After eliciting: Variation in elementary mathematics teachers’ discursive pathways during collaborative problem solving

Pre-service mathematics teachers responding to student thinking in their teaching experiences

“…As Munson (2019) indicated, not all responses are equally productive for promoting student learning, this study showed that responding to ST does not always mean focusing and deepening them. A good response should be based on ST and involve interaction with the student to leave space for the student"s future thinking (Monson et al, 2020).…”

“…Accordingly, many studies have discussed which of the ways the teacher respond to student thinking could be better (e.g., Jacobs & Empson, 2016;Lim et al, 2020;Monson et al, 2020). Not all responses are equally productive for promoting student learning or building on student ideas (Munson, 2019). Monson et al (2020) defined characteristics of good response as it (1) works toward student learning objective, (2) draws on and is consistent with the student thinking presented, (3) draws on and is consistent with research on students" mathematical development, and (4) proposed interaction with student leaves space for student"s future thinking (not just teacher"s thinking).…”

Conceptualizing micro-adaptive teaching practices in content-specific ways: Case study on fractions

“…In contrast to Schwarz et al (2021) and Prediger and Erath (2014), some sense-making units were split into several teaching practices (the non-considered part is then marked in grey on the concept map).  Follow-up move to make students reflect and correct their own (partially) incorrect strategies by generic or specific questions  Unlike -elaborate-the aim is not to deepen a student's strategy  ( "repair," Buttlar, 2019; "assessing" and "challenging," Parsons et al, 2018) strong ambiguous -Portion- Series of closed follow-up questions that aim at getting students to utter the correct answer by reducing the linguistic and mathematical complexity  Unlike -elicit-, produces mostly short answers, rarely aligned to student thinking  ( "funneling," Munson, 2019) ambiguous strong -Repeat- Teacher utterance with verbatim reproduction of one or more students' utterances  Unlike -complete-or -reformulate-, mathematics or language not enhanced  ( "repeat utterances," Prediger & Pöhler, 2015) strong weak -Reformulate- Teacher utterance taking students' utterances to a higher language level (everyday to academic) while maintaining students' content, usually includes lexical support  Unlike -complete-focuses on improving language, not mathematics  ( "modeling," Parsons et al, 2018;"reformulate," Prediger & Pöhler, 2015) strong ambiguous -Complete- Teacher utterance for relating, summing up, abstracting, repairing, explicating, or expanding students' utterances, bringing in new aspects/strategies themselves  Unlike -continue and connect-, the teacher brings in new information; unlike -input-, the utterance is (at least implicitly) closely related to students' uttered strategies  ( "making connections" and "explaining, Between the identified teaching practices, the number of applied moves and arrows can differ, as some practices are characterized by only typical arrow and move, while others may contain several. The practices are characterized by typical changes in navigation across the content-specific navigation space or a characteristic change of used moves or both.…”

“…As we will show in this paper, the moves collected as common typologies of responses from Parsons et al (2018) need to be complemented and sometimes unfolded to investigate their role in microadaptive teaching practices with a focus on students' content-specific learning pathways (see Section 2.3; moves from Table 1 are marked by -…-). For instance, the move "questioning" can have two different functions: As an initiation move, it intends to -elicit-students' thinking (Munson, 2019;Jacobs & Empson, 2016), whereas as a follow-up move, it intends to -elaborate-on students thinking regarding the depth of students' understanding or the connection to other concepts (Munson, 2019;Smith & Stein, 2018;Schwarz et al, 2021). The latter can also be part of the "challenging" move depending on the actual phrasing of the question.…”

“…The steering trajectory in Figure 13 illustrates the characteristics of the teaching practice Pull Out Small Pieces From Student Ideas (Turns 256-264): -Portioning-by posing a series of closed questions that result in little involvement of the students in shared discourse that follows a teacher guided direction, which is at best (and at most of the time) directed towards students' next development state (similar to funneling; Munson, 2019). Hence, the goal focus is strong.…”