Quantitative study on teacher quality: case of middle grades mathematics

This quantitative study examines whether and how different proxies of teacher quality such as cognitive type of teacher knowledge, coursework and certification are associated with student achievement. In the context of this study, the cognitive type of teacher content knowledge refers to the amount and organization of mathematical facts and procedures, concepts and connections, and models and generalizations in the minds of teachers. Teachers were tested using a specifically designed Teacher Content Knowledge Survey. Teacher preparation and teacher demographic characteristics, such as teaching experience, teacher certification, teacher coursework were collected and analyzed with respect to the cognitive type of teacher knowledge and student achievement. The type of teachers' content knowledge was assessed and tested for correlation with student achievement on the state-mandated standardized test using multivariate methods including, but not limited to, tests for variance and independence, and correlation analysis

Engineering and didactics: blended approach

In this proposal, relationship between engineering and didactics is closely examined in order to conceptualize the construct of didactical engineering as an application of engineering methodology to studying of teaching and learning. Key terms (e.g., engineering, didactics, engineering design, and engineering didactics) are analyzed to validate the new construct. Subject domain of the didactical engineering is determined as design and construction of outcome-oriented teaching products via application of a scientific method and design thinking to the analysis of didactical systems, processes and situations for creating effective learning environments. The place of didactical engineering in the chain of related concepts as well as an impact of the new construct on redefining didactics is also discussedВ данном исследовании детально изучается взаимосвязь инженерии и дидактики с целью осмысления конструкции дидактической инженерии как применения инженерной методологии к изучению преподавания и обучения. Ключевые термины (например, инженерия, дидактика, инженерное проектирование и инженерная дидактика) анализируются для проверки новой конструкции. Предметная область дидактической инженерии определяется как проектирование и построение ориентированных на результат обучающих продуктов путем применения научного метода и проектного мышления к анализу дидактических систем, процессов и ситуаций для создания эффективной учебной среды. Также обсуждается место дидактической инженерии в цепочке смежных понятий, а также влияние новой строительной переопределяющей дидактик

CONTENT INTERACTIVITY AND CONTENT COMMUNICATION IN ENGINEERING OF ONLINE MATHEMATICS METHOD CLASS

In today's world, current revolutionary changes are associated with the intensive use of digital technologies in many spheres of human life, which democratize knowledge and access to open education. The ICT is increasingly implemented in the daily lives of individuals and the society. We are witnessing the formation of a new phenomenon - a global virtual learning community, which today includes more than one billion users. And the numbers continue to grow. Along with this, the market of online educational services is steadily growing. To meet the demands of the market, content development, content interactivity and content communication play important role in the engineering of online learning. In this paper, we will consider some of the approaches that will help to enhance content interactivity, such as cognitive visualization and other emerging techniques, for example, video streaming, screencasting, and gamification. We will also discuss different formats of content communication.8-2

Un estudio cuantitativo del conocimiento del contenido del maestro de matemáticas y su “saber actuar” en el aula

El objetivo de este estudio fue medir el conocimiento del contenido matemático del maestro de secundaria y su relación con el “saber actuar” del maestro. La pregunta de investigación es: ¿Qué tan asociados están los tipos cognitivos del conocimiento matemático con el “saber actuar” del maestro? Un estudio correlacional se desarrolló para establecer la relación entre estos dos tipos del conocimiento del maestro. Dos encuestas se aplicaron a 70 maestros de secundaria en la frontera norte de México. Una encuesta mide el conocimiento del contenido matemático del maestro (TCKS) y la otra examina el “saber actuar” (KtAS) del maestro

Learning Sciences Perspective on Engineering of Distance Learning. Part 2

There is an on-going debate in the literature on theoretical underpinnings of distance learning. Scholars consider different theoretical perspectives including but not limited to theory of independence and autonomy, theory of industrialization, and theory of interaction and communication through the lens of a traditional Learning Theory approach. There is a lack of discussion on a potential role of a newly emerging field of Learning Sciences in framing the theory of distance learning. Thus, in this paper we provide a theoretical analysis of the Learning Sciences as a new approach to understand distance learning in the era of Information and Communication Technology (ICT). Learning Sciences is an interdisciplinary field that studies teaching and learning. This emerging innovative field includes but is not limited to multiple disciplines such as cognitive science, educational psychology, anthropology, computer science, to name a few. The Learning Sciences’ major objective is to understand and design effective learning environments, including distance learning, based on the latest findings about the processes involved in human learning

Learning Sciences Perspective on Engineering of Distance Learning. Part 1

There is an on-going debate in the literature on theoretical underpinnings of distance learning. Scholars consider different theoretical perspectives including but not limited to theory of independence and autonomy, theory of industrialization, and theory of interaction and communication through the lens of a traditional Learning Theory approach. There is a lack of discussion on a potential role of a newly emerging field of Learning Sciences in framing the theory of distance learning. Thus, in this paper we provide a theoretical analysis of the Learning Sciences as a new approach to understand distance learning in the era of Information and Communication Technology (ICT). Learning sciences is an interdisciplinary field that studies teaching and learning. This emerging innovative field includes but is not limited to multiple disciplines such as cognitive science, educational psychology, anthropology, computer science, to name a few. The Learning Sciences’ major objective is to understand and design effective learning environments, including distance learning, based on the latest findings about the processes involved in human learning

QUALITATIVE STUDY OF SECONDARY MATHEMATICS TEACHERS' NOT-KNOWING WHILE SOLVING GEOMETRIC REASONING TASKS

Not-knowing is an underexplored concept defined by an individual's ability to be aware of what they do not know as a means to plan and more effectively face complex situations. This qualitative study focuses on analyzing students' ability to express their "not-knowing" while completing tasks and reflecting periodically. It becomes evident rather quickly that these students have difficulty expressing their not-knowing. Through transcription analysis, reflection coding, and interviews, four recurring themes emerge that could possibly determine why students have difficulty expressing their not-knowing. These four themes are deflection, student pressure, heuristic sense, and fractured knowledge. Each one of these themes will be discussed followed by a conclusion of their overall importance in relation to a students' ability to express not-knowing.147-15

SECONDARY SCHOOL MATHEMATICS TEACHERS' DISPOSITION TOWARD MISTAKES: CROSS-CULTURAL MIXED METHODS STUDY

The reported mixed methods study focused on exploration of mathematics teachers' dispositions toward errors in two countries - Mexico and USA. More specifically, this study addressed borderland secondary teachers' dispositions toward mistakes in teaching and learning mathematics. An explanatory sequential method design was used that involved collecting quantitative data first and then explaining the quantitative results with in-depth qualitative analysis. The instrument - Error Orientation Questionnaire (EOQ) - was used to collect quantitative data on teachers' disposition toward errors in the context of their own learning and their students learning. Following up on EOQ, the semi-structured interview was used to collect qualitative data. Two research questions guided the study. First, we were interested in what dispositions toward mathematical mistakes do secondary teachers in the US and Mexico have. The second question addressed ways the interview aimed at teachers' dispositions toward errors helped to explain the quantitative results.The reported mixed methods study focused on exploration of mathematics teachers' dispositions toward errors in two countries - Mexico and USA. More specifically, this study addressed borderland secondary teachers' dispositions toward mistakes in teaching and learning mathematics. An explanatory sequential method design was used that involved collecting quantitative data first and then explaining the quantitative results with in-depth qualitative analysis. The instrument - Error Orientation Questionnaire (EOQ) - was used to collect quantitative data on teachers' disposition toward errors in the context of their own learning and their students learning. Following up on EOQ, the semi-structured interview was used to collect qualitative data. Two research questions guided the study. First, we were interested in what dispositions toward mathematical mistakes do secondary teachers in the US and Mexico have. The second question addressed ways the interview aimed at teachers' dispositions toward errors helped to explain the quantitative results.188-19

Narrative analysis of college students' inconsistecies in representing duality of infinity

Interpreting students? views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among the students? process-object perceptions. The fluctuations between students? views however reveal an undeveloped duality conception. This paper seeks to examine college students? conception of duality in understanding and representing infinity with the intent to elucidate strategy that could guide researchers in categorizing students? views of infinity into different levels. Data for the study were collected from N=69 college pre-calculus students at one of the southwestern universities in the U.S. using self-report questionnaire and interviews. Data was triangulated using multiple measures analyzed by three independent experts using self-designed coding sheet to assess students? externalization of the duality conception of infinity.223-23

Examination of Lower Secondary Mathematics Teachers’ Content Knowledge and Its Connection to Students’ Performance

© 2015 Ministry of Science and Technology, Taiwan This mixed methods study examined an association between cognitive types of teachers’ mathematical content knowledge and students’ performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge. The first cognitive type (T1) assessed participants’ knowledge of basic facts and procedures. The second cognitive type (T2) measured teachers’ understanding of concepts and connections. The third cognitive type (T3) gauged teachers’ knowledge of mathematical models and generalizations. The study comprised two levels of quantitative data analysis. First, we explored each cognitive type of teachers’ content knowledge and the overall TCKS score as they related to student performance. Second, we studied the correlation between each cognitive type of teacher content knowledge to deepen the understanding of content associations. Results of the study show a statistically significant correlation between cognitive types T1 and T2 of teacher content knowledge and student performance (p < .05). The correlation between cognitive type T3 and student performance was not significant (p = .0678). The most substantial finding was the correlation between teachers’ total score on the TCKS and student performance (Pearson’s r = .2903, p = .0055 < .01). These results suggest that teachers’ content knowledge plays an important role in student performance at the lower secondary school. The qualitative phase included structured interviews with two of the teacher participants in order to further elaborate on the nature of the quantitative results of the study