Mathematical Knowledge For Teaching Research Articles

Developing survey-based measures of mathematics teachers’ pedagogical technology knowledge: a focus on computational thinking and programming tools

ABSTRACT The aim of this research is to develop a survey to explore Norwegian teachers’ perceptions regarding integrating computational thinking (CT) and programming tools into mathematics teaching by using Rasch analysis. For this purpose, three measures are developed: mathematical knowledge for teaching (with technology), instrumental genesis and personal orientations, aligning with the components of Pedagogical Technology Knowledge framework. The empirical data to validate and refine the developed measures includes a relatively large sample of 356 Norwegian primary and secondary school mathematics teachers. Through the three measures, analysis of the survey data revealed insights into teacher perceptions and challenges in tool adoption. These results, first, highlighted the complexity of tool integration and the necessity of unpacking country-specific competencies linking CT and programming to mathematics. Second, the results underlined a need for qualitative research to delve deeper into teacher perceptions and understandings of CT and programming to address challenges and enhance classroom practices.

Mathematical knowledge of pre-service teachers when performing measurement estimation tasks

Mathematical knowledge of pre-service teachers when performing measurement estimation tasks

Implementing Blended Learning within the TPMK Framework to Enhance Mathematics Teachers' Competence

The post Covid-19 pandemic opens opportunities for teachers to conduct innovative studis in the context of mathematics education. The blended learning model has become the primary choice implemented by teachers during mathematics learning activities in schools. However, discourse related to this matter is still limited. This research investigates the impact of implementing the blended learning model on the Technological Pedagogical and Mathematics Knowledge (TPMK) of mathematics teachers in Madrasah Aliyah (MA) in Indonesia. post-Covid-19 pandemic. The research focuses on aspects of blended learning implementation, the level of TPMK of teachers, and the extent of its impact on the professional development of mathematics teachers. The research method used is correlational design, with data collection conducted through questionnaires given to MA teachers. The results show that implementing blended learning has a significant positive impact on improving the TPMK of mathematics teachers. Research recommendations include expanding training programs for teachers in technology integration, improving digital infrastructure in madrasas, providing incentives for learning innovations, and enhancing cooperation among madrasas. The implications of this research are crucial in providing significant contributions to the development of mathematics education in the madrasah environment. This research can be a foundation for developing more effective educational strategies and policies, particularly in facing and adapting to post-pandemic learning changes.

Pre-service teachers’ use of the jump strategy on the empty number line for mental computation

Background: South African teachers’ mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics.Aim: The aim of this article is to share how pre-service teachers (PSTs) used the empty number line (ENL) to demonstrate the jump strategy (JS) for efficient mental computation, related to the national Mental Starters Assessment Project (MSAP).Setting: This study was conducted at a tertiary institution in the Eastern Cape province of South Africa, with 40 first-year intermediate phase PSTs, during their mathematics didactics course.Methods: The data comprised 40 micro-teaching videos, analysed thematically, following an analytical model for video-recorded data. Videos were categorised according to the way they faithfully followed or departed from the MSAP teacher resources.Results: Findings suggest that more than 70% of the PSTs faithfully followed the teacher resources to teach the JS on the ENL, with regards to use of at least three of the four key elements, namely: ENL, jumps, gesturing, and key phrases and terminology.Conclusion: We suggest PSTs receive explicit instruction on the above-mentioned key elements for teaching mental calculation strategies with the ENL and opportunities to practise teaching these to their peers.Contribution: Most PSTs successfully used the ENL to demonstrate the JS for efficient mental computation, enabled by the opportunity to engage in developing (and reflecting on their) micro-teaching videos.

Investigating Preservice Teachers’ Conceptualizations of Mathematical Knowledge for Teaching Through Video Analysis

Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher knowledge either as purely pedagogical or solely content knowledge in their initial analyses of the video lesson. After engaging in a discussion that introduced the MKT framework, the M-PSTs began to illustrate how a teacher’s content knowledge influenced her instructional decisions and actions. Through this discussion, M-PSTs began identifying MKT as professional content knowledge unique to teaching and, thus, distinguished MKT from generic pedagogical or content knowledge. I argue that the language and concepts offered through the framework enhanced the M-PSTs’ conceptions of MKT and suggest that the instructional activities from this study contribute to developing M-PSTs as reflective practitioners.

Mathematical Knowledge for Teaching in the Senior Phase: Entry-Level Teacher Candidates’ Subject Content Knowledge

Mathematical Knowledge for Teaching in the Senior Phase: Entry-Level Teacher Candidates’ Subject Content Knowledge

Mathematical knowledge for teaching among Rwandan Teacher Training Colleges: data collected for a doctoral program

Mathematical knowledge for teaching among Rwandan Teacher Training Colleges: data collected for a doctoral program

Preservice Secondary Teachers’ Mathematical Knowledge for Teaching: Focus on Reflective Practice

ABSTRACT Mathematics education researchers have highlighted that preservice secondary mathematics teachers (PSTs) need opportunities to learn how their content knowledge is contextualized during instruction. Mathematical Knowledge for Teaching (MKT) subdomains provide a way to understand mathematics discipline-specific knowledge that is unique to the profession of teaching. Using a single case study design, we investigated how 11 secondary PSTs described MKT subdomains as they engaged in approximations of practice in the form of lesson planning, peer teaching, and associated guided reflections. The findings demonstrated that the PSTs referenced the MKT subdomains related to planned teacher actions (e.g., posing scripted questions) in their initial reflections. As they progressed through the approximations of practice and associated reflections, they began reflecting on MKT subdomains related to contingency actions and decisions (e.g., modifying mathematical tasks based on students’ thinking). Findings also demonstrated that, after experiences reflecting, the PSTs described a broader set of MKT subdomains (e.g., curricular trajectory) in addition to their responses to the specific prompts. We argue that providing PSTs with opportunities to reflect on their practices through the lens of MKT is an effective way to develop their understanding of how content knowledge is contextualized during mathematics teaching.

Mathematical Knowledge of Early Algebra Exhibited by Pre-Service Early Childhood Education Teachers

AbstractThis study analyzes the mathematical knowledge to teach early algebra exhibited by pre-service early childhood education teachers, from the perspective of the Mathematical Knowledge for Teaching (MKT) model. The research adopts a mixed exploratory-descriptive methodological approach, based on the application of the MKT-early algebra questionnaire (3–6), consisting of six open-ended items that place teachers in various teaching situations reflecting the knowledge that characterizes early algebra at this stage of schooling. The analysis of the answers given by the pre-service teachers of early childhood education revealed a level general of insufficient mathematical knowledge, with the common content knowledge exhibiting fewer limitations compared to the other subdomains that comprise the model, and the horizon content knowledge the weakest. We conclude that it is necessary to offer teacher training programs that deepen the didactics of early algebra and provide tools to further the effective teaching of this content block in early childhood education.

Analysis of Mathematics Content Knowledge of Mathematics Teachers Based on Bloom's Taxonomy Revision

This study aims to assess mathematics teachers' understanding of Mathematics Content Knowledge based on the Revised Bloom Taxonomy. The method used is quantitative descriptive research with a survey approach. The respondents of this study were mathematics teachers who taught at SMP/MTs in Losari District, Brebes Regency. Data was collected using non-test instruments in the form of questionnaires and question tests. Data analysis involves presenting data, testing differences, and concluding. The results showed that teachers' understanding of Mathematics Content Knowledge in teaching and mastery of the material was categorized as strong. Based on Bloom's revised taxonomy, teachers have good mastery, especially in knowledge dimensions such as factual, conceptual, procedural, and metacognitive knowledge, which are categorized as high. There was no significant difference in the average Mathematics Content Knowledge score of teachers, either with a working period of less than 10 years, 10-15 years, or more than 15 years.

Foundational mathematical knowledge of prospective teachers: Evidence from a professional development training

Foundational mathematical knowledge of prospective teachers: Evidence from a professional development training

Toward a Better Understanding of the Nature of Pedagogical Content Knowledge for Fractions: The Role of Experience

ABSTRACT Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions assessment. The PCK-Fractions measure is designed to examine the effectiveness of teacher education program and field experiences in facilitating preservice teachers’ (PSTs) PCK for children’s fraction reasoning in grades 4–6. Emplying165 undergraduate students, the research investigates how different levels of coursework and field experience influence PCK-Fractions scores. Results suggest that both completing coursework in a teacher education program and having grades 4–6 field experience each led to higher PCK-Fractions scores. Additionally, this study provides further evidence supporting the validity of the PCK-Fractions measure as a reliable indicator of PSTs’ proficiency in teaching fractions. Implications for mathematics teacher education and educational research are discussed.

The Effect of Training Program Based on Instructional Practices According to the (NCTM) Standards on Improving the Pedagogical Knowledge among Mathematics Teachers in Jordan

The current study aims at revealing the effect of a training program based on teaching practices according to NCTM standards in improving the pedagogical knowledge of mathematics teachers. The study followed the semi- experimental method. To achieve the aims of the research, a training program that is based on the standards of NCTM was designed. The program consists of eight packages which are (Establish mathematics goals to focus learning, implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, facilitate meaningful mathematical discourse, pose purposeful questions, build procedural FLuency from conceptual understanding, support productive struggle in learning mathematics, Elicit and use evidence of student thinking). After confirming the validity of the tool, a sample of (20) male and female teachers from Deir Ala Directorate of Education in the academic year 2020-2021.To reveal the effectiveness of the program, a test in pedagogical knowledge was prepared. The test consists of six respects which are identification of mathematics content, the pedagogical knowledge of the mathematical content and knowing students' thinking. The test validity and reliability were checked. The results of the study showed that there were statistically significant differences between measuring averages in the post application of the test. These results were pro- sample in all dimensions and in the total degree. Depending on these results, the study asserted the necessity for the training department in the Jordanian Ministry of Education to benefit from the suggested and used program in the study to focus more on the teaching practices.

Assessing knowledge to teach early algebra from the Mathematical Knowledge for Teaching (MKT) perspective: A support tool for primary school teachers

Assessing knowledge to teach early algebra from the Mathematical Knowledge for Teaching (MKT) perspective: A support tool for primary school teachers

Analysis of STEM Knowledge of Pre-Service Science and Mathematics Teacher

This research is motivated by the importance of STEM knowledge for pre-service science and mathematics teachers in the 21st century. This research aims to analyze the STEM knowledge of pre-service science and mathematics teachers. The research method was carried out by distributing questionnaires with STEM knowledge indicators to the sample. The sample in this research was 86. They were 59 pre-service science teachers and 27 pre-service mathematics teachers, with different years of education, namely the 1st, 2nd, 3rd, and 4th year of Universitas Negeri Semarang. The results of this research show that the average understanding of pre-service science and mathematics teachers regarding to the STEM-based learning in the definition aspect is 4.11, objectives are 3.94, benefits are 3.94, aspects are 3.69, components are 3.71, characteristics is 3.75, and implementation is 3.86. This proves that pre-service science and mathematics teachers' understanding of the definition of STEM-based learning is very good, while pre-service science and mathematics teachers' understanding of the objectives, benefits, aspects, components, characteristics, and implementation of STEM-based learning is good.

Preservice teachers' mathematical knowledge for teaching: Focus on lesson planning and reflection

AbstractMathematics teacher educators have suggested preservice mathematics teachers' (PMTs') practices provide evidence of their mathematical knowledge for teaching (MKT). PMTs engage in approximations of practice to rehearse teaching. To explore connections between MKT and PMTs’ practices, we operationalized six MKT subdomains in terms of approximations of practice. We used that operationalization to investigate, which subdomains were evidenced in PMTs’ lesson plans and their lesson plan reflections. Eleven secondary PMTs participated in our study. Using a qualitative content analysis method, we found Knowledge of Content and Teaching most evidenced, suggesting that the PMTs demonstrated MKT when they described mathematical tasks and associated instructional activities. Also, the PMTs demonstrated Knowledge of Content and Students when they described how their students would engage with proposed mathematical tasks. However, the PMTs struggled to plan for activities by building on students’ potential mathematical thinking and reasoning. Only limited instances of Horizon Content Knowledge suggest that the PMTs had limited opportunities to demonstrate how their advanced mathematical knowledge connected with their mathematics teaching in the approximations of practice provided. We propose alternative forms of approximations of practice to optimize PMTs’ opportunities to demonstrate and develop MKT.

A model for problem creation: implications for teacher training

AbstractThe invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on the assumptions of the Onto-Semiotic Approach, considers both the elements that characterize a problem and a categorization of different types of problem-posing tasks. In addition, the model proposes a description of the mathematical processes that occur during the sequence of actions carried out when a new problem is created. The model is illustrated by its application to analyze the practices developed by pre-service teachers in three problem-posing tasks aimed at specific didactic-mathematical purposes (mobilizing certain mathematical knowledge or reasoning, contributing to achieving learning goals, or addressing students’ difficulties). We conclude discussing the potential of our model to analyze the mathematical processes involved in problem creation from the perspective of teacher education.

Relationship between mathematical pedagogical content knowledge, beliefs, and motivation of elementary school teachers

Pedagogical content knowledge (PCK) is one form of teachers’ professional knowledge in subject teaching, and teachers’ rich PCK enables effective instruction and improves students’ academic performance. However, there has been limited research on the relationships of individual difference characteristics of teachers to PCK among in-service elementary school teachers. Therefore, in addition to the demographic variables (gender and years of teaching experience) and psychological variables (beliefs about teaching and learning and teacher efficacy) examined in previous studies, this study attempted to clarify whether motivation for teaching is related to PCK. We conducted a web survey of in-service elementary school teachers in Japan (n = 267). The results showed that the traditional beliefs that students are to be controlled by their teachers and indifference, which describes a state of lack of motivation to prepare for class, were negatively associated with two elements of mathematical PCK (knowledge of learners and knowledge of instruction). Furthermore, multiple regression analysis revealed that traditional beliefs about teaching and learning were negatively associated with the knowledge of learners and indifference to subject instruction with knowledge of instruction. This suggests that teachers’ motivation for teaching is related to PCK, in addition to the variables that have been previously examined.

Specialized Knowledge of Prospective Mathematics Teachers on the Concept of Mathematical Proof

[Objetivo] En este artículo, se presentan los resultados de una investigación cualitativa de carácter descriptivo que tiene como objetivo caracterizar el conocimiento especializado de los profesores de matemáticas en formación inicial de la Universidad Nacional en Costa Rica (UNA), sobre el concepto de la demostración matemática, mediante el modelo Mathematics Teacher’s Specialized Knowledge (MTSK). [Metodología] La investigación se posiciona en el paradigma interpretativo y tiene un enfoque cualitativo. Se aplicó un cuestionario, durante el primer semestre del 2021, a 42 profesores de matemáticas en formación inicial de cuarto y quinto año de la carrera Bachillerato y Licenciatura en Enseñanza de la Matemática de la Universidad Nacional de Costa Rica. Para examinar la información, se empleó el análisis de contenido y se hicieron agrupaciones de las respuestas, con el propósito de generar ideas centrales sobre el concepto de demostración. [Resultados] De los resultados se desprenden cuatro ideas centrales sobre lo que es una demostración matemática para los sujetos de la investigación, cercanas a aspectos formales lógico-sintácticos y matemáticos (ALSM) o aspectos informales semánticos (AIS). Se encontraron evidencias de las cinco funciones de De Villiers (1993) para la demostración y surgieron nuevas funciones relacionadas con esta en las matemáticas y en las matemáticas escolares. [Conclusiones] Los resultados brindan insumos a formadores de profesores de matemáticas e investigadores, en la revisión y análisis de programas de formación docente, y contribuyen en la búsqueda de nuevas áreas de investigación relacionadas con el tema.

From “learning to variate” to “variate for learning”: Teachers learning through collaborative, iterative context-based mathematical problem posing

Problem posing (PP) has been found to contribute to teachers’ mathematical pedagogical knowledge. However, little is known about what and how teachers learn when engaged in continuous iterative PP. We use the variation theory of learning to conceptualize what and how teachers learn during iterative PP, illustrating these processes via a case study. The main argument is that what teachers learn from engaging in iterative PP are different task variables we refer to as “dimensions of possible variation.” Awareness of these dimensions allows teachers to skillfully generate new problems or re-formulate previously posed ones to achieve desired pedagogical goals. We show how, during a collaborative design process with the PD coordinator, a teacher-designer became aware of some new-to-her dimensions and developed corresponding techniques for diversifying tasks. These awarenesses were still evident in an interview six months after the end of the PD. Recommendations for teacher educators are suggested.