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Full-Text Articles in Physical Sciences and Mathematics
Feedback To Support Learning In The Leadership Institute For Teachers, Cathy Kinzer, Janice Bradley, Patrick Morandi
Feedback To Support Learning In The Leadership Institute For Teachers, Cathy Kinzer, Janice Bradley, Patrick Morandi
The Mathematics Enthusiast
Feedback is a type of formative assessment used to inform instruction and advance learning. Feedback serves as a mechanism to connect teaching and learning at the student level. Learners receive feedback, formally or informally, as they engage in learning experiences. Within the Leadership Institute for Teachers, a National Science Foundation funded research project, we are exploring feedback as a research‐informed process to support learning and improvement for individuals, teams, and university courses. There is an explicit focus on creating a culture of critical thinking and reasoning, taking ownership for learning both individually and collectively, and understanding how to improve teaching …
Nsf's Math-Science Partnership Projects- Measuring The Trickle-Down Effect Of American Tax Dollars, Bharath Sriraman
Nsf's Math-Science Partnership Projects- Measuring The Trickle-Down Effect Of American Tax Dollars, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Integrating Disciplinary Perspectives: The Poincaré Institute For Mathematics Education, Montserrat Teixidor-I-Bigas, Analúcia D. Schliemann, David W. Carraher
Integrating Disciplinary Perspectives: The Poincaré Institute For Mathematics Education, Montserrat Teixidor-I-Bigas, Analúcia D. Schliemann, David W. Carraher
The Mathematics Enthusiast
We describe the development of the Poincaré Institute, an NSF‐MSP supported program developed through Tufts University Departments of Mathematics, Education, and Physics and by TERC, in partnership with nine school districts in Massachusetts, New Hampshire, and Maine. We focus on the challenges of developing an inter‐disciplinary program aimed at improving the teaching and learning of mathematics from grades 5 to 9, the choice of mathematical and educational content of the program, the course structure, and the progress of the first cohort of participant teachers. We also outline the changes we are implementing for future cohorts.
Developing Effective Mathematics Teachers Through National Science Foundation Funded Math And Science Partnership Grants, Ruth M. Heaton, Wendy M. Smith
Developing Effective Mathematics Teachers Through National Science Foundation Funded Math And Science Partnership Grants, Ruth M. Heaton, Wendy M. Smith
The Mathematics Enthusiast
Every year the National Science Foundation (NSF) gathers together leadership teams of funded Math and Science Partnership programs (MSP) at a Learning Network Conference in Washington, D.C. The purpose of the annual conference is to bring together teams of MSP leaders who represent institution higher education (IHE) faculty from STEM disciplines, IHE education faculty, school partners, and project evaluators, to give them an opportunity to learn across projects, and provide opportunities for individual projects to reflect on their progress. For the last two years, 2011 and 2012, we were part of the conference’s organizing committee. During the two‐day conference, project …
Teacher Learning In Lesson Study, Jennifer M. Lewis, Davida Fischman, Iris Riggs, Kelli Wasserman
Teacher Learning In Lesson Study, Jennifer M. Lewis, Davida Fischman, Iris Riggs, Kelli Wasserman
The Mathematics Enthusiast
This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students’ autonomous problem‐solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among the teams’ composition, leadership, and content foci.
Developing Effective Mathematics Teaching: Assessing Content And Pedagogical Knowledge, Student-Centered Teaching, And Student Engagement, Serigne M. Gningue, Roger Peach, Barbara Schroder
Developing Effective Mathematics Teaching: Assessing Content And Pedagogical Knowledge, Student-Centered Teaching, And Student Engagement, Serigne M. Gningue, Roger Peach, Barbara Schroder
The Mathematics Enthusiast
The Mathematics Teacher Transformation Institutes (MTTI) program attempts to develop math teacher leaders in part by providing content, inquiry and leadership courses aimed at making them more effective teachers. We assessed progress by observing teacher leaders’ teaching practices, and encouraging them to introduce or extend studentcentered pedagogy in their classrooms. We found there was little relationship between our measures of mathematics content knowledge and student‐centered pedagogy. But teachers who employed student‐centered pedagogy tended to have more highly‐engaged math students in their classrooms.
Supporting Middle School Mathematics Specialists’ Work: A Case For Learning And Changing Teachers’ Perspectives, Joy W. Whitenack, Aimee J. Ellington
Supporting Middle School Mathematics Specialists’ Work: A Case For Learning And Changing Teachers’ Perspectives, Joy W. Whitenack, Aimee J. Ellington
The Mathematics Enthusiast
In this paper, we highlight one whole‐class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state‐wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge …
A Partnership's Effort To Improve The Teaching Of K-12 Mathematics In Rapid City, South Dakota, Ben Sayler, June Apaza, Vicki Kapust, Susan Roth, Becky Carroll, Pam Tambe, Mark St. John
A Partnership's Effort To Improve The Teaching Of K-12 Mathematics In Rapid City, South Dakota, Ben Sayler, June Apaza, Vicki Kapust, Susan Roth, Becky Carroll, Pam Tambe, Mark St. John
The Mathematics Enthusiast
Over the span of ten years, a National Science Foundation‐funded partnership effort has collected and analyzed multiple forms of evidence, both direct and indirect, about improved teaching of mathematics within Rapid City Area Schools. This article describes the project's impact on K‐12 teaching and factors contributing to that impact. The authors argue that improvements in teaching are attributable largely to a robust infrastructure established to support teacher growth. Direct evidence includes classroom observations conducted by the project's external evaluation team. Indirect evidence exists in the form of data on student outcomes: achievement on the state's multiple‐choice accountability measure and achievement …
Mathematical Habits Of Mind For Teaching: Using Language In Algebra Classrooms, Ryota Matsuura, Sarah Sword, Mary Beth Piecham, Glenn Stevens, Al Cuoco
Mathematical Habits Of Mind For Teaching: Using Language In Algebra Classrooms, Ryota Matsuura, Sarah Sword, Mary Beth Piecham, Glenn Stevens, Al Cuoco
The Mathematics Enthusiast
The notion of mathematical knowledge for teaching has been studied by many researchers, especially at the elementary grades. Our understandings of this notion parallel much of what we have read in the literature, but are based on our particular experiences over the past 20 years, as mathematicians engaged in doing mathematics with secondary teachers. As part of the work of Focus on Mathematics, Phase II MSP, we are developing, in collaboration with others in the field, a research program with the ultimate goal of understanding the connections between secondary teachers’ mathematical knowledge for teaching and secondary students’ mathematical understanding and …
Making Explicit The Commonalities Of Msp Projects: Learning From Doing, Marilyn Strutchens, W. Gary Martin
Making Explicit The Commonalities Of Msp Projects: Learning From Doing, Marilyn Strutchens, W. Gary Martin
The Mathematics Enthusiast
The seven projects discussed in the preceding articles are funded by the National Science Foundation (NSF) Math and Science Partnership (MSP) program (Hamos et al., 2009), which began in 2002. One of the main goals of the MSP program is to build capacity and integrate the work of higher education, especially its STEM disciplinary faculty, with that of K‐12 to strengthen and reform mathematics and science education (Hamos et al., 2009). Thus, the MSP program brought together three sets of people (disciplinary faculty, teacher educators, and school system personnel) who do not usually work together to reform the mathematics and …
Introduction To International Perspectives On Problem Solving Research In Mathematics Education, Luis Moreno Armella, Manuel Santos-Trigo
Introduction To International Perspectives On Problem Solving Research In Mathematics Education, Luis Moreno Armella, Manuel Santos-Trigo
The Mathematics Enthusiast
Any field of research and innovation must be exposed to revisions, criticisms and to an intense scrutiny not only to discuss the state of the art but, hopefully, to identify prospective changes and new areas of study and exploration as well.
Becoming Aware Of Mathematical Gaps In New Curricular Materials: A Resource-Based Analysis Of Teaching Practice, José Guzman, Carolyn Kieran
Becoming Aware Of Mathematical Gaps In New Curricular Materials: A Resource-Based Analysis Of Teaching Practice, José Guzman, Carolyn Kieran
The Mathematics Enthusiast
The study featured in this article, with its central focus on resources-in-use, draws upon salient aspects of the documentational approach of didactics. It includes an a priori analysis of the curricular resources being used by a teacher for the first time, followed by detailed in situ observations of the unfolding of her teaching practice involving these resources. The central mathematical problem of the lesson being analyzed deals with families of polynomial functions. The analysis highlights the teacher’s growing awareness of the mathematical gaps in the resources she is using, which we conjecture to be a first step for her in …
Mathematical Problem Solving In Training Elementary Teachers From A Semiotic Logical Approach, Martín Socas, Josefa Hernández
Mathematical Problem Solving In Training Elementary Teachers From A Semiotic Logical Approach, Martín Socas, Josefa Hernández
The Mathematics Enthusiast
The aim of this article is to consider the professional knowledge and competences of mathematics teachers in compulsory education, and to propose basic tasks and activities in an initial training programme in the framework of a global proposal for “Immersion” in the curriculum of the educational phase which the trainee teacher would go on to work in. Problem-solving, in this context, is considered as being an inherent part of mathematics and this is described in terms of problem-solving, establishing connections between concepts, operations and implicit processes in the mathematical activity (conceptual field) and their relationships problem-solving; and it is assumed …
Proof And Problem Solving At University Level, Annie Selden, John Selden
Proof And Problem Solving At University Level, Annie Selden, John Selden
The Mathematics Enthusiast
This paper will be concerned with undergraduate and graduate students’ problem solving as they encounter it in attempting to prove theorems, mainly to satisfy their professors in their courses, but also as they conduct original research for theses and dissertations. We take Schoenfeld’s (1985) view of problem, namely, a mathematical task is a problem for an individual if that person does not already know a method of solution for that task. Thus, a given task may be a problem for one individual, who does not already know a solution method for that task, or it may be an exercise for …
Trajectory Of A Problem: A Study In Teacher Training, Alain Kuzniak, Bernard Parzysz, Laurent Vivier
Trajectory Of A Problem: A Study In Teacher Training, Alain Kuzniak, Bernard Parzysz, Laurent Vivier
The Mathematics Enthusiast
Problems are frequently used in mathematics to introduce and convey new notions and skills. Hence, teachers transform and adjust those problems to their students' level. The present study focuses on this transformation process on the particular case of a geometric problem posed by two teacher educators in one French Institute for Teacher Training. The whole process is described as a trajectory of the problem through various institutions from training center to secondary school and back. Before presenting the notion of trajectory of the problem, some elements about a general theoretical frame which refers to didactics of mathematics are presented.
A Proposal For A Problem-Driven Mathematics Curriculum Framework, Judith S. Zawojewski, Marta T. Magiera, Richard Lesh
A Proposal For A Problem-Driven Mathematics Curriculum Framework, Judith S. Zawojewski, Marta T. Magiera, Richard Lesh
The Mathematics Enthusiast
A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework.
Young Children Investigating Advanced Mathematical Concepts With Haptic Technologies: Future Design Perspectives, Stephen Hegedus
Young Children Investigating Advanced Mathematical Concepts With Haptic Technologies: Future Design Perspectives, Stephen Hegedus
The Mathematics Enthusiast
In this chapter, we focus on how new technologies can be used with young children to investigate mathematical ideas and concepts that would normally be introduced at a later age. In particular, we focus on haptic technologies that allow learners to touch and feel objects through force feedback in addition to visual images on a screen. The main purpose of this paper is to describe how these technologies can be used to enable young learners to construct meaning about geometric shapes and surfaces as well as attributes of particular mathematical constructions in multiple dimensions (particularly 2D and 3D for purposes …
Cognitive Processes Developed By Students When Solving Mathematical Problems Within Technological Environments, Fernando Barrera-Mora, Aarón Reyes-Rodríguez
Cognitive Processes Developed By Students When Solving Mathematical Problems Within Technological Environments, Fernando Barrera-Mora, Aarón Reyes-Rodríguez
The Mathematics Enthusiast
In this paper we document and discuss how the use of digital technologies in problem solving activities can help students to develop mathematical competences; particularly, we analyze the characteristics of reasoning that students develop as a result of using Cabri Geometry software in problem solving. We argue that the dynamical nature of representations constructed with Cabri, and the availability of measure tools integrated to it are important elements that enhance students’ ability to think mathematically and foster the implementation of several heuristic strategies in problem solving processes.
Developing The Art Of Seeing The Easy When Solving Problems, Alfinio Flores, Jaclyn Braker
Developing The Art Of Seeing The Easy When Solving Problems, Alfinio Flores, Jaclyn Braker
The Mathematics Enthusiast
For Leonardo da Vinci “saper vedere”, that is, knowing how to see, or having the art to see, was the key to unlocking the secrets of the visible world. Saper vedere included a precise sensory intuitive faculty as well as artistic imagination (Heydenreich, 1954) which were at the root of Leonardo’s inventiveness and creativity. According to Leonardo, to understand, you only have to see things properly (Bramly 1994, p. 264). Knowing how to see is also important in mathematics. The Italian mathematician Bruno de Finetti (1967) stresses this importance in his book on “Saper vedere” in mathematics. He highlights several …
Reflections On Problem Solving Theory And Practice, Alan H. Schoenfeld
Reflections On Problem Solving Theory And Practice, Alan H. Schoenfeld
The Mathematics Enthusiast
In this article, the author reflects on the current state of mathematical problem solving, both in theory and in instruction. The impact of the book Mathematical Problem solving (Schoenfeld, 1985) is also discussed, along with implications of problem solving today with the advent of 21st century technologies.
Problem Solving In The Primary School (K-2), Richard Lesh, Lyn English, Chanda Riggs, Serife Sevis
Problem Solving In The Primary School (K-2), Richard Lesh, Lyn English, Chanda Riggs, Serife Sevis
The Mathematics Enthusiast
This article focuses on problem solving activities in a first grade classroom in a typical small community and school in Indiana. But, the teacher and the activities in this class were not at all typical of what goes on in most comparable classrooms; and, the issues that will be addressed are relevant and important for students from kindergarten through college. Can children really solve problems that involve concepts (or skills) that they have not yet been taught? Can children really create important mathematical concepts on their own – without a lot of guidance from teachers? What is the relationship between …
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón
The Mathematics Enthusiast
Research on technology-assisted teaching and learning has identified several families of factors that contribute to the effective integration of such tools. Focusing on one such family, affective factors, this article reports on a qualitative study of 30 prospective secondary school mathematics teachers designed to acquire insight into the affect associated with the visualization of geometric loci using GeoGebra. Affect as a representational system was the approach adopted to gain insight into how the use of dynamic geometry applications impacted students’ affective pathways. The data suggests that affect is related to motivation through goals and self-concept. Basic instrumental knowledge and the …
Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman
Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Problem Solving And Its Elements In Forming Proof, Joanna Mamona-Downs, Martin Downs
Problem Solving And Its Elements In Forming Proof, Joanna Mamona-Downs, Martin Downs
The Mathematics Enthusiast
The character of the mathematics education traditions on problem solving and proof are compared, and aspects of problem solving that occur in the processes of forming a proof, which are not well represented in the literature, are portrayed.
Developing Problem Solving Experiences In Practical Action Projects, François Pluvinage
Developing Problem Solving Experiences In Practical Action Projects, François Pluvinage
The Mathematics Enthusiast
Problem solving doubtless is an essential element of mathematical learning, so that mathematics educators often are satisfied when finding situations that lead their students to such activity. But in many cases, the chosen situations and the ways to guide students' works are not sufficiently analyzed from a didactic point of view. Our goal in the present analysis is to underline the possible ways for managing the situations, and to exhibit the parameters that educators have at their disposition within their role as mediator between students and mathematical knowledge and know-how.
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco
The Mathematics Enthusiast
Recent studies relating the affective domain with the teaching and learning of mathematics, and more specifically with mathematics problem solving, have focused on teacher education. The authors of these studies have been ever more insistently pointing to the need to design educational programs that take an integrated cognitive and affective approach to mathematics education. Given this context, we have designed and implemented a program of intervention on mathematics problem solving for prospective primary teachers. We here describe some results of that program.
Thoughts About Research On Mathematical Problem- Solving Instruction, Frank K. Lester Jr.
Thoughts About Research On Mathematical Problem- Solving Instruction, Frank K. Lester Jr.
The Mathematics Enthusiast
In this article, the author, who has written extensively about mathematical problem solving over the past 40 years, discusses some of his current thinking about the nature of problem-solving and its relation to other forms of mathematical activity. He also suggests several proficiencies teachers should acquire in order for them to be successful in helping students become better problem solvers and presents a framework for research on problem-solving instruction. He closes the article with a list of principles about problem-solving instruction that have emerged since the early 1970s.
Framing The Use Of Computational Technology In Problem Solving Approaches, Manuel Santos-Trigo, Matías Camacho Machín
Framing The Use Of Computational Technology In Problem Solving Approaches, Manuel Santos-Trigo, Matías Camacho Machín
The Mathematics Enthusiast
Mathematical tasks are key ingredient to foster teachers and students’ development and construction of mathematical thinking. The use of distinct computational tools offers teachers a variety of ways to represent and explore mathematical tasks which often extends problem solving approaches based on the use of paper and pencil. We sketch a framework to characterize ways of reasoning that emerge as result of using computational technology to solve a task that involves dealing with variation phenomena.
Two-Step Arithmetic Word Problems, Enrique Castro-Martínez, Antonio Frías-Zorilla
Two-Step Arithmetic Word Problems, Enrique Castro-Martínez, Antonio Frías-Zorilla
The Mathematics Enthusiast
This study uses the perspective of schemes to analyze characteristics of arithmetic word problems that can influence the process of translation from the verbal statement to an arithmetical representation. One characteristic that we have detected in the two-step word problems is the presence of one or two connections (nodes) in schemes that represent them, and this paper explores whether the number of nodes affects the activation of the associated schemas. With students from the 5th and 6th grades of elementary school (11 and 12 years of age), we analyze the written productions and would stress that the number of connections …