Specialized Content Knowledge Research Articles

The role of uncertainty in mathematical tasks for prospective elementary teachers

Mathematics teacher educators (MTEs) charged with the content preparation of prospective elementary teachers (PTs) receive widespread recommendations on a variety of issues, including which mathematical topics to include in their courses, the types of pedagogical strategies to use when working with PTs, and how to foster the development of particular mathematical practices. The nature of the mathematical tasks that MTEs can use to best support and extend PTs’ content knowledge is another area that deserves attention. This article considers uncertainty as a task feature and explains how it can be incorporated into mathematical tasks in order to support PTs’ specialized content knowledge. Using Zaslavsky’s (2005) three types of uncertainty – competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes – we provide three classroom examples of ways in which MTEs incorporated uncertainty into their mathematical tasks. Each example provides detail about the task design, background research on PTs’ knowledge of the underlying mathematical content, the type of uncertainty the task generated for PTs, and the ways in which that uncertainty may have contributed to PTs’ understandings of the content. Each example concludes with recommendations for MTEs on specific ways to incorporate that particular type of uncertainty into their own teaching.

Mathematical Knowledge for Teaching: How do Primary Pre-service Teachers in Malawi Understand it?

While a consensus within the field exists that pre-service teachers need adequate knowledge and skills to become effective teachers in mathematics, less is known about how they understand the mathematical knowledge needed for teaching in elementary education. This paper explores how Malawian pre-service teachers understand the mathematical knowledge needed for teaching in primary schools. Written answers to a questionnaire survey, and data from six individual interviews collected at the beginning of the teacher-training programme will be presented. The analytical framework is based on the practice-based theory of mathematical knowledge for teaching, with a specific focus on the domains of the common, horizon and specialised content knowledge. The data revealed that, while taking theoretical courses, pre-service teaches develop only intuitive but complementary views of what is proposed by the theory, which is even the case with pre-service teachers with some prior teaching experience. Findings provide insights into the development of pre-service teachers’ mathematical knowledge for teaching, and suggest that further research is needed on how pre-service teachers articulate their understanding of teaching in practice.

Impact of a Field-Based Mathematics Methods Course on Preservice Elementary Teachers’ Specialized Content Knowledge: The Case of Area and Perimeter

Impact of a Field-Based Mathematics Methods Course on Preservice Elementary Teachers’ Specialized Content Knowledge: The Case of Area and Perimeter

Predictors of Success in the NCLEX-RN for Canadian Graduates.

The National Council Licensure Examination for Registered Nurses (NCLEX-RN) has been the nursing licensure exam in most Canadian jurisdictions since 2015. Nursing faculty across the country have invested considerable effort into understanding the NCLEX-RN, so they could help to prepare students to be successful in the exam. A retrospective study was conducted at one Canadian university to identify predictors of success on the NCLEX-RN. Findings revealed that the strongest predictors of success were a grade point average of >3.5 and a course grade in the community development course. The strong predictive value of the community development course was unexpected, and this suggests that content specifically related to acute care may not play as heavy a role in the NCLEX-RN outcome as previously expected. It is possible that students' higher levels of cognitive abilities, such as application, analysis and synthesis of nursing knowledge, play a larger role in the exam outcome than content-specific knowledge.

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Teachers use their content and pedagogical content knowledge for teaching algebra. For this reason, the examination of how teachers use this knowledge may help shed light on how students learn algebra, especially in determining why they usually have difficulties. The aim of the current study is to reveal what teachers know, and propose what they actually need to know for teaching the simplification and equivalence of algebraic expressions. The multiple-case study design was used for this study to compare and contrast the two middle school teachers’ lesson planning and instruction. The data corpus included lesson plans, actual instruction records, and post-observation interviews. Data analysis was conducted using the Mathematical Knowledge for Teaching (MKT) model. The findings indicated that both teachers had a lack of specialized content knowledge about mathematical representations such as algebra tiles. They did not use algebra tiles effectively and could not link algebraic and geometric representations that underlie the idea of multiplication. It was observed that both teachers generally used unknowns and variables interchangeably indicating the inadequacy of their common content knowledge. In the planning process, the two teachers were able to state the common misconceptions that the students generally had and the ways of addressing them. Through the cases of these two teachers, it was observed that teachers need to have a good conceptual mathematical understanding and also knowledge of students’ thinking in order to design effective lessons. Based on the findings, the types of knowledge that the teachers need to have are outlined and the theoretical and practical implications of the study are discussed.

Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.

Talking About Sustainability in Teacher Preparation in Finland and the United States

This article reports on empirical research findings from a case study of teacher education in Finland and the United States. A sociological perspective was deployed for investigating how the concept of sustainability was addressed in two teacher education programs. One of the programs was located in Finland and the other in the US. The study was carried out in 2015 and 2016. Seventeen semi-structured, open-ended, audio-recorded interviews form the core of the research materials. A thematic analysis of interviews was conducted for identifying articulations related to sustainability in subject-matter specialized teacher preparation. Findings from this study contribute to research on teacher preparation. Notably, by articulating how context-specific culture and social norms contribute to local models of teacher education. Findings from this study indicate that teacher training practices in Finland have encouraged students to articulate sustainability in relation to critical thinking, whereas in the US, sustainability has been articulated in relation to social justice. The key point supported by the evidence is that sustainability was by teachers and teacher educators conceptualized as being about the popularization of knowledge about ecology and biodiversity. The kind of communication that was by teachers and teacher educators described as effective for popularizing knowledge about scientific phenomena were forms of teaching that expanded on content-specific knowledge by connecting it to ethical and civic frameworks of the societies in which students live.

SOUTH AFRICAN TEACHERS’ MATHEMATICAL KNOWLEDGE: REFLECTIONS FROM SHORT LEARNING INTERVENTION PROGRAMME (SLIP)

This qualitative research reports the results of a short learning intervention programme conducted by South African National Roads Agency Limited (SANRAL) Chair in Science and Mathematics Education to enhance the mathematical knowledge of teachers in some South African schools. The short learning programme comprised the fostering of teachers’ mathematical knowledge and the formation of lesson study groups to apply the knowledge gained from the intervention programme in different schools in the country. The sample comprised 53 male and 72 female Mathematics teachers who were nominated from several school districts in the country. The participants were trained using Mathematical Knowledge for Teaching (MKT) which included the topics of probability/ratio and proportion (grades 1-9). The MKT consisted of these sets of expertise: Common Content Knowledge (CCK), Specialised Content Knowledge (SCK), Knowledge of Contents and Students (KCS), and Knowledge of Content and Teaching (KCT). The lesson study groups applied the knowledge acquired from the short learning intervention programme to engage in group activities, lesson studies, and to report the major challenges in doing the lesson studies. This model research comprised three stages: the first stage involved active participation in the workshops that took place at the University of the Free State; the teachers that attended the training workshops implemented the knowledge gained in the respective schools in their districts in the second stage; and the third stage involved the compilation and submission of a Portfolio of Evidence (PoE) by the teachers that participated in the training workshops. Keywords: mathematical knowledge, short learning intervention programme, South African teachers.

Recycling Plastics: Middle School Students Create Solutions During a Summer Camp

Four distinct plastics recycling projects created by middle school students emerged from a one-week long plastics recycling activity incorporated within a science, technology, engineering, and mathematics (STEM) residential summer camp at a research-intensive university. The plastics recycling activity was a project-based learning (PBL) activity facilitated by STEM experts in geometry, architecture, and materials science. Specific instruction involving mathematics and science concepts was provided to emphasize content-specific knowledge related to plastics recycling. A rubric was applied and used to determine evidence of learning manifested in participants’ final presentations. Participants’ final presentations demonstrated mixed results in terms of student learning outcomes, but indicated that campers demonstrated a clear sense of social environmental awareness and responsibility toward recycling plastics.

Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course

This study examined the development of prospective teachers’ (PTs) understanding of productive struggle using video episodes which PTs analyzed through the lens of professional teacher noticing. Our qualitative study included 66 PTs in four sections of a semester-long mathematics content course for prospective elementary and middle school teachers that focused on numbers and operations. The goal was to give PTs opportunities to observe students struggling with the course content the PTs were studying and to enact their specialized content knowledge and pedagogical knowledge for teaching simultaneously. Findings suggest that the PTs develop the ability to attend to and interpret the mathematics underlying the student struggles through video analyses. They also begin to identify teaching strategies and practices that appear potentially useful for supporting productive struggle. The use of a productive struggle framework helped the PTs develop a language for discussing productive struggle. Findings also suggest that PTs who had very little knowledge of productive struggle became more aware of what it looks like in practice, discuss ways to support students’ struggle and suggest its potential value in supporting students’ understanding of mathematics. One implication for this study is to carefully weave opportunities to develop teaching practices such as support of productive struggle into the content course for teaching. The PTs may better bridge the stance between being a student and becoming a teacher in what productive struggle looks like in learning mathematics.

Development of mathematics trainee teachers’ knowledge while creating a MOOC

This article describes how creating a MOOC (Massive Open Online Course) about ratio and proportion in a collaborative, technological environment during mathematics teacher training, benefited the development of content, pedagogical and technological knowledge for teaching. Twenty-nine trainee mathematics teachers, divided into groups, created teaching units as part of a MOOC in the subject of ratio and proportion. Before MOOC creation, the trainee teachers held misconceptions about the meaning of ratio and proportion, but through a process of reflective thinking, collaboration and peer assessment, they developed a sequence of teaching units about different aspects of the subject. This process allowed them to acquire a broad perspective on the subject, develop their Specialized Content Knowledge (SCK) [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] and let go of their own misconceptions. The trainee teachers also integrated into their units realistic situations of ratio and proportion, facilitating involvement and understanding, hence MOOC development also promoted Knowledge of Content and Teaching (KCT) [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]. Lastly, the need to select and adapt computerized tools to meet teaching objectives, promoted Technological Pedagogical Content Knowledge (TPCK) [Mishra, P., & Koehler, M. J. (2006). Technological Pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054]. From their reports, we can gather the trainee teachers learned how to translate theoretical knowledge to practical pedagogical tools.

Collaboration and teacher knowledge in a teacher learning community: A case of mathematics teachers in KwaZulu-Natal province

The literature on professional development of teachers has shifted to focusing on collaboration and learning communities as a productive way for teachers to learn. This qualitative case study examines the nature of collaborative activities and the kinds of teacher knowledge learnt in a community of high school mathematics teachers. Data was collected through observations of professional development workshops, questionnaires, interviews with teachers and document analysis. The findings established that collegial collaboration and the focus on specialised content knowledge in this learning community enabled teachers to approach their teaching more effectively. In this paper we claim that that the learning community is a productive learning space because it was supported by the Department of Education and a Non-Governmental Organisation, and because it focused on specialised content knowledge. The collaborative focus enabled teachers to share knowledge and ideas resulting in teachers taking charge of their own learning.

학습자 중심 코칭: 지도자들의 전문내용지식 비교

학습자 중심 코칭: 지도자들의 전문내용지식 비교

758. High-Throughput Mining of Electronic Medical Records Using Generalizable Autonomous Scripts

BackgroundThe electronic medical record (EMR) has become a modern compendium of health information, from broad clinical assessments down to an individual’s heart rate. The wealth of information in these EMRs hold promise for clinical discovery and hypothesis generation. Unfortunately, as these systems have become more robust, mining them for relevant clinical information is hindered by the overall data architecture, and often requires the expertise of a clinical informatician to extract relevant data. However, as the information presented to the clinician through the digital workspace is derived from the core EMR database, the format is well structured and can be mined using text recognition and parsing scripts.MethodsHere we present a program which can parse output from Epic Hyperspace®, generating a relational database of clinical information. To facilitate ease of use, our protocol capitalizes on the familiarity of Microsoft Excel® as an intermediary for storing the raw output from the EMR, with data parsing and processing scripts written in SAS V9.4 (Cary, North Carolina).ResultsAs a proof of concept, we extracted the diagnosis codes and standard laboratories for 190 patients seen in our Congenital Cytomegalovirus Clinic at Texas Children’s Hospital in Houston, Texas. Manual extraction of these data into Microsoft Excel® took 1 hour, and the scripts to parse the data took less than 5 seconds to run. Data from these patients included: 3800 ICD-10 codes (along with their metadata) and 33,000 individual laboratory values. In total, more than 850,000 characters were extracted from the EMR using this technique. Manual review of 10 randomly selected charts, found the data in perfect concordant with the EMR, a direct reflection of the fidelity of the parsing scripts. On average, an experienced user was able to enter three ICD-10 codes each minute, and six individual laboratory values per minute. At best, this same process would have taken at least 110 hours using a conventional chart review technique.ConclusionHigh-throughput data mining tools have the potential to improve the feasibility of studies dependent upon information stored in the EMR. When coupled with specific content knowledge, this approach can consolidate months of data collection into a day’s task.Disclosures All authors: No reported disclosures

2337. Health Outcomes in Congenital Cytomegalovirus, a Systematized and Unbiased Approach in the Electronic Medical Record Era

BackgroundThere is limited data on the indirect and non-medical costs associated with congenital cytomegalovirus (cCMV). Attempts to predict the economic impact of disease often rely on secondary analyses of large private databases, and may not capture the full spectrum of a disease. The granularity of billing codes in the Electronic Medical Record (EMR) make it possible to track health outcomes over time, however, with over 80,000 unique codes in ICD-10, selecting the appropriate codes requires specific content knowledge and can lead to bias in categorization. The Systematized Nomenclature of Medicine—Clinical Terms (SNOMED-CT)® provides physicians a tool to find specific ICD-10 on the basis of semantic terms. These terms can be used to build disease state-specific clusters of ICD-10 codes by which to study the economic impact of any disease, including this potentially devastating congenital infection.MethodsUsing a series of data parsing and processing scripts written in SAS V9.4 (Cary, NC), we extracted the diagnosis codes for 190 patients seen in our Congenital Cytomegalovirus Clinic at Texas Children’s Hospital in Houston, Texas. This data were consolidated into a relational database of clinical information. Through a second program we developed, clusters of ICD-10 codes were imputed from the SNOMED-CT® on the basis of semantic terms associated with cCMV (e.g., “hearing problem,” “developmental disability,” “neurological problem”).ResultsA total of 190 patients have been seen in our clinic with an ICD-10 diagnosis of CMV infection, 144 of these had cCMV, and 102 of these were born after 1/1/2008 (the inception date of our EMR). 60% of these patients were Caucasian (21% Hispanic), and 25% African American. 54 (53%) had hearing deficits, 17 (16%) had hearing aids, and 55 (54%) had developmental abnormalities. The average time (in years) to development of specific deficits are shown in Figure 1.ConclusionThe spectrum of disease of cCMV is broad and has been well studied in the past. The EMR gives us the potential to further study this disease in finer detail and identify rates of disease progression by mining the ICD-10 codes associated with these patients throughout time. These results should prove invaluable for generating cost-models for the economic impact of cCMV. Disclosures All authors: No reported disclosures.

Turkish Pre-service Middle Level Mathematics Teachers’ Knowledge for Teaching Fractions

Fractions are a crucial mathematical topic, which is known as being challenging for both students, pre- and in-service teachers. The current study attempted to explore the extent of pre-service middle level mathematics teachers’ knowledge for teaching fractions. Fifty-one senior pre-service teachers took part in the study. The Knowledge for Teaching Fractions Test, which includes almost all characteristics of fractions, was employed to measure participants’ knowledge for teaching fractions. The Pre-service Teachers’ Mathematics Knowledge for Teaching Framework was used to conceptualize participants’ responses to the tasks in the Knowledge for Teaching Fractions Test. The findings showed that participants’ mathematical knowledge for teaching fractions was not satisfactory. Meanwhile, while they had sound common content knowledge for teaching fractions, their specialized content knowledge for teaching this topic was very poor. The implications for teaching fractions are discussed in the context of pre-service middle level teacher preparation.

Content Development as a Function of Content Knowledge Courses in Preservice Physical Education Teachers

ABSTRACTThe purpose of this study was to investigate preservice teachers’ (PSTs) knowledge of instructional task progressions (i.e., content development) and depth of content knowledge as a function of content courses in parkour and basketball. 18 preservice teachers (PSTs) (five female and 13 male) in Physical Education from a Belgian university engaged in a parkour and basketball content course. Each class consisted of a 4-day unit with a total duration of 12 hours and focused on the acquisition of specialized content knowledge through microteaching sessions. Before and after the content course, PSTs content development defined in terms of knowledge of instructional tasks was measured through content mapping. Two trained observers coded content maps independently and reliability was 86%, based on 75% of the total sample. For parkour, the median total number of tasks, informing and extending tasks, increased significantly after the content course (p = .001). For basketball, the median total number of tasks remained the same (p = .011). Median extending tasks decreased significantly (p = .003) while extending-applying tasks increased significantly (p = .007). Median depth of content knowledge did not improve and was 1.67 for parkour and 1.15 for basketball, which is below the recommended index of 3.0. For parkour, content courses positively increased PST’s content development in terms of total and extending tasks. For basketball, the increase of extending-applying tasks reflected a game-based approach. Further research is needed to investigate how content courses should be designed to improve PST’s knowledge of instructional tasks.

Exploring differences in mathematical knowledge for teaching for prospective and practicing teachers

Teaching mathematics requires a wide range of knowledge, including types of mathematical knowledge specialized to the work of teaching. Because specialized content knowledge is a form of professional knowledge, it is important to emphasize in professional preparation. In this paper, we present results comparing the performance of prospective and practicing teachers on the Learning Mathematics for Teaching (LMT) assessments. While the results show that practicing teachers score higher on the LMT assessments than prospective teachers, only about half of the individual items are significantly more difficult for prospective teachers. To gain a more nuanced understanding of the mathematical knowledge assessed by the LMT items, we also compared the performance of prospective and practicing teachers for items organized by the mathematical work of teaching. We discuss implications for identifying types of professional mathematical knowledge important to emphasize in teacher education.

Assessment of In-service Science Teachers’ Teaching Competencies in Integrated STEM Program

The purpose of the study was to investigate the effects of a professional development instructional program Integrated STEM for elementary schools in a rural context of Thailand which carried out at the Faculty of Education, Buriram Rajabhat University during February 2018. Research instruments were (1) assessment observational record consisted of 5 elements of competencies with 4 levels of rubric criteria including beginning, approaching proficient, proficient, and distinguished levels, (2) achievement test related STEM designed to assess specific science content knowledge. The research findings revealed that the integrated STEM program was recommended to use for developing in-service science teachers’ teaching competencies. From evaluation of experts, the results indicated that competencies’ levels of teaching of in-service science teachers was achieved as approaching proficient level. Moreover, the results of one sample t-test indicated that teachers’ achievement score on science content knowledge after implementing the integrated STEM program was significantly higher than before at the 0.01 level. It can be suggested that in-service training programs should be developed and used for science teachers to raise their awareness of the necessity of STEM education and to enhance their competencies in teaching preparation program.

테니스 초임 지도자와 경력 지도자의 전문내용 지식 비교

Purpose: The purpose of this study is to compare the specialized content knowledge (SCK) of novice and expert tennis coaches. Research questions are: (1) Are there differences in the recognition of performance errors between novice and expert coaches? (2) Are there differences in the task presentation that correct the performance errors between novice and expert coaches?BR Methods: Participants were novice (N = 10) and expert (N = 10) tennis coaches. We collected data on (1 ) the knowledge of performing errors and (2) the knowledge of tasks representation that constitutes the SCK of tennis coaches. The coaches watched the game video of the beginning tennis player, described the technical error of the player in the video clip, and the performance action to be improved. And coaches have created a content map to improve performance errors. The content knowledge of performance error was analyzed by content analysis and the content map of task presentation knowledge was analyzed using a nonparametric statistical method.BR Results: Results indicated that novice and expert tennis coaches were similar in performance error detection knowledge. Also, they showed 3.0 or higher in the SCK index scores. Findings also showed that both novice and expert coaches used extended tasks more than any other content development categories. Expert coaches used more refining tasks than novice ones.BR Conclusion: SCK of novice and expert coaches was not different in error detection and instructional task presentation. Implications of this study were discussed for future research agenda.