.
Talkbank - - 6 120 T all right Angela, you can work with um Eun and (.) all right?
Talkbank - - 6 121 T then you've got just one down there.
Talkbank - - 6 122 T here's a all right?
Talkbank - - 6 123 SN how am I going to work?
Talkbank - - 6 124 T bring a chair.
Talkbank - - 6 125 T yeah, you can bring that yeah, bring the table over.
Talkbank - - 6 126 SN xxx.
Talkbank - - 6 127 T no.
Talkbank - - 6 128 T all right, I'll go through the instructions with you.
Talkbank - - 6 129 T I'll read through the instructions and girls, read through the instructions as I go through it.
Talkbank - - 6 130 T what you're doing is you're actually finding the rules for a pair of congruent triangles and you're trying to find the minimum rules.
Talkbank - - 6 131 T so the task you need to produce a list of instructions so that anyone following them will construct exactly the same triangle.
Talkbank - - 6 132 UNK %xTEA:I explained the aim of the lesson so that the students would understand the goal that they were trying to achieve. I read the instructions to the students because some students have difficulty understanding written instructions. I could have told them to use the length of the sides and the size of the angles to describe the triangles, however, I think it worked better because the students constructed triangles from their own experiences and in their own language. They were familiar with constructing angles and sides of a triangle using protractors and compasses.
Talkbank - - 6 133 UNK %xNRC:There is little formal geometry done at this level in most Australian schools. Finding the conditions for congruent triangles is typically not done before Year Nine.
Talkbank - - 6 134 SN oh.