ethanporcaro/eric-fulltext-meta huggingface dataset:
Two Prospective Middle School Teachers Reinvent Combinatorial Formulas: Permutations and Arrangements = Dos futuros maestros de escuela intermedia reinventan fórmulas combinatorias: permutaciones y arreglos
Author: Antonides, Joseph
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Middle Schools,Identification,Cognitive Processes,Abstract Reasoning,Logical Thinking,Thinking Skills,Mathematics,Mathematical Concepts,Innovation

We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were designed and facilitated to guide each PT toward reinventing multiple combinatorial formulas. Drawing on a subset of this data, we describe the development of the PTs' mental processes and reasoning as they came to construct formulas for counting permutations and arrangements without repetition, and we analyze our findings through a psychological constructivist framework. [For the complete proceedings, see ED629884.]
Investing Undergraduate Students&apos; Generalizing Activity in a Computational Setting
Author: Lockwood, Elise
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Undergraduate Students,Computation,Problem Solving,Programming,Generalization,Mathematics Activities,Student Behavior,Skill Development,Cognitive Processes

Computational activity is increasingly relevant in education and society, and researchers have investigated its role in students' mathematical thinking and activity. More work is needed within mathematics education to explore ways in which computational activity might afford development of mathematical practices. In this paper, we specifically examine the generalizing activity of undergraduate students who solved combinatorial problems in the context of Python programming. We demonstrate instances of generalizing in terms of Ellis et al.'s (2017) framework, and we argue that some opportunities were facilitated and supported by the computational setting in which the students worked. [For the complete proceedings, see ED629884.]
Construction of Arithmetic-Algebraic Thinking in a Socio-Cultural Instructional Approach = Construction d&apos;une pensée arithémico-algébrique dans une approche socioculturelle de l&apos;enseignement
Author: Hitt, Fernando
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Arithmetic,Algebra,Grade 6,Elementary School Mathematics,Secondary School Mathematics,Mathematics Instruction,Social Influences,Culturally Relevant Education,Foreign Countries,Mathematical Concepts,Concept Formation,Learning Problems,Generalization,Mathematical Logic

We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely, children from 11 to 14 years old. We target secondary students (first year or K7) in this article. Our objective relates to the development of a gradual generalization in arithmetic-algebraic thinking in a socio-cultural approach to the learning of mathematics. We experimented with investigative situations using a paper-and-pencil approach and technology. We analyze the emergence, in this context, of a visual abstraction, the production of institutional and non-institutional representations, a sensitivity to contradiction, and, finally, the concepts of variable and of covariation between variables. [For the complete proceedings, see ED629884.]
Report of a Classroom Experience for the Development of Distribution Models = Experiencia en el aula para el desarrollo de modelos para el reparto
Author: Aviña González, María José
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Student Experience,Curriculum Design,Curriculum Evaluation,Mathematics Instruction,College Freshmen,Accounting,Class Activities,Mathematics Activities,Problem Solving,Cooperative Learning,Foreign Countries

This paper presents the design and analysis of a Model-Eliciting Activity (MEA), which aims to support the refinement of the conceptual system associated with directly proportional distribution problems (example: linear function, percentage, proportion, variation, etc.). The situation explores a context that is close to the student, encouraging the construction of a generalizable mathematical model that can be transferred to diverse contexts. For the design, the principles of the Models and Modeling perspective (Lesh and Doerr, 2003) were considered. The target population were students enrolled in the first semesters of a university degree in Accounting. For the analysis, we considered the construction of models (performed in teams); the mathematical representations within the process observed (such as diagrams and tabular organizations); as well as the individual solutions of the students. [For the complete proceedings, see ED629884.]
Educational Neuroscience: Past, Present, and Future Prospects
Author: Campbell, Stephen R.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Neurosciences,Education,Brain,Mathematics Education,Educational Research,Neurology,Cognitive Science

This talk provides the speaker's perspective on how the fledgling new area of educational neuroscience has emerged from a disenchantment with brain-based education, through various multidisciplinary, interdisciplinary, and transdisciplinary initiates and collaborations involving educationists and neuroscientists. Specific examples and results pertaining to research in mathematics education will be presented. Beyond the current state-of-the-art, the speaker will conclude with some speculations on what might be anticipated as this area of research continues to unfold into the near and far futures. [For the complete proceedings, see ED629884.]
Mental Mathematics in the Classroom: Content, Practices and Papert&apos;s &quot;Mathland&quot;
Author: Proulx, Jérôme
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Mental Computation,Mathematics Education,Problem Solving,Secondary School Students,Grade 10,Mathematics Activities,Cognitive Processes,Geometry

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety of mathematical topics (e.g., algebra, geometry, measurement, statistics, trigonometry, fractions), where students are given short amounts of time to solve tasks given orally and/or on the board, without the use of paper-and-pencil or any material aids. Whereas the central objectives centers on inquiring into the nature of the strategies students engage in to solve the tasks, more seem to be happening in these sessions. In particular, students' solutions and strategies to the task given in the mental mathematics context led to numerous questions, discussions, follow-up explorations, and so forth, by students, which in turn enabled the emergence of significant mathematical issues. This raised interest in investigating these (additional and unplanned) mathematical issues. This represents the core of this lecture, which focuses on the nature of the mathematics (in terms of content and of practices) that frequently unfolds in the mental mathematics sessions conducted. Using an illustrative extract from a mental mathematics session on analytical geometry in a Grade-10 classroom (15-16 years old), the analysis outlines how not only mathematical content is being worked on through these mental mathematics sessions, but also how mathematical practices are being enacted by students. This raises issues about the nature of the environment that these mental mathematics session plunge students into, one that could be tentatively, and boldly, aligned with Papert's concept of mathland. [For the complete proceedings, see ED629884.]
Exploring Secondary Students&apos; Proving Competencies through Clinical Interviews with Smartpens
Author: Cirillo, Michelle
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Students,Secondary School Mathematics,Mathematical Logic,Mathematics Skills,Geometry,Spatial Ability,Protocol Analysis,Assistive Technology,Competence,Learning Analytics

Twenty students who earned A or B course-grades in the proof unit(s) of a secondary course that addressed proof in geometry were asked to work on two proof tasks while sharing their thinking aloud and using smartpens. Students were classified into two categories: those who were successful with both proofs and those who were unsuccessful with both proofs. Large differences were observed in how often students in the two groups exhibited certain competencies. The largest gaps occurred in the ways that students: attended to the proof assumptions; used warrants in their proofs; and demonstrated logical reasoning. [For the complete proceedings, see ED629884.]
How Mathematical Modeling Enables Learning?
Author: Kandasamy, Sindura Subanemy
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Mathematical Models,Mathematics Education,Conflict,Cognitive Processes,Undergraduate Students,Calculus,Validity

In this theoretical paper we compare the Piagetian perspective on knowledge construction to mathematical model construction, with the aim to understand how mathematical modeling enables learning of mathematics and learning of science, as is often claimed. We do this by examining data through two lenses: (1) examining the role of cognitive conflict as it arises during validation of a model; and (2) viewing model validation as a reflection on activity-effect relationship. We explain why we chose to look deeply into model validation specifically, present examples for each lens, and consider implications. [For the complete proceedings, see ED629884.]
Developing a Framework for Characterizing Student Analogical Activity in Mathematics
Author: Hicks, Michael D.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Logical Thinking,Learning Activities,Mathematics,Algebra,Undergraduate Students,Graduate Students,Teaching Methods

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from mathematical analogies. This considers activities along several dimensions including: inter/intra domain activity, foregrounded/backgrounded domain, and attention to similarity/difference. These dimensions are integrated with Gentner's (1983) analogical mapping framework to characterize student activity when they are presented with tasks where reasoning by analogy can productively support their mathematical investigations. By characterizing these activities, we can better develop tasks to support students in productively analogizing between mathematical domains. [For the complete proceedings, see ED629884.]
Coaches&apos; and Teachers&apos; Noticing through Annotations: Exploring Analytic Stance across Coaching Cycles
Author: Amador, Julie M.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Coaching (Performance),Observation,Interaction,Middle School Teachers,Faculty Development,Documentation,Mathematics Teachers,Video Technology

We share results of a study on the analytic stances of coaches' and teachers' as they annotated key moments from classroom video of the teacher's lessons. In the analysis, emphasis was on the analytic stances of the coaches and how their annotations related to trends in teachers' annotations. Findings indicate differences in how coaches and teachers noticed across the coaching cycles, suggesting the annotations were influenced by the interactions between the coaches and teachers and the teachers' perceptions of coaching process. As a result of our analysis, we characterized one coach as having a high ratio of questions to suggestions, another as having annotations coded as interpretation, another as having more evaluations and suggestions, and the fourth as having asked more questions. Some teachers mirrored the analytic stance of their coach over time and other teachers shifted their analytic stance in ways that suggest they were responsive to their coach's analytic stance. [For the complete proceedings, see ED629884.]
Establishing a Cartesian Coordination in the Ant Farm Task: The Case of Ginny
Author: Lee, Hwa Young
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Preservice Teachers,Elementary School Teachers,Cognitive Processes,Geometry,Graphs,Mathematics Activities,Spatial Ability,Problem Solving

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the complete proceedings, see ED629884.]
Profiling Productive Mathematical Teaching Moves in 4th-8th Mathematics Classrooms
Author: Melhuish, Kathleen
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Instruction,Teaching Methods,Elementary School Mathematics,Middle School Mathematics,Mathematics Skills,Productivity,Profiles

As the field draws to greater consensus around components of productive mathematics classrooms, the need increases to answer questions about how we operationalize and measure these components and how we can actualize such practice in classrooms. This research report shares an analysis from a larger project aimed at describing and quantifying student and teacher components of productive classrooms at a fine-grain level. We share results from this analysis of 39 mathematics lessons with a focus on teacher moves and catalytic teaching habits that characterize these lessons. A cluster analysis identified four profiles of lessons differentiated by the existence of these catalytic teaching habits and subsequent work with student ideas. Further, these clusters appeared to account for differences in student contributions in lessons. [For the complete proceedings, see ED629884.]
Mathematical Knowledge and Skills of University Students When Solving a MEA = Conocimientos y Habilidades Matemáticas de Estudiantes Universitarios al Realizar una MEA
Author: Rodríguez-González, Iván I.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Mathematics Education,Mathematics Skills,Mathematical Models,Algebra,Problem Solving,Undergraduate Students,Cooperative Learning,Mathematics Activities

In this paper we present the results of an investigation related to the developing of mathematical knowledge and skills by first semester university students when solving a Model Eliciting Activity [MEA] which involves quadratic function knowledge. This was a qualitative research. The theoretical framework was Models and Modeling Perspective [MMP]. The results show that the students used their mathematical knowledge and skills related to linear and quadratic functions to describe the situation; they moved from a quantitative cycle of understanding (associated with linear and quadratic behaviors), to an algebraic cycle of understanding (associated with quadratic behaviors). [For the complete proceedings, see ED629884.]
Prospective K-8 Teachers&apos; Problem Posing: Interpretations of Tasks That Promote Mathematical Argumentation
Author: Magiera, Marta T.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Elementary Secondary Education,Elementary School Teachers,Secondary School Teachers,Mathematics,Preservice Teachers,Mathematics Instruction,Learner Engagement

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation, (b) tasks PSTs posed to engage students in mathematical argumentation, and (c) accompanying explanations in which PSTs motivated tasks they posed. The analysis revealed that PSTs interpret tasks that foster argumentation in terms of activities of argumentation that a task elicits and space for argumentation that the task provides. Several features that PSTs associated with each of the two major task characteristics were identified. While posing tasks to engage students in argumentation, PSTs did not place equal emphasis on all of the identified features. [For the complete proceedings, see ED629884.]
Methodology for the Design of Didactic Sequences for Secondary Mathematics in a Technological Context = Metodología Para El Diseño De Secuencias Didácticas Para Matemática De Secundaria En Un Contexto Tecnológico
Author: Sánchez, Jamil Fabiola Alvarado
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Secondary School Mathematics,Mathematics Instruction,Instructional Design,Technology Integration,Technology Uses in Education,Teaching Methods,Mathematics Curriculum,Curriculum Development,Mathematics Teachers,Teacher Workshops,Sequential Approach,Foreign Countries

In this paper a didactic proposal is presented which consists of a methodology aimed at secondary level mathematics teachers, the aim of this proposal is to provide the teacher with a tool to design teaching sequences in order to take them to the classroom; These designs have the particularity of incorporating digital technology for the development of the sequence and its implementation. The methodology was developed based on the articulation of: the didactic structure of Díaz-Barriga, the teaching method ACODESA of Hitt and the curricular developments of Taba. The methodology has been tested with a group of 11 teachers in a course-workshop of 40 hours, the results obtained were three didactic sequences elaborated by three teams of teachers in a technological context (using Geogebra), where it is perceived that it is possible to design using this methodological proposal, however, teachers presented some difficulties during the process of articulation with technology. [For the complete proceedings, see ED629884.]
Elementary Students and Their Self-Identified Emotions as They Engaged in Mathematical Problem Solving
Author: O'Dell, Jenna R.
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Elementary School Students,Emotional Development,Mathematics,Problem Solving,Psychological Patterns,Student Attitudes

In this study, we investigated two students', ages ten and eleven, emotions while they engaged in mathematical problem solving. During three task-based interviews, the students explored parts of the unsolved problem the Graceful Tree Conjecture. While they were engaged in the interviews, they self-identified the emotions of frustration and joy they were feeling using the Wong-Baker Scale. The students displayed the interplay of the emotions of frustration and joy or which we consider to be productive struggle. A descripted case of Georgia is included to describe her emotions while problem solving. [For the complete proceedings, see ED629884.]
Disentangling the Role of Context and Community in Teacher Professional Development Uptake
Author: Koellner, Karen
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: Faculty Development,Workshops,Teacher Attitudes,Program Effectiveness,Mathematics Education,Knowledge Level,Geometry,Communities of Practice,Educational Technology,English Language Learners,Context Effect

The study presented here utilized a cross case comparison of three different professional development programs to examine the contextual factors associated with uptake related to what teachers learned related to content, pedagogy and the resources used in their professional development (PD) workshops. From a theoretical perspective this study draws on a situative perspective to guide our analyses on how uptake across different PD projects impacted teacher learning. Findings indicate that teachers' perceptions of learning may be associated with explicit goals and intentions of the PD program, their perceptions of community and the relevance of the content, pedagogy and resources provided to their everyday work in mathematics classrooms. Differences were found to be related to where they fell on the adaptive-specified continuum. [For the complete proceedings, see ED629884.]
Types of Orchestrations in a Case Study of a Statistics Constructionist Teaching Practice = Tipos de orquestación en un estudio de caso de una enseñanza construccionista de la estadística
Author: Ruiz-Arias, Perla Marysol
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: College Faculty,Statistics Education,College Mathematics,Data Analysis,Technology Integration,Mathematics Instruction,Teaching Methods,Programming,Coding,Constructivism (Learning),Active Learning

This paper presents a case study that is part of a research studying how university statistics teachers integrate digital tools in their practice. The case study is of a teacher who claims to follow constructionist ideas for her teaching of statistics, using the R programming language. The teacher developed a series of activities with R, aiming to promote the understanding of statistical concepts. We observed 11 of her classes, in a three-week period. These classes were analyzed using as framework the notion of Instrumental Orchestration and Papert's constructionist principles. We identified four ways in which this teacher orchestrates her class and the constructionist elements present in them. [For the complete proceedings, see ED629884.]
Covariational Reasoning Patterns of High School Students in Problems of Correlation and Linear Regression = Patrones de razonamiento covariacional de estudiantes de bachillerato en problemas de correlacion y regresión lineal
Author: Medina, Miguel
Date: 2020-12-00
Type: Speeches/Meeting Papers
Subjects: High School Students,Thinking Skills,Mathematical Concepts,Cognitive Processes,Problem Solving,Foreign Countries,Correlation,Regression (Statistics)

The topics of correlation and linear regression constitute a complex and subtle system of statistical and mathematical ideas whose teaching-learning raises numerous practical and theoretical problems. In this research paper, the patterns of reasoning that students exhibit, under the approach of informal inferences when they face problems of correlation and regression line are identified. To achieve this, activities were implemented in two stages: in the first stage, two problems (one of estimation and other of best-fit line) were applied to be solved using pencil and paper; the second stage incorporates the use of the Fathom software. [For the complete proceedings, see ED629884.]