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Tasks And Competencies In The Teaching And Learning Of Algebra


Tasks And Competencies In The Teaching And Learning Of Algebra
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Tasks And Competencies In The Teaching And Learning Of Algebra


Tasks And Competencies In The Teaching And Learning Of Algebra
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Author : Alex Friedlander
language : en
Publisher: National Council of Teachers of English
Release Date : 2018-02-28

Tasks And Competencies In The Teaching And Learning Of Algebra written by Alex Friedlander and has been published by National Council of Teachers of English this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-28 with Algebra categories.


Tasks and Competencies in the Teaching and Learning of Algebra provides a conceptual approach that will encourage students learning algebra to employ a variety of thinking processes and strategies and, most importantly, will enable them to truly understand the concepts that underlie the problems they are solving. The authors' framework develops those skills and competencies, aligned with the goals of the Common Core State Standards, that are necessary for an integrated, conceptual learning of algebra. The book's four chapters include tasks focusing on algebraic expressions, equations, and functions, followed by tasks that integrate several mathematical concepts. Each of the 48 tasks in this book contains: a classroom-ready task, with items arranged by increasing order of complexity a discussion of the task's main ideas and objectives solutions for each item in the task, with suggestions of various methods that students might use; and a listing of the essential competencies that students can develop by working on the task. All 48 tasks are also available at NCTM's More4U website as downloadable and printable worksheets to hand out to students. With its strong conceptual framework, Tasks and Competencies in the Teaching and Learning of Algebra is designed to enable teachers, teacher educators, and curriculum designers to help students at all levels master the ideas and practices found in algebra and to develop skills they can use throughout their mathematics education.



Implementation Research On Problem Solving In School Settings


Implementation Research On Problem Solving In School Settings
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Author : Inga Gebel
language : en
Publisher: WTM-Verlag Münster
Release Date : 2019

Implementation Research On Problem Solving In School Settings written by Inga Gebel and has been published by WTM-Verlag Münster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Education categories.


Content of the Book The University of Potsdam hos­ted the 25th ProMath and the 5th WG Problem Solving confe­ren­ce. Both groups met for the second time in this constellation which contributed to profound discussions on problem solving in each country taking cultural particularities into account. The joint conference took place from 29th to 31st August 2018, with participants from Finland, Germany, Greece, Hungary, Israel, Sweden, and Turkey. The conference revolved around the theme “Implementation research on problem solving in school settings”. These proceedings contain 14 peer-reviewed research and practical articles including a plenary paper from our distinguished colleague Anu Laine. In addition, the proceedings include three workshop reports which likewise focused on the conference theme. As such, these proceedings provide an overview of different research approaches and methods in implementation research on problem solving in school settings which may help close the gap between research and practice, and consequently make a step forward toward making problem solving an integral part of school mathematics on a large-scale. Content PLENARY REPORT Anu Laine: How to promote learning in problem-solving? pp 3 – 18 This article is based on my plenary talk at the joint conference of ProMath and the GDM working group on problem-solving in 2018. The aim of this article is to consider teaching and learning problem-solving from different perspectives taking into account the connection between 1) teacher’s actions and pupils’ solutions and 2) teacher’s actions and pupils’ affective reactions. Safe and supportive emotional atmosphere is base for students’ learning and attitudes towards mathematics. Teacher has a central role both in constructing emotional atmosphere and in offering cognitive support that pupils need in order to reach higher-level solutions. Teachers need to use activating guidance, i.e., ask good questions based on pupils’ solutions. Balancing between too much and too little guidance is not easy. https://doi.org/10.37626/GA9783959871167.0.01 RESEARCH REPORTS AND ORAL COMMUNICATIONS Lukas Baumanns and Benjamin Rott: Is problem posing about posing “problems”? A terminological framework for researching problem posing and problem solving pp 21 – 31 In this literature review, we critically compare different problem-posing situations used in research studies. This review reveals that the term “problem posing” is used for many different situations that differ substantially from each other. For some situations, it is debatable whether they provoke a posing activity at all. For other situations, we propose a terminological differentiation between posing routine tasks and posing non-routine problems. To reinforce our terminological specification and to empirically verify our theoretical considerations, we conducted some task-based interviews with students. https://doi.org/10.37626/GA9783959871167.0.02 Kerstin Bräuning: Long-term study on the development of approaches for a combinatorial task pp 33 – 50 In a longitudinal research project over two years, we interviewed children up to 6 times individually to trace their developmental trajectories when they solve several times the same tasks from different mathematical areas. As a case study, I will present the combinatorial task and analyze how two children, a girl and a boy, over two years approached it. As a result of the case studies we can see that the analysis of the data product-oriented or process-oriented provides different results. It is also observable that the developmental trajectory of the girl is a more continuous learning process, which we cannot identify for the boy. https://doi.org/10.37626/GA9783959871167.0.03 Lars Burman: Developing students’ problem-solving skills using problem sequences: Student perspectives on collaborative work pp 51 – 59 Using problem solving in mathematics classrooms has been the object of research for several decades. However, it is still necessary to focus on the development of problem-solving skills, and in line with the recent PISA assessment, more attention is given to collaborative problem solving. This article addresses students’ collaborative work with problem sequences as a means to systematically develop students’ problem-solving skills. The article offers student perspectives on challenges concerning the social atmosphere, differentiation on teaching, and learning in cooperation. In spite of the challenges, the students’ experiences indicate that the use of problem sequences and group problem solving can be fruitful in mathematics education. https://doi.org/10.37626/GA9783959871167.0.04 Alex Friedlander: Learning algebraic procedures through problem solving pp 61 – 69 In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations. https://doi.org/10.37626/GA9783959871167.0.05 Thomas Gawlick and Gerrit Welzel: Backwards or forwards? Direction of working and success in problem solving pp 71 – 89 We pose ourselves the question: What can one infer from the direction of working when solvers work on the same task for a second time? This is discussed on the basis of 44 problem solving processes of the TIMSS task K10. A natural hypothesis is that working forwards can be taken as evidence that the task is recognized and a solution path is recalled. This can be confirmed by our analysis. A surprising observation is that when working backwards, pivotal for success is (in case of K10) to change to working forwards soon after reaching the barrier. https://doi.org/10.37626/GA9783959871167.0.06 Inga Gebel: Challenges in teaching problem solving: Presentation of a project in progress by using an extended tetrahedron model pp 91 – 109 In order to implement mathematical problem solving in class, it is necessary to consider many different dimensions: the students, the teacher, the theoretical demands and adequate methods and materials. In this paper, an implementation process is presented that considers the above dimensions as well as the research perspective by using an extended tetrahedron model as a structural framework. In concrete terms, the development and initial evaluation of a task format and a new teaching concept are presented that focus on differentiated problem-solving learning in primary school. The pilot results show initial tendencies towards possible core aspects that enable differentiated problem solving in mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.07 Heike Hagelgans: Why does problem-oriented mathematics education not succeed in an eighth grade? An insight in an empirical study pp 111 – 119 Based on current research findings on the possibilities of integration of problem solving into mathematics teaching, the difficulties of pupils with problem solving tasks and of teachers to get started in problem solving, this article would like to show which concrete difficulties delayed the start of the implementation of a generally problem-oriented mathematics lesson in an eighth grade of a grammar school. The article briefly describes the research method of this qualitative study and identifies and discusses the difficulties of problem solving in the examined school class. In a next step, the results of this study are used to conceive a precise teaching concept for this specific class for the introduction into problem-oriented mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.08 Zoltán Kovács and Eszter Kónya: Implementing problem solving in mathematics classes pp 121 – 128 There is little evidence of teachers are using challenging problems in their mathematics classes in Hungary. At the University of Debrecen and University of Nyíregyháza, we elaborated a professional development program for inservice teachers in order to help them implementing problem solving in their classes. The basis of our program is the teacher and researcher collaboration in the lessonplanning and evaluation. In this paper we report some preliminary findings concerning this program. https://doi.org/10.37626/GA9783959871167.0.09 Ana Kuzle: Campus school project as an example of cooperation between the University of Potsdam and schools pp 129 – 141 The “Campus School Project” is a part of the “Qualitätsoffensive Lehrerbildung” project, whose aim is to improve and implement new structures in the university teacher training by bringing all the essential protagonists, namely university stuff, preservice teachers, and in-service teachers – together, and having them work jointly on a common goal. The department of primary mathematics education at the University of Potsdam has been a part of the Campus School Project since 2017. Thus far several cooperations emerged focusing on different aspects of problem solving in primary education. Here, I give an overview of selected cooperations, and the first results with respect to problem-solving research in different school settings. https://doi.org/10.37626/GA9783959871167.0.10 Ioannis Papadopoulos and Aikaterini Diakidou: Does collaborative problem-solving matter in primary school? The issue of control actions pp 143 – 157 In this paper we follow three Grade 6 students trying to solve (at first individually, and then in a group) arithmetical and geometrical problems. The focus of the study is to identify and compare the various types of control actions taken during individual and collaborative problem-solving to show how the collective work enhances the range of the available control actions. At the same time the analysis of the findings give evidence about the impact of the collaborative problemsolving on the way the students can benefit in terms of aspects of social metacognition. https://doi.org/10.37626/GA9783959871167.0.11 Sarina Scharnberg: Adaptive teaching interventions in collaborative problem-solving processes pp 159 – 171 Even though there exists limited knowledge on how exactly students acquire problem-solving competences, researchers agree that adaptive teaching interventions have the potential to support students‘ autonomous problem-solving processes. However, most recent research aims at analyzing the characteristics of teaching interventions rather than the interventions’ effects on the students’ problem-solving process. The study in this paper addresses this research gap by focusing not only on the teaching interventions themselves, but also on the students’ collaborative problem-solving processes just before and just after the interventions. The aim of the study is to analyze the interventions‘ effect on the learners’ integrated problem-solving processes. https://doi.org/10.37626/GA9783959871167.0.12 Nina Sturm: Self-generated representations as heuristic tools for solving word problems pp 173 – 192 Solving non-routine word problems is a challenge for many primary school students. A training program was therefore developed to help third-grade students to find solutions to word problems by constructing external representations (e.g., sketches, tables) and to specifically use them. The objective was to find out whether the program positively influences students’ problemsolving success and problem-solving skills. The findings revealed significant differences between trained and untrained classes. Therefore, it can be assumed that self-generated representations are heuristic tools that help students solve word problems. This paper presents the results on the impact of the training program on the learning outcome of students. https://doi.org/10.37626/GA9783959871167.0.13 Kinga Szűcs: Problem solving teaching with hearing and hearing-impaired students pp 193 – 203 In the last decade the concept of inclusion has become more and more prevalent in mathematics education, especially in Germany. Accordingly, teachers in mathematics classrooms have to face a wide range of heterogeneity, which includes physical, sensory and mental disabilities. At the Friedrich-Schiller-University of Jena, within the framework of the project “Media in mathematics education” it is examined how new technologies can support teaching in inclusive mathematics classrooms. In the academic year 2017/18, the heterogeneity regarding hearing impairment was mainly focussed on. Based on a small case study with hearing and hearing-impaired students a problem-solving unit about tangent lines was worked out according to Pólya, which is presented in the paper. https://doi.org/10.37626/GA9783959871167.0.14 WORKSHOP REPORTS Ana Kuzle and Inga Gebel: Implementation research on problem solving in school settings: A workshop report 207 On the last day of the conference, we organized a 90-minute workshop. The workshop focused on the conference theme “Implementation research on problem solving in school settings”. Throughout the conference, the participants were invited to write down their questions and/or comments as a response to held presentations. https://doi.org/10.37626/GA9783959871167.0.15 Ana Kuzle, Inga Gebel and Anu Laine: Methodology in implementation research on problem solving in school settings pp 209 – 211 In this report, a summary is given on the contents of the workshop. In particular, the methodology and some ethical questions in implementation research on problem solving in school settings are discussed. The discussion showed how complex this theme is so that many additional questions emerged. https://doi.org/10.37626/GA9783959871167.0.16 Lukas Baumanns and Sarina Scharnberg: The role of protagonists in implementing research on problem solving in school practice pp 213 – 214 Based on seminal works of Pólya (1945) and Schoenfeld (1985), problem solving has become a major focus of mathematics education research. Even though there exists a variety of recent research on problem solving in schools, the research results do not have a direct impact on problem solving in school practice. Instead, a dissemination of research results by integrating different protagonists is necessary. Within our working group, the roles of three different protagonists involved in implementing research on problem solving in school practice were discussed, namely researchers, pre-service, and in-service teachers, by examining the following discussion question: To what extent do the different protagonists enable implementation of research findings on problem solving in school practice? https://doi.org/10.37626/GA9783959871167.0.17 Benjamin Rott and Ioannis Papadopoulos: The role of problem solving in school mathematics pp 215 – 217 In this report of a workshop held at the 2018 ProMath conference, a summary is given of the contents of the workshop. In particular, the role of problem solving in regular mathematics teaching was discussed (problem solving as a goal vs. as a method of teaching), with implications regarding the selection of problems, its implementation into (written) exams as well as teacher proficiency that is needed for implementing problem solving into mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.18



Challenges And Strategies In Teaching Linear Algebra


Challenges And Strategies In Teaching Linear Algebra
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Author : Sepideh Stewart
language : en
Publisher: Springer
Release Date : 2018-02-01

Challenges And Strategies In Teaching Linear Algebra written by Sepideh Stewart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Education categories.


This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.



Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds


Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds
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Author : Carolyn Kieran
language : en
Publisher: Springer
Release Date : 2017-12-04

Teaching And Learning Algebraic Thinking With 5 To 12 Year Olds written by Carolyn Kieran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Education categories.


This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.



Mathematics Education


Mathematics Education
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Author : Khoon Yoong Wong
language : en
Publisher: World Scientific
Release Date : 2009

Mathematics Education written by Khoon Yoong Wong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Education categories.


This title provides much food for thought and pointers to meet future challenges in mathematics education not only within Singapore, but also in other countries.



Assessment In Mathematics Education


Assessment In Mathematics Education
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Author : Christine Suurtamm
language : en
Publisher: Springer
Release Date : 2016-07-07

Assessment In Mathematics Education written by Christine Suurtamm and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-07 with Education categories.


This book provides an overview of current research on a variety of topics related to both large-scale and classroom assessment. First, the purposes, traditions and principles of assessment are considered, with particular attention to those common to all levels of assessment and those more connected with either classroom or large-scale assessment. Assessment design based on sound assessment principles is discussed, differentiating between large-scale and classroom assessment, but also examining how the design principles overlap. The focus then shifts to classroom assessment and provides specific examples of assessment strategies, before examining the impact of large-scale assessment on curriculum, policy, instruction, and classroom assessment. The book concludes by discussing the challenges that teachers currently face, as well as ways to support them. The book offers a common language for researchers in assessment, as well as a primer for those interested in understanding current work in the area of assessment. In summary, it provides the opportunity to discuss large-scale and classroom assessment by addressing the following main themes: ·Purposes, Traditions and Principles of Assessment ·Design of Assessment Tasks ·Classroom Assessment in Action ·Interactions of Large-Scale and Classroom Assessment ·Enhancing Sound Assessment Knowledge and Practices It also suggests areas for future research in assessment in mathematics education.



Resources In Education


Resources In Education
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Author :
language : en
Publisher:
Release Date : 1999

Resources In Education written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Education categories.




Tasks In Primary Mathematics Teacher Education


Tasks In Primary Mathematics Teacher Education
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Author : Barbara Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-25

Tasks In Primary Mathematics Teacher Education written by Barbara Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-25 with Education categories.


Tasks in Primary Mathematics Teacher Education is intended to advance relevant research and innovative international practices in the preparation and professional development of mathematics teachers. Emerging from discussion at the ICMI study on teacher professional development, this volume, focused on primary and elementary teachers, culls a richness that can only be found by gathering wisdom from varied experiences around the world. The choice of tasks, and the associated pedagogies, is a key aspect of teaching and learning mathematics. Arguing that what students learn is largely defined by the tasks they are given, several major themes are presented. One such major strand, the form, function and focus of tasks, is discussed throughout several chapters, offering analysis, discussion of implementation, and exemplars of a broader category of illustrative techniques for developing critical understanding.



The Future Of The Teaching And Learning Of Algebra


The Future Of The Teaching And Learning Of Algebra
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Author : Kaye Stacey
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-19

The Future Of The Teaching And Learning Of Algebra written by Kaye Stacey and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-19 with Education categories.


This book presents a wide-ranging, international perspective on the state of the field of algebra from invited participants to the 12th ICMI Study Conference held in Melbourne, Australia in 2001. The authors are renowned academics from all around the world who have written individual chapters associated with the teaching and learning of algebra that relate to their particular areas of research and teaching expertise. The book includes information about different approaches to the teaching and learning of algebra - from early algebra to tertiary algebra, the impact of tools and technology (including Computer Algebra Systems), the role of symbols and language, teachers of algebra, and the history of algebra. The Future of the Teaching and Learning of Algebra: the 12th ICMI Study is of interest to researchers, curriculum developers, educational policy makers, teachers of mathematics, and trainee mathematics teachers.



Psychology And Mathematics Education


Psychology And Mathematics Education
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Author : Gila Hanna
language : en
Publisher: Frontiers Media SA
Release Date : 2023-09-05

Psychology And Mathematics Education written by Gila Hanna and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-05 with Science categories.


Modern Mathematics is constructed rigorously through proofs, based on truths, which are either axioms or previously proven theorems. Thus, it is par excellence a model of rational inquiry. Links between Cognitive Psychology and Mathematics Education have been particularly strong during the last decades. Indeed, the Enlightenment view of the rational human mind that reasons, makes decisions and solves problems based on logic and probabilities, was shaken during the second half of the twentieth century. Cognitive psychologists discovered that humans' thoughts and actions often deviate from rules imposed by strict normative theories of inference. Yet, these deviations should not be called "errors": as Cognitive Psychologists have demonstrated, these deviations may be either valid heuristics that succeed in the environments in which humans have evolved, or biases that are caused by a lack of adaptation to abstract information formats. Humans, as the cognitive psychologist and economist Herbert Simon claimed, do not usually optimize, but rather satisfice, even when solving problem. This Research Topic aims at demonstrating that these insights have had a decisive impact on Mathematics Education. We want to stress that we are concerned with the view of bounded rationality that is different from the one espoused by the heuristics-and-biases program. In Simon’s bounded rationality and its direct descendant ecological rationality, rationality is understood in terms of cognitive success in the world (correspondence) rather than in terms of conformity to content-free norms of coherence (e.g., transitivity).