Melissa Hosten
\nLoewenberg Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of teacher education, 59(5), 389-407.
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Melissa Hosten
\nLoewenberg Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of teacher education, 59(5), 389-407.
\nProblem Statement: Research is inconsistent in regards to subject matter knowledge for teaching. In fact, there is not a widely accepted single definition for mathematical knowledge, and as such, Shulman's two categories (Content knowledge and pedagogical content knowledge are not sufficient to fully understand the mathematical knowledge required for teaching.
\nMain Argument: There is further elaboration necessary to fully understand these two categories, to inform research, and to help direct efforts. Content knowledge can be expanded to common content knowledge and specialized content knowledge. Pedagogical content knowledge can be elaborated to include knowledge of content and students, knowledge of content and teaching, and knowledge of the curriculum. This brings a strong focus on the work of teaching.
\nContribution: The article served to expand the understanding of content for mathematics teaching, with specific examples of the five categories. The article further elluded to specialized content knowledge including knowledge beyond what is taught, but necessary for teaching with understanding. The article also offered a clear and concise definition for mathematical knowledge for teaching.
\nQuestions and critique: I wonder how much agreement can be found on the horizon knowledge. The authors seem to indicate that this is agreed upon levels according to content being taught, but I find it hard to believe the field would agree widely, since mathematics is complex and rich in connections. This highly connected and complex content area might cause people to value relationships further removed from the content of the class/grade that what others value.
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\n\n
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389-407.
\n\n
Summary of the problem statement:
\nBall claims a gap in the research lies in the small amount of attention given to how teachers need to understand the subjects they teach. Researchers have also failed to establish more precise and agreed-upon definitions of Shulman’s term, pedagogical content knowledge (PCK). Shulman’s (1986) “coherent theoretical framework” is underdeveloped.” The field has done little to advance measures of PCK and to use these measures to test definitions and our understanding of the nature and the effects of content knowledge on teaching and learning” (Ball, Thames & Phelps, 2008, p.3).
\n\n
Summary of the authors’ main argument:
\nBall and colleagues concluded it’s likely that content knowledge for teaching is multidimensional. The researchers argue content knowledge for teaching extends beyond Shulman’s (1986) categories of subject matter knowledge and pedagogical content knowledge. They further claim the categories do not represent the mathematical demands teachers encounter when teaching. Further aspects of subject matter knowledge are prevalent when teaching mathematics.
\n\n
Summary of the contribution:
\nBall and colleagues further refined Shulman’s framework by including common content knowledge (CCK) and specialized content knowledge (SCK) under Shulman’s category of subject matter knowledge. The researchers further elaborate on Shulman’s pedagogical content knowledge to include knowledge of content and students (KCS), knowledge of content and teaching (KCT) and knowledge of curriculum. In addition to further defining Shulman’s framework, Ball and colleagues included Mathematical Tasks of Teaching, which delineates tasks that teachers routinely do.
\n\n
Questions and/or Critiques:
\nI’m not convinced that further developing a framework for pedagogical content knowledge is required to better understand the questions of what teachers need to know and how they need to know it when teaching content. Definitions in academia also span a range of ambiguity. I understand the value of theoretical frameworks and agreed-upon definitions. However, I’m not quite following Ball’s line of thinking of needing to further refine what has already been established for educational reform. To what point is a framework and definition refined enough to create better understanding that leads towards change?
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\n1) Summary of the problem statement (What is the hole in the literature? What is the purpose of the author? ~3 sentences)
\nResearchers tend to focus on pedagogical skills rather than on the content knowledge needed to teach math, and even when they do address content knowledge, they tend to only address teachers' advanced study in a content area rather than on the specific kinds of knowledge needed in order to teach a subject.
\n2) Summary of the authors' main argument (~3 -5 sentences)
\nSpecialized content knowledge is not the same as pedagogical content knowledge because this specialized content knowledge does not involve knowledge of students or teaching. They need a much richer knowledge of the math topics taught than, say, an accountant or an engineer needs. Some examples of this include being able to utilize multiple representations, how to explain and justify mathematical ideas, and to be able to unpack mathematics in ways that make sense to students.
\n3) Summary of the contribution: What does this argument help us understand? What are the implications/contributions of the argument? Why is this argument important? (~3 sentences).
\nPrior studies had conflated pedagogical content knowledge with what, these authors argue, is actually mathematical knowledge that's needed for teaching rather than being pedagogical knowledge, per se. The authors hope that we will better be able to understand how to prepare teachers to have such knowledge with a more nuanced sense of what things fall into what categories.
\n4) Questions and/or Critiques: What questions does this argument raise for you? What are the strength & weaknesses of the argument (3 sentences)
\nSomething bothers me about trying to make such a clean separation between content and pedagogy; I think that mathematical knowledge is constructed through a process of dialogue and that you can't necessarily have content knowledge absent considerations of process. There's so much more, as Nowicki says, to whether the content you know actually ends up being manifested in the classroom.
\nThe article seems to be saying that content knowledge is getting the short shrift here, but in my experience it's actually PCK that's being devalued in favor of the pure mathematical knowledge. I'd personally like to see more PCK presented in content classes; there's already a lot of MKT being presented in pedagogy classes...
\nI also wonder to what extent this theory itself needs to be taught to preservice teachers, or whether this is more something primarily directed at teacher educators for them to think about when planning curricula?
\n5) Quotes:
\n\"Given all of this, a question that others regularly ask is: 'Why are any new categories needed? Why not just refer to all of this as “pedagogical content knowledge”?' Three reasons capture our current thinking about the usefulness of refining the conceptual map of the content knowledge needed by teachers. First, in studying the relationships between teachers’ content knowledge and their students’ achievement, it would be useful to be able to ascertain whether there are aspects of teachers’ content knowledge that may predict students’ achievement more than others. If, for instance, teachers’ common content knowledge is the greatest predictor of students’ achievement, this might direct our efforts in ways different than if knowledge of content and students has the largest effect. Second, if this were the case, it could be useful to study whether and how different approaches to teacher development make different impacts on particular aspects of teachers’ content knowledge. Third, and closely related, a clearer sense of the categories of content knowledge for teaching might inform the design of support materials for teachers, as well as teacher education and professional development. \"(p. 12-13).
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Kristen C
\nBall, D.L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59 (5), 389-407.
\n\n
Problem Statement:
\nIn this article the main problem being questioned is: How do teachers demand mathematical reasoning, insight, understanding and skill while teaching mathematics? Teachers need to have a basis for what they know and be able to effectively demonstrate their knowledge while teaching mathematics. Teachers need to know their subject matter, content, ask questions, thinking about what else they can learn while using their mathematical knowledge while teaching. Even though these ideas are questioned there is no clear idea on how these ideas of content knowledge and pedagogical content knowledge are being researched?
\nMain Argument:
\nQuestions that arose in this article are: Where do teachers develop explicit and fluent use of mathematical notation? Where do they learn to inspect definitions and establish the equivalence of alternative definitions for a given concept? Where do they learn what constitutes good mathematical explanation? Teachers need to learn how to model steps while teaching in a way that makes sense to students. Teachers need to have hindsight into how students will react to specific problems given. Effective teachers will be able to point out errors easily and show a multiple ways of solving problems. The mathematical teacher needs to have the knowledge to ask higher order questions to challenge student's thinking. Two main ideas of subject matter knowledge and pedagogical content knowledge play a part in helping the teacher develop the content necessary to be successful at teaching.
\nContribution:
\nThis article helps us make sense of content knowledge for teaching mathematics. It introduced definitons of Common content knowledge, specialized content knowledge, knowledge of content and students, knowledge of content and teaching and knowledge of curriculum. This research makes implications to other questions such as: Are there other aspects of teacher content knowledge that may predict students achievement mroe than others? How would different approaches to teacher development make an impact on teachers content knowledge?
\nQuestions/ Critiques:
\nI found this article hard to evaluate. This article shows no research evidence that any progress or anything was actually done besides providing definitions for improvements to teachers.
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\nProblem Statement: There is agreement in the field that teachers require pedagogical content knowledge in order to effectively teach mathematics. However, this knowledge has not been well defined and it is unclear what content this knowledge actually covers. Furthermore, there is no metric or tool by which to measure this important teacher knowledge.
\nSummary of Main Argument: The mathematics that a teacher knows and uses to teach is specialized. Building off Shulman's notion of pedagogical content knowledge (1986), this mathematical knowledge for teaching is multidimensional and likely can be subdivided into six sub areas (horizon knowledge, common content knowledge, specialized content knowledge, knowledge of content and students, knowledge of curriculum, knowledge of content and teaching).
\nSummary of the Contribution: This paper gave the field a more detailed way of thinking about the mathematical knowledge teachers use when teaching mathematics. This also shifted how we thought about the math content preparation that teachers needed in order to teach mathematics in elementary grades.
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