Gestures and Insight in Advanced Mathematical Thinking
ERIC Educational Resources Information Center
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-01-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
Gestures and insight in advanced mathematical thinking
NASA Astrophysics Data System (ADS)
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-10-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding - in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities. One participant uses gestures to clarify the relationships between a function, its derivative and its antiderivative. We show how these gestures help create a virtual mathematical construct, which in turn leads to a new problem-solving strategy. These results suggest that gestures are a productive, but potentially undertapped resource for generating new insights in advanced levels of mathematics.
Mathematical Proof as Formal Procept in Advanced Mathematical Thinking
ERIC Educational Resources Information Center
Chin, Erh-Tsung
2003-01-01
In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis of distinct cognitive…
Student Learning in Linear Algebra: The Gateways To Advance Mathematical Thinking Project.
ERIC Educational Resources Information Center
Manes, Michelle
This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…
ERIC Educational Resources Information Center
Nabb, Keith A.
2013-01-01
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
ERIC Educational Resources Information Center
Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree
2016-01-01
Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…
Supporting Mathematical Thinking
ERIC Educational Resources Information Center
Houssart, Jenny; Roaf, Caroline; Watson, Anne
2005-01-01
This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…
Cognitive Psychology and Mathematical Thinking.
ERIC Educational Resources Information Center
Greer, Brian
1981-01-01
This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)
The Transition to Formal Thinking in Mathematics
ERIC Educational Resources Information Center
Tall, David
2008-01-01
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…
Mathematical Thinking: From Cacophony to Consensus
ERIC Educational Resources Information Center
Argyle, Sean F.
2012-01-01
Various standards have demanded that teachers improve "mathematical thinking," but definitions are vague--if present at all. What little research on the subject exists is disjointed and dissenting, leading some researchers to lament the possibility of ever coming to an agreement on how to define "mathematical thinking" as a…
Visible Thinking in High School Mathematics
ERIC Educational Resources Information Center
Sliman, Emily
2013-01-01
If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…
Inhibiting Intuitive Thinking in Mathematics Education
ERIC Educational Resources Information Center
Thomas, Michael O. J.
2015-01-01
The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…
Assessing Higher Order Thinking in Mathematics.
ERIC Educational Resources Information Center
Kulm, Gerald, Ed.
This book explores current theory, research, practice, and policy in the assessment of higher order thinking in mathematics, focusing on the elementary and secondary grades. Current knowledge and research on mathematics learning and testing is synthesized. Examples of innovative test items for classroom use and state assessment programs are…
Screencasts: Formative Assessment for Mathematical Thinking
ERIC Educational Resources Information Center
Soto, Melissa; Ambrose, Rebecca
2016-01-01
Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction.…
Connecting Research to Teaching: The "MOST" Productive Student Mathematical Thinking
ERIC Educational Resources Information Center
Stockero, Shari L.; Peterson, Blake E.; Leatham, Keith R.; Van Zoest, Laura R.
2014-01-01
Instruction that meaningfully incorporates students' mathematical thinking is widely valued within the mathematics education community (NCTM 2000; Sherin, Louis, and Mendez 2000; Stein et al. 2008). Although being responsive to student thinking is important, not all student thinking has the same potential to support mathematical learning.…
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon
2016-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking
ERIC Educational Resources Information Center
Leatham, Keith R.; Peterson, Blake E.; Stockero, Shari L.; Van Zoest, Laura R.
2015-01-01
The mathematics education community values using student thinking to develop mathematical concepts, but the nuances of this practice are not clearly understood. The authors conceptualize an important group of instances in classroom lessons that occur at the intersection of student thinking, significant mathematics, and pedagogical…
Conditional Inference and Advanced Mathematical Study: Further Evidence
ERIC Educational Resources Information Center
Inglis, Matthew; Simpson, Adrian
2009-01-01
In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…
Defining Computational Thinking for Mathematics and Science Classrooms
NASA Astrophysics Data System (ADS)
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-02-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.
Racial Differences in Mathematics Test Scores for Advanced Mathematics Students
ERIC Educational Resources Information Center
Minor, Elizabeth Covay
2016-01-01
Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…
Teacher Leaders: Advancing Mathematics Learning
ERIC Educational Resources Information Center
Kinzer, Cathy J.; Rincón, Mari; Ward, Jana; Rincón, Ricardo; Gomez, Lesli
2014-01-01
Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…
A Mathematical Mystery Tour: Higher-Thinking Math Tasks.
ERIC Educational Resources Information Center
Wahl, Mark
This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…
Defining Computational Thinking for Mathematics and Science Classrooms
ERIC Educational Resources Information Center
Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri
2016-01-01
Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…
Preparing Beginning Teachers to Elicit and Interpret Students' Mathematical Thinking
ERIC Educational Resources Information Center
Sleep, Laurie; Boerst, Timothy A.
2012-01-01
This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices--in particular, their eliciting and interpreting of students' mathematical thinking--in the context of an elementary mathematics methods assignment,…
Emergent Mathematical Thinking in the Context of Play
ERIC Educational Resources Information Center
van Oers, Bert
2010-01-01
In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children's development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early…
Mathematical Language and Advanced Mathematics Learning
ERIC Educational Resources Information Center
Ferrari, Pier Luigi
2004-01-01
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
ERIC Educational Resources Information Center
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
NASA Astrophysics Data System (ADS)
Paterson, Judy; Sneddon, Jamie
2011-10-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.
Children thinking mathematically beyond authoritative identities
NASA Astrophysics Data System (ADS)
MacMillan, Agnes
1995-10-01
A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.
Cognitive Correlates of Performance in Advanced Mathematics
ERIC Educational Resources Information Center
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Educational interventions to advance children's scientific thinking.
Klahr, David; Zimmerman, Corinne; Jirout, Jamie
2011-08-19
The goal of science education interventions is to nurture, enrich, and sustain children's natural and spontaneous interest in scientific knowledge and procedures. We present taxonomy for classifying different types of research on scientific thinking from the perspective of cognitive development and associated attempts to teach science. We summarize the literature on the early--unschooled--development of scientific thinking, and then focus on recent research on how best to teach science to children from preschool to middle school. We summarize some of the current disagreements in the field of science education and offer some suggestions on ways to continue to advance the science of science instruction.
Scaffolding Students' Thinking in Mathematical Investigations
ERIC Educational Resources Information Center
McCosker, Natalie; Diezmann, Carmel M.
2009-01-01
Mathematical investigations are loosely-defined, engaging problem-solving tasks that allow students to ask their own questions, explore their own interests and set their own goals. The value of investigations for students lies in their complexity. Scaffolding plays an important role in supporting students' high-level engagement by encouraging…
Mathematical Thinking with Lower-Attaining Pupils
ERIC Educational Resources Information Center
Woodham, Liz
2008-01-01
The main strand of the NRICH project is the NRICH website (http://nrich.maths.org), which was set up in 1996 to cater for secondary-aged pupils who were attending mathematics master-classes at the Royal Institution. By 1998, problems aimed at primary children were included and the site began to provide for students aged five to 18-plus. At this…
How Elementary School Children Think about Mathematics.
ERIC Educational Resources Information Center
Melancon, Janet G.; And Others
The attitudes toward mathematics of a large cross-sectional sample of students in grades 6 through 12 were explored. Most previous studies have not used samples as large as the 623 urban public school students in the southern United States, included in this study. The sample included 55.1 percent females, 58.3 percent Whites, 27.6 percent African…
Inversion in Mathematical Thinking and Learning
ERIC Educational Resources Information Center
Greer, Brian
2012-01-01
Inversion is a fundamental relational building block both within mathematics as the study of structures and within people's physical and social experience, linked to many other key elements such as equilibrium, invariance, reversal, compensation, symmetry, and balance. Within purely formal arithmetic, the inverse relationships between addition and…
The Role of Visualisation in Developing Critical Thinking in Mathematics
ERIC Educational Resources Information Center
Makina, A.
2010-01-01
Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done to clarify the fact that…
The Stakes of Movement: A Dynamic Approach to Mathematical Thinking
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Maheux, Jean-François
2015-01-01
Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…
Teachers' Considerations of Students' Thinking during Mathematics Lesson Design
ERIC Educational Resources Information Center
Amador, Julie M.
2016-01-01
Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers…
Thinking Process of Pseudo Construction in Mathematics Concepts
ERIC Educational Resources Information Center
Subanji; Nusantara, Toto
2016-01-01
This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…
Activating Pre-Service Mathematics Teachers' Critical Thinking
ERIC Educational Resources Information Center
Applebaum, Mark
2015-01-01
Teachers' critical thinking skills are essential for fostering the development of the same skills in their students. To demonstrate how teachers' ability to examine solutions critically can be developed and supported, we analyse a classroom activity performed by a group of pre-service secondary school mathematics teachers (N = 37) who were asked:…
ERIC Educational Resources Information Center
Rasiman
2015-01-01
This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…
A Framework for Mathematical Thinking: The Case of Linear Algebra
ERIC Educational Resources Information Center
Stewart, Sepideh; Thomas, Michael O. J.
2009-01-01
Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…
Tasks to Advance the Learning of Mathematics
ERIC Educational Resources Information Center
Greenes, Carole
2014-01-01
Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…
ERIC Educational Resources Information Center
Hitt, Fernando; Morasse, Christian
2009-01-01
Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…
A Study of Rural Preschool Practitioners' Views on Young Children's Mathematical Thinking
ERIC Educational Resources Information Center
Hunting, Robert P.; Mousley, Judith A.; Perry, Bob
2012-01-01
The project "Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice" aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian…
NASA Astrophysics Data System (ADS)
Fredenberg, Michael Duane
The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the
Advanced mathematical study and the development of conditional reasoning skills.
Attridge, Nina; Inglis, Matthew
2013-01-01
Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.
NASA Astrophysics Data System (ADS)
Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz
2016-04-01
Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that embodied solutions of mathematical modelling tasks. The data were collected from 25 prospective mathematics teachers enrolled in an undergraduate course through four 2-week-long cycles. Analysis of data revealed that the prospective teachers interpreted students' thinking in four ways: describing, questioning, explaining, and comparing. Moreover, whereas some of the prospective teachers showed a tendency to increase their attention to the meaning of students' ways of thinking more while they engaged in students' work in depth over time and experience, some of them continued to focus on only judging the accuracy of students' thinking. The implications of the findings for understanding and developing prospective teachers' ways of interpreting students' thinking are discussed.
NASA Astrophysics Data System (ADS)
Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz
2016-09-01
Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that embodied solutions of mathematical modelling tasks. The data were collected from 25 prospective mathematics teachers enrolled in an undergraduate course through four 2-week-long cycles. Analysis of data revealed that the prospective teachers interpreted students' thinking in four ways: describing, questioning, explaining, and comparing. Moreover, whereas some of the prospective teachers showed a tendency to increase their attention to the meaning of students' ways of thinking more while they engaged in students' work in depth over time and experience, some of them continued to focus on only judging the accuracy of students' thinking. The implications of the findings for understanding and developing prospective teachers' ways of interpreting students' thinking are discussed.
NASA Astrophysics Data System (ADS)
Osman, Sharifah; Mohammad, Shahrin; Abu, Mohd Salleh
2015-05-01
Mathematics and engineering are inexorably and significantly linked and essentially required in analyzing and accessing thought to make good judgment when dealing in complex and varied engineering problems. A study in the current engineering education curriculum to explore how the critical thinking and mathematical thinking relates to one another, is therefore timely crucial. Unfortunately, there is not much information available explicating about the link. This paper aims to report findings of a critical review as well as to provide brief description of an on-going research aimed to investigate the dispositions of critical thinking and the relationship and integration between critical thinking and mathematical thinking during the execution of civil engineering tasks. The first part of the paper reports an in-depth review on these matters based on rather limited resources. The review showed a considerable form of congruency between these two perspectives of thinking, with some prevalent trends of engineering workplace tasks, problems and challenges. The second part describes an on-going research to be conducted by the researcher to investigate rigorously the relationship and integration between these two types of thinking within the perspective of civil engineering tasks. A reasonably close non-participant observations and semi-structured interviews will be executed for the pilot and main stages of the study. The data will be analyzed using constant comparative analysis in which the grounded theory methodology will be adopted. The findings will serve as a useful grounding for constructing a substantive theory revealing the integral relationship between critical thinking and mathematical thinking in the real civil engineering practice context. The substantive theory, from an angle of view, is expected to contribute some additional useful information to the engineering program outcomes and engineering education instructions, aligns with the expectations of
ERIC Educational Resources Information Center
Fatah, Abdul; Suryadi, Didi; Sabandar, Jozua; Turmudi
2016-01-01
The present study aims at examining the use of open-ended approach in cultivating senior high school students' mathematical creative thinking ability (MCTA) and self-esteem (SE) in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten…
ERIC Educational Resources Information Center
Berkley, Darrin K.
2012-01-01
This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…
ERIC Educational Resources Information Center
Palinussa, Anderson L.
2013-01-01
This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…
A study of rural preschool practitioners' views on young children's mathematical thinking
NASA Astrophysics Data System (ADS)
Hunting, Robert P.; Mousley, Judith A.; Perry, Bob
2012-03-01
The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.
Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry
ERIC Educational Resources Information Center
Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann
2008-01-01
Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…
Connecting Research to Teaching: Lenses for Examining Students' Mathematical Thinking
ERIC Educational Resources Information Center
Linsenmeier, Katherine A.; Sherin, Miriam; Walkoe, Janet; Mulligan, Martha
2014-01-01
The authors present three strategies for making sense of students' mathematical thinking. These lenses make the abstract idea of "making sense of student thinking" more manageable and concrete. We start by taking an initial look at a student's idea, going deeper, and finally looking across several ideas.
Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand
ERIC Educational Resources Information Center
Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee
2015-01-01
The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…
What We Think We Know About Maya Mathematics and Astronomy
NASA Astrophysics Data System (ADS)
Van Stone, M.
2016-01-01
In most cultures, mathematics and astronomy are obscure and arcane. Not so to the ancient Maya. Despite what we consider technological “deficiencies”—they lacked both metal tools and the wheel—their public inscriptions paid uniquely sophisticated attention to these sciences. At any given monument, fully half the text is devoted to situating events in time, particularly specifying the precise number of days between events, whether historical or mythological. Often these intervals have numerological significance, and many are precise multiples of the periodicities of heavenly bodies. The Maya apparently were fully aware of the exact length of the tropical year, the sidereal year, the cycles of Venus, and eclipses; and there is evidence that they even celebrated events reflecting the 26,000-year precession cycle. However, Maya illuminati had an agenda quite alien to our way of thinking. Clues to their knowledge are arcane, rare, and often difficult for us to recognize with eyes clouded by our modern worldview. The body of work left to us consists of just a few tantalizing sherds of a once-rich and diverse astromythological tradition. Moreover, there was no single pan-Mayan mythos. An astronomical alignment seen repeatedly in one city will be completely absent in others. Each city-state emphasized specific and often unique features, and they often contradict one another. But we soldier on. The diversity we find so frustrating is simply the fine structure of their worldview. Intellectual historians have for too long been, like Procrustes, trying to force all Maya science and religion into a single universal straitjacket.
Exploring the Possibilities of Using Tic-Tac-Toe to Think and Communicate about Mathematics
ERIC Educational Resources Information Center
Clarkson, Philip C.
2008-01-01
Doing mathematics, and thinking about how you are doing it at the same time, are not the easiest things to do. It is even more difficult if students are not aware that they should be attempting both processes at the same time. They are likely to concentrate on the immediate task of "doing" the mathematics, rather than trying to access the deeper…
ERIC Educational Resources Information Center
Anthony, Glenda; Hunter, Jodie; Hunter, Roberta
2015-01-01
In recent years there have been calls for ambitious mathematics teaching which places student thinking and reasoning at the centre of instruction. Drawing on a larger study concerning implementation of practice-based pedagogies within our initial teacher education mathematics programme, this paper examines the range of opportunities for…
Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades
ERIC Educational Resources Information Center
Graf, Edith Aurora; Arieli-Attali, Meirav
2015-01-01
Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…
ERIC Educational Resources Information Center
Aizikovitsh-Udi, Einav; Clarke, David; Kuntze, Sebastian
2014-01-01
Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should…
Increasing Logico-Mathematical Thinking in Low SES Preschoolers
ERIC Educational Resources Information Center
Kirkland, Lynn D.; Manning, Maryann; Osaki, Kyoko; Hicks, Delyne
2015-01-01
Traditionally, children in low socioeconomic status (SES) inner-city areas in the United States lack experiences that prepare them for academic success, especially in math and science. The purpose of this research was to determine the extent to which a constructivist curriculum emphasizing logical thinking produces higher level thinking in low-SES…
Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication
ERIC Educational Resources Information Center
Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.
2014-01-01
This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities…
ERIC Educational Resources Information Center
Sherman, Milan
2014-01-01
The use of instructional technology in secondary mathematics education has proliferated in the last decade, and students' mathematical thinking and reasoning has received more attention during this time as well. However, few studies have investigated the role of instructional technology in supporting students' mathematical thinking. In…
ERIC Educational Resources Information Center
Lince, Ranak
2016-01-01
Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…
ERIC Educational Resources Information Center
Husnaeni
2016-01-01
Critical thinking ability of students' mathematical is a component that must be mastered by the student. Learn to think critically means using mental processes, such as attention, categorize, selection, and rate/decide. Critical thinking ability in giving proper guidance in thinking and working, and assist in determining the relationship between…
Connecting Science with Mathematics: Thinking Outside the Toolbox
ERIC Educational Resources Information Center
Wake, Geoff; Newton, Len
2014-01-01
Our view of learning takes into account how learners, when learning, are engaged in both doing science and mathematics and becoming mathematicians and scientists. Drawing on our work on a number of European projects that developed inquiry approaches across mathematics and science, we propose a new research and development agenda seeking new ways…
Advanced Mathematics Course-Taking: A Focus on Gender Equifinality
ERIC Educational Resources Information Center
You, Sukkyung; Sharkey, Jill D.
2012-01-01
High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers.…
Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…
Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School.
ERIC Educational Resources Information Center
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
ERIC Educational Resources Information Center
Putnam, Ralph T.; Reineke, James W.
Recent calls for reform in mathematics education suggest students must learn to recognize mathematical elements in situations, flexibly apply appropriate mathematical tools, and engage in mathematical reasoning. These things suggest teachers must make their students' thinking a prominent part of their classroom instruction; they must make their…
Advance care planning: thinking ahead to achieve our patients' goals.
Cairns, Rosemary
2011-09-01
The End of Life Care Strategy for England describes advance care planning (ACP) as a 'voluntary process of discussion about future care...concerns and wishes...values or personal goals for care, their understanding of their illness and prognosis...wishes for types of care or treatment and the availability of these' (Department of Health (DH), 2008). In Scotland, Living and Dying Well: Building on Progress (Scottish Government (SG), 2011) referred to adopting a 'thinking ahead' philosophy.
ERIC Educational Resources Information Center
Wood, Terry, Ed.; Nelson, Barbara Scott, Ed.; Warfield, Janet, Ed.
This book describes and analyzes the teaching that has evolved in mathematics classrooms of teachers who have been forerunners in the effort to implement the National Council of Teachers of Mathematics (NCTM) Standards in Elementary Mathematics. Research and insights from psychology, mathematics, and sociology are presented. Chapters include: (1)…
NASA Astrophysics Data System (ADS)
Cable, John
2013-07-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.
ERIC Educational Resources Information Center
McLeman, Laura Kondek
2009-01-01
Teacher educators use children's thinking activities as a means to prepare prospective teachers to teach mathematics. Research in methods courses and student teaching practica has shown these types of activities help prospective teachers deepen their own mathematical knowledge as well as better understand how children think. This study…
Enhancing Thinking Skills in the Sciences and Mathematics.
ERIC Educational Resources Information Center
Halpern, Diane F., Ed.
The need to provide an improved science and mathematics curriculum is imperative. Over recent years cognitive psychologists and educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. This book contains many of the guiding principles…
Mathematical Thinking and Human Nature: Consonance and Conflict
ERIC Educational Resources Information Center
Leron, Uri
2004-01-01
Human nature had traditionally been the realm of novelists, philosophers, and theologicians, but has recently been studied by cognitive science, neuroscience, research on babies and on animals, anthropology, and evolutionary psychology. In this paper I will show--by surveying relevant research and by analyzing some mathematical "case studies"--how…
ERIC Educational Resources Information Center
Koichu, Boris
2010-01-01
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
Teacher Questioning to Elicit Students' Mathematical Thinking in Elementary School Classrooms
ERIC Educational Resources Information Center
Franke, Megan L.; Webb, Noreen M.; Chan, Angela G.; Ing, Marsha; Freund, Deanna; Battey, Dan
2009-01-01
Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students' mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers'…
ERIC Educational Resources Information Center
Baltaci, Serdal
2016-01-01
It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…
ERIC Educational Resources Information Center
Tanujaya, Benidiktus
2016-01-01
The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…
Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture
ERIC Educational Resources Information Center
Mustafa, Sriyanti; Nusantara, Toto; Subanji; Irawati, Santi
2016-01-01
The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students' activity are recorded using handy cam and digital camera (full HD capacity).…
ERIC Educational Resources Information Center
Sahin, Senar Alkin; Tunca, Nihal; Altinkurt, Yahya; Yilmaz, Kürsad
2016-01-01
The purpose of this study is to determine the relationship between the professional values and critical thinking disposition of science-technology and mathematics teachers working in middle schools. The survey research method was employed in the study. The sample of the study is comprised of 193 teachers (90 science-technology and 103 mathematics…
Using Math Journals to Enhance Second Graders' Communication of Mathematical Thinking
ERIC Educational Resources Information Center
Kostos, Kathleen; Shin, Eui-kyung
2010-01-01
As an action research project, using mixed methodology, this study investigated how the use of math journals affected second grade students' communication of mathematical thinking. For this study, math journal instruction was provided. The data gathering included pre- and post- math assessment, students' math journals, interviews with the…
A Language-Thinking Approach to Mathematical Problem Solving: A Staff Development Package.
ERIC Educational Resources Information Center
Howell, Mary R.; Bell, Pat
Designed for fifth grade mathematics teachers, the three inservice sessions described in this booklet balance the theoretical with the practical and show teachers how to help students through the activity of writing word problems based on their own experiences. Using a total language-thinking approach to helping students read and solve word…
The Impact of Critical Thinking and Logico-Mathematical Intelligence on Algorithmic Design Skills
ERIC Educational Resources Information Center
Korkmaz, Ozgen
2012-01-01
The present study aims to reveal the impact of students' critical thinking and logico-mathematical intelligence levels of students on their algorithm design skills. This research was a descriptive study and carried out by survey methods. The sample consisted of 45 first-year educational faculty undergraduate students. The data was collected by…
ERIC Educational Resources Information Center
Sevimli, Eyup; Delice, Ali
2012-01-01
Students' cognitive differences in problem solving have been the focus of much research. One classification of these differences is related to whether visualisation is used. Like mathematical thinking differences, multiple representation preferences are important when considering individual differences. Choosing an appropriate representation is an…
ERIC Educational Resources Information Center
Suh, Jennifer
2010-01-01
The following study describes design research in an elementary school near the metropolitan D.C. area with a diverse student population. The goal of the project was to design tasks that leveraged technology and enhance the access to critical thinking in specific mathematical concepts: data analysis and probability. It highlights the opportunities…
ERIC Educational Resources Information Center
Aguirre, Julia M.; Turner, Erin E.; Bartell, Tonya Gau; Kalinec-Craig, Crystal; Foote, Mary Q.; Roth McDuffie, Amy; Drake, Corey
2013-01-01
This study examines the ways prospective elementary teachers (PSTs) made connections to children's mathematical thinking and children's community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that…
ERIC Educational Resources Information Center
van Velzen, Joke H.
2016-01-01
The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…
ERIC Educational Resources Information Center
Cable, John
2014-01-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…
Exposing calculus students to advanced mathematics
NASA Astrophysics Data System (ADS)
Griffiths, Barry J.; Selcuk Haciomeroglu, Erhan
2014-07-01
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major.
Reassessing the Economic Value of Advanced Level Mathematics
ERIC Educational Resources Information Center
Adkins, Michael; Noyes, Andrew
2016-01-01
In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium…
All Students Need Advanced Mathematics. Math Works
ERIC Educational Resources Information Center
Achieve, Inc., 2013
2013-01-01
This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…
ERIC Educational Resources Information Center
Turner, Erin E.; Drake, Corey
2016-01-01
Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers' learning about children's mathematical thinking (CMT) or, less frequently, about children's cultural funds of knowledge (CFoK) related to mathematics. Despite this…
ERIC Educational Resources Information Center
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
ERIC Educational Resources Information Center
Verschaffel, Lieven; Lehtinen, Erno; Van Dooren, Wim
2016-01-01
In this commentary we take a critical look at the various studies being reported in this issue about the relationship between cognitive neuroscience and mathematics, from a mathematics education viewpoint. After a discussion of the individual contributions, which we have grouped into three categories--namely neuroscientific studies of (a)…
ERIC Educational Resources Information Center
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
ERIC Educational Resources Information Center
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
ERIC Educational Resources Information Center
Gibney, Janette
2014-01-01
This action research project looks at what happened when a small group of adult numeracy teachers with widely different experiences of learning and teaching mathematics explored their own informal numeracy practices and undertook a series of collaborative mathematical tasks. Evidence from qualitative data collected during the enquiry suggests that…
ERIC Educational Resources Information Center
Ma, Xin
2010-01-01
Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advanced mathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although early…
NASA Astrophysics Data System (ADS)
Bektasli, Behzat
Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking
An initial framework for the language of higher-order thinking mathematics practices
NASA Astrophysics Data System (ADS)
Staples, Megan E.; Truxaw, Mary P.
2012-09-01
This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: language of generalisation, language of comparison, language of proportional reasoning, and language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.
An Enquiry Into Adverse Attitudes Towards Advanced Level Mathematics
ERIC Educational Resources Information Center
Selkirk, Jack
1975-01-01
The adverse attitudes of many students in advanced mathematics courses were explored. Results indicated students felt the gap between regular and advanced courses was too great, and that students pursuing arts or social sciences would benefit from courses with broader application. (SD)
ERIC Educational Resources Information Center
Clements, Douglas H., Ed.; DiBiase, Ann-Marie, Ed.; Sarama, Julie, Ed.
2004-01-01
This book brings together the combined wisdom of a diverse group of experts involved with early childhood mathematics. The book originates from the landmark 2000 Conference on Standards for Pre-kindergarten and Kindergarten Mathematics Education, attended by representatives from almost every state developing standards for young children's…
NASA Astrophysics Data System (ADS)
Wilkie, Karina J.
2016-06-01
A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.
ERIC Educational Resources Information Center
Tandiseru, Selvi Rajuaty
2015-01-01
The problem in this research is the lack of creative thinking skills of students. One of the learning models that is expected to enhance student's creative thinking skill is the local culture-based mathematical heuristic-KR learning model (LC-BMHLM). Heuristic-KR is a learning model which was introduced by Krulik and Rudnick (1995) that is the…
Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series
ERIC Educational Resources Information Center
Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.
2005-01-01
The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…
Global Perspectives: Developing Media Literacy Skills to Advance Critical Thinking
ERIC Educational Resources Information Center
Radeloff, Cheryl L.; Bergman, Barbara J.
2009-01-01
Women's studies and feminist curricula have been lauded for the development and application of critical thinking skills for social and political change in its students (Fisher; Kellner and Share; Mayberry). Critical thinking can be defined as the ability to identify and challenge assumptions, to search for alternative ways of thinking, and to…
Teachers' Uses of a Learning Trajectory to Support Attention to Students' Mathematical Thinking
ERIC Educational Resources Information Center
Edgington, Cynthia Page
2012-01-01
Teachers' ability to elicit and build on students' mathematical thinking during instruction is critical in order to support students' mathematical growth. An emerging hypothesis in the field is that the construct of a "learning trajectory" (LT) has the potential to support teachers in making sense of and using student…
ERIC Educational Resources Information Center
Innabi, Hanan; El Sheikh, Omar
2007-01-01
This study investigates how mathematics secondary schools' teachers in Jordan perceive critical thinking and compares teachers' perceptions before and after educational reform. Data were collected from 12 schools twice: in 1988 and in 2004 by interviewing 47 Mathematics teachers. The interview included questions related to teachers' understanding…
ERIC Educational Resources Information Center
Crawford, Caroline M.; Brown, Evelyn
Emphasizing higher order thinking skills is of primary concern within mathematics. Learning environments emphasizing the learners understanding of the subject matter are constantly under review, with one learner-centered emphasis upon instruction leading the way: WebQuests. The design and development of WebQuests for the mathematical classroom…
ERIC Educational Resources Information Center
Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua
2015-01-01
The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…
Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers
NASA Astrophysics Data System (ADS)
Harada, Shoji
Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.
Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.
ERIC Educational Resources Information Center
Natour, Denise M.
This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require mastery for…
Who Succeeds in Advanced Mathematics and Science Courses?
ERIC Educational Resources Information Center
Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje; Bosker, Roel
2011-01-01
Few students (particularly few girls) currently choose to take their Final School Examination (FSE) in advanced mathematics, chemistry and physics, a combination of subjects that is the best preparation for a science-oriented study in higher education. Are these subjects attainable by more students than is currently the case? This study examined…
NASA Astrophysics Data System (ADS)
Koichu, Boris
2010-03-01
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of three mathematical worlds; relatively advanced problem-solving behaviours are defined in terms of taxonomies of proof schemes and heuristic behaviours. The relationships between mathematical knowledge and problem-solving behaviours are analysed in the contexts of solving an insight geometry problem, posing algebraic problems and calculus exploration. A particularly knowledgeable and skilled university student was involved in all the episodes. The presented examples substantiate the claim that advanced mathematical knowledge and advanced problem-solving behaviours do not always support each other. More advanced behaviours were observed when the student worked within her conceptual-embodied mathematical world, and less advanced ones when she worked within her symbolic and formal-axiomatic worlds. Alternative explanations of the findings are discussed. It seems that the most comprehensive explanation is in terms of the Principle of Intellectual Parsimony. Implications for further research are drawn.
Advanced Mathematical Knowledge in Teaching Practice: Perceptions of Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Zazkis, Rina; Leikin, Roza
2010-01-01
For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages…
NASA Astrophysics Data System (ADS)
Gazit, Avikam
2012-12-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers' answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical-mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.
Mathematical foundations of quantum mechanics: An advanced short course
NASA Astrophysics Data System (ADS)
Moretti, Valter
2016-08-01
This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.
Students' Exploratory Thinking about a Nonroutine Calculus Task
ERIC Educational Resources Information Center
Nabb, Keith
2013-01-01
In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…
ERIC Educational Resources Information Center
Yuliani, Kiki; Saragih, Sahat
2015-01-01
The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…
ERIC Educational Resources Information Center
Sezer, Renan
2008-01-01
Critical thinking receives increasing emphasis from educators looking to infuse analytical thinking skills into the curriculum. Many research projects have been conducted on the transferability of critical thinking skills to other disciplines and how critical thinking may be taught. There are numerous studies on teaching critical thinking, yet…
ERIC Educational Resources Information Center
Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi
2014-01-01
This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…
ERIC Educational Resources Information Center
Promraksa, Siwarak; Sangaroon, Kiat; Inprasitha, Maitree
2014-01-01
The objectives of this research were to study and analyze the characteristics of computational thinking about the estimation of the students in mathematics classroom applying lesson study and open approach. Members of target group included 4th grade students of 2011 academic year of Choomchon Banchonnabot School. The Lesson plan used for data…
ERIC Educational Resources Information Center
Koichu, Boris; Harel, Guershon; Manaster, Alfred
2013-01-01
Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…
ERIC Educational Resources Information Center
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
The Impact of Advanced Curriculum on the Achievement of Mathematically Promising Elementary Students
ERIC Educational Resources Information Center
Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen
2009-01-01
The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…
Year 11 Advanced Mathematics: Hearing from Students Who Buck the Trend
ERIC Educational Resources Information Center
Ho, Kai Fai
2010-01-01
There are concerns about the trends and patterns in enrolments in senior school mathematics. Shortages of suitably qualified teachers and dwindling students' demand for Advanced Mathematics have led some Western Australian schools to collaborate to provide an otherwise unavailable opportunity for their students to study Advanced Mathematics. It is…
ERIC Educational Resources Information Center
Schreiber, James B.
The student variables associated with scoring above the international mean on the Third International Mathematics and Science Study (TIMSS) were studied in a group of U.S. students who took advanced mathematics or advanced mathematics and physics. The total sample was 2,349, with 1,158 females and 1,191 males. Formal parent education level and…
Advancing socio-technical systems thinking: a call for bravery.
Davis, Matthew C; Challenger, Rose; Jayewardene, Dharshana N W; Clegg, Chris W
2014-03-01
Socio-technical systems thinking has predominantly been applied to the domains of new technology and work design over the past 60 years. Whilst it has made an impact, we argue that we need to be braver, encouraging the approach to evolve and extend its reach. In particular, we need to: extend our conceptualization of what constitutes a system; apply our thinking to a much wider range of complex problems and global challenges; and engage in more predictive work. To illustrate our agenda in novel domains, we provide examples of socio-technical perspectives on the management of crowd events and environmental sustainability. We also outline a research and development agenda to take the area forward.
Thinking Ourselves to Liberation?: Advancing Sociopolitical Action in Critical Consciousness
ERIC Educational Resources Information Center
Watts, Roderick J.; Hipolito-Delgado, Carlos P.
2015-01-01
Freire advanced critical consciousness as a tool for the liberation of oppressed communities. Based on his ideas, scholars of theory and practice from myriad disciplines have written about how to advance critical consciousness (CC) among oppressed peoples. We reviewed CC theory and practice articles in scholarly journals with the goal of…
Systems Thinking: An Approach for Advancing Workplace Information Literacy
ERIC Educational Resources Information Center
Somerville, Mary M.; Howard, Zaana
2008-01-01
As the importance of information literacy has gained increased recognition, so too have academic library professionals intensified their efforts to champion, activate, and advance these capabilities in others. To date, however, little attention has focused on advancing these essential competencies amongst practitioner advocates. This paper helps…
ERIC Educational Resources Information Center
Advanced Technology, Inc., Indianapolis, IN.
Designed to assist technical assistance center staff members and other inservice providers, this workshop leader's guide contains step-by-step procedures for preparing, organizing, and presenting a one-hour workshop on advanced skills for teachers, administrators, and others associated with Chapter 1 programs. Sections of the guide include: (1) an…
ERIC Educational Resources Information Center
Rasmussen, Chris; Kwon, Oh Nam; Allen, Karen; Marrongelle, Karen; Burtch, Mark
2006-01-01
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students' beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the…
ERIC Educational Resources Information Center
Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.
2011-01-01
This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…
ERIC Educational Resources Information Center
Pape, S. J.; Bell, C. V.; Yetkin, IE.
2003-01-01
Mathematics educators have found sociocultural models of teaching and learning to be powerful in their ability to describe and support the pursuit of instruction based on recent standards documents (e.g., National Council of Teachers of Mathematics [NCTM], 1989, 2000). These models of instruction, however, have been criticized for their lack of…
ERIC Educational Resources Information Center
Klein, Pnina S.; Adi-Japha, Esther; Hakak-Benizri, Simcha
2010-01-01
The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher-child mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children's mathematics, spatial, and verbal…
Literacy in Language and Mathematics: More in Common Than You Think
ERIC Educational Resources Information Center
Thompson, Denisse R.; Rubenstein, Rheta N.
2014-01-01
This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…
Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…
ERIC Educational Resources Information Center
Weber, Keith
2009-01-01
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
Institutional and Student Factors and Their Influence on Advanced Mathematics Achievement.
ERIC Educational Resources Information Center
Schreiber, James B.
2002-01-01
Examined advanced mathematics achievement among high school students using data from the Third International Mathematics and Science Study. Examination of school- and student-level factors indicated that gender and economic disparities existed, even with the most advanced students. This disparity varied by school. Parent education related to…
A Cross-National Comparison of Reported Effort and Mathematics Performance in TIMSS Advanced
ERIC Educational Resources Information Center
Eklöf, Hanna; Pavešic, Barbara Japelj; Grønmo, Liv Sissel
2014-01-01
The purpose of the study was to measure students' reported test-taking effort and the relationship between reported effort and performance on the Trends in International Mathematics and Science Study (TIMSS) Advanced mathematics test. This was done in three countries participating in TIMSS Advanced 2008 (Sweden, Norway, and Slovenia), and the…
ERIC Educational Resources Information Center
de Wolf, Virginia A.
Freshmen placed into the second or third quarter of the first year calculus sequence at the University of Washington were studied. Two major findings were: freshmen eligible for advanced placement earned mean mathematics Grade Point Averages (GPAs) which were quite high; and advanced placement students earned mean mathematics GPAs substantially…
Issues in Designing Assessments of Historical Thinking
ERIC Educational Resources Information Center
Ercikan, Kadriye; Seixas, Peter
2015-01-01
Similar to educators in mathematics, science, and reading, history educators around the world have mobilized curricular reform movements toward including complex thinking in history education, advancing historical thinking, developing historical consciousness, and teaching competence in historical sense making. These reform movements, including…
What do trainees think about advanced trauma life support (ATLS)?
Campbell, B.; Heal, J.; Evans, S.; Marriott, S.
2000-01-01
Advanced trauma life support (ATLS) has become a desirable or even essential part of training for many surgeons and anaesthetists, but aspects of the ATLS course have attracted criticism. In the absence of published data on the views of trainees, this study sought their opinions in a structured questionnaire, which was completed by trainees in accident and emergency (A & E) (26), anaesthetic (82), general surgical (26), orthopaedic (42) and other (5) posts in different hospitals (response rate 66%). Of the trainees, 78% had done an ATLS course and, of these, 83% considered ATLS a 'major advantage' or 'essential' for practising their proposed specialty--100% for A & E, 94% for orthopaedics, 92% for general surgery, and 75% for anaesthetics. ATLS was considered a major curriculum vitae (CV) advantage by 94%, 85%, 50%, and 45%, respectively. Over 90% had positive attitudes towards ATLS, and 74% selected 'genuine improvement of management of trauma patients' as the most important reason for doing the course: 93% thought ATLS saved lives. Of the respondents, 83% thought that all existing consultants dealing with trauma patients should have done the course, and 41% thought it offered major advantages to doctors not involved in trauma. Funding problems for ATLS courses had been experienced by 14% trainees. This survey has shown that most trainees view ATLS positively. They believe that it provides genuine practical benefit for patients, and very few regard ATLS primarily as a career advantage or mandate. PMID:10932661
Promoting Critical-Thinking Dispositions by Using Problem Solving in Middle School Mathematics
ERIC Educational Resources Information Center
Leader, Lars F.; Middleton, James A.
2004-01-01
This review of research generates principles for the design of instructional programs that foster critical-thinking dispositions. The dispositional aspect of critical thinking may be considered part of attitudinal memory, readily activated if sufficiently strong. We describe evidence suggesting that ill-structured problem-solving can provide…
ERIC Educational Resources Information Center
Burris, Justin T.
2010-01-01
As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…
ERIC Educational Resources Information Center
Artzt, Alice F.; Armour-Thomas, Eleanor
This activity-oriented book for preservice mathematics teachers who are taking methods courses or who have been student teaching offers a framework for teacher reflection and self- assessment. It supplies detailed observation instruments for observing other teachers, reflective activities, and guidelines and instruments for supervisors. There are…
ERIC Educational Resources Information Center
Cohen, Sophia
2004-01-01
This book illustrates the experiences of elementary school teachers across one year's time as they participated in a teacher development seminar focused on mathematics, and as a result changed their beliefs, their knowledge, and their practices. It explores these experiences as a means of understanding the learning that takes a teacher from a more…
Some observations on the interdigitation of advances in medical science and mathematics.
Glamore, Michael James; West, James L; O'leary, James Patrick
2013-12-01
The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.
Advanced Skills for Chapter 1 Mathematics: Estimation. Workshop Leader's Guide.
ERIC Educational Resources Information Center
Advanced Technology, Inc., Indianapolis, IN.
This Workshop Leader's Guide contains step-by-step procedures for preparing, organizing, and presenting 1-hour and 3-hour workshops on estimation in mathematics. It was designed to assist Technical Assistance Center staff members and other inservice providers in conducting successful workshops on estimation in mathematics for administrators,…
ERIC Educational Resources Information Center
Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith
2016-01-01
We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…
Valuing Choice as an Alternative to Fixed-Ability Thinking and Teaching in Primary Mathematics
ERIC Educational Resources Information Center
Milik, Amy; Boylan, Mark
2013-01-01
This article offers a personal account of a primary mathematics teacher's current practice and how it developed through participation in a professional development programme. This alternative to fixed-ability teaching is based on creating opportunities for learners to exercise choice and on an understanding of mathematics as connected. Key…
The Interaction between Intuitive and Formal Mathematical Thinking: A Case Study
ERIC Educational Resources Information Center
Farmaki, V.; Paschos, T.
2007-01-01
This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic…
ERIC Educational Resources Information Center
Mulligan, Joanne; Mitchelmore, Mike; Kemp, Coral; Marston, Jennie; Highfield, Kate
2008-01-01
Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In this article, the…
Where Learning Starts? A Framework for Thinking about Lectures in University Mathematics
ERIC Educational Resources Information Center
Pritchard, David
2010-01-01
Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying…
ERIC Educational Resources Information Center
Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim
2013-01-01
The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…
Inhibitory Control in Mathematical Thinking, Learning and Problem Solving: A Survey
ERIC Educational Resources Information Center
Van Dooren, Wim; Inglis, Matthew
2015-01-01
Inhibitory control--the ability to ignore salient but unhelpful stimuli and responses--seems to be important for learning mathematics. For instance there is now robust evidence that performance on classic measures of inhibition, such as the Stroop Task, correlate with school-level mathematics achievement. At the same time, a great deal of…
ERIC Educational Resources Information Center
Norton, Anderson; McCloskey, Andrea; Hudson, Rick A.
2011-01-01
In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child's mathematics…
Gender Differences in the Use and Benefit of Advanced Learning Technologies for Mathematics
ERIC Educational Resources Information Center
Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park
2013-01-01
We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…
ERIC Educational Resources Information Center
Fiero, Diane M.
2013-01-01
Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…
ERIC Educational Resources Information Center
Anderson, Rick
2006-01-01
The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…
Origins of the brain networks for advanced mathematics in expert mathematicians.
Amalric, Marie; Dehaene, Stanislas
2016-05-01
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Origins of the brain networks for advanced mathematics in expert mathematicians
Amalric, Marie; Dehaene, Stanislas
2016-01-01
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Origins of the brain networks for advanced mathematics in expert mathematicians.
Amalric, Marie; Dehaene, Stanislas
2016-05-01
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.
A Survey of Advanced Mathematics Topics: A New High School Mathematics Class
ERIC Educational Resources Information Center
Bellomo, Carryn; Strapp, Remy
2008-01-01
The number of students pursuing undergraduate degrees in mathematics is decreasing. Research reveals students who pursue mathematics majors complained about inadequate high school preparation in terms of disciplinary content or depth, conceptual grasp, or study skills. Unfortunately, the decrease in the number of students studying advanced…
ERIC Educational Resources Information Center
DuBridge, Lee A.
An appeal for more research to determine how to educate children as effectively as possible is made. Mathematics teachers can readily examine the educational problems of today in their classrooms since learning progress in mathematics can easily be measured and evaluated. Since mathematics teachers have learned to think in quantitative terms and…
Where learning starts? A framework for thinking about lectures in university mathematics
NASA Astrophysics Data System (ADS)
Pritchard, David
2010-07-01
Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying out various functions is discussed with reference to some recent educational research. There is evidence that lectures can be effective in communicating information, modelling reasoning and motivating students. Therefore, when supported appropriately by other activities, lectures provide an effective component of a mathematical education.
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin
2013-04-01
The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.
ERIC Educational Resources Information Center
An, Shuhua; Wu, Zhonghe
2012-01-01
This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth-eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of…
Thinking and Writing Mathematically: "Achilles and the Tortoise" as an Algebraic Word Problem.
ERIC Educational Resources Information Center
Martinez, Joseph G. R.
2001-01-01
Introduces Hogben's adaptation of Zeno's paradox, "Achilles and the Tortoise", as a thinking and writing exercise. Emphasizes engaging students' imagination with creative, thought-provoking problems and involving students in evaluating their word problem-solving strategies. Describes the paradox, logical solutions, and students' mathematical…
ERIC Educational Resources Information Center
Dyer, Elizabeth B.; Sherin, Miriam Gamoran
2016-01-01
Basing instruction on the substance of student thinking, or responsive teaching, is a critical strategy for supporting student learning. Previous research has documented responsive teaching by identifying observable teaching practices in a broad range of disciplines and classrooms. However, this research has not provided access to the teacher…
ERIC Educational Resources Information Center
Wilson, P. Holt; Mojica, Gemma F.; Confrey, Jere
2013-01-01
Recent work by researchers has focused on synthesizing and elaborating knowledge of students' thinking on particular concepts as core progressions called learning trajectories. Although useful at the level of curriculum development, assessment design, and the articulation of standards, evidence is only beginning to emerge to suggest how learning…
ERIC Educational Resources Information Center
Sriraman, Bharath
2004-01-01
This article is the sequel to the use of "Flatland" with beginning algebra students reported in Sriraman (2003). The use of "Flatland" with beginning algebra students resulted in the positive outcomes of cultivating critical thinking in the students as well as providing the teacher with the context necessary to introduce sophisticated mathematical…
Advanced Mathematics. Training Module 1.303.3.77.
ERIC Educational Resources Information Center
Kirkwood Community Coll., Cedar Rapids, IA.
This document is an instructional module prepared in objective form for use by an instructor familiar with mathematics as applied to water and wastewater treatment plant operation. Included are objectives, instructor guides and student handouts. This is the third level of a three module series and is concerned with statistics, total head, steady…
Block Scheduling and Advanced Placement Mathematics: When Tradition and Reform Collide.
ERIC Educational Resources Information Center
Howard, Elizabeth
1997-01-01
This case study reflects block scheduling's effects on advanced-placement mathematics courses of one veteran teacher tracking personal progress since 1989. Block scheduling began in 1994, creating problems for the teacher, whose resistance to the reform was based on declining advanced-placement scores. Teacher attitude and insufficient…
The Influence of Applied STEM Coursetaking on Advanced Mathematics and Science Coursetaking
ERIC Educational Resources Information Center
Gottfried, Michael A.
2015-01-01
Advanced mathematics and science course taking is critical in building the foundation for students to advance through the STEM pathway-from high school to college to career. To invigorate students' persistence in STEM fields, high schools have been introducing applied STEM courses into the curriculum as a way to reinforce concepts learned in…
Innovations in Science and Mathematics Education: Advanced Designs for Technologies of Learning.
ERIC Educational Resources Information Center
Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.
This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…
Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners
ERIC Educational Resources Information Center
Johnsen, Susan K., Ed.; Sheffield, Linda J., Ed.
2012-01-01
"Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners" provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K-12 schools. The book describes--and demonstrates with specific examples from the…
Mathematical thinking: challenging prospective teachers to do more than `talk the talk'
NASA Astrophysics Data System (ADS)
Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh
2014-07-01
This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme.
Eliciting Student Thinking in Elementary School Mathematics Classrooms. CRESST Report 725
ERIC Educational Resources Information Center
Franke, Megan L.; Webb, Noreen M.; Chan, Angela; Battey, Dan; Ing, Marsha; Freund, Deanna; De, Tondra
2007-01-01
The importance of student talk in mathematics classrooms figures prominently in curriculum and teaching standards. Student talk is a vehicle for increasing student learning and for helping teachers monitor student understanding and inform student instructional practices. Although researchers have begun to study the moves teachers may make to…
Increasing Cognitive Inhibition with a Difficult Prior Task: Implications for Mathematical Thinking
ERIC Educational Resources Information Center
Attridge, Nina; Inglis, Matthew
2015-01-01
Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning.
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning. PMID:24591504
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students’ apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students’ understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students’ inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students’ biology learning. PMID:24591504
Seeing Relationships: Using Spatial Thinking to Teach Science, Mathematics, and Social Studies
ERIC Educational Resources Information Center
Newcombe, Nora S.
2013-01-01
The author discusses four specific strategies for enhancing and supporting the spatial aspects of the science, mathematics, and social studies curricula. However, these four strategies are examples of what can be done, not an exhaustive list. The overarching concept is to embrace the spatial visualizations used for discovery and communication in…
Forecast: Changing Mathematics Curriculum and Increasing Pressure for Higher-Level Thinking Skills.
ERIC Educational Resources Information Center
Niess, Margaret L.
1993-01-01
Presents a unit developed by the 1991 Oregon Mathematics Teachers of Middle School project in which students investigate the average temperature, precipitation, and snowfall in their town using spreadsheets and graphing packages. Students compare the averages over a period of 30 years to a particular year. (MDH)
The School Library: A Space for Critical Thinking about Data and Mathematical Questions
ERIC Educational Resources Information Center
Kimmel, Sue C.
2012-01-01
Which potato chip is healthiest: (1) regular; (2) baked; or (3) sour cream and onion? This problem requires critical and numerical skills in order to read and compare nutrition labels. The question has applications in mathematics and science classrooms but also in teachers' lounges and school cafeterias. It is a problem that addresses the five…
Advancing our thinking in presence-only and used-available analysis.
Warton, David; Aarts, Geert
2013-11-01
1. The problems of analysing used-available data and presence-only data are equivalent, and this paper uses this equivalence as a platform for exploring opportunities for advancing analysis methodology. 2. We suggest some potential methodological advances in used-available analysis, made possible via lessons learnt in the presence-only literature, for example, using modern methods to improve predictive performance. We also consider the converse - potential advances in presence-only analysis inspired by used-available methodology. 3. Notwithstanding these potential advances in methodology, perhaps a greater opportunity is in advancing our thinking about how to apply a given method to a particular data set. 4. It is shown by example that strikingly different results can be achieved for a single data set by applying a given method of analysis in different ways - hence having chosen a method of analysis, the next step of working out how to apply it is critical to performance. 5. We review some key issues to consider in deciding how to apply an analysis method: apply the method in a manner that reflects the study design; consider data properties; and use diagnostic tools to assess how reasonable a given analysis is for the data at hand. PMID:23488567
Advancing our thinking in presence-only and used-available analysis.
Warton, David; Aarts, Geert
2013-11-01
1. The problems of analysing used-available data and presence-only data are equivalent, and this paper uses this equivalence as a platform for exploring opportunities for advancing analysis methodology. 2. We suggest some potential methodological advances in used-available analysis, made possible via lessons learnt in the presence-only literature, for example, using modern methods to improve predictive performance. We also consider the converse - potential advances in presence-only analysis inspired by used-available methodology. 3. Notwithstanding these potential advances in methodology, perhaps a greater opportunity is in advancing our thinking about how to apply a given method to a particular data set. 4. It is shown by example that strikingly different results can be achieved for a single data set by applying a given method of analysis in different ways - hence having chosen a method of analysis, the next step of working out how to apply it is critical to performance. 5. We review some key issues to consider in deciding how to apply an analysis method: apply the method in a manner that reflects the study design; consider data properties; and use diagnostic tools to assess how reasonable a given analysis is for the data at hand.
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
2016-09-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record
2016-01-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
2016-09-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record PMID:26913930
NASA Astrophysics Data System (ADS)
Bitner, Betty L.
To test the hypothesis that formal operational reasoning modes are predictors of critical thinking abilities and grades assigned by teachers in science and mathematics, in September 1986 the Group Assessment of Logical Thinking (GALT) and in December 1986 the Watson-Glaser Critical Thinking Appraisal (WGCTA) were administered to 101 rural students in Grades 9 through 12. The grades assigned by teachers were collected in May 1987. Construct and criterion-related validities and internal-consistency reliability using Cronbach's alpha method were established on the GALT. On the WGCTA, content and construct validities and internal consistency reliability using the split-half procedure, coefficient of stability, and coefficient of equivalence were established. The five formal operational reasoning modes in the GALT were found to be significant predictors of critical thinking abilities and grades assigned by teachers in science and mathematics. The variance in the five critical thinking abilities attributable to the five formal operational reasoning modes ranged between 28% and 70%. The five formal operational reasoning modes explained 29% of the variance in mathematics achievement and 62% of the variance in science achievement.
ERIC Educational Resources Information Center
Cai, Jinfa, And Others
1996-01-01
Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…
ERIC Educational Resources Information Center
Sisofo, Eric Joseph
2010-01-01
The use of student thinking in teaching has been linked to improved instruction and learning. It is reasonable to assume that the University of Delaware's undergraduate program might be interested in figuring out ways to develop this skill in its mathematics specialist pre-service teachers. Currently, the student teaching experience at the…
ERIC Educational Resources Information Center
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
ERIC Educational Resources Information Center
Chonkaew, Patcharee; Sukhummek, Boonnak; Faikhamta, Chatree
2016-01-01
The purpose of this study was to investigate the analytical thinking abilities and attitudes towards science learning of grade-11 students through science, technology, engineering, and mathematics (STEM) education integrated with a problem-based learning in the study of stoichiometry. The research tools consisted of a pre- and post-analytical…
Visual thinking and gender differences in high school calculus
NASA Astrophysics Data System (ADS)
Selcuk Haciomeroglu, Erhan; Chicken, Eric
2012-04-01
This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were collected from 183 Advanced Placement calculus students in five high schools. Students' visual preferences were not influenced by gender. Statistically significant differences in visual preference scores were found among high- and low-performing students. Thus, the results suggest that stronger preference for visual thinking was associated with higher mathematical performances.
Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.
ERIC Educational Resources Information Center
Scharf, John; And Others
This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…
ERIC Educational Resources Information Center
Grinstead, Mary L.
2013-01-01
This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…
ERIC Educational Resources Information Center
Schoenfeld, Alan H.
2010-01-01
Teachers try to help their students learn. But why do they make the particular teaching choices they do? What resources do they draw upon? What accounts for the success or failure of their efforts? In "How We Think", esteemed scholar and mathematician, Alan H. Schoenfeld, proposes a groundbreaking theory and model for how we think and act in the…
Mathematics Problem Solving: A More Advanced Skill for Chapter 1. Workshop Leader's Guide.
ERIC Educational Resources Information Center
Advanced Technology, Inc., Indianapolis, IN.
This guide is designed to assist inservice providers in conducting successful workshops for teachers, administrators, and others associated with Chapter 1 mathematics programs. It contains step-by-step procedures for preparing, organizing, and presenting the workshop. Included in this guide are: (1) an advanced planner, which includes a detailed…
ERIC Educational Resources Information Center
Davis, Cinda-Sue; And Others
This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…
ERIC Educational Resources Information Center
DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.
2015-01-01
This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…
ERIC Educational Resources Information Center
Niess, Margaret; Gillow-Wiles, Henry
2013-01-01
This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…
NASA Astrophysics Data System (ADS)
Fiondella, F.; Davi, N. K.; Wattenberg, F.; Pringle, P. T.; Greidanus, I.; Oelkers, R.
2015-12-01
Tree-ring science provides an engaging, intuitive, and relevant entryway into understanding both climate change and environmental research. It also sheds light on the process of science--from inspiration, to fieldwork, to analysis, to publishing and communication. The basic premise of dendrochronology is that annual rings reflect year-to-year environmental conditions and that by studying long-lived trees we can learn about environmental and climatic conditions going back hundreds to thousands of years. Conceptually, this makes tree-ring studies accessible to students and faculty for a number of reasons. First, in order to collect their data, dendrochronologists often launch expeditions to stunningly picturesque and remote places in search of long-lived, climate sensitive trees. The exciting stories and images that scientists bring back from the field can help connect students to the studies, their motivation, and the data collected. Second, tree rings can be more easily explained as a proxy for climate than ice cores, speleothems and others. Most people have prior knowledge about trees and annual growth rings. It is even possible, for example, for non-expert audiences to see climate variability through time with the naked eye by looking at climate-sensitive tree cores. Third, tree rings are interdisciplinary and illustrate the interplay between the mathematical sciences, the biological sciences, and the geosciences—that is, they show that the biosphere is a fundamental component of the Earth system. Here, we present online, multi-media learning modules for undergraduates that introduce students to several foundational studies in tree-ring science. These include evaluating tree-ring cores from ancient hemlock trees growing on a talus slope in New Paltz, NY to learn about drought in the Northeastern US, evaluating long-term streamflow and drought of the Colorado River based on tree-ring records, and using tree-ring dating techniques to develop construction
Developing Mathematical Thinking
ERIC Educational Resources Information Center
Jones, Graham
2006-01-01
Working with his daughter and her friend on a problem-solving task gave Graham Jones the opportunity to reconsider how best he might help. This document describes how he went about assisting the girls in solving the problem. In assisting, Graham decided to present the girls with a three part lesson, which would lead to the solution. He stresses…
Non-Traditional Socio-Mathematical Norms in Undergraduate Real Analysis
ERIC Educational Resources Information Center
Dawkins, Paul Christian
2009-01-01
This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative…
ERIC Educational Resources Information Center
Sheldrake, Richard; Mujtaba, Tamjid; Reiss, Michael J.
2015-01-01
Increasing the number of students who study mathematics once it is no longer compulsory remains a priority for England. A longitudinal cohort from England (1085 students) was surveyed at Years 10 and 12. Students' self-beliefs of ability influenced their GCSE mathematics grades and their intended and actual mathematics subject-choices; the degree…
ERIC Educational Resources Information Center
Owens, Kay
2014-01-01
Identity as a mathematics teacher is enhanced when a teacher explores the cultural setting of their mathematics. The reports of projects that link culture and mathematics were analysed to explore the impact of sociocultural situations together with affective and cognitive aspects of self-regulation on identity. The reports were written by…
ERIC Educational Resources Information Center
Tularam, Gurudeo Anand; Hulsman, Kees
2015-01-01
This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…
ERIC Educational Resources Information Center
Peak, David J.
2010-01-01
Improving student achievement in mathematics in secondary schools remains a priority for public education in our country. With continued federal and state mandates to improve overall student achievement in mathematics, as well as to close the achievement gap, many school districts have sought programs, such as Advancement Via Individual…
ERIC Educational Resources Information Center
Githua, Bernard N.; Nyabwa, Rachel Angela
2008-01-01
Students have continued to perform poorly in KCSE examinations in certain mathematics topics taught in secondary schools in Kenya. One such topic is commercial arithmetic. Successful teaching of mathematics depends partly on correct use of teaching methods in classroom settings. This study sought to examine how the use of advance organisers during…
Schissel, D.P.
1996-08-01
This report discusses advancing precollege science and mathematics education in San Diego Count. Described in this report are: curriculum and teacher development; pre-tour material; facility tour; student workbook; evaluation and assessment; and internet access.
ERIC Educational Resources Information Center
Hoffman, Bobby
2010-01-01
This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
ERIC Educational Resources Information Center
Wicklein, Robert C.; Schell, John W.
A study examined the perceptions of participants in a multidisciplinary project regarding the degree to which the integration of technology, mathematics, and science had enabled advanced mental skills in technical thinking and problem solving. A literature review focused on advanced learning and thinking, ill-structured workplace problems,…
Not Available
1990-12-01
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) Climate Modeling Program is designed to contribute directly to this rapid improvement. The goal of the CHAMMP Climate Modeling Program is to develop, verify, and apply a new generation of climate models within a coordinated framework that incorporates the best available scientific and numerical approaches to represent physical, biogeochemical, and ecological processes, that fully utilizes the hardware and software capabilities of new computer architectures, that probes the limits of climate predictability, and finally that can be used to address the challenging problem of understanding the greenhouse climate issue through the ability of the models to simulate time-dependent climatic changes over extended times and with regional resolution.
Preschoolers' Thinking during Block Play
ERIC Educational Resources Information Center
Piccolo, Diana L.; Test, Joan
2010-01-01
Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…
ERIC Educational Resources Information Center
Weiss, Michael K.; Moore-Russo, Deborah
2012-01-01
What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…
Preparing the practitioner for advanced academic study: the development of critical thinking.
Girot, E A
1995-02-01
Using an evaluative approach, this paper explores the concept of critical thinking and its development within a recently revised study skills programme, preparing practitioners for the academic post-registration courses in one college of health. The current and almost explosive move of nurse education in the United Kingdom into the halls of higher education seems to recognize the need for higher-order thinking skills in preparation for the unpredictability of nursing practice. Using a quasi-experimental design, the qualitative data analysed from two groups of students who undertook the study skills programme were measured against a control group of students undertaking the same short professional development course through the more traditional university approach of 2 years part-time academic study. The findings acknowledge that the development of critical thinking needs time and exposure to others seeking similar goals. In addition, to encourage the process of critical thought, study skills applied to content should be offered, as well as attention to teaching/learning strategies. If higher education means a change in culture, of attitude towards learning, then a more comprehensive foundation programme may better commence this process. It is anticipated that through such a programme current practitioners may be enabled to achieve successfully within the new academic courses and ultimately be better equipped for the complex decision-making in practice.
Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support
NASA Technical Reports Server (NTRS)
Cruthirds, John E.
2003-01-01
A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.
ERIC Educational Resources Information Center
Soares, Maria Tereza Carneiro; Moro, Maria Lucia Faria; Spinillo, Alina Galvao
2012-01-01
This study examines the relationship between the grasp of consciousness of the reasoning process in Grades 5 and 8 pupils from a public and a private school, and their performance in mathematical problems of Cartesian product. Forty-two participants aged from 10 to 16 solved four problems in writing and explained their solution procedures by…
ERIC Educational Resources Information Center
Kelley, Julie B.
2015-01-01
Self-regulated learning is an elaborate metacognitive process consisting of an individual's awareness of the thought process, flexibility in one's approach to problem solving, and motivation to persist through obstacles until a goal has been met. Strategies and instructional practices used to develop mathematically proficient thinkers also develop…
ERIC Educational Resources Information Center
Rahman, Abdul; Ahmar, Ansari Saleh
2016-01-01
Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…
The Development Of Logico-Mathematical Thinking at Ages 1-3 In Play With Blocks and An Incline
ERIC Educational Resources Information Center
Miyakawa, Yoko; Kamii, Constance; Nagahiro, Mariko
2005-01-01
Fifty 1-to 3-year-olds were asked to imitate: (1) the rolling of a cylinder down an incline and (2) the making of an incline with a board and a block. Their incorrect imitations and progress were videotaped and analyzed, and interpreted in light of Piaget's theory about the elaboration of logico-mathematical relationships in an interrelated way.…
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication
ERIC Educational Resources Information Center
Kaya, Defne; Aydin, Hasan
2016-01-01
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
ERIC Educational Resources Information Center
Richardson, Sandra
2009-01-01
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
ERIC Educational Resources Information Center
DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.
2015-01-01
Introduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advanced mathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…
ERIC Educational Resources Information Center
Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.
2010-01-01
The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…
ERIC Educational Resources Information Center
Scarborough, Jule Dee
2004-01-01
This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…
Intuitive vs Analytical Thinking: Four Perspectives
ERIC Educational Resources Information Center
Leron, Uri; Hazzan, Orit
2009-01-01
This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…
ERIC Educational Resources Information Center
Aneckstein, Laura; Baird, Andrea; Butler, Margaret; Chambers, David; Johnson, Wanda; Kraus, Rebecca; Mann, Eric; Trost, Tami; Zalokar, Nadja; Zieseniss, Mireille
This report focuses on the Office for Civil Rights' (OCR's) activities relating to Title IX and advanced mathematics, science, and technology education for girls. It examines some of the barriers and inequities that undermine girls' opportunities to choose college majors and enter careers in the advanced mathematics, science, and technology…
ERIC Educational Resources Information Center
Ronis, Diane
This booklet includes a wheel of problem solving strategies and a seven-step process for approaching and solving complicated problems. The information provided gives students a variety of ways to approach, analyze, and think critically about mathematics problems. The chapters present guides to promoting critical thinking in cooperative groups…
ERIC Educational Resources Information Center
Parks, David J.
2016-01-01
The tallest hurdle in completing a doctoral degree is the dissertation, which continues to be the primary capstone experience for the degree. Dissertation research is a mystery to many considering an advanced degree and can be intimidating to those who are unfamiliar with the nature of universities and doctoral research. In this report, the author…
Analyzing the Teaching of Advanced Mathematics Courses via the Enacted Example Space
ERIC Educational Resources Information Center
Fukawa-Connelly, Timothy Patrick; Newton, Charlene
2014-01-01
Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
Kavlock, R J
1997-01-01
During the last several years, significant changes in the risk assessment process for developmental toxicity of environmental contaminants have begun to emerge. The first of these changes is the development and beginning use of statistically based dose-response models [the benchmark dose (BMD) approach] that better utilize data derived from existing testing approaches. Accompanying this change is the greater emphasis placed on understanding and using mechanistic information to yield more accurate, reliable, and less uncertain risk assessments. The next stage in the evolution of risk assessment will be the use of biologically based dose-response (BBDR) models that begin to build into the statistically based models factors related to the underlying kinetic, biochemical, and/or physiologic processes perturbed by a toxicant. Such models are now emerging from several research laboratories. The introduction of quantitative models and the incorporation of biologic information into them has pointed to the need for even more sophisticated modifications for which we offer the term embryologically based dose-response (EBDR) models. Because these models would be based upon the understanding of normal morphogenesis, they represent a quantum leap in our thinking, but their complexity presents daunting challenges both to the developmental biologist and the developmental toxicologist. Implementation of these models will require extensive communication between developmental toxicologists, molecular embryologists, and biomathematicians. The remarkable progress in the understanding of mammalian embryonic development at the molecular level that has occurred over the last decade combined with advances in computing power and computational models should eventually enable these as yet hypothetical models to be brought into use.
Computational thinking and thinking about computing.
Wing, Jeannette M
2008-10-28
Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing.
Computational thinking and thinking about computing
Wing, Jeannette M.
2008-01-01
Computational thinking will influence everyone in every field of endeavour. This vision poses a new educational challenge for our society, especially for our children. In thinking about computing, we need to be attuned to the three drivers of our field: science, technology and society. Accelerating technological advances and monumental societal demands force us to revisit the most basic scientific questions of computing. PMID:18672462
Kasturirangan, Rajesh
2008-01-01
Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.
ERIC Educational Resources Information Center
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
2016-01-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…
Students in Rural Schools Have Limited Access to Advanced Mathematics Courses. Issue Brief No. 7
ERIC Educational Resources Information Center
Graham, Suzanne E.
2009-01-01
This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job…
Zlotnicki, Jason P.; Geeslin, Andrew G.; Murray, Iain R.; Petrigliano, Frank A.; LaPrade, Robert F.; Mann, Barton J.; Musahl, Volker
2016-01-01
Focal chondral defects of the articular surface are a common occurrence in the field of orthopaedics. These isolated cartilage injuries, if not repaired surgically with restoration of articular congruency, may have a high rate of progression to posttraumatic osteoarthritis, resulting in significant morbidity and loss of function in the young, active patient. Both isolated and global joint disease are a difficult entity to treat in the clinical setting given the high amount of stress on weightbearing joints and the limited healing potential of native articular cartilage. Recently, clinical interest has focused on the use of biologically active compounds and surgical techniques to regenerate native cartilage to the articular surface, with the goal of restoring normal joint health and overall function. This article presents a review of the current biologic therapies, as discussed at the 2015 American Orthopaedic Society for Sports Medicine (AOSSM) Biologics Think Tank, that are used in the treatment of focal cartilage deficiencies. For each of these emerging therapies, the theories for application, the present clinical evidence, and specific areas for future research are explored, with focus on the barriers currently faced by clinicians in advancing the success of these therapies in the clinical setting. PMID:27123466
ERIC Educational Resources Information Center
Fuson, Karen C.
2009-01-01
This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…
ERIC Educational Resources Information Center
Alsaeed, Maha Saad
2012-01-01
Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they…
Ambiguity and Paradox in Mathematics
ERIC Educational Resources Information Center
Byers, William
2007-01-01
Many people believe that mathematics provides a model of what thinking is, or should be. They imagine that mathematical thinking always proceeds in a logically rigorous, step-by-step fashion from one truth to another, like a formal proof or a computer program. In fact, insights in mathematics -- whether they are the scholar's breakthroughs or the…
ERIC Educational Resources Information Center
Hillman, Thomas
2014-01-01
This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…
ERIC Educational Resources Information Center
Wood, William B.
2002-01-01
A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
Improving Mathematical Thinking through Assessment
ERIC Educational Resources Information Center
Har, Yeap Ban
2010-01-01
National tests, an influential assessment practice in many countries in East Asia, are often blamed as obstacles to good instructional practices. In this paper, the positive impact of assessment, national tests in particular, is discussed using the case of Singapore. The first part of the paper includes an analysis of items from the primary grade…
ERIC Educational Resources Information Center
Montiel, Mariana; Bhatti, Uzma
2010-01-01
This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…
Clickers and Classroom Voting in a Transition to Advanced Mathematics Course
ERIC Educational Resources Information Center
Lockard, Shannon R.; Metcalf, Rebecca C.
2015-01-01
Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…
Learner-Centered Strategies and Advanced Mathematics: A Study of Students' Perspectives
ERIC Educational Resources Information Center
Ortiz-Robinson, Norma L.; Ellington, Aimee J.
2009-01-01
A number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centered…
ERIC Educational Resources Information Center
Leddy, Mark H.
2010-01-01
Americans with disabilities are underemployed in science, technology, engineering and mathematics (STEM) at higher rates than their nondisabled peers. This article provides an overview of the National science Foundation's Research in Disabilities Education (RDE) program, of technology use by students with disabilities (SWD) in STEM, and of…
NASA Astrophysics Data System (ADS)
Perdigão, Rui A. P.
2016-04-01
The fundamental stochastic-dynamic coevolution laws governing complex coevolutionary systems are introduced in a mathematical physics framework formally unifying nonlinear stochastic physics with fundamental deterministic interaction laws among spatiotemporally distributed processes. The methodological developments are then used to shed light onto fundamental interactions underlying complex spatiotemporal behaviour and emergence in multiscale hydroclimate dynamics. For this purpose, a mathematical physics framework is presented predicting evolving distributions of hydrologic quantities under nonlinearly coevolving geophysical processes. The functional formulation is grounded on first principles regulating the dynamics of each system constituent and their interactions, therefore its applicability is general and data-independent, not requiring local calibrations. Moreover, it enables the dynamical estimation of hydroclimatic variations in space and time from knowledge at different spatiotemporal conditions, along with the associated uncertainties. This paves the way for a robust physically based prediction of hydroclimatic changes in unsupervised areas (e.g. ungauged basins). Validation is achieved by producing, with the mathematical physics framework, a comprehensive spatiotemporal legacy consistent with the observed distributions along with their statistic-dynamic relations. The similarity between simulated and observed distributions is further assessed with novel robust nonlinear information-theoretic diagnostics. The present study brings to light emerging signatures of structural change in hydroclimate dynamics arising from nonlinear synergies across multiple spatiotemporal scales, and contributes to a better dynamical understanding and prediction of spatiotemporal regimes, transitions, structural changes and extremes in complex coevolutionary systems. This study further sheds light onto a diversity of emerging properties from harmonic to hyper-chaotic in general
ERIC Educational Resources Information Center
Dickerson, David S.; Doerr, Helen M.
2014-01-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were…
ERIC Educational Resources Information Center
Rasmussen, Ann Marie
2011-01-01
This article describes an undergraduate, German-language course that aimed to improve students' language skills, critical thinking, and declarative knowledge of German history and culture by studying multiple manifestations of the legend of Siegfried the Dragonslayer. The course used web-based e-learning tools to address two major learning…
Geometrical Analogies in Mathematics Lessons
ERIC Educational Resources Information Center
Eid, Wolfram
2007-01-01
A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…
ERIC Educational Resources Information Center
Jitendra, Asha K.; Dupuis, Danielle N.; Star, Jon R.; Rodriguez, Michael C.
2016-01-01
This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment…
ERIC Educational Resources Information Center
Fonkert, Karen L.
2012-01-01
This study analyzes the nature of student interaction and discourse in an environment that includes the use of Java-based, curriculum-embedded mathematical software. The software "CPMP-Tools" was designed as part of the development of the second edition of the "Core-Plus Mathematics" curriculum. The use of the software on…
ERIC Educational Resources Information Center
Gough, Deborah
1991-01-01
This document summarizes five studies that offer insight into the nature of higher-order thinking skills and the most effective methods for teaching them to students. The reviews outline the conclusions, definitions, recommendations, specific methods of teaching, instructional strategies, and programs detailed in the documents themselves.…
NASA Astrophysics Data System (ADS)
Campbell, D. Michael
The lack of preparation, participation, and equal access of students in mathematics and the science education continues to afflict America's high school system (Ratliff, 2001). Additionally, gender and ethnic status have become significant factors as females and minority subgroups such as African Americans and Hispanics continue to be underrepresented in these two subject fields. Recognizing and understanding these trends is extremely important for the future of this country. As fewer minorities and females become involved in advanced mathematics and science curriculum there will be a continued lack of minorities and females in mathematics and science careers. Additionally, this insufficient representation leads to fewer numbers of females and minorities in industry and educational leadership positions in mathematics and science to promote participation and equality in these fields. According to Brainard and Carlin (2003) as trends currently stand, these two groups will be under-represented in the fields of math and science and will continue to be denied economic and social power. Thus, a better understanding of these trends in participation in mathematics and science among these groups of students is warranted. This study is intended to accomplish four objectives. The first objective is to identify the extent to which opportunities are increasing or decreasing for students in high schools taking mathematics and science Advanced Placement exams by examining six years of student testing data from the College Board. A second objective is to identify features of high schools that relate to greater expansion in Advanced Placement test taking for females and minority groups in the areas of both math and science. A third objective is to explore whether, and to what extent, any social or educational features such as economic status, regional school and living locations, and ethnic backgrounds have enhanced or reduced Advanced Placement testing in these schools. Lastly
ERIC Educational Resources Information Center
Ruthven, Kenneth
2014-01-01
Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…
Thinking Critically about Critical Thinking
ERIC Educational Resources Information Center
Mulnix, Jennifer Wilson
2012-01-01
As a philosophy professor, one of my central goals is to teach students to think critically. However, one difficulty with determining whether critical thinking can be taught, or even measured, is that there is widespread disagreement over what critical thinking actually is. Here, I reflect on several conceptions of critical thinking, subjecting…
How can mathematical models advance tuberculosis control in high HIV prevalence settings?
Houben, R M G J; Dowdy, D W; Vassall, A; Cohen, T; Nicol, M P; Granich, R M; Shea, J E; Eckhoff, P; Dye, C; Kimerling, M E; White, R G
2014-05-01
Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly. PMID:24903784
Mathematical Lens: Iron Gate, Metulla, Israel
ERIC Educational Resources Information Center
Mathematics Teacher, 2005
2005-01-01
The "Mathematical Lens" feature of "Mathematics Teacher," uses photographs as a springboard for mathematical inquiry. The goal of this feature is to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. In this edition of "Mathematical Lens," students analyze the shapes in an iron…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
ERIC Educational Resources Information Center
Ayers, Don; And Others
This study conducted a statistical analysis to look at the participation and achievement of Black, Hispanic, and female secondary education students in mathematics, science, and advanced technology programs in schools in Virginia, compared to those of White students and male students. In particular, the study applied descriptive and inferential…
Dr. Edward de Bono's Six Thinking Hats and Numeracy
ERIC Educational Resources Information Center
Paterson, Anne
2006-01-01
In education, the term "metacognition" describes thinking about thinking. Within mathematics, the term "metacomputation" describes thinking about computational methods and tools. This article shows how Dr. Edward de Bono's Six Thinking Hats can be used to demonstrate metacognition and metacomputation in the primary classroom. The article suggests…
Mathematics in the Early Years.
ERIC Educational Resources Information Center
Copley, Juanita V., Ed.
Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…
ERIC Educational Resources Information Center
Colwell, Dhamma
This paper describes a case study in which one woman in a focus group of 11 women recounted her use of numerical and mathematical tools in her personal and work life. According to the researcher, the subject's experiences engendered strong feelings and revealed that aspects of her self-identity were bound up with her use of tools and feelings…
ERIC Educational Resources Information Center
Marks, Rachel
2013-01-01
The use of structured ability grouping is increasing in English primary schools and is regularly seen in primary mathematics classrooms. Ability is a normalised discourse with beliefs that some individuals are "born to do maths" permeating society and infiltrating school practices. In this article, observation and interview data…
NASA Astrophysics Data System (ADS)
Grogg, Jennifer K. Drake
This proposal examines the relationships between self-efficacy and persistence of students enrolled in science, computer science (as a technology-based program of study), and mathematics programs (STM) in a Midwestern university. It also examines gender differences between persisters and non-persisters as to self-efficacy levels, academic performance, attrition/persistence, and contributing factors related to self-efficacy. A review of related research was found to be somewhat contradictory and inadequate in examining the relationship between academic self-efficacy and student persistence in college STM programs.
Thinking Is Literacy, Literacy Thinking
ERIC Educational Resources Information Center
Roberts, Terry; Billings, Laura
2008-01-01
Recognizing the profound relationship between thinking and language, the authors have developed the traditional Paideia seminar into a literacy cycle of instruction that involves students in reading, speaking, listening, writing, and thinking. As staff members of the National Paideia Center, they have observed that learning to think requires…
Critically Thinking about Critical Thinking
ERIC Educational Resources Information Center
Weissberg, Robert
2013-01-01
In this article, the author states that "critical thinking" has mesmerized academics across the political spectrum and that even high school students are now being called upon to "think critically." He furthers adds that it is no exaggeration to say that "critical thinking" has quickly evolved into a scholarly…
ERIC Educational Resources Information Center
Dori, Yehudit Judy; Dangur, Vered; Avargil, Shirly; Peskin, Uri
2014-01-01
Chemistry students in Israel have two options for studying chemistry: basic or honors (advanced placement). For instruction in high school honors chemistry courses, we developed a module focusing on abstract topics in quantum mechanics: Chemistry--From the Nanoscale to Microelectronics. The module adopts a visual-conceptual approach, which…
ERIC Educational Resources Information Center
Lewis, Richard
2008-01-01
For their course, mathematics students at Bath Spa University were asked to choose a topic and explore the mathematics. As well as learning some mathematics, the author hoped that the assignment would shed light on the process of mathematical investigation itself. Their course leader had suggested that the topic of conic sections was rich, and…
Jitendra, Asha K; Dupuis, Danielle N; Star, Jon R; Rodriguez, Michael C
2016-07-01
This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students' difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students' performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas.
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
Horsley, Helen L; Shepherd, Kate; Brown, Heather; Carey, Irene; Matthews, Beverley; O’Donoghue, Donal; Vinen, Katie; Murtagh, Felicity EM
2015-01-01
Background: There is a need to improve end-of-life care for people with end-stage kidney disease, particularly due to the increasingly elderly, frail and co-morbid end-stage kidney disease population. Timely, sensitive and individualised Advance Care Planning discussions are acceptable and beneficial for people with end-stage kidney disease and can help foster realistic hopes and goals. Aim: To explore the experiences of people with end-stage kidney disease regarding starting haemodialysis, its impact on quality of life and their preferences for future care and to explore the Advance Care Planning needs of this population and the timing of this support. Study design: Semi-structured qualitative interview study of people receiving haemodialysis. Interviews were analysed using thematic analysis. Recruitment ceased once data saturation was achieved. Setting/participants: A total of 20 patients at two UK National Health Service hospitals, purposively sampled by age, time on haemodialysis and symptom burden. Results: Themes emerged around: Looking Back, emotions of commencing haemodialysis; Current Experiences, illness and treatment burdens; and Looking Ahead, facing the realities. Challenges throughout the trajectory included getting information, communicating with staff and the ‘conveyor belt’ culture of haemodialysis units. Participants reported a lack of opportunity to discuss their future, particularly if their health deteriorated, and variable involvement in treatment decisions. However, discussion of these sensitive issues was more acceptable to some than others. Conclusion: Renal patients have considerable unmet Advance Care Planning needs. There is a need to normalise discussions about preferences and priorities in renal and haemodialysis units earlier in the disease trajectory. However, an individualised approach is essential – one size does not fit all. PMID:25527527
ERIC Educational Resources Information Center
Shores, Melanie L.; Shannon, David M.; Smith, Tommy G.
2010-01-01
A total of 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were examined to investigate the relationships between individual learner variables (gender, ethnicity, socioeconomic status [SES]) and mathematics performance. Specifically, this portion of the study examined individual learner variables…
2014-01-01
make sense of policy intentions and incorporate them into their everyday routines and practices. This requires a leadership of sensemaking that enables front line staff to exercise their collective discretionary power in strengthening PHC. We hope this theoretically-framed analysis of one set of experiences stimulates wider thinking about the leadership needed to sustain primary health care in other settings. PMID:24935658
Murray, Iain R.; LaPrade, Robert F.; Musahl, Volker; Geeslin, Andrew G.; Zlotnicki, Jason P.; Mann, Barton J.; Petrigliano, Frank A.
2016-01-01
Rotator cuff tears are common and result in considerable morbidity. Tears within the tendon substance or at its insertion into the humeral head represent a considerable clinical challenge because of the hostile local environment that precludes healing. Tears often progress without intervention, and current surgical treatments are inadequate. Although surgical implants, instrumentation, and techniques have improved, healing rates have not improved, and a high failure rate remains for large and massive rotator cuff tears. The use of biologic adjuvants that contribute to a regenerative microenvironment have great potential for improving healing rates and function after surgery. This article presents a review of current and emerging biologic approaches to augment rotator cuff tendon and muscle regeneration focusing on the scientific rationale, preclinical, and clinical evidence for efficacy, areas for future research, and current barriers to advancement and implementation. PMID:27099865
ERIC Educational Resources Information Center
Suhor, Charles
One of a series dealing with current issues affecting language arts instruction, this paper focuses on thinking skills. The paper begins by raising two issues: whether thinking skills should be taught as part of each subject area, as a separate skill, or both, and whether English and language arts teachers have a special role in the teaching of…
Wood, William B
2002-01-01
A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors.
Computational Thinking Concepts for Grade School
ERIC Educational Resources Information Center
Sanford, John F.; Naidu, Jaideep T.
2016-01-01
Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding "computational thinking" as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of…
ERIC Educational Resources Information Center
Brown, Kenneth E.; Johnson, Philip G.
1953-01-01
The Cooperative Committee on the Teaching of Science and Mathematics of the American Association for the Advancement of Science that participated in planning for and publishing this bulletin is composed of representatives of seventeen national scientific and mathematical societies including representatives from the associated teaching…
ERIC Educational Resources Information Center
Jackson, Philip W.
2012-01-01
Background: The intellectual context of this essay is the nature of human thought as examined by philosophers and psychologists past and present. Focus of study: The study focuses on the treatment of thinking by John Dewey in his two editions of "How We Think" and by William James in his "Talks to Teachers". Research Design: This is a…
The Only Absolute Truth in Mathematics is the Myth of Mathematics as Universal
ERIC Educational Resources Information Center
Kantner, M. Joanne
2008-01-01
Culture and national origin can affect thinking about mathematics and mathematics learning. The myth that mathematics is objective and culture free becomes a barrier to adults learning mathematics. Adult educators must reflect upon culture's influence on learning and recognize the implications of universality myths on students' learning in…
Visual Thinking and Gender Differences in High School Calculus
ERIC Educational Resources Information Center
Haciomeroglu, Erhan Selcuk; Chicken, Eric
2012-01-01
This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…
Multiplicative Thinking: Much More than Knowing Multiplication Facts and Procedures
ERIC Educational Resources Information Center
Hurst, Chris; Hurrell, Derek
2016-01-01
Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…
Fostering Instructor Knowledge of Student Thinking Using the Flipped Classroom
ERIC Educational Resources Information Center
Strayer, Jeremy F.; Hart, James B.; Bleiler, Sarah K.
2015-01-01
In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Generalizing: The Core of Algebraic Thinking
ERIC Educational Resources Information Center
Kinach, Barbara M.
2014-01-01
Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…
Two Meanings of Algorithmic Mathematics.
ERIC Educational Resources Information Center
Maurer, Stephen B.
1984-01-01
Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…
ABCs of Early Mathematics Experiences
ERIC Educational Resources Information Center
Hensen, Laurie E.
2005-01-01
Children begin to develop mathematical thinking before they enter school. Art, baking, playing with blocks, counting numbers, games, puzzles, singing, playing with pretend money, water play all these early mathematical experiences help the children to learn in the elementary school years.
ERIC Educational Resources Information Center
Whitin, Phyllis; Whitin, David J.
2011-01-01
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
Celebrate Mathematical Curiosity
ERIC Educational Resources Information Center
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…
ERIC Educational Resources Information Center
Gavin, M. Katherine; Casa, Tutita M.; Firmender, Janine M.; Carroll, Susan R.
2013-01-01
The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of…
ERIC Educational Resources Information Center
Rumsey, Chepina Witkowski
2012-01-01
The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Polak, E.; Zadeh, L. A.
1974-01-01
A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.
Cultivating strategic thinking skills.
Shirey, Maria R
2012-06-01
This department highlights change management strategies that may be successful in strategically planning and executing organizational change initiatives. With the goal of presenting practical approaches helpful to nurse leaders advancing organizational change, content includes evidence-based projects, tools, and resources that mobilize and sustain organizational change initiatives. In this article, the author presents an overview of strategic leadership and offers approaches for cultivating strategic thinking skills.
Hunt, Tam
2014-01-01
Evolution as an idea has a lengthy history, even though the idea of evolution is generally associated with Darwin today. Rebecca Stott provides an engaging and thoughtful overview of this history of evolutionary thinking in her 2013 book, Darwin's Ghosts: The Secret History of Evolution. Since Darwin, the debate over evolution—both how it takes place and, in a long war of words with religiously-oriented thinkers, whether it takes place—has been sustained and heated. A growing share of this debate is now devoted to examining how evolutionary thinking affects areas outside of biology. How do our lives change when we recognize that all is in flux? What can we learn about life more generally if we study change instead of stasis? Carter Phipps’ book, Evolutionaries: Unlocking the Spiritual and Cultural Potential of Science's Greatest Idea, delves deep into this relatively new development. Phipps generally takes as a given the validity of the Modern Synthesis of evolutionary biology. His story takes us into, as the subtitle suggests, the spiritual and cultural implications of evolutionary thinking. Can religion and evolution be reconciled? Can evolutionary thinking lead to a new type of spirituality? Is our culture already being changed in ways that we don't realize by evolutionary thinking? These are all important questions and Phipps book is a great introduction to this discussion. Phipps is an author, journalist, and contributor to the emerging “integral” or “evolutionary” cultural movement that combines the insights of Integral Philosophy, evolutionary science, developmental psychology, and the social sciences. He has served as the Executive Editor of EnlightenNext magazine (no longer published) and more recently is the co-founder of the Institute for Cultural Evolution, a public policy think tank addressing the cultural roots of America's political challenges. What follows is an email interview with Phipps. PMID:26478766
A Taxonomy of Software for Mathematics Instruction
ERIC Educational Resources Information Center
Kurz, Terri L.; Middleton, James A.; Yanik, H. Bahadir
2005-01-01
The potential to use mathematics software to enhance student thinking and development is discussed and a taxonomy of software categories is outlined in this paper. Briefly, there are five categories of tool-based mathematics software that can be used fruitfully in a mathematics curriculum: (a) review and practice, (b) general, (c) specific, (d)…
ERIC Educational Resources Information Center
Niedermeyer, Fred; Ice, Kay
1992-01-01
Describes a series of environmental education instructional units for grades K-6 developed by the Think Earth Consortium that cover topics such as conservation, pollution control, and waste reduction. Provides testimony from one sixth-grade teacher that field tested the second-grade unit. (MDH)
Serb, Chris
2008-08-01
Hospitals typically don't come to mind when you think about cutting-edge environmental programs, but that's changing. Rising energy costs, the need to replace older facilities, and a growing environmental consciousness have spurred hospitals nationwide to embrace a green ideology. The executive suite is a vocal and active player in these efforts. PMID:19062433
NASA Astrophysics Data System (ADS)
Collins, Harry
2008-02-01
Physicists are often quick to discount social research based on qualitative techniques such as ethnography and "deep case studies" - where a researcher draws conclusions about a community based on immersion in the field - thinking that only quantitative research backed up by statistical analysis is sound. The balance is not so clear, however.
ERIC Educational Resources Information Center
Arnheim, Rudolf
Based on the more general principle that all thinking (including reasoning) is basically perceptual in nature, the author proposes that visual perception is not a passive recording of stimulus material but an active concern of the mind. He delineates the task of visually distinguishing changes in size, shape, and position and points out the…
Serb, Chris
2008-08-01
Hospitals typically don't come to mind when you think about cutting-edge environmental programs, but that's changing. Rising energy costs, the need to replace older facilities, and a growing environmental consciousness have spurred hospitals nationwide to embrace a green ideology. The executive suite is a vocal and active player in these efforts.
Mathematical Modeling in the Undergraduate Curriculum
ERIC Educational Resources Information Center
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
The Fostering Algebraic Thinking Toolkit: A Guide for Staff Development.
ERIC Educational Resources Information Center
Driscoll, Mark; Zawojeski, Judith; Humez, Andrea; Nikula, Johannah; Goldsmith, Lynn; Hammerman, James
This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials…
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. PMID:24620862
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics.
Young Children's Mathematics References during Free Play in Family Childcare Settings
ERIC Educational Resources Information Center
Hendershot, Shawnee M.; Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie
2016-01-01
Very little is known about children's discussion of mathematics topics during unstructured play. Ginsburg, Lin, Ness, and Seo [2003. Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235-258. Retrieved from…
NASA Astrophysics Data System (ADS)
Dickerson, David S.; Doerr, Helen M.
2014-12-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.
NASA Astrophysics Data System (ADS)
Meulien-Ohlmann, Odile
2000-10-01
Holographic thinking is everywhere although we do not realize it. Turn on your TV and you will see many representations of holographic images. It is in many science fiction movies, as well as in books and the news. Now, start your computer and search the Web. What do you see, a screen with plenty of little boxes or frames, each one containing information. You can choose to go deeper by clicking here and there, but ultimately all the little boxes are related to each other. What do you have? A holographic principle where each point stands by itself, containing the whole entity while composing part of it at the same time. The following paragraphs, discussing and evaluating the characteristics of holographic thinking can be read in any order you wish. Each paragraph contributes an understanding of just one aspect of all the ideas which cannot be limited to this paper alone.
Stimulating Mathematical Thinking through Domino Games
ERIC Educational Resources Information Center
Gough, John
2015-01-01
Most readers would be familiar with the standard domino set which is played with rectangular domino tiles. The domino set, sometimes called a deck or pack, consists of 28 dominoes, colloquially nicknamed bones, cards, tiles, stones, or spinners. A domino set is a generic gaming device, similar to playing cards or dice, in that a variety of games…
Fractals Illustrate the Mathematical Way of Thinking.
ERIC Educational Resources Information Center
Nievergelt, Yves
1991-01-01
Presented are exercises that demonstrate the application of standard concepts in the design of algorithms for plotting certain fractals. The exercises can be used in any course that explains the concepts of bounded or unbounded planar sets and may serve as an application in a course on complex analysis. (KR)
Hot Ideas. A Mathematical Response to a Piece of Text
ERIC Educational Resources Information Center
Grey, Melinda
2005-01-01
Children's literature can enhance mathematics lessons by providing a meaningful context, demonstrating that mathematics develops from human experiences and contributes an aesthetic dimension to learning mathematics. Written as a series of real life inspired snapshots of mathematical thinking, "Counting on Frank" (Rod Clement, 1990) provides a…
The Mathematical Education of Teachers. Issues in Mathematics Education. Volume 11 [and] Part I.
ERIC Educational Resources Information Center
Conference Board of the Mathematical Sciences, Washington, DC.
This report is designed to be a resource for mathematics faculty and other parties involved in the education of mathematics teachers. It provides a distillation of current thinking on curriculum and policy issues affecting the mathematical education of teachers with the goal of stimulating efforts on individual campuses to improve programs for…
ERIC Educational Resources Information Center
Reeve, Edward M.
2015-01-01
Science, Technology, Engineering, and Mathematics (STEM) is a term seen almost daily in the news. In 2009, President Obama launched the Educate to Innovate initiative to move American students from the middle to the top of the pack in science and math achievement over the next decade (The White House, n.d.). Learning about the attributes of STEM…
Lee, Stephen R
2010-01-01
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled mUlti-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CP AM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections): (1) Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the laboratory; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial differential equations
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
ERIC Educational Resources Information Center
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
How Problem Solving Can Develop an Algebraic Perspective of Mathematics
ERIC Educational Resources Information Center
Windsor, Will
2011-01-01
SProblem solving has a long and successful history in mathematics education and is valued by many teachers as a way to engage and facilitate learning within their classrooms. The potential benefit for using problem solving in the development of algebraic thinking is that "it may broaden and develop students' mathematical thinking beyond the…
Critical Thinking in Adulthood.
ERIC Educational Resources Information Center
Fulton, Rodney D.
Critical thinking is often defined as that which a particular instrument measures. The most prominent tests are the Watson-Glaser Critical Thinking Appraisal, the Ennis-Weir Critical Thinking Essay Test, and the Cornell Critical Thinking Tests. Watson and Glaser's (1980) view of critical thinking is "a composite of attitudes, knowledge, and…
Fuzzy Thinking in Non-Fuzzy Situations: Understanding Students' Perspective.
ERIC Educational Resources Information Center
Zazkis, Rina
1995-01-01
In mathematics a true statement is always true, but some false statements are more false than others. Fuzzy logic provides a way of handling degrees of set membership and has implications for helping students appreciate logical thinking. (MKR)
2014-01-01
Background Although there is widespread agreement that strong district manager decision-making improves health systems, understanding about how the design and implementation of capacity-strengthening interventions work is limited. The Ghana Health Service has adopted the Leadership Development Programme (LDP) as one intervention to support the development of management and leadership within district teams. This paper seeks to address how and why the LDP ‘works’ when it is introduced into a district health system in Ghana, and whether or not it supports systems thinking in district teams. Methods We undertook a realist evaluation to investigate the outcomes, contexts, and mechanisms of the intervention. Building on two working hypotheses developed from our earlier work, we developed an explanatory case study of one rural district in the Greater Accra Region of Ghana. Data collection included participant observation, document review, and semi-structured interviews with district managers prior to, during, and after the intervention. Working backwards from an in-depth analysis of the context and observed short- and medium-term outcomes, we drew a causal loop diagram to explain interactions between contexts, outcomes, and mechanisms. Results The LDP was a valuable experience for district managers and teams were able to attain short-term outcomes because the novel approach supported teamwork, initiative-building, and improved prioritisation. However, the LDP was not institutionalised in district teams and did not lead to increased systems thinking. This was related to the context of high uncertainty within the district, and hierarchical authority of the system, which triggered the LDP’s underlying goal of organisational control. Conclusions Consideration of organisational context is important when trying to sustain complex interventions, as it seems to influence the gap between short- and medium-term outcomes. More explicit focus on systems thinking principles that
Critical Thinking in Chemistry Using Symbolic Math Documents
ERIC Educational Resources Information Center
Journal of Chemical Education, 2004
2004-01-01
Teaching environments are provided by symbolic mathematics templates to promote development of HOCS (Higher Orders Cognitive Skills). The way of looking LOCS and HOCS is to distinguish them by recognizing that the LOCS corresponds to complex correct thinking and the HOCS form the essence of full critical thinking.
Learning with Touchscreen Devices: Game Strategies to Improve Geometric Thinking
ERIC Educational Resources Information Center
Soldano, Carlotta; Arzarello, Ferdinando
2016-01-01
The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The…
Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process
ERIC Educational Resources Information Center
Bal, Aytgen Pinar; Doganay, Ahmet
2014-01-01
The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…
ERIC Educational Resources Information Center
Jao, Limin
2012-01-01
The National Council of Teachers of Mathematics (NCTM, 2000) has created a set of standards to reform mathematics teaching procedures to ensure that all students understand mathematics and learn to think mathematically. The standards also require teachers to use strategies that allow all students to reason and communicate mathematically and…
Driven by History: Mathematics Education Reform
ERIC Educational Resources Information Center
Permuth, Steve; Dalzell, Nicole
2013-01-01
The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…
Making Mathematics Relevant for Students in Bali
ERIC Educational Resources Information Center
Sema, Pryde Nubea
2008-01-01
The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…
Self and Peer Assessment of Mathematical Processes
ERIC Educational Resources Information Center
Onion, Alice; Javaheri, Elnaz
2011-01-01
This article explores using Bowland assessment tasks and Nuffield Applying Mathematical Processes (AMP) activities as part of a scheme of work. The Bowland tasks and Nuffield AMP activities are designed to develop students' mathematical thinking; they are focused on key processes. Unfamiliar demands are made on the students and they are challenged…
Developing the Young Gifted Child's Mathematical Mind
ERIC Educational Resources Information Center
Fisher, Carol
2016-01-01
Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…
Mathematical Lens: Roller Coasters and Railways
ERIC Educational Resources Information Center
Daire, Sandra Arguelles
2009-01-01
This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…
Mathematics Teacher TPACK Standards and Development Model
ERIC Educational Resources Information Center
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Discussion from a Mathematics Education Perspective
ERIC Educational Resources Information Center
Clements, Douglas; Sarama, Julie
2015-01-01
In a review of the special issue, we conclude that the articles are research gems in the domain of preschool mathematics education. Most share several features, such as their perspective on research methodology and their view of mathematics thinking and learning. They address the cognitive architecture and processes and the developmental levels…
Algebraic Thinking through Koch Snowflake Constructions
ERIC Educational Resources Information Center
Ghosh, Jonaki B.
2016-01-01
Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…
Developing Multiplicative Thinking from Additive Reasoning
ERIC Educational Resources Information Center
Tobias, Jennifer M.; Andreasen, Janet B.
2013-01-01
As students progress through elementary school, they encounter mathematics concepts that shift from additive to multiplicative situations (NCTM 2000). When they encounter fraction problems that require multiplicative thinking, they tend to incorrectly extend additive properties from whole numbers (Post et al. 1985). As a result, topics such as …
Gesture Supports Spatial Thinking in STEM
ERIC Educational Resources Information Center
Stieff, Mike; Lira, Matthew E.; Scopelitis, Stephanie A.
2016-01-01
The present article describes two studies that examine the impact of teaching students to use gesture to support spatial thinking in the Science, Technology, Engineering, and Mathematics (STEM) discipline of chemistry. In Study 1 we compared the effectiveness of instruction that involved either watching gesture, reproducing gesture, or reading…
Improvisation in the Mathematics Classroom
ERIC Educational Resources Information Center
Young, Andrea
2013-01-01
This article discusses ways in which improvisational comedy games and exercises can be used in college mathematics classrooms to obtain a democratic and supportive environment for students. Using improv can help students learn to think creatively, take risks, support classmates, and solve problems. Both theoretical and practical applications are…
Governing Equality: Mathematics for All?
ERIC Educational Resources Information Center
Diaz, Jennifer D.
2013-01-01
With the notion of governmentality, this article considers how the equal sign (=) in the U.S. math curriculum organizes knowledge of equality and inscribes cultural rules for thinking, acting, and seeing in the world. Situating the discussion within contemporary math reforms aimed at teaching mathematics for all, I draw attention to how the…
ERIC Educational Resources Information Center
Herman, Dan
1999-01-01
Explains how advances in diesel and alternative fuels has caused schools to reconsider their use for their bus fleets. Reductions in air pollution emissions, cost-savings developments, and the economies experienced from less downtime and maintenance requirements are explored. (GR)
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
The Process of Thinking among Junior High School Students in Solving HOTS Question
ERIC Educational Resources Information Center
Bakry, Md Nor Bin Bakar
2015-01-01
Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…
ERIC Educational Resources Information Center
Castro Superfine, Alison; Li, Wenjuan; Bragelman, John; Fisher, Amanda
2015-01-01
Noticing children's mathematical thinking is an important aspect of what teachers need to know. This study explores the role of videocases in supporting preservice elementary teachers' noticing of children's mathematical thinking. Findings from a quasi-experimental study of preservice teachers' engagement with videocases indicate no significant…
Symbols and the Bifurcation between Procedural and Conceptual Thinking.
ERIC Educational Resources Information Center
Tall, David; Gray, Eddie; Bin Ali, Maselan; Crowley, Lillie; DeMarois, Phil; McGowen, Mercedes; Pitta, Demetra; Pinto, Marcia; Thomas, Michael; Yusof, Yudariah
Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…
Brown, Tim
2008-06-01
In the past, design has most often occurred fairly far downstream in the development process and has focused on making new products aesthetically attractive or enhancing brand perception through smart, evocative advertising. Today, as innovation's terrain expands to encompass human-centered processes and services as well as products, companies are asking designers to create ideas rather than to simply dress them up. Brown, the CEO and president of the innovation and design firm IDEO, is a leading proponent of design thinking--a method of meeting people's needs and desires in a technologically feasible and strategically viable way. In this article he offers several intriguing examples of the discipline at work. One involves a collaboration between frontline employees from health care provider Kaiser Permanente and Brown's firm to reengineer nursing-staff shift changes at four Kaiser hospitals. Close observation of actual shift changes, combined with brainstorming and rapid prototyping, produced new procedures and software that radically streamlined information exchange between shifts. The result was more time for nursing, better-informed patient care, and a happier nursing staff. Another involves the Japanese bicycle components manufacturer Shimano, which worked with IDEO to learn why 90% of American adults don't ride bikes. The interdisciplinary project team discovered that intimidating retail experiences, the complexity and cost of sophisticated bikes, and the danger of cycling on heavily trafficked roads had overshadowed people's happy memories of childhood biking. So the team created a brand concept--"Coasting"--to describe a whole new category of biking and developed new in-store retailing strategies, a public relations campaign to identify safe places to cycle, and a reference design to inspire designers at the companies that went on to manufacture Coasting bikes. PMID:18605031
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
Provocative Mathematics Questions: Drawing Attention to a Lack of Attention
ERIC Educational Resources Information Center
Klymchuk, Sergiy
2015-01-01
The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…
Marina's Fish Shop: A Mathematically- and Technologically-Rich Lesson
ERIC Educational Resources Information Center
Wander, Roger; Pierce, Robyn
2009-01-01
In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think mathematically.…
Intentional Experiences: Teaching|Learning Mathematics with Young Children
ERIC Educational Resources Information Center
McGarvey, Lynn M.
2010-01-01
A recent emphasis on mathematics learning in the preschool years has sparked a flurry of research in children's thinking; yet, the same attention has not been paid to teaching mathematics in preschools. This paper examines the reciprocal relationship of teaching|learning mathematics with young children and attempts to move discussions beyond…
Community and Place in Mathematics Instruction in Selected Rural Schools
ERIC Educational Resources Information Center
Howley, Aimee; Clonch, Sandra; Howley, Craig; Perko, Heike; Klein, Robert; Foley, Greg; Belcher, Johnny; Pendarvis, Edwina; Howley, Marged; Miyafusa, Sumiko; Tusay, Mark; Jimerson, Lorna
2010-01-01
The teaching of mathematics, which arguably is so abstract as to transcend place and community and even culture (according at least to a Platonic view of mathematics), will seem to some observers particularly ill-suited to instruction in place- or community- or culture-based approaches. Nevertheless, current thinking in mathematics education,…
The Effects of an Educational Video Game on Mathematical Engagement
ERIC Educational Resources Information Center
Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Deater-Deckard, Kirby; Samur, Yavuz
2016-01-01
In an effort to maximizing success in mathematics, our research team implemented an educational video game in fifth grade mathematics classrooms in five schools in the Eastern US. The educational game was developed by our multi-disciplinary research team to achieve a hypothetical learning trajectory of mathematical thinking of 5th grade students.…
A Guide to Teaching Mathematics in the Primary Grades.
ERIC Educational Resources Information Center
Baroody, Arthur J.
This book was written as a tool to help teachers of prekindergarten to grade 3 make use of recent developments in the cognitive psychology of mathematical learning. Chapters included are: (1) "The Nature of Children's Mathematical Thinking"; (2) "Designing Effective Mathematics Instruction"; (3) "Oral Counting"; (4) "Numbering"; (5) "Numerical…
Investigations in Mathematics Education. Volume 17, Number 3.
ERIC Educational Resources Information Center
Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.
1984-01-01
This issue of "Investigations in Mathematics Education" contains: (1) a review of E. Fischbein's book "The Intuitive Sources of Probabilistic Thinking in Children;" (2) nine abstracts of research studies in mathematics education; (3) a list (by EJ number) of mathematics education research studies reported in the January to March 1984 issues of…
Constructing Meanings of Mathematical Registers Using Metaphorical Reasoning and Models
ERIC Educational Resources Information Center
Lai, Mun Yee
2013-01-01
Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…
Multiple Representations as Sites for Teacher Reflection about Mathematics Learning
ERIC Educational Resources Information Center
Ryken, Amy E.
2009-01-01
This documentary account situates teacher educator, prospective teacher, and elementary students' mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill--creating and analyzing representations. The author examines responses of prospective…
Teacher Actions to Maximize Mathematics Learning Opportunities in Heterogeneous Classrooms
ERIC Educational Resources Information Center
Sullivan, Peter; Mousley, Judith; Zevenbergen, Robyn
2006-01-01
The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and…
Investigating Mathematics through Digital Media: Cognitive Visual Perturbations
ERIC Educational Resources Information Center
Calder, Nigel
2011-01-01
How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425
ERIC Educational Resources Information Center
National Council on Disability, Washington, DC.
This paper summarizes a May 2000 conference about advancing the civil and human rights of people with disabilities from diverse cultures. The conference included people with disabilities from diverse cultures and members of national civil rights organizations. The conference identified five priority areas for attention: (1) cultivating leadership…
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships.
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. PMID:26263071
TIMSS Advanced 2008 Assessment Frameworks
ERIC Educational Resources Information Center
Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka
2006-01-01
Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
Mathematics anxiety and mathematics achievement
NASA Astrophysics Data System (ADS)
Sherman, Brian F.; Wither (Post.), David P.
2003-09-01
This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.
Improved Appreciation of Mathematics through an IBL Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Blyth, Russell D.
2015-01-01
The author has taught an inquiry-based liberal arts mathematics class using the text "The Heart of Mathematics: An Invitation to Effective Thinking" by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with…
Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis
ERIC Educational Resources Information Center
Hamburg, Maryanna P.
2009-01-01
This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…
Mathematical E-Learning Using Interactive Mathematics on the Web.
ERIC Educational Resources Information Center
Bringslid, Odd
2002-01-01
Explains the use of the Web as an advanced calculator using numeric, graphic, and symbolic mathematics interactively with the development of XML-standard MathML. Suggests that the problem of decreasing achievement in mathematics courses can be solved using interactive and personalized documents on the Web and improve the understanding of…
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Audiovisual Materials in Mathematics.
ERIC Educational Resources Information Center
Raab, Joseph A.
This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…
New Technologies in Mathematics.
ERIC Educational Resources Information Center
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Visual Thinking Strategies = Creative and Critical Thinking
ERIC Educational Resources Information Center
Moeller, Mary; Cutler, Kay; Fiedler, Dave; Weier, Lisa
2013-01-01
Implementation of Visual Thinking Strategies (VTS) into the Camelot Intermediate School curriculum in Brookings, South Dakota, has fostered the development of creative and critical thinking skills in 4th- and 5th-grade students. Making meaning together by observing carefully, deciphering patterns, speculating, clarifying, supporting opinions, and…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Foundations for Critical Thinking
ERIC Educational Resources Information Center
Bers, Trudy; Chun, Marc; Daly, William T.; Harrington, Christine; Tobolowsky, Barbara F.
2015-01-01
"Foundations for Critical Thinking" explores the landscape of critical-thinking skill development and pedagogy through foundational chapters and institutional case studies involving a range of students in diverse settings. By establishing a link between active learning and improved critical thinking, this resource encourages all higher…
ERIC Educational Resources Information Center
de Bono, Edward
1986-01-01
Suggests our society strongly needs thinking that is constructive, generative, and organizing; describes an educational program, CoRT (Cognitive Research Trust), which teaches creative thinking as a skill; and presents reasons for teaching thinking as a specific subject area. (MBR)
Critical Thinking Concept Reconstructed
ERIC Educational Resources Information Center
Minter, Mary Kennedy
2010-01-01
This paper explores the proposition that teaching of critical thinking (CT) should include: (1) identifying and addressing the many environmental variables acting as barriers to our human thinking, i.e., an open system approach, and (2) utilizing the interrelatedness of the CT building blocks, i.e., creative thinking techniques, levels of…
ERIC Educational Resources Information Center
Hyde, Rod
1997-01-01
Effective Thinking Outdoors (ETO) is an organization that teaches thinking skills and strategies via significant outdoor experiences. Identifies the three elements of thinking as creativity, play, and persistence; presents a graphic depiction of the problem-solving process and aims; and describes an ETO exercise, determining old routes of travel…
Critical assumptions: thinking critically about critical thinking.
Riddell, Thelma
2007-03-01
The concept of critical thinking has been featured in nursing literature for the past 20 years. It has been described but not defined by both the American Association of Colleges of Nursing and the National League for Nursing, although their corresponding accreditation bodies require that critical thinking be included in nursing curricula. In addition, there is no reliable or valid measurement tool for critical thinking ability in nursing. As a result, there is a lack of research support for the assumptions that critical thinking can be learned and that critical thinking ability improves clinical competence. Brookfield suggested that commitments should be made only after a period of critically reflective analysis, during which the congruence between perceptions and reality are examined. In an evidence-based practice profession, we, as nurse educators, need to ask ourselves how we can defend our assumptions that critical thinking can be learned and that critical thinking improves the quality of nursing practice, especially when there is virtually no consensus on a definition.
Mathematics Knowledge for Understanding and Problem Solving.
ERIC Educational Resources Information Center
Putnam, Ralph T.
1987-01-01
Two important aspects of transfer in mathematics learning are the application of mathematical knowledge (MK) to problem solving and the acquisition of more advanced concepts. General assumptions and themes of current cognitive research on mathematics learning in schoolchildren are discussed, focusing on issues facilitating the transfer of MK. (TJH)
Clinical Assessment in Mathematics: Learning the Craft.
ERIC Educational Resources Information Center
Hunting, Robert P.; Doig, Brian A.
1997-01-01
Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…
Mathematics in Context: Measurement, Packaging and Caring for Our Environment.
ERIC Educational Resources Information Center
Anderson, Ann
1994-01-01
Presents examples using the context of packaging materials and their impact on the environment to help teachers and teacher educators combine mathematics and science through activities that involve higher order thinking and worthwhile tasks. (Author/MKR)
Statewide Mathematics Professional Development: Teacher Knowledge, Self-Efficacy, and Beliefs
ERIC Educational Resources Information Center
Carney, Michele B.; Brendefur, Jonathan L.; Thiede, Keith; Hughes, Gwyneth; Sutton, John
2016-01-01
We examined the impact of a state-mandated K-12 mathematics professional development course on knowledge, self-efficacy, and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics…
Action-Based Digital Tools: Mathematics Learning in 6-Year-Old Children
ERIC Educational Resources Information Center
Dejonckheere, Peter J. N.; Desoete, Annemie; Fonck, Nathalie; Roderiguez, Dave; Six, Leen; Vermeersch, Tine; Vermeulen, Lies
2014-01-01
Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…
Reading the News: The Statistical Preparation of Pre-Service Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Chesler, Joshua
2015-01-01
Undergraduate mathematics programs must prepare teachers for the challenges of teaching statistical thinking as advocated in standards documents and statistics education literature. This study investigates the statistical thinking of pre-service secondary mathematics teachers at the end of their undergraduate educations. Although all had completed…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Teaching Critical Thinking: Sense-Making, Explanations, Language, and Habits
ERIC Educational Resources Information Center
Maloney, David
2015-01-01
The conjunction of three events has encouraged me to devote significant time to thinking about the pedagogical framework in my introductory courses. The three events were: doing a workshop addressing the Advanced Placement restructuring of the Physics B course with a stronger focus on critical thinking, finding out that "The Physics…
ERIC Educational Resources Information Center
Dalton, Ben; Ingels, Steven J.; Downing, Jane; Bozick, Robert
2007-01-01
While increased academic requirements for high school graduation have long been advocated, current research shows a mixed record in mathematics and science achievement among American middle and high school students relative to some of their international peers. In response to these concerns and other calls for reform, states have increased the…
ERIC Educational Resources Information Center
Fry, Dale Eugene
College students' performance in their first two calculus-level mathematics courses was studied by comparing students skipping, on any basis, one or more courses in the regular calculus sequence and students reaching these same courses through the regular sequence. Those skipping via CEEB AP and those skipping for any other reason were also…
Mole, John
2002-01-01
People in different cultures are taught to think differently. How we gather information, process, rationalise, justify and communicate our ideas is culturally determined. Europe is divided between the pragmatic, inductive thinking of North Sea cultures and the rationalist thinking of the rest of the continent. Westerners and Asians have different mental skills and capacities deriving from the nature of written and spoken language, the relative importance of learning by rote or investigation and the social environment. Western children are expected to ask questions and test ideas for themselves, while in Asia it is unacceptable to question anyone senior in age or authority, including teachers. Westerners base thinking on reason; Asians base thinking on harmony. Whenever people of different cultures work together, different ways of thinking create barriers to understanding and communication. This applies to many spheres of work, including the medical profession. PMID:12195863
Global Thinking, or the Utility of Trivia.
ERIC Educational Resources Information Center
Harris, John S.
2001-01-01
Suggests the case of the British Westland Lysander P12 Ground Strafer aircraft illustrates the problem of narrow thinking. Claims that had the initial designers approached the problem in a broad way, they would have seen in advance that the project would fail. Concludes the case is instructive as an industrial problem, but it also demonstrates the…
Atance, Cristina M.; O'Neill, Daniela K.
2001-12-01
Thinking about the future is an integral component of human cognition - one that has been claimed to distinguish us from other species. Building on the construct of episodic memory, we introduce the concept of 'episodic future thinking': a projection of the self into the future to pre-experience an event. We argue that episodic future thinking has explanatory value when considering recent work in many areas of psychology: cognitive, social and personality, developmental, clinical and neuropsychology. Episodic future thinking can serve as a unifying concept, connecting aspects of diverse research findings and identifying key questions requiring further reflection and study.
NASA Astrophysics Data System (ADS)
Clarke, Doug; Roche, Anne; Wilkie, Karina; Wright, Vince; Brown, Jill; Downton, Ann; Horne, Marj; Knight, Rose; McDonough, Andrea; Sexton, Matthew; Worrall, Chris
2013-06-01
As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the lesson, during the lesson, following the debrief, and several weeks later, data were collected on teachers' intended and actual observation foci and any anticipated changes in their beliefs and practices arising from the experience. There were several common themes in teachers' intended observations, including a focus on questioning, catering for individual differences, and building student engagement. As evident in other research, teachers' intended and actual observations gave greater attention to teacher actions and decision making than to student learning and thinking. In this paper, we situate demonstration lessons within teacher professional learning models, describe the features of our model, summarise teacher data, and discuss issues arising from our work.
Lateral Thinking of Prospective Teachers
ERIC Educational Resources Information Center
Lawrence, A. S. Arul; Xavier, S. Amaladoss
2013-01-01
Edward de Bono who invented the term "lateral thinking" in 1967 is the pioneer of lateral thinking. Lateral thinking is concerned with the generation of new ideas. Liberation from old ideas and the stimulation of new ones are twin aspects of lateral thinking. Lateral thinking is a creative skills from which all people can benefit…
Critical Thinking in Business Education.
ERIC Educational Resources Information Center
Sormunen, Carolee
Critical thinking is currently a prominent issue in education. For business educators, four issues must be considered: the meaning of critical thinking, how critical thinking can be introduced into the curriculum, how critical thinking is developed in courses, and how critical thinking can be evaluated. The literature identifies three theoretical…
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
NASA Astrophysics Data System (ADS)
Rodríguez, Nancy
2015-03-01
The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].
ERIC Educational Resources Information Center
Luo, Yu L. L.; Kovas, Yulia; Haworth, Claire M. A.; Plomin, Robert
2011-01-01
The genetic and environmental origins of individual differences in mathematical self-evaluation over time and its association with later mathematics achievement were investigated in a UK sample of 2138 twin pairs at ages 9 and 12. Self-evaluation indexed how good children think they are at mathematical activities and how much they like those…
Everyday Pedagogical Practices in Mathematical Play Situations in German "Kindergarten"
ERIC Educational Resources Information Center
Brandt, Birgit
2013-01-01
This study describes situations in German daycare facilities (Kindergarten) in which the development of mathematical thinking in children is specifically encouraged through examination of common play objects. Using micro-sociological methods of analysis, the mathematical potential of such interactions between teacher and child is elaborated within…
Building a Case for Blocks as Kindergarten Mathematics Learning Tools
ERIC Educational Resources Information Center
Kinzer, Cathy; Gerhardt, Kacie; Coca, Nicole
2016-01-01
Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic "seat time" in order to address standards. Mathematics research…
From Static to Dynamic Mathematics: Historical and Representational Perspectives
ERIC Educational Resources Information Center
Moreno-Armella, Luis; Hegedus, Stephen J.; Kaput, James J.
2008-01-01
The nature of mathematical reference fields has substantially evolved with the advent of new types of digital technologies enabling students greater access to understanding the use and application of mathematical ideas and procedures. We analyze the evolution of symbolic thinking over time, from static notations to dynamic inscriptions in new…
Dialogue on Early Childhood Science, Mathematics, and Technology Education.
ERIC Educational Resources Information Center
American Association for the Advancement of Science, Washington, DC.
Educators, scholars, and researchers in the United States convened at the Forum on Early Childhood Science, Mathematics, and Technology Education to discuss how, when, and even if science, mathematics, and technology should be taught to pre-kindergarten children. The product of that forum, this book summarizes some of the latest thinking about…
Graphing Calculators in the Mathematics Classroom. ERIC Digest.
ERIC Educational Resources Information Center
Smith, Jeffrey P.
Graphing calculators present a challenging task for mathematics teachers in the classroom. This digest offers four distinct methods for using graphing calculators in mathematics classrooms, including: (1) tools for expediency; (2) amplifiers for conceptual understanding; (3) catalysts for critical thinking; and (4) vehicles for integration.…
Teacher Interventions in Cooperative-Learning Mathematics Classes
ERIC Educational Resources Information Center
Ding, Meixia; Li, Xiaobao; Piccolo, Diana; Kulm, Gerald
2007-01-01
The authors examined the extent to which teacher interventions focused on students' mathematical thinking in naturalistic cooperative-learning mathematics classroom settings. The authors also observed 6 videotapes about the same teaching content using similar curriculum from 2 states. They created 2 instruments for coding the quality of teacher…
A Tree at Bedtime Investigation: Connecting Mathematics, Science, and Literature
ERIC Educational Resources Information Center
Kieff, Judith
2006-01-01
Activities that promote "active thinking" help children learn mathematics and science by allowing them to work at forming relationships, making connections, and integrating concepts and procedures. Dynamic and exciting children's books invite and motivate children to learn mathematics and science by responding to stories, characters, and their…
On the "Relevance" of the Mathematics Curriculum to Young People
ERIC Educational Resources Information Center
Sealey, Paula; Noyes, Andrew
2010-01-01
In this article we draw upon focus group data from a large study of learner trajectories through 14-19 mathematics education to think about the notion of relevance in the mathematics curriculum. Drawing on data from three socially distanced sites we explore how different emphases on what might be termed "practical," "process" and/or "professional"…
Mathematiques 14-24 (Mathematics 14-24).
ERIC Educational Resources Information Center
Alberta Learning, Edmonton.
To set goals and make informed choices, students need an array of thinking and problem-solving skills. Fundamental to this is an understanding of mathematical techniques and processes that will enable them to apply the basic skills necessary to address everyday mathematical situations, as well as acquire higher order skills in logical analysis and…
Equations and Inequalities: Making Mathematics Accessible to All. PISA
ERIC Educational Resources Information Center
Piacentini, Mario; Monticone, Chiara
2016-01-01
More than ever, students need to engage with mathematics concepts, think quantitatively and analytically, and communicate using mathematics. All these skills are central to a young person's preparedness to tackle problems that arise at work and in life beyond the classroom. But the reality is that many students are not familiar with basic…
Teaching Writing and Communication in a Mathematical Modeling Course
ERIC Educational Resources Information Center
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Aiming for Understanding: Lessons Learned about Writing in Mathematics
ERIC Educational Resources Information Center
O'Connell, Susan R.; Baemon, Celia; Beyea, Jennifer M.; Denvir, Susan S.; Dowdall, Leila A.; Friedland, Nikki G.; Ward, Joelle D.
2005-01-01
A Professional Development Schools partnership between the University of Maryland and other elementary schools in the district worked together to explore, discuss and reflect on the challenges of helping students to write about mathematics. Finding ways to help students effectively communicate their mathematical thinking is a challenge for…
The I Hate Mathematics! Book. A Brown Paper School Book.
ERIC Educational Resources Information Center
Burns, Marilyn
This 1975 book is written for children who do not like mathematics and presents activities which may help them to begin understanding mathematics. Activities are organized under the following headings: "Street Math"; "Maybe Grownups Aren't as Smart as You Think"; "Things to Do When You Have the Flu"; "A Math-Magic Show"; "How to Always Be a…
Inquiry-Based Learning and the Art of Mathematical Discourse
ERIC Educational Resources Information Center
von Renesse, Christine; Ecke, Volker
2015-01-01
Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…
Investigating Preservice Mathematics Teachers' Manipulative Material Design Processes
ERIC Educational Resources Information Center
Sandir, Hakan
2016-01-01
Students use concrete manipulatives to form an imperative affiliation between conceptual and procedural knowledge (Balka, 1993). Hence, it is necessary to design specific mathematics manipulatives that focus on different mathematical concepts. Preservice teachers need to know how to make and use manipulatives that stimulate students' thinking as…
The Layering of Mathematical Interpretations through Digital Media
ERIC Educational Resources Information Center
Calder, Nigel
2012-01-01
How might understanding emerge when learners engage mathematical phenomena through digital technologies? This paper considers the ways children's mathematical thinking was influenced by their interpretations through various pedagogical discourses and how understanding emerged through those various filters. Current research into using digital…
Influence of Demographic Factors on Students' Beliefs in Learning Mathematics
ERIC Educational Resources Information Center
Tahir, Izah Mohd; Bakar, Nor Mazlina Abu
2009-01-01
Learning mathematics has been recognized by many as important. It does not only develop students' ability to think in quantitative terms but can also enhance skills such as analytical and problem solving skills. However, to enable us to tell our students how important mathematics is we have to understand students' beliefs in learning mathematics…
Conceptualizing Mathematics as Discourse in Different Educational Settings
ERIC Educational Resources Information Center
Güçler, Beste; Wang, Sasha; Kim, Dong-Joong
2015-01-01
In this work, we focus on a relatively new theory in mathematics education research, which views thinking as communication and characterizes mathematics as a form of discourse. We discuss how this framework can be utilized in different educational settings by giving examples from our own research to highlight the insights it provides in the…
Graphing Calculators: The Newest Revolution in Mathematics.
ERIC Educational Resources Information Center
Clutter, Martha
1999-01-01
Asserts that there are numerous advantages to using graphing calculators, including the teaching of higher-level thinking skills and allowing students to draw conclusions about what they are learning. However, mathematics educators face such challenges as teaching students when it is appropriate to use graphing calculators, course-content…
Teaching Mathematics from a Chemist's Viewpoint.
ERIC Educational Resources Information Center
DeLorenzo, Ronald A.
This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…
Learning to Read in Mathematics Classrooms
ERIC Educational Resources Information Center
Meaney, Tamsin; Flett, Kirsten
2006-01-01
Reading in mathematics classrooms needs to be an active part of the learning process. If it continues to be viewed as a passive way to gain information, then its benefit to the learning process will also continue to be under-utilised. The "Read--Think--Do (x2)" model, designed by these authors and described in this article, can be a support to…
Pablo's Tree: Mathematics in a Different Light.
ERIC Educational Resources Information Center
Wickett, Maryann
1996-01-01
Relates mathematics to literature through the story "Pablo's Tree." The students turn flat paper into three-dimensional boxes through the use of riddles, reasoning, and communication, thereby providing the teacher an easy, informal way to assess their level of thinking and understanding. (AIM)
ERIC Educational Resources Information Center
Orem, Donna
2016-01-01
This article describes a concept called the "blue ocean thinking strategy," developed by W. Chan Kim and Renée Mauborgne, professors at INSEAD, an international graduate school of business in France. The "blue ocean" thinking strategy considers opportunities to create new markets for services, rather than focusing solely on…
ERIC Educational Resources Information Center
Maclennan, Ian
1977-01-01
Suggests that there exists a "finite" number of elementary concepts and distinguishable modes of thinking, that all human beings tend to acquire the same set of elements of thinking and the same strategies with which to understand and control their physical environment, and that the method of analysis used here is a standard scientific method.…
ERIC Educational Resources Information Center
Harden, Helen
2009-01-01
This article provides an overview of the "It Makes You Think" resource. The lessons provided by this resource show how students can learn about the global dimension through science. The "It Makes You Think" resource contains ten topics: (1) Metals in jewellery worldwide; (2) Global food market; (3) The worldwide travels of paper; (4) Mobile phones…
Against Critical Thinking Pedagogy
ERIC Educational Resources Information Center
Hayes, David
2015-01-01
Critical thinking pedagogy is misguided. Ostensibly a cure for narrowness of thought, by using the emotions appropriate to conflict, it names only one mode of relation to material among many others. Ostensibly a cure for fallacies, critical thinking tends to dishonesty in practice because it habitually leaps to premature ideas of what the object…
Thinking Skills & Intelligence.
ERIC Educational Resources Information Center
Blai, Boris, Jr.
A review of research and the views of researchers prominent in the field of thinking skill development discusses the role of thinking skills in the ability to formulate problems, resolve issues, determine the most effective decisions, and create effective solutions to problems. The views of Edward deBono, Robert Ennis, Reuven Feuerstein, Matthew…
ERIC Educational Resources Information Center
Downs, Christopher J.
2008-01-01
Critical thinking is of primary importance in higher education, yet the concept remains slippery and the skill elusive. The author argues that most current critical thinking textbooks are out of line with the seminal work of John Dewey. Rather than logical argument and justification, it is suggested that carefulness, open-mindedness and creativity…
ERIC Educational Resources Information Center
Demski, Jennifer
2012-01-01
When one thinks of 21st century schools, one thinks of geometric modern architecture, sustainable building materials, and high-tech modular classrooms. It's rare, though, that a district has the space or the money to build that school from the ground up. Instead, the challenge for most is the transformation of the 20th century architecture to…
Critical Thinking and Learning
ERIC Educational Resources Information Center
Mason, Mark
2007-01-01
This paper introduces some of the debates in the field of critical thinking by highlighting differences among thinkers such as Siegel, Ennis, Paul, McPeck, and Martin, and poses some questions that arise from these debates. Does rationality transcend particular cultures, or are there different kinds of thinking, different styles of reasoning? What…
ERIC Educational Resources Information Center
Winkeljohann, Rosemary
1979-01-01
The focus article in this newsletter contains a discussion of the theory of reading as a thinking process and offers practical suggestions for implementing instruction in teaching reading as a thinking process. The section on theory is based on observations of the reading process as perceived by psycholinguists such as Frank Smith and Kenneth…
NASA Astrophysics Data System (ADS)
Wang, Xia; Yang, Yuanyuan
2013-04-01
The Mathematical Olympiad is the Championship Mathematics Competition for High School students. In china, to alleviate the burden of the students, some people argue the Mathematical Olympiad should be called off in this year. Others think that Mathematical Olympiad and further study should be completely separated, thus eliminating its utilitarian overtones. For this reason, we lead our students to investigate and study the influence of Mathematical Olympiad on the development of the students by questionnaires.
A consensus statement on critical thinking in nursing.
Scheffer, B K; Rubenfeld, M G
2000-11-01
The purpose of this study was to define critical thinking in nursing. A Delphi technique with 5 rounds of input was used to achieve this purpose. An international panel of expert nurses from nine countries: Brazil, Canada, England, Iceland, Japan, Korea, Netherlands, Thailand, and 23 states in the U.S. participated in this study between 1995 and 1998. A consensus definition (statement) of critical thinking in nursing was achieved. The panel also identified and defined 10 habits of the mind (affective components) and 7 skills (cognitive components) of critical thinking in nursing. The habits of the mind of critical thinking in nursing included: confidence, contextual perspective, creativity, flexibility, inquisitiveness, intellectual integrity, intuition, open-mindedness, perseverance, and reflection. Skills of critical thinking in nursing included: analyzing, applying standards, discriminating, information seeking, logical reasoning, predicting and transforming knowledge. These findings can be used by practitioners, educators and researchers to advance understanding of the essential role of critical thinking in nursing.
ERIC Educational Resources Information Center
Aguirre, Julia M.; Zavala, Maria del Rosario; Katanyoutanant, Tiffany
2012-01-01
This study documents and describes efforts to develop robust forms of pre-service teachers' pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children's mathematical thinking, and…
ERIC Educational Resources Information Center
Tasova, Halil Ibrahim; Delice, Ali
2012-01-01
Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed. PMID:23512504
TIMSS Advanced 2015 Assessment Frameworks
ERIC Educational Resources Information Center
Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.
2014-01-01
The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…
ERIC Educational Resources Information Center
Donawa, Annette Mallory
2009-01-01
The enhancement of critical thinking skills is necessary for students pursuing degrees in science, technology, engineering, and mathematics (STEM) disciplines. A three-year mixed methods study conducted at a Historically Black College and University in Baltimore, Maryland focused on enhancing critical thinking skills for African American students.…
The Thinking-about-Derivative Test for Undergraduate Students: Development and Validation
ERIC Educational Resources Information Center
Aydin, Utkun; Ubuz, Behiye
2015-01-01
Two studies were conducted for the development and validation of a multidimensional test to assess undergraduate students' mathematical thinking about derivative. The first study involved two phases: question generation and refinement of the Thinking-about-Derivative Test (TDT). The second study included four phases as follows: test…
Computational Thinking in K-12: A Review of the State of the Field
ERIC Educational Resources Information Center
Grover, Shuchi; Pea, Roy
2013-01-01
Jeannette Wing's influential article on computational thinking 6 years ago argued for adding this new competency to every child's analytical ability as a vital ingredient of science, technology, engineering, and mathematics (STEM) learning. What is computational thinking? Why did this article resonate with so many and serve as a rallying cry for…
ERIC Educational Resources Information Center
Ben Youssef, Belgacem; Berry, Barbara
2012-01-01
Spatial thinking skills are vital for success in everyday living and work, not to mention the centrality of spatial reasoning in scientific discoveries, design-based disciplines, medicine, geosciences and mathematics to name a few. This case study describes a course in spatial thinking and communicating designed and delivered by an…
Learning to Think Spatially: What Do Students "See" in Numeracy Test Items?
ERIC Educational Resources Information Center
Diezmann, Carmel M.; Lowrie, Tom
2012-01-01
Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results…
Project IMPACT. Improve Minimal Proficiences by Activating Critical Thinking. Grades 7-12.
ERIC Educational Resources Information Center
Orange County Dept. of Education, Santa Ana, CA.
The major goal of Project IMPACT (Improve Minimal Proficiencies by Activating Critical Thinking) is to improve student achievement on district tests of basic skill competency. The program seeks to improve student performance on tests requiring critical thinking with emphasis on reading and mathematics. Students involved in Project IMPACT work in a…
Picture This: Increasing Math and Science Learning by Improving Spatial Thinking
ERIC Educational Resources Information Center
Newcombe, Nora S.
2010-01-01
Spatial thinking--such as visualizing the earth rotating--is crucial to student success in science, technology, engineering, and mathematics (STEM). Since spatial thinking is associated with skill and interest in STEM fields (as well as in other areas, such as art, graphic design, and architecture), the immediate question is whether it can be…
Schlimm, Dirk
2013-04-01
This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter.
Depastas, A.N.
1990-01-01
According to the practicalist school, thinking emerges from activity and each human practice is giving food to its own distinctive kinds of perception, conduct, and perspective of the world. The author, while studying and describing developments after the commencement of the nuclear age in many fields of human behavior and knowledge, including the social sciences, particularly psychology and international politics, became an adherent to the practicalist philosophy when he perceived new relevant thoughts coming to his mind at the same time. Indeed writing is a learning experience. He has, therefore, systematically included these thoughts in the following pages and synoptically characterized them in the title: Nuclear Age Thinking. He considers this kind of thinking as automatic, conscious activity which is gradually influencing our choices and decisions. The author has reservations as regards Albert Einstein's saying that the unleashed power of the atom changed everything save our modes of thinking, because the uncontrollability of nuclear energy is apparently in the subconscious of mankind nowadays, influencing the development of a new mode of thinking, and that is the nuclear age thinking which is the subject of this book. Nuclear age thinking drives from the collective fear of extinction of life on earth due to this new power at man's disposal, and it is not only limited to the change in the conventional meaning of the words war and peace.
In Focus...Mathematics, History, Ethnomathematics and Education: A Comprehensive Program.
ERIC Educational Resources Information Center
D'Ambrosio, Ubiratan
1999-01-01
Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)
Thinking through a Lesson: Successfully Implementing High-Level Tasks
ERIC Educational Resources Information Center
Smith, Margaret S.; Bill, Victoria; Hughes, Elizabeth K.
2008-01-01
This article focuses on the Thinking Through a Lesson Protocol (TTLP) that is intended to facilitate the design of lessons based on cognitively challenging mathematics tasks. Included is a discussion of the key features of the TTLP, suggestions on ways in which the protocol can be used as a tool for collaborative lesson planning, and a discussion…
Pre-Service Teachers' Opinions on Teaching Thinking Skills
ERIC Educational Resources Information Center
Akinoglu, Orhan; Karsantik, Yasemin
2016-01-01
The purpose of the present study is to determine pre-service teachers' opinions on teaching thinking skills. 134 senior pre-service pre-school, English and mathematics teachers studying at a state university in Istanbul participated in the study which is designed based on survey model. A questionnaire which was developed by the researchers was…
Think-Share-Write: An Effective Strategy for Group Quizzes
ERIC Educational Resources Information Center
Gopalakrishnan, Hema
2004-01-01
Group Quizzes using the Think-Share-Write strategy can be very effective in engaging students and enhancing their learning in the classroom. In this article, I describe my experiences in implementing this method in both lower division and upper division Mathematics courses. (Contains 1 figure.)
Science and the City: Thinking Geospatially about Opportunity to Learn
ERIC Educational Resources Information Center
Tate, William F.; Jones, Brittni D.; Thorne-Wallington, Elizabeth; Hogrebe, Mark C.
2012-01-01
The purpose of this article is to describe several conceptual areas that warrant attention by scholars and practitioners interested in improving access and opportunity to science, technology, engineering, and mathematics (STEM) learning in urban cities. Thinking conceptually about the urban context has been a part of intellectual traditions in the…
The ‘structure-function’ relationship in glaucoma – past thinking and current concepts
Malik, Rizwan; Swanson, William H.; Garway-Heath, David F
2013-01-01
An understanding of the relationship between functional and structural measures in primary open angle glaucoma (POAG) is necessary for both grading the severity of disease and for understanding the natural history of the condition. This article outlines the current evidence for the nature of this relationship, and highlights the current mathematical models linking structure and function. Large clinical trials demonstrate that both structural and functional change are apparent in advanced stages of disease, while, at an individual level, detectable structural abnormality may precede functional abnormality in some patients whilst the converse in true in other patients. Although the exact nature of the ‘structure-function’ relationship in POAG is still the topic of scientific debate and the subject of continuing research, this article aims to provide the clinician with an understanding of the past concepts and contemporary thinking in relation to the structure-function relationship in POAG. PMID:22339936
Clinical thinking in psychiatry.
Wells, Lloyd A
2015-06-01
I discuss the lack of precision in the term 'clinical reasoning' and its relationship to evidence-based medicine and critical thinking. I examine critical thinking skills, their underemphasis in medical education and successful attempts to remediate them. Evidence-based medicine (and evidence-based psychiatry) offer much but are hampered by the ubiquity and flaws of meta-analysis. I explore views of evidence-based medicine among psychiatry residents, as well as capacity for critical thinking in residents before and after a course in philosophy. I discuss decision making by experienced doctors and suggest possible futures of this issue.
ERIC Educational Resources Information Center
Bennett, Elaine; Weidner, Jenny
2011-01-01
Children are born naturally mathematical, so why is it sometimes so difficult to observe children being mathematical? Why do so many of us think we are "bad" at maths and how does this subconsciously affect the provision, experiences and opportunities we provide for young children who are starting their mathematical learning journey? This easily…
Textbook and Course Materials for 21-127 "Concepts of Mathematics"
ERIC Educational Resources Information Center
Sullivan, Brendan W.
2013-01-01
Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…
ERIC Educational Resources Information Center
Bufford, Carolyn A.; Mettler, Everett; Geller, Emma H.; Kellman, Philip J.
2014-01-01
Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…
ERIC Educational Resources Information Center
Borden, Lisa Lunney
2011-01-01
As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…
Cognitive functioning in mathematical problem solving during early adolescence
NASA Astrophysics Data System (ADS)
Collis, Kevin F.; Watson, Jane M.; Campbell, K. Jennifer
1993-12-01
Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student's problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students' degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.
ERIC Educational Resources Information Center
Berryman, Sue E.
This paper describes trends in and causes of minority and female representation among holders of advanced science and math degrees. The minority groups studied are Blacks, Hispanic Americans, American Indians, and Asian Americans, all of whom are compared with Whites. The degrees looked at include those in math, the computer sciences, physical…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
The Critical Thinking Workout.
ERIC Educational Resources Information Center
Masters, Terry McDaniel
1991-01-01
Presents a critical thinking exercise program, modeled on a physical exercise workout, for elementary teachers to use in the classroom. It includes warm-up exercises, a more strenuous workout, and a cool-down period for the brain. (SM)
Shaw, Natalie
2014-07-15
The Stop, Breathe & Think app is free, thanks to underwriting from Tools for Peace, the non-profit organisation that teaches people of all ages how to develop and apply kindness and compassion in their daily lives.
ERIC Educational Resources Information Center
Jones, Clive
1972-01-01
A look at the latest package from a British managment training organization, which explains and demonstrates creative thinking techniques, including brainstorming. The package, designed for groups of twelve or more, consists of tapes, visuals, and associated exercises. (Editor/JB)
ERIC Educational Resources Information Center
Slisko, Josip; Cruz, Adrian Corona
2013-01-01
There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…
The Curiosity in Marketing Thinking
ERIC Educational Resources Information Center
Hill, Mark E.; McGinnis, John
2007-01-01
This article identifies the curiosity in marketing thinking and offers ways to teach for marketing thinking through an environment that fosters students' curiosity. The significance of curiosity in its relationship with thinking is that when curiosity is absent, so is thinking. Challenges are discussed in recognizing the fragility of curiosity…
ERIC Educational Resources Information Center
Martin, Daisy; Wineburg, Sam
2008-01-01
Teaching a way of thinking requires making thinking visible. Educators need to pull back the curtains from historical cognition to show students not only what historians think, but "how" they think. Given that many students believe that history is a single story to be committed to memory and that texts speak for themselves, teaching historical…
ERIC Educational Resources Information Center
Carrier, Jim
2014-01-01
For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…
Decentering: A Construct to Analyze and Explain Teacher Actions as They Relate to Student Thinking
ERIC Educational Resources Information Center
Teuscher, Dawn; Moore, Kevin C.; Carlson, Marilyn P.
2016-01-01
Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus.…
ERIC Educational Resources Information Center
Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Darrough, Rebecca L.; Pfannenstiel, Kathleen Hughes
2015-01-01
Many students with learning disabilities (LD) in mathematics receive their mathematics education in general education inclusive classes; therefore, these students must be capable of learning algebraic concepts, including developing algebraic thinking abilities, that are part of the general education curriculum. To help students develop algebraic…
NIRS evaluates the thinking process of Mushi-kuizan task
NASA Astrophysics Data System (ADS)
Eda, Hideo; Kuroda, Yasufumi; Okamoto, Naoko; Maesako, Takanori
2008-02-01
We discuss the possibility of Near Infrared Spectroscopy (NIRS) application to the educational research. NIRS system was used for prefrontal cortex measurement of children, when they were solving Mushi-kuizan problems. The Mushi-kuizan task is one of the mathematical puzzles. Subjects were four children in fifth grade. Hemoglobin parameters such as oxygenated hemoglobin and deoxygenated hemoglobin were calculated during Mushi-kuizan problems. The parameters were compared with the performance data of each subject. Changes Hb parameters described how children use their brain. NIRS evaluated the thinking process of mathematics task. It is very useful for mathematics teachers to catch the children's thinking process dynamically because they can consider the way of teaching for each child. It was shown that NIRS may be able to apply to education.
Neurally and Mathematically Motivated Architecture for Language and Thought
Perlovsky, L.I; Ilin, R
2010-01-01
Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788
The Progressive Development of Early Embodied Algebraic Thinking
NASA Astrophysics Data System (ADS)
Radford, Luis
2014-06-01
In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning—the theory of objectification. Within this theory, thinking is conceived of as a form of reflection and action that is simultaneously material and ideal: It includes inner and outer speech, sensuous forms of imagination and visualisation, gestures, rhythm, and their intertwinement with material culture (symbols, artifacts, etc.). The theory articulates a cultural view of development as an unfolding dialectic process between culturally and historically constituted forms of mathematical knowing and semiotically mediated classroom activity. Looking at the experimental data through these theoretical lenses reveals a developmental path where embodied forms of thinking are sublated or subsumed into more sophisticated ones through the mediation of properly designed classroom activity.
J.K. Brimacombe; I.V. Samarasekera; E.B. Hawbolt; T.R. Meadowcroft; M. Militzer; W.J. Pool; D.Q. Jin
1999-07-31
This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.
Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry
ERIC Educational Resources Information Center
Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.
2013-01-01
Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…
Learning to Leverage Children's Multiple Mathematical Knowledge Bases in Mathematics Instruction
ERIC Educational Resources Information Center
Turner, Erin E.; Foote, Mary Q.; Stoehr, Kathleen Jablon; McDuffie, Amy Roth; Aguirre, Julia Maria; Bartell, Tonya Gau; Drake, Corey
2016-01-01
In this article, the authors explore prospective elementary teachers' engagement with and reflection on activities they conducted to learn about a single child from their practicum classroom. Through these activities, prospective teachers learned about their child's mathematical thinking and the interests, competencies, and resources she or he…
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
ERIC Educational Resources Information Center
Coffman, Diane M.
2013-01-01
Thinking skills have long been regarded as an essential outcome of the educational process. Yet, research shows that the teaching of thinking skills in K-12 education does not follow a coherent path. Several factors affect the teaching and use of thinking skills in the classroom, with teacher knowledge and beliefs about thinking skills among the…
Lowi-Young, Mimi; DuBois-Wing, Gwen
2016-01-01
Amol Verma and Sacha Bhatia's (2016) paper presents policy recommendations that merit serious consideration on a system-wide level. While they make compelling arguments about why provincial governments are ideally suited to adapt Triple Aim innovation, we are concerned that the current health system climate limits this possibility. In our commentary, we present our thoughts about the authors' admittedly aspirational goals and the realities of the pan-Canadian healthcare system. We commence our commentary by confirming our agreement about the potential inherent within the Triple Aim framework. Second, we argue how important progress can take place that may not reflect a provincial-wide system. Next, we maintain that a learning health system is an essential ingredient to advancing Triple Aim and other health system-wide improvements. Third, we wonder whether the stewardship role of government is real and possible. Finally, we question the concept of our current health system's readiness for system change. While we have raised some questions about Verma and Bhatia's thinking around provincial adoption of the Triple Aim, we applaud their ideas. We believe that transformation in provincial health systems requires bold thinking. PMID:27009585
Mathematical Modeling of Electronic Devices and Circuits
NASA Astrophysics Data System (ADS)
Singh, B. P.; Singh, Meena; Roy, Sanjay Kumar
2010-11-01
The necessity of modeling lies in the nature of technology and its advancement. The modeling minimizes time and cost of the process involved. The mathematical model provides an insight into the behavior of the physical system that reduces the problem to its essential characteristics. The floating admittance matrix (FAM) approach is an elegant method of mathematical modeling of electronic devices and circuits.
Technology in K-12 Mathematics Classrooms
ERIC Educational Resources Information Center
Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.
2008-01-01
Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…
Mathematical Rigor in the Common Core
ERIC Educational Resources Information Center
Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin
2013-01-01
A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…
The Myth of Objectivity in Mathematics Assessment.
ERIC Educational Resources Information Center
Romagnano, Lew
2001-01-01
Investigates meaningful assessment to give teachers information on students' understanding of mathematical ideas and how their understanding changes over time. Presents examples collected from a teacher-made quiz, the Advanced Placement calculus test, and the SAT-I Mathematics test. Illustrates both the inherent subjectivity of these methods and…
ERIC Educational Resources Information Center
Le Storti, Anthony J.; And Others
The set of three units, designed for middle and junior high school gifted students, includes 30 lessons on logic and critical thinking. Each lesson includes information on objectives, materials, and teaching presentation suggestions. Ten deductive reasoning lessons focus on such topics as fact and opinion, tests for validity of deductive…
Science and Mathematics in Astronomy
NASA Technical Reports Server (NTRS)
Woolack, Edward
2009-01-01
A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.
Foundations of resilience thinking.
Curtin, Charles G; Parker, Jessica P
2014-08-01
Through 3 broad and interconnected streams of thought, resilience thinking has influenced the science of ecology and natural resource management by generating new multidisciplinary approaches to environmental problem solving. Resilience science, adaptive management (AM), and ecological policy design (EPD) contributed to an internationally unified paradigm built around the realization that change is inevitable and that science and management must approach the world with this assumption, rather than one of stability. Resilience thinking treats actions as experiments to be learned from, rather than intellectual propositions to be defended or mistakes to be ignored. It asks what is novel and innovative and strives to capture the overall behavior of a system, rather than seeking static, precise outcomes from discrete action steps. Understanding the foundations of resilience thinking is an important building block for developing more holistic and adaptive approaches to conservation. We conducted a comprehensive review of the history of resilience thinking because resilience thinking provides a working context upon which more effective, synergistic, and systems-based conservation action can be taken in light of rapid and unpredictable change. Together, resilience science, AM, and EPD bridge the gaps between systems analysis, ecology, and resource management to provide an interdisciplinary approach to solving wicked problems.
Foundations of resilience thinking.
Curtin, Charles G; Parker, Jessica P
2014-08-01
Through 3 broad and interconnected streams of thought, resilience thinking has influenced the science of ecology and natural resource management by generating new multidisciplinary approaches to environmental problem solving. Resilience science, adaptive management (AM), and ecological policy design (EPD) contributed to an internationally unified paradigm built around the realization that change is inevitable and that science and management must approach the world with this assumption, rather than one of stability. Resilience thinking treats actions as experiments to be learned from, rather than intellectual propositions to be defended or mistakes to be ignored. It asks what is novel and innovative and strives to capture the overall behavior of a system, rather than seeking static, precise outcomes from discrete action steps. Understanding the foundations of resilience thinking is an important building block for developing more holistic and adaptive approaches to conservation. We conducted a comprehensive review of the history of resilience thinking because resilience thinking provides a working context upon which more effective, synergistic, and systems-based conservation action can be taken in light of rapid and unpredictable change. Together, resilience science, AM, and EPD bridge the gaps between systems analysis, ecology, and resource management to provide an interdisciplinary approach to solving wicked problems. PMID:24975863
Values taught, values learned, attitude and performance in mathematics
NASA Astrophysics Data System (ADS)
Limbaco, K. S. A.
2015-03-01
The purpose of the study was to identify, describe and find the relationship among values taught, values learned, attitude and performance in mathematics. The researcher used descriptive-correlational method of research to gather information and to describe the nature of situation. The following instruments were used in this study: Math Attitude Inventory, Inventory of Values Taught and Learned which were content validated by experts in the field of Mathematics, Values and Education. Generally, most of the values were taught by the teachers. All of the values were learned by the students. The following got the highest mean ratings for values taught: moral strength, sharing, charity, valuing life, love of God, truth and honesty, reason, alternativism and articulation. The following got highest mean ratings for values learned: patience/tolerance, sharing, charity, valuing life, faith, love of God, truth and honesty, analogical thinking, confidence and individual liberty. Majority of the respondents have moderately positive attitude towards mathematics. Positive statements in the Mathematics Attitude Inventory are "Generally true" while negative statements are "Neutral." In conclusion, values were taught by mathematics teacher, thus, learned by the students. Therefore, mathematics is very much related to life. Values can be learned and strengthened through mathematics; there is a significant relationship between values taught by the teachers and values learned by the students and attitude towards mathematics and performance in mathematics; values taught does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance in mathematics even if the mathematics teacher did not teach values; values learned does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance
Dilemma in Teaching Mathematics
ERIC Educational Resources Information Center
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…