A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

Analyzing Elementary Preservice Teachers’ Development of Content and Pedagogical Content Knowledge in Mathematics through Microteaching Lesson Study

This study examines the effect of Microteaching Lesson Study participation on the mathematics content and pedagogical content knowledge of 52 elementary preservice teachers. Preliminary findings, which are positive, are discussed.

The Effect of Authentic Literacy Experiences as Book Buddies with Hispanic Fourth Graders on Preservice Teachers’ Literacy Content Knowledge and Reading Maturity

From a sociocultural perspective, individuals learn best from contextualized experiences. In preservice teacher education, contextualized experiences include authentic literacy experiences, which include a real reader and writer and replicate real life communication. To be prepared to teach well, preservice teachers need to gain literacy content knowledge and possess reading maturity. The purpose of this study was to examine the effect of authentic literacy experiences as Book Buddies with Hispanic fourth graders on preservice teachers’ literacy content knowledge and reading maturity. The study was a pretest/posttest design conducted over 12 weeks. Preservice teacher participants, the focus of the study, were elementary education majors taking the third of four required reading courses in non-probabilistic convenience groups, 43 (n = 33 experimental, n = 10 comparison) Elementary Education majors. The Survey of Preservice Teachers’ Knowledge of Teaching and Technology (SPTKTT), specifically designed for preservice teachers majoring in elementary or early childhood education and the Reading Maturity Survey (RMS) were used in this study. Preservice teachers chose either the experimental or comparison group based on the opportunity to earn extra credit points (experimental = 30 points, comparison = 15). After exchanging introductory letters preservice teachers and Hispanic fourth graders each read four books. After reading each book preservice teachers wrote letters to their student asking higher order thinking questions. Preservice teachers received scanned copies of their student’s unedited letters via email which enabled them to see their student’s authentic answers and writing levels. A series of analyses of covariance were used to determine whether there were significant differences in the dependent variables between the experimental and comparison groups. This quasi-experimental study tested two hypotheses. Using the appropriate pretest scores as covariates for adjusting the posttest means of the subcategory Literacy Content Knowledge (LCK), of the SPTKTT and the RMS, the mean adjusted posttest scores from the experimental group and comparison group were compared. No significant differences were found on the LCK dependent variable using the .05 level of significance, which may be due to Type II error caused by the small sample size. Significant differences were found on RMS using the .05 level of significance.

Mathematical pedagogical content knowledge in early childhood education: A study in initial teacher education in Portugal

The study aims to explore the specificity of mathematics Pedagogical Content Knowledge in Early Childhood Education Pedagogy. The pedagogy of ECE (Siraj-Blatchford, 2010) and the didactics of ECE (Pramling & Pramling-Samuelsson, 2011) suggest dimensions of knowledge that require strong content and PC knowledge of teachers. Recent studies about PCK of ECE teachers highlight similar specific dimensions: organization of educational environment and interactions with children (Lee, 2010, McCray, 2008, Rojas, 2008). The current framework for ECE Teacher Education in Portugal (since 2007) focuses both content knowledge and subject didactics. PCK has been labelled the 'great unknown' in ECE (Rojas, 2008) in traditions where the child's development is considered as the main knowledge base for ECE (Chen & McNamee, 2006, Cullen, 2005, Hedges & Cullen, 2005). We studied the perspectives of 27 initial teacher education students about knowledge for teaching and about ECE Pedagogy. We used one open-ended questionnaire and students' analysis of episodes focusing children's answers or discourse relevant for mathematics (about high numbers and square root). The questionnaire was anonymous and students’ permission to use the answers was obtained. In the questionnaire, interactions with children (62%) and organization of the educational environment (38%) are highlighted as the most important focus for the teacher. Students suggested tasks that were adult planned and oriented to further the situations presented in the episodes. Very few references to children's exploratory actions (Bonawitz et al., 2011) were made. The specificity of ECE (child initiated activities, e.g.) needs to be further developed in initial teacher education.

The pedagogical content knowledge of Danish geography teachers in a changing schooling context

This study examines the self-reported, topic-specific professional knowledge (TSPK) of Danish geography teachers seen as an aspect of their pedagogical content knowledge (PCK) when teaching weather formation and climate change. This topic is considered representative of geography teaching in Denmark. In the last ten years Danish primary and lower-secondary schooling has undergone several significant changes, including the introduction of a final multiple-choice exam in geography in 2007, and a fundamental reconstruction of the curriculum in 2014. These changes are expected to influence the TSPK of geography teachers in ways that potentially have an impact on their classroom practice. Teachers´ responses to specific questions relating to their choice of learning goals and the content and organisation of their lessons show that geography teachers take into account not only the knowledge aspects which point to the final multiple-choice exam, but also the ‘bildung’ perspectives of the subject equipping students to develop their own opinions when dealing with socio-scientific issues (SSI).

Preservice teachers' knowledge on elementary geometry concepts

This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometry

Preservice teachers' knowledge on elementary geometry concepts

This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometry.

The construction process of pedagogical knowledge among nursing professors

Didactic knowledge about contents is constructed through an idiosyncratic synthesis between knowledge about the subject area, students' general pedagogical knowledge and the teacher's biography. This study aimed to understand the construction process and the sources of Pedagogical Content Knowledge, as well as to analyze its manifestations and variations in interactive teaching by teachers whom the students considered competent. Data collection involved teachers from an undergraduate nursing program in the South of Brazil, through non-participant observation and semistructured interviews. Data analysis was submitted to the constant comparison method. The results disclose the need for initial education to cover pedagogical aspects for nurses; to assume permanent education as fundamental in view of the complexity of contents and teaching; to use mentoring/monitoring and the value learning with experienced teachers with a view to the development of quality teaching.

Knowledge Construction Technology through Hypermedia-Based Intelligent Conversational Channel

There have been multifarious approaches in building expert knowledge in medical or engineering field through expert system, case-based reasoning, model-based reasoning and also a large-scale knowledge-based system. The intriguing factors with these approaches are mainly the choices of reasoning mechanism, ontology, knowledge representation, elicitation and modeling. In our study, we argue that the knowledge construction through hypermedia-based community channel is an effective approach in constructing expert’s knowledge. We define that the knowledge can be represented as in the simplest form such as stories to the most complex ones such as on-the-job type of experiences. The current approaches of encoding experiences require expert’s knowledge to be acquired and represented in rules, cases or causal model. We differentiate the two types of knowledge which are the content knowledge and socially-derivable knowledge. The latter is described as knowledge that is earned through social interaction. Intelligent Conversational Channel is the system that supports the building and sharing on this type of knowledge.

An analysis of the themes of environmental sustainability in the United States curriculum science content standards

This study examined how the themes of environmental sustainability are evident in the national, state and local standards that guide k–12 science curriculum. The study applied the principles of content analysis within the framework of an ecological paradigm. In education, an ecological paradigm focuses on students' use of a holistic lens to view and understand material. The intent of this study was to analyze the seventh grade science content standards at the national, state, and local textbook levels to determine how and the extent to which each of the five themes of environmental sustainability are presented in the language of each text. The themes are: (a) Climate Change Indicators, (b) Biodiversity, (c) Human Population Density, (d) Impact and Presence of Environmental Pollution, (e) Earth as a Closed System. The research study offers practical insight on using a method of content analysis to locate keywords of environmental sustainability in the three texts and determine if the context of each term relates to this ecological paradigm. Using a concordance program, the researcher identified the frequency and context of each vocabulary item associated with these themes. Nine chi squares were run to determine if there were differences in content between the national and state standards and the textbook. Within each level chi squares were also run to determine if there were differences between the appearance of content knowledge and skill words. Results indicate that there is a lack of agreement between levels that is significant p < .01. A discussion of these results in relation to curriculum development and standardized assessments followed. The study found that at the national and state levels, there is a lack of articulation of the goals of environmental sustainability or an ecological paradigm. With respect to the science textbook, a greater number of keywords were present; however, the context of many of these keywords did not align with the discourse of an ecological paradigm. Further, the environmental sustainability themes present in the textbook were limited to the last four chapters of the text. Additional research is recommended to determine whether this situation also exists in other settings.

Microteaching Lesson Study: Mentor interaction structure and its relation to elementary preservice mathematics teacher knowledge development

This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a southern urban university were part of the study. This included 72 participants who completed MLS across three different mentor interaction structures as part of their course requirements and 31 elementary preservice teachers who did not complete MLS as part of their methods course and served as a comparison group for a portion of the study. A sequential mixed-methods research design was used to analyze the relationship between MLS mentor interaction structure and growth in preservice teachers' mathematics teacher knowledge. Data sources included pre and post assessments, group developed lesson plans and final reports, a feedback survey with Likert-type and open-ended questions, and transcripts of audio-recorded debriefing sessions. The pre and post assessments were analyzed using Analysis of Variance (ANOVA) and descriptive statistics were used to analyze the Likert-type feedback survey questions. Group MLS lesson plans, final reports, and transcripts of debriefing sessions along with the open-ended questions from the feedback survey were coded in a three-step process as described by Miles and Huberman (1994). In alignment with findings from M. Fernandez (2005, 2010), elementary preservice teachers participating in MLS grew in content knowledge related to MLS topics taught by one another. Results from the analysis of pre and post content knowledge assessments revealed that participants grew in their understanding of the mathematics topics taught during MLS irrespective of their mentor interaction structure and when compared to the participants who did not complete MLS in their methods course. Findings from the analysis of lesson plans for growth in pedagogical content knowledge revealed the most growth in this area occurred for participants assigned to the interaction structure in which the MLS mentor participated in the first two debriefing sessions. Analysis of the transcripts of the discourse during the debriefing sessions and the feedback surveys support the finding that the elementary preservice teachers assigned to the interaction structure in which the MLS mentor participated in the first and second debriefing sessions benefited more from the MLS experience when compared to elementary preservice teachers assigned to the other two interaction structures (MLS mentor participated in only the first debriefing session and MLS mentor participated in only the last debriefing session).

O professor como construtor do currículo: integração da tecnologia em atividades de aprendizagem de matemática

O desenvolvimento profissional dos professores de matemática, por meio de progra¬mas nacionais e formações contínuas, deve proporcionar experiências que envolvam investigação, pensamento, planeamento, prática e reflexão. No caso da tecnologia, não nos devemos focar nas ferramentas em si, mas no modo como são usadas pelos docentes em contexto de sala de aula. Existem taxonomias de atividades de apren¬dizagem baseadas no conteúdo assentes na ideia do professor como construtor do currículo, que, para integrar com sucesso a tecnologia educativa nas aulas, desenvolve o conhecimento pedagógico e tecnológico do conteúdo (TPACK), e apresenta-se a de matemática. Desse modo, reflete-se, por meio de vários estudos nacionais e internacionais, que as tecnologias deverão ser usadas pelos professores de acordo com objetivos, conteúdos e pedagogias específicas para terem um efeito positivo na aprendizagem dos alunos sobre as atividades baseadas no conteúdo que melhor se enquadram com essas tecnologias.

Using problem-based learning for introducing producer theory and market structure in intermediate microeconomics

This paper shows how instructors can use the problem‐based learning method to introduce producer theory and market structure in intermediate microeconomics courses. The paper proposes a framework where different decision problems are presented to students, who are asked to imagine that they are the managers of a firm who need to solve a problem in a particular business setting. In this setting, the instructors’ role isto provide both guidance to facilitate student learning and content knowledge on a just‐in‐time basis