Main thesis: Teachers with similar professional vision can have different classroom practices, specifically, honoring and eliciting student thinking at different frequencies. Using the definitions below, the author claims that teachers with the same offline vision can have different online visions and classroom practices.
\nDefinitions: The author categorizes two types of professional vision (or professional noticing):
\n-Online noticing: Noticing in-the-moment while teaching.
\n-Offline noticing: Noticing while not teaching (such as video reflection). This form is often used in PD.
\nFrom Sherin and van Es's framework (2009), author defined professional vision twofold:
\n-Selective attention: What teachers pay attention to. This was measured by what teachers tagged (up to 10 seconds) in the \"offline\" videos.
\n-Knowledge-based reasoning: How teachers interpret what they attend to.
\nMethodology:
\n-Four high school classroom mathematics teachers participated in five 40-minute video club meetings over 10 weeks. After each meeting participants were to prepare a 2-3 clips of their own teaching that showcases support of student thinking. Participants were interviewed via phone after each personal video clip was recorded prior to self review.
-Participants watched 4-6 minute videos that showcased different instructional modes (small group, full group, student presentation, etc.) and rated each on a 4-point scale as to how likely the clip supports student thinking.
\n-Classrooms were observed at the beginning and near the end of the study.
\nFindings:
\n-Two teachers (Sam and Matt) had similar selective attention based on what they tagged in the offline videos, focusing heavily on the student over the teacher as the actor highlighting student math thinking as the preponderance of their tags. The author also claims that they had similar interpretation of those events (though Matt coded interpretation of student ideas three times more often than Sam).
-While these two teachers had similar offline visions, their interviews about online vision were different in that Sam only mentioned student thinking once.
\n-Their classroom practices were quite different as well even though classroom structures (small group work) were similar. In particular Sam never asked for or probed for explanations where Matt did this 4 and 7 times respectively.
\nConclusion:
\n-Teachers can have similar offline visions about noticing and eliciting student thinking but can have different online visions in practice.
\nAdditional Thoughts:
\n-The research seems to suggest that online noticing can be improved through continued professional development; however, much of the PD in this field is \"offline\" rather through static analysis of student work or through review and discussion of video taped lessons, often of another teacher outside of the review group.
\n-The author points out the stark difference between online vision and classroom practices between Sam and Matt; however, there are some reasons why these differences might exist:
a) The author points out that Sam is only a first year teacher and Matt has over five years of experience. Does this not suggest that teaching experience IS a critical factor to successful listening and noticing?
b) Sam's interviews seemed to be delayed after recording while Matt's interviews were in closer proximity to when the lesson occurred. Matt would be able to recall more details about the lesson than Sam since the interviews occurred closer to when the lesson was enacted.
\nc) Matt had almost twice the amount of segments in his observations compared to Sam (8 vs. 5). Would this not allow Matt to have more opportunity to elicit student thinking? This was not properly normalized for equal comparison.
\n-The author raises an interesting point about differences in vision when one observes someone else's video vs. their own. Has such research been conducted? I hypothesize that teachers would be more open to analyzing offline videos of another teacher rather than their own. They would give other teachers the benefit of the doubt for collegiality purposes as well as be more critical of their own practices.
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Main thesis: Teachers (mostly inservice in this study) do not attend to or build upon student thinking about mathematics and do not recognize or leverage different student strategies. The transition from directive to observational to responsive listening takes years to master but has multiple benefits in both student and teacher effectiveness and understanding. As supported in other research, such as Star & Strickland (2008), such support is often not acquired in teacher preparation programs.
\nDefinition: Three types of teacher listening:
-Directive listening: Determining if student response matches an expected response (even if what is expected is inconsistent with student understanding). Part of this redirection is motivated by teachers wanting students to succeed via an algorithm or traditional solution approach.
-Observational listening: Attempt to hear student thinking with little attempt to support or extend thinking.
-Responsive listening: Active attempts to make sense of and respond to student thinking. This requires a big shift in teachers' conception of their role.
-Give case study of Laura Rose, student who uses reasoning about different groupings in a multiplication problem about beads and braids. Inservice teachers quick to dismiss or misunderstand student process since it varies greatly from their own strategies.
\n-Exemplary interview sample with student Darcy about rocks in pockets. The discourse builds upon the types of questions cited in Jacobs & Ambrose (2008).
\n-There are four main benefits to listening to children's mathematical thinking:
a) improving children's understandings; b) ongoing formative assessment; c) increase in teacher content knowledge; d) supportive in teachers' continuous lifelong (or generative) learning.
-There are three suggested activities for listening PD:
a) Written student work: easy to collect and compare but not dynamic. Allow for discussion with peers moving from evaluative comments to making evidence-based inferences about student understanding.
b) Student interview videos: Captures both teacher and student interactions. Careful thought is required in selecting the video (professional vs. teacher-created). Teachers tend to relate better to more authentic videos, but this requires \"critical colleagueship\".
\nc) One-on-one interaction with students: Authentic dialogue between teacher and student. Useful to have a math teacher educator on hand as a coach as teacher transitions through listening frameworks (directive, observational, responsive).
\nConclusion:
\n-\"Teaching is listening and learning is talking\" (Boles, Troen, & Kamii, 1997). Teachers are used to telling.
\n-Most difficult for teachers to transition from observational to responsive listening modalities.
\n-Research has shown the many benefits of honoring student thinking via teacher listening; however, listening requires years of work which may not be supported through continuous PD or understood by administrators or parents. Further, development in teacher listening does not provide precise instructions which can cause frustration with teachers since it is an ongoing work in progress.
\nAdditional Thoughts:
\n-The dichotomy between student reasoning and adult or teacher reasoning is a major consideration, especially as parents try to help their own children with strategies in the CCSS-M that they never learned themselves (such as area/bar models or partial products). See p. 260.
\n-Teachers must be highly aware of the different problem situations that occur and how children view these as distinct even though they are of the same fact family or even the same operation (such as 3x7 = 7x3). See p. 88 & 89 in CCSS-M for common operational situations.
\n-The research seems heavily grounded in elementary strategies, specifically related to the four operations. Where is the research about listening to student thinking in secondary/high school mathematics? The last time student strategies is mentioned in the CCSS-M is in 7th grade (7.EE.3 - estimation strategies in real-world situations).
\n-\"The development of this expertise involves a certain amount of trial and error\" (p. 270). Are teachers comfortable with this uncertainty? Do they have a supportive space where they can practice different types of questioning techniques? This is where a simulated and action-consequence environment to provide scaffolding might be useful for both preservice and inservice tachers.
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\n1) Preservice teachers are more likely to notice teacher actions (especially classroom management) rather than student actions, especially when compared to expert teachers. 2) Moreover, with articulated training and an organizational framework, preservice teachers are able to make gains in their noticing schema.
-Sherin and van Es have key contributions in video club work with both preservice and inservice teachers in early 2000's. Developed the VAST tool. This work showed the ability for teachers to shift from noticing teacher actions to student actions and moving from judgmental inferences to evidence-based claims.
\nMethodology:
\n-28 preservice teachers were enrolled in a semester methods course. Additionally, 6 doc students with at least 3 years experience were identified as \"expert\" teachers.
\n-Participants watched a secondary TIMMS lesson (~50 mins) and were allowed to take notes.
-Pre-test followed lesson observation consisting of objective questions from 5 categories:
classroom environment (physical setting and classroom makeup), classroom management (procedures and teacher actions), mathematical content (representations), tasks (student activities), and communication (S to S and T to S).
-Participants then re-watched video and reflected in small paper, often highlighting observations that were first missed in pre-test.
\n-Post-test was a different (but similar) video with similar questions in same sequence and number.
\n-Final observation papers were completed using the observational framework.
\nResults:
\n-Experienced teachers scored 86% on pre-test. Lowest in communication (78%) and highest in management (91%).
\n-Preservice teachers in pre-test scored lowest in environment (44%) and highest in management (80%).
\n-Biggest gains from pre to post were in classroom environment, specifically awareness of static features (equipment, names of students, etc.).
\n-Even after a framework to focus observations, preservice students showed least gains in mathematical content. Communication was similar in this respect, with preservice teachers often making large generalizations.
\nConclusion:
\n-Preservice teachers have spent considerable time observing teaching, but from the lens of a learner rather than a more broad perspective of observing the practice of teaching and learning.
\n-One's past experiences forms a belief framework which influences what one observes.
\n-Preservice teachers can improve their ability to notice, but require a guiding framework to organize what they can and should notice.
Additional Thoughts:
\n-\"More experienced teachers notice more, and make different kinds of observations, than preservice, inexperienced teachers\" (p. 109). This seems to be in conflict with Phillip et al. in which it was purported that teacher PD was more correlated to effective noticing than teacher experience. How does one effectively delineate experience with professional development to avoid confounding variables?
\n-The choice of math ed doc students as experienced teachers seems a bit questionable, especially if they have been removed from the classroom for a considerable time. The sample size of 6 expert teachers vs. 28 preservice teachers seems a bit disproportionate.
\n-There is a delicate balance here about honoring the subjective and personal nature of noticing. While the authors claim that the instruments used were highly objective, their focus on the five categories inherently directs preservice teachers to notice what the researchers feel is important to notice. As an example, the large gains from pre to post tests in noticing classroom environment seem a bit forced, since the preservice teachers were cued that the researchers felt that this was an important lens. Further, how were these five observational categories (environment, management, tasks, content, communication) determined? It was only crosschecked with one other framework (Fredriksen et al., 1998).
\n-\"Preservice teachers were not able to identify the kinds of equipment available in the classroom\" (p. 117). How important are such observations, especially when some of this equipment was not even used in the lesson? Is it not more important to focus on the student and teacher interactions and mathematical content? Perhaps their categorical framework could be weighted more heavily in some areas than others rather than a uniform average.
\n-The mathematical content and student understanding of that content was least noticed before and after the study. The researchers cite that perhaps this is because of unfamiliarity with some of the advanced content in the video. Does this not undermine the study, since the content is not well correlated with the mathematical understanding of preservice teachers? Other studies (Chao, Phillips et al.) were intentional in correlating tasks with the mathematical expertise of the participant.
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Definition: professional noticing of children’s mathematical thinking as “in-the-moment” decision making. Each professional field requires the practice of capturing and synthesizing complex stimuli (known as professional vision). Often this perception of one’s world is subjective (Gibson, 1979).
\n\n
Three elements (often integrated into one \"teacher move\"): (p. 173).
\n\n
Attending to children’s strategies. Authors found that years of experience were not necessarily correlated to attending to strategies, sometimes dismissing a strategy based on its complexity.
\nInterpreting what the child knows from 1). Few participants were able to differentiate their interpretation about mathematical understanding. Authors found that interpreting student work is not solely learned from teaching expertise.
\nResponding to the child’s thinking based on what is evidenced from 2)
\nMethodology: The experimental variable was the different amount of experience educators had in professional development in noticing. Participants ranged in prospective (no experience or PD) to emerging teacher leaders (4+ years of noticing PD) with varying teacher experience with an average of 15 years.
\nParticipants given prompts for each noticing action:
Attending to thinking: “Please describe in detail what you think each child did in response to this problem.” Rated 1 (evidence) or 0 (lack of evidence).
\nInterpreting thinking: “Please explain what you learned about these children’s understandings.” Rated 2 (robust evidence), 1 (limited evidence) or 0 (lack of evidence).
\nResponding: “What problem(s) might you pose next?” Rated 2 (robust evidence), 1 (limited evidence) or 0 (lack of evidence).
\nConclusion: Teachers can improve noticing techniques by changing what they notice and how they analyze what they notice. (van E’s & Sherin). This improvement requires sustained professional development and leads to positive gains in student achievement.
Additional Thoughts:
-All the student work presented was static in nature. Noticing requires more senses than just visual information, such as body language and verbal communication. What are better ways that student work can be captured? Livescribe pens? One take videos (McCammon)?
\n-The authors did not concern themselves with the execution of the response after step 3. Is not the execution of how to respond equally as critical as the theoretical response the teacher might invoke? This is similar to Stein et. al’s categorization of cognitive demand of a task in that a task of high cognitive demand might be selected, but when implemented with actual students, the task’s demand might decrease. Specifically, what is intended and what is executed might be quite different.
\n-The methodology relied specifically on K-3 teachers, only a subset of which were prospective teachers. Is years experience not a confounding variable in this study? Further, the sample was overwhelmingly female (119 female vs. 12 male). How would the results differ in a secondary setting?
\n\n
-The results show that the first two years of PD are most impacting and there is asymptotic gains in successful noticing techniques with increased PD (p. 193). How does this impact how teacher PD is executed? How much PD is ongoing enough to pay dividends but not too long to have little effect?
\n\n
-What are teacher challenges to discussing student understanding, in particular, in secondary mathematics? Lack of knowledge of various strategies, lack of content expertise to make sense of student thinking, lack of supportive curriculum and remediation for an adequate response of extension or intervention.
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Main thesis: Story problems provide a lens into student thinking and innate problem solving strategies.
\nThere are two main categories of teacher moves in one-on-one interviews.
\na) Supporting Moves (before correct answer is determined)
\n-Ensure understanding of problem: Rephrase or elaborate
\n-Change the problem (to an easier one)
\n-Articulate what the student has already done
\n-Remind student of other strategies/manipulatives
\nb) Extending Moves (after correct answer is found)
\n-Have student reflect on strategy used
\n-Generate other strategies (such as a mental strategy) and compare these strategies
\n-Use symbolic notation
\n-Generate other problems
\nConclusion:
-These moves cannot be pre-planned and require sustained expertise and training.
\n-Attend to details of student thinking. Don't overgeneralize student strategies.
\n-Continue the conversation once a correct answer is determined. Reflection and extension can occur here.
\nAdditional Thoughts:
\n-The SMP's (Standards for Mathematical Practice) are heavily embedded in this work, especially 1. Make Sense of Problems, 2. Reason Abstractly and Quantitatively, 5. Use Tools Strategically, 7/8. Look for Structure & Repeated Reasoning. What work has been done to correlate these SMP's to teacher noticing and one-on-one interviews?
\n-Polya's problem solving heuristics seem naturally embedded here as well. Has a correlation study been done to investigate how his heuristic strategies correlate to the SMP's or a students' trajectory in problem solving?
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