Dialogic Teaching Model For Ninth Class Students To Conceptualize Inequalities

It is known that difficulties are often experienced in conceptual learning of mathematics, which is an abstract lesson. For this reason, it is difficult for students to conceptually learn inequalities, one of the difficult subjects of mathematics. The aim of this study is to investigate the effect of dialogic teaching to overcome the general mistakes and difficulties of 9th grade students in deepening the conceptual teaching of inequalities. This study was designed as an action research. The answers and solutions given to 7 open-ended questions prepared to determine students’ misconceptions and mistakes were scored between 0 and 2 points. When a detailed analysis of solutions written by the students was done, it was determined that the students had difficulty in establishing the concept of numbers, that they ignored the real numbers in a defined range and only focused on integers, that they ignored zero when finding the square of the inequality in a defined range, and that they had difficulty in understanding the principle of reversing when the inequality was multiplied by a negative number and also had difficulty in the solution of inequalities when two inequalities were combined into a single inequality. According to the results of the research, dialogic teaching played a supporting role for the students to reach the conceptual learning of inequalities. It was also seen that high school students were able to reconstruct the concept of inequality conceptually in the learning process. Keywords: dialogic teaching, inequalities, conceptual teaching, reconstructin

Students’ Creative Thinking Stages in Inquiry-Based Learning: A Mixed-Methods Study of Elementary School Students in Indonesia

Background: Creative thinking skills significantly affect the learning process's success. Improving higher-order thinking skills requires wise consideration of learning techniques and a commitment to an active and learner-centered learning environment. Objectives: The objective of this research is to explore the creative process of children when playing games using coding skills. Design: This study employed a mixed-methods approach to data collection, combining semi-structured and comparison methods. Setting and Participants: The research sample consisted of 20 five-grade students (twelve boys and eight girls) from SD Negeri 149 Tokinjong, Sinjai Regency. Data collection and analysis: Descriptive statistics and the N-Gain test were used to analyse participants’ creative thinking pre- and post-test scores. Interview analysis was performed through data reduction, data display, and conclusion drawing and verification. Results: The results showed that IBL has the potential to improve elementary school students’ creative thinking skills with a mean score of 77.25. Besides, participants engaged in a cyclical thinking phase between the preparation and imagination phases. The two cognitive tasks distinguished the cyclical thinking process are information collection and information examination. This process was repeated until participants decided that no more viable alternatives. Conclusions: The implementation of inquiry-based learning has the potential to improve elementary school students’ creative thinking skills; participants engaged in a cyclical thinking phase between the preparation and imagination stages

A Study of the Relationships between Epistemological Beliefs and Self-Regulated Learning among Advanced Placement Calculus Students in the Context of Mathematical Problem Solving

Secondary mathematics educators advocating constructivist-oriented instruction face the dilemma of developing students’ problem-solving skills. Students’ epistemological beliefs and self-regulated learning (SRL) processing capacity influence mathematical problem-solving prowess. This multiple-case study explored the relationships between epistemological beliefs and SRL processing while advanced mathematics students engaged in problem-solving tasks and investigated students’ SRL strategy use, heuristic strategy use, and problem-solving performance. Data sources included think-aloud and interview transcriptions, student work, and classroom observation protocols. Validity and reliability were enhanced via member-checking interviews, triangulation, peer review, and completion of a case study database. Five major findings emerged from the data: (1) participants’ unique/arbitrary beliefs regarding problem solutions, procedural/conceptual beliefs in problem solving, and empirical/rational beliefs in problem solving were related to various facets of SRL processing; (2) differences in SRL strategy use were noted dependent upon cognitive load of problem-solving tasks; (3) heuristic strategy use was related to participants’ mathematical problem-solving beliefs; (4) problem-solving performance was related to participants’ mathematical problem-solving beliefs; (5) discrepancies were noted between espoused beliefs and manifested beliefs among participants with non-availing beliefs. Recommendations for practicing mathematics educators include the assessment and development of students’ mathematical epistemological beliefs and SRL processing capacity, differentiation of cognitive load for tasks based on assessments of students’ cognitive capacity, and professional development training for teachers. Further research is needed which involves students of various achievement levels and extends methodologies to grounded theory or structural equation modeling. Additionally, a request is made for more research from classroom teachers

An Investigation of Students\u27 Use and Understanding of Evaluation Strategies

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including evaluation of problem solutions. To investigate students’ use of evaluation strategies, we developed and administered tasks prompting students to check the validity of a given expression. We collected written (N\u3e673) and interview (N=31) data at the introductory, sophomore, and junior levels. Tasks were administered in three different physics contexts: the velocity of a block at the bottom of an incline with friction, the electric field due to three point charges of equal magnitude, and the final velocities of two masses in an elastic collision. Responses were analyzed using modified grounded theory and phenomenology. In these three contexts, we explored different facets of students’ use and understanding of evaluation strategies. First, we document and analyze the various evaluation strategies students use when prompted, comparing to canonical strategies. Second, we describe how the identified strategies relate to prior work, with particular emphasis on how a strategy we describe as grouping relates to the phenomenon of chunking as described in cognitive science. Finally, we examine how the prevalence of these strategies varies across different levels of the physics curriculum. From our quantitative data, we found that while all the surveyed student populations drew from the same set of evaluation strategies, the percentage of students who used sophisticated evaluation strategies was higher in the sophomore and junior/senior student populations than in the first-year population. From our case studies of two pair interviews (one pair of first years, and one pair of juniors), we found that that while evaluating an expression, both juniors and first-years performed similar actions. However, while the first-year students focused on computation and checked for arithmetic consistency with the laws of physics, juniors checked for computational correctness and probed whether the equation accurately described the physical world and obeyed the laws of physics. Our case studies suggest that a key difference between expert and novice evaluation is that experts extract physical meaning from their result and make sense of them by comparing them to other representations of laws of physics, and real-life experience. We conclude with remarks including implications for classroom instruction as well as suggestions for future work

Teacher practice in primary mathematics classrooms: A story of positioning

The past twenty-five years have seen a dramatic increase in the interest given to dialogue between teachers and students, and students and students during mathematics teaching and learning. This interest is evident within the growing body of research and the call for the increased quality and quantity of student discourse in curriculum and policy documents. Recent research in mathematics education is underpinned by the belief that students learn best when they have the opportunity to participate in their own and others’ mathematical talk, text, and actions in purposeful and meaningful ways. This study explores how teachers position themselves and students in their lowest and highest mathematics strategy groups and how that positioning influences the sharing of mathematical know-how. Mathematical know-how within this study comprises teacher and student independence, judgement, and creativity. Social-constructivist theories of teaching and learning underpin the focus of this study. The importance of teachers and students constructing and co-constructing individual and shared mathematical understandings through dialogically rich interactions with each other and the environment are considered. Positioning theory provides the theoretical lens through which mathematical know-how will be analysed and understood. The constructs of positioning theory important to this research were the teachers’ and students’ positions, enacted as their rights and duties, the storylines that develop through the positions, rights, and duties and the teachers’ and students’ social acts which come to have significance and be a social force within the teaching and learning. The decision to employ qualitative case study methodology arose naturally from the subjective social phenomenon of teaching and learning. The analysis of data generated through video and audio recordings, transcriptions, participant observations, and documents and archival records supported the development of the two cases: teacher affording positioning, and teacher constraining positioning. The particularised and investigative design of qualitative case study supported the development of an emerging taxonomy of teacher affording and constraining positioning. The taxonomy contributed to the growing body of knowledge regarding student participation by categorising new thinking in regards to the phenomenon of teachers and positioning in mathematics. Teachers in this study afforded the sharing of mathematical know-how from the position of appropriator, procurer, and provoker. The positions of controller, proprietor, and protector were found to constrain the sharing of mathematical know-how. Significant differences were revealed in how teachers positioned themselves and how their positioning influenced opportunities for student engagement. Higher levels of student talk, text, and actions were evident when teachers positioned themselves to ensure the mathematics was visible, fluid, and contestable. Collaboration between teachers and students, and students and students, was a strong feature of the emerging taxonomy

The Effects of Common Core State Standards in Mathematics on Inclusive Environments

The Common Core State Standards for Mathematics (CCSSM) require students with learning disabilities in mathematics to use a range of cognitive, skills, and foundational numerical competencies to learn and understand complex standards. Students with learning disabilities in mathematics experience deficits in cognitive processes skills and foundational numerical competencies which have emerged as underlying barriers associated with mastering CCSSM. Examining the impact of high-stakes assessments on readiness for college and careers and student achievement may provide evidence that deficits in cognitive processing skills and numerical competencies can impact achievement levels. Using the cognitive theoretical frameworks of Bandura and Gagné, along with the concepts of cognitive learning, instructional interventions, and inclusion, the relationship between students\u27 scores in the algebraic foundations (AF) intervention inclusion method and the regular algebra (RA) nonintervention inclusion method, as measured on the end of the year assessments were examined in this study. An ANCOVA design was used to test the statistical significance of the relationship between the two intervention methods and the use of cognitive and numerical competencies for the two groups and to analyze the disparity in achievement scores between the AF intervention inclusion method and RA nonintervention inclusion method. The results revealed a statistically significant relationship between cognitive processing skills and foundational numerical competencies as measured on the final exam for both methods. The intended audience include academic communities using evidence-based inventions to improve college and career readiness results, leading to positive social change

Learning to Teach Mathematics with Reasoning and Sense Making

This study uses teacher research to examine teacher learning in the context of instructional coaching. The author, a mathematics instructional coach, engaged in an intense three-week coaching relationship with a high school Algebra teacher. A detailed description of the teaching and learning of quadratics that took place during this research provide information about what and how a teacher learns to teach mathematics with reasoning and sense making. Mapping the terrain of quadratics deepened the teacher’s understanding of the mathematical content and encouraged him to adapt his textbook in order to build mathematical reasoning. Through the coaching process, the teacher also enhanced his specialized content knowledge and developed pedagogical reasoning skills when faced with teaching dilemmas. Finally, a discussion about instructional coaching considers an instructional coach’s role in regard to teacher learning. Adviser: Ruth M. Heato

One Teacher\u27s Transformation of Practice Through the Development of Covariational Thinking and Reasoning in Algebra : A Self-Study

CCSSM (2010) describes quantitative reasoning as expertise that mathematics educators should seek to develop in their students. Researchers must then understand how to develop covariational reasoning. The problem is that researchers draw from students’ dialogue as the data for understanding quantitative relationships. As a result, the researcher can only conceive the students’ reasoning. The objective of using the self-study research methodology is to examine and improve existing teaching practices. To improve my practice, I reflected upon the implementation of my algebra curriculum through a hermeneutics cycle of my personal history and living educational theory. The critical friend provoked through dialogues and narratives the reconceptualization of my smooth covariational reasoning from a “transformational perspective” to a “solving algebraic equations” perspective. This study showed that by creating images in motion, graphs, or algebraic representation, I recognized the importance of students’ cognitive development in the conceptual embodied and proceptual symbolic worlds. The results presented the transformation of my teaching practices by building new algebraic connections. By using these findings, researchers can gain additional understanding as to how they can transform their teaching practices