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Articles 1 - 5 of 5
Full-Text Articles in Education
Quality, Meaningful Educational Experiences: An Autobiographical Study Of Teaching And Learning Algebra 1, Marya Ray
Curriculum and Instruction (Ed.D.) Dissertations
This autobiographical study of teaching and learning Algebra 1 was developed to examine classroom experiences through the lens of the researcher and to explore the perceptions of teachers and students involved in the study. The goal was to identify the quality, meaningful educational experiences in the classroom which led to the development of algebraic thinking and self-efficacy among students who previously demonstrated a struggle to learn mathematics. The inspiration for this study was my personal experience as a student, as I also struggled to develop algebraic thinking as a high school student. The school district in which this study was …
Improving Assessment Outcomes In Algebra And Functions Through Concrete Materials And Direct Instruction, Sandra Deacon, Courtney Pillers
Improving Assessment Outcomes In Algebra And Functions Through Concrete Materials And Direct Instruction, Sandra Deacon, Courtney Pillers
Masters of Arts in Education Action Research Papers
Critical thinking consists of the mental processes, strategies, and representations individuals use to solve problems, make decisions, and learn new concepts. We observed our 6th-year students struggling with algebra functions and problem-solving. These observations motivated us to engage in active research to improve the students' critical thinking and problem-solving skills. We administered interventions that supported the language transfer between traditional mathematical language and Montessori mathematical terms. We utilized direct instruction with concrete algebra materials to lead the students to abstract work in algebra. We also used formal assessments and observations to decide what lessons the students should get next. Our …
An Empirically Based Practical Learning Progression For Generalisation, An Essential Element Of Algebraic Reasoning, Max Stephens, Lorraine Day, Marj Horne
An Empirically Based Practical Learning Progression For Generalisation, An Essential Element Of Algebraic Reasoning, Max Stephens, Lorraine Day, Marj Horne
Education Papers and Journal Articles
Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic …
Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer
Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer
Mathematics, Statistics and Computer Science Faculty Research and Publications
In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …
Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Improving Students’ Algebraic Thinking: The Case Of Talia, Kien H. Lim
Kien H Lim
This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her algebraic thinking after five one-hour sessions of solving problems involving inequalities and equations. She improved from association-based to coordination-based predictions, from impulsive to analytic anticipations, and from inequality-as-a-signal-for-a-procedure to inequality-as-a-comparison-of-functions conceptions. In the one-on-one teaching intervention, she progressed from the sub-context of manipulating symbols, to working with specific numbers, to reasoning with “general” numbers, and eventually to reasoning with symbols. Three features were identified to account for her improvement: (a) attention to meaning, (b) opportunity to repeat similar reasoning, and (c) opportunity to explore.