This study examined the effects of question prompts, knowledge integration prompts, and problem solving prompts, embedded in a Web-based learning environment in scaffolding preservice teachers' conceptual understanding and problem solving in an ill-structured domain. A mixed-method study was employed to investigate the outcomes of students' conceptual knowledge and ill-structured problem solving. The quantitative results indicated that students who received knowledge integration prompts had...
Topics: ERIC Archive, Internet, Educational Principles, Preservice Teachers, Problem Solving, Cues,...
This study was conducted on informal aspects of an inquiry-based physics course and reports findings about learning interactions and discourse observed during the first three semesters the course was offered. The course offered an alternative to the large lecture instruction typical in introductory university physics and promoted learning in an informal environment. The course organization attempted to engage students in investigations with only a small fraction of time devoted to...
Topics: ERIC Archive, Physics, Investigations, Informal Education, Problem Solving, Interaction Process...
This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student strategy use, which included: (a) input value, (b) mathematical structure of the task, (c) prior strategies, (d) visual image of the situation, and (e)...
Topics: ERIC Archive, Grade 5, Mathematics Education, Algebra, Mathematical Concepts, Elementary School...
This paper takes up the question of the way in which "the problem with educational research" is represented. It takes as its point of departure two recent views on "the problem"--one expressed by an educational journalist and one presented by the Australian Council of Deans of Education. It locates these within a larger frame of international debate about educational research and its problems and considers how these arise out of particular dispositions towards educational...
Topics: ERIC Archive, Fantasy, Educational Research, Problem Solving, Disadvantaged, Research Problems,...
This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring items. More specifically, the study consisted of two parts. The first part involved the development of a mathematics problem-solving framework that was...
Topics: ERIC Archive, Problem Solving, Mathematics Education, Cognitive Psychology, Item Response Theory,...
This paper offers some concrete ideas and suggestions for incorporating discussions of experimental technologies in the middle level technology education classroom. Technology education students should be aware of experimental technologies. They should understand the ramifications of items such as hybrid vehicles, photovoltaic solar panels, biometrics, nanotechnology, biological engineering, and hydrogen vehicles. Nonetheless, the focus of the middle level technology classroom should not be on...
Topics: ERIC Archive, Technology Education, Preservice Teacher Education, Logical Thinking, Thinking...
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed....
Topics: ERIC Archive, Foreign Countries, Equations (Mathematics), Grade 9, Algebra, Mathematics...
In today's rapidly changing world, people must continually come up with creative solutions to unexpected problems. Success is based not only on what one knows or how much one knows, but on one's ability to think and act creatively. In short, people are now living in the Creative Society. Unfortunately, few of today's classrooms focus on helping students develop as creative thinkers. In addition, the proliferation of new technologies is quickening the pace of change, accentuating the need for...
Topics: ERIC Archive, Creative Thinking, Problem Solving, Technology Uses in Education, Children,...
Problem solving and student-centred learning have received a great deal of attention in mathematics curricula for schools and in some universities. Much of this emphasis developed from the pioneering work of George Polya in heuristics, problem solving, and mathematics education. In this study, the author reviews Polya's work, and some of its later extensions, in the light of current research findings. It is argued that, despite the attention it has received, problem solving remains a difficult...
Topics: ERIC Archive, Mathematics Education, Problem Solving, Mathematics Instruction, Conceptual Tempo,...
In this article, the author presents a six by six array in which individuals can obtain 182 in total even if they use a different set of numbers. The author then explain why this is possible. The author uses the k-translation of a sequence for this equation. (Contains 8 figures, 2 tables and 6 footnotes.)
Topics: ERIC Archive, Computation, Equations (Mathematics), Problem Solving, Arithmetic, Mathematical...
In this article, the authors consider the exponential curves y = ba[superscript x] where a, b [is a member of] R, a [greater than] 0, a [not equal to] 1, and b [not equal to] 1. The authors show that by fixing one of a or b the points (x[subscript 0],y[subscript 0) of tangency of y = ba[superscript x] and the line passing through the origin lie on a straight line. The y-ordinates of these points are equal to be. (Contains 3 figures.)
Topics: ERIC Archive, Geometric Concepts, Equations (Mathematics), Mathematical Logic, Validity, Problem...
In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the only rules, then the solved puzzle would be called a Latin square. This name was invented by the Swiss mathematician Leonhard Euler (1707-1783) who...
Topics: ERIC Archive, Logical Thinking, Mathematical Concepts, Mathematics Skills, Mathematical Logic,...
Most parents of gifted children are aware of the benefit of having books and other hands-on learning materials available to their children. However, there is more involved in creating a thoughtful and intellectual learning environment at home than just books and science kits. The way a group communicates, what it communicates, and what it values are all components of a culture of thinking. In "The Thinking Classroom: Learning and Teaching in a Culture of Thinking," Tishman, Perkins,...
Topics: ERIC Archive, Academically Gifted, Parent School Relationship, Parent Participation, Creative...
Increasing people's ability to solve complex problems is more and more often being seen as an integral part of vocational education. While there have been numerous empirically-based approaches to the didactic structuring of teaching and learning arrangements by which students' ability to solve problems can be increased, knowledge of how to evaluate a person's ability to solve problems is far more limited. There is a lack of testing instruments that are inexpensive to implement and evaluate and...
Topics: ERIC Archive, Problem Solving, Followup Studies, Vocational Education, Teaching Methods, Thinking...
Students have problems in their lives, but can teachers help them? Should teachers help? The No Child Left Behind (NCLB) act and its emphasis on standardized test results have forced school systems to produce high scores, and in turn school administrators pressure teachers to prepare students for taking standardized tests. Teachers may want to deal with students' problems, but a required curriculum emphasizing skill drills has compromised teaching time. Teachers are not free to determine what...
Topics: ERIC Archive, Student Needs, Federal Legislation, Teacher Responsibility, Problem Solving,...
For many children, mathematics is an inherently difficult subject to learn. Between 5 and 8 percent of children between the ages of 6 and 14 have a particular type of cognitive deficiency that limits their aptitude to acquire knowledge and understanding of fundamental ideas in numeracy. Increasingly, researchers in the cognitive sciences are studying this deficiency under the name dyscalculia, a disorder in which normally intelligent children demonstrate specific disabilities in learning...
Topics: ERIC Archive, Instructional Design, Mathematical Aptitude, Mathematics Skills, Academic...
The purpose of this study is to investigate the relationship between different levels of organizational commitment (compliance, identification, internalization) of teachers and their different conflict management strategies (compromising, problem solving, forcing, yielding, avoiding). Based on a questionnaire survey of 418 teachers, this study indicated that male teachers are more likely to experience commitment based on compliance, and are more likely to avoid conflicts than female teachers....
Topics: ERIC Archive, Problem Solving, Conflict, Conflict Resolution, Predictor Variables, Teacher...
This study investigated obstacles to teaching civic education in the United States, a country whose government was established on democratic principles over 250 years ago, and Hungary, a European country presently making the transition to a government based on democratic principles. The purpose is to compare the obstacles within these two countries as they seek ways to provide their young citizens with the training and experiences necessary to be responsible, effective citizens in a democratic...
Topics: ERIC Archive, Foreign Countries, Comparative Analysis, Democracy, Citizenship Education, Civics,...
We conducted an experimental analysis of children's relative problem-completion rates across two workstations under conditions of equal (Experiment 1) and unequal (Experiment 2) problem difficulty. Results were described using the generalized matching equation and were evaluated for degree of schedule versus stimulus control. Experiment 1 involved a symmetrical choice arrangement in which the children could earn points exchangeable for rewards contingent on correct math problem completion....
Topics: ERIC Archive, Student Behavior, Elementary School Students, Assignments, Workstations, Rewards,...
Most teachers have attended countless workshops that advocated new teaching methods, materials, or techniques in addressing special student populations. They politely listen as a series of presenters enthusiastically introduce their information in written and verbal form. They return to the classroom, fully intending to use their new skills, but perhaps feeling a bit anxious about their actual applications and ensuing results. This author believes that teachers, like students, must be both...
Topics: ERIC Archive, Academically Gifted, Interdisciplinary Approach, Problem Solving, Teaching Methods,...
There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyze the behavior of two Year 8 students who had demonstrated spontaneous abstracting. The analysis highlighted the crucial role of synthetic and evaluative analysis, two processes that seem...
Topics: ERIC Archive, Cooperative Learning, Documentation, Mathematics Instruction, Secondary Education,...
Canadian universities are struggling to address seemingly contradictory challenges pertaining to undergraduate education: high demand and underfunding. A number of instruments, including the National Survey of Student Engagement (National Survey of Student Engagement, n.d.), have led to greater priority being placed on the undergraduate experience. Yet, strategies to ensure student satisfaction with their education, through initiatives such as small classes and personal contact with faculty,...
Topics: ERIC Archive, Undergraduate Study, Problem Based Learning, Teaching Methods, Foreign Countries,...
The purpose of this article is to present various techniques that will engage young children, ages 3-8, in learning science and mathematics. Children actively engage in acquiring basic science and mathematics concepts as they explore their environment. The methods presented are intended to meet the developmental levels of young learners as they make connections with science and mathematics. Also included is a review of science and mathematics content and process skills appropriate for early...
Topics: ERIC Archive, Young Children, Science Instruction, Mathematics Instruction, Mathematical Concepts,...
Teachers are often unaware that bilingual students often switch between their languages when doing mathematics. Little research has been undertaken into this phenomenon. Results are reported here from a study of language switching by sixteen Year 4/5 Iranian bilingual students as they solved mathematical problems in an interview situation. Reasons given for switching between English and their L1 language (Persian or Farsi) were the difficulty of the problem, familiarity with particular numbers...
Topics: ERIC Archive, Immigrants, Grade 4, Grade 5, Foreign Countries, Elementary School Students,...
Marie Evans Schmidt and Elizabeth Vandewater review research on links between various types of electronic media and the cognitive skills of school-aged children and adolescents. One central finding of studies to date, they say, is that the content delivered by electronic media is far more influential than the media themselves. Most studies, they point out, find a small negative link between the total hours a child spends viewing TV and that child's academic achievement. But when researchers...
Topics: ERIC Archive, Video Games, Academic Achievement, Hyperactivity, Transfer of Training, Attention...
Evidence of public and private interest in programs designed to strengthen the institution of marriage and reduce the number of children growing up without both their parents is growing. Robin Dion addresses the question of whether such programs can be effective, especially among disadvantaged populations. She begins by describing a variety of marriage education programs. Although new to the social welfare umbrella, such programs have existed for several decades. Social scientists have...
Topics: ERIC Archive, Low Income, Disadvantaged, Marriage, Social Scientists, Low Income Groups, Program...
To address the lack of connection between theory and practice, a number of recent reforms in teacher education have included inquiry-based programs and/or new types of education courses, which encourage student teachers to be reflective problem solvers and change agents. Based on a pilot course for student teachers, the authors, also aspiring teacher educators, studied the process of implementing an inquiry approach toward teaching and learning to teach while simultaneously responding to the...
Topics: ERIC Archive, Teacher Education, Student Teachers, Education Courses, Change Agents, Theory...
Teacher retention has been the subject of much study, yet recent estimates of teachers who choose to leave the profession within the first three years to pursue other careers remains at an unacceptably high level of 33.5 percent. These figures are alarming in light of the fact that schools desperately need qualified teachers. Several authors maintain that in order to solve the teacher shortage problem, the focus should be on retaining already qualified teachers rather than encouraging...
Topics: ERIC Archive, Teacher Education, Teacher Education Programs, Self Efficacy, Teacher Persistence,...
Criticism of the public schools has been unrelenting since "A Nation at Risk" was published in 1983. From that pivotal moment to the present the business community has played a crucial role in setting the parameters of the critique of the schools and shaping the reform agendas that have been proposed and implemented. However, this author has found the criticisms of student achievement leveled by the business community to reveal tremendous ignorance of the complexity of schools, of the...
Topics: ERIC Archive, School Restructuring, Business, Educational Change, Scientific Research, School...
Unlike traditional lecture-based instruction, where information is passively transferred from instructor to student, problem-based learning (PBL) students are active participants in their own learning, thrust into unknown learning situations where the parameters of the problem may not be well-defined and the task at hand ambiguous--just like in the real world. In this article, the author discusses PBL, a student-centered approach to learning that is grounded in real-world situations. PBL...
Topics: ERIC Archive, Testing, Problem Based Learning, Teaching Methods, Problem Solving, Independent...
A variety of developments in nursing education in Australia including some innovative and exciting models, educational enterprises between education and industry, and evidence of developing strengths in research and professional alliances on a national level have been discussed recently. This paper presents Simulation to Practice as an example of an educational program that can maximise skill mastery for nurses in mental health fields as practised by Deakin University in Victoria, Australia....
Topics: ERIC Archive, Nursing Students, Nursing Education, Mental Health, Problem Solving, Foreign...
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 valuable source of mathematical activities and problem solving tasks. The main character is constantly solving problems by considering...
Topics: ERIC Archive, Data Analysis, Cooperative Learning, Mathematical Logic, Childrens Literature,...
The author advocates for writing as an essential communication skill for learning mathematics. Mathematical diary writing is cited as a good way for students to privately represent their thinking through pictures, language, or symbols, and also as a channel for children to communicate with themselves and with their teachers. Cited research demonstrates that diary writing also has benefits for teaching and learning by nurturing number sense, helping teachers investigate children's understanding...
Topics: ERIC Archive, Symbols (Mathematics), Problem Solving, Communication Skills, Elementary School...
The authors discuss proportional reasoning as a challenging yet central concept for students in the middle grades that lays a foundation for mathematics studied later in high school. Four types of proportional reasoning problems are discussed: (1) Part-part-whole (comparing a subset (part) of a whole with its complement (other part) or the whole itself); (2) Associated sets (relating two quantities, not ordinarily associated, through a problem context or situation); (3) Well-known measures...
Topics: ERIC Archive, Numeracy, Mathematical Concepts, Mathematics Instruction, Middle School Students,...
Adults and children often encounter situations where they have to make judgments about "how much" or "how long" or "how many." The significance of estimation as an ordinary, everyday, and natural aspect of measurement needs to be conveyed to students through their mathematical experiences. Many students, however, tend to view estimation as a difficult technique where success is dependent upon how close the student's estimate is to the teacher's estimate rather than...
Topics: ERIC Archive, Teaching Methods, Measurement, Educational Strategies, Mathematics Education, Foreign...
This article presents an example of a versatile multi-solution problem that can be used right across the primary years. The basic problem is: "Noah saw 16 legs go past him into the Ark. How many creatures did he see?" Any even number can be used, although, 2 legs allows only one answer and with 16 legs there are already 14 different solutions, so teachers need to exercise caution in using large numbers. The teacher should encourage discussion around the interpretation of the problem...
Topics: ERIC Archive, Animals, Recreational Facilities, Primary Education, Foreign Countries, Problem...
The difficulties that primary students experience when dealing with real-world related word problems have been discussed extensively. These difficulties are not only related to complex, non-routine problems but already occur with respect to routine problems that involve the application of a simple algorithm. Due to difficulties with the comprehension of the text and the identification of the "mathematical core" of the problem, primary students frequently engage in a rather arbitrary...
Topics: ERIC Archive, Problem Solving, Word Problems (Mathematics), Mathematics Instruction, Foreign...
Measurement is a mathematics skill students encounter often in their daily lives. The act of measuring involves the use of concrete, hands-on materials that students find engaging and appealing. According to Martinie (2004), the best way to teach measurement "is to find or create situations in which students need to measure and let them experience this process." Preston and Thompson (2004) concur that "the most fundamental aspect of measurement is the act of measuring.". In...
Topics: ERIC Archive, Mathematics Skills, Grade 5, Foreign Countries, Primary Education, Measurement,...
Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the counting-by-one strategy for addition to a variety of strategies that do not rely on counting by ones. Assisting the child to develop sophisticated...
Topics: ERIC Archive, Mental Computation, Number Concepts, Subtraction, Arithmetic, Mathematics Skills,...
One way of providing middle-school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. Students are expected to learn serious, substantive mathematics in classrooms in which the emphasis is on thoughtful engagement and meaningful learning. Lesh and Harel (2003) have indicated that the kind of problem-solving situations that should be emphasised in the...
Topics: ERIC Archive, Spatial Ability, Mathematical Concepts, Mathematics Instruction, Problem Solving,...
It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on the part of the student except for addition and multiplication, reflection and rotation; but, using questions and exercises throughout, finishes by...
Topics: ERIC Archive, Mathematical Concepts, Primary Education, Mathematics Education, Arithmetic,...
Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem enabled a Grade 5/6 student to think about the relationship between multiplication, division, and fractions. Here, they describe the project and...
Topics: ERIC Archive, Grade 5, Multiplication, Mathematics Instruction, Arithmetic, Primary Education,...
The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as "changing" and how it explicitly illustrates the way in which addition and subtraction are inverse operations, with each "undoing"...
Topics: ERIC Archive, Constructivism (Learning), Active Learning, Algebra, Mathematics Instruction, Foreign...
Everyone knows that teachers do not have unlimited time, a log of experience, or a deep understanding of all the mathematics they teach. To solve this problem, teachers often use textbooks, and the accompanying teacher's resource books, as sources of activities and advice about how to help students learn mathematics. The activity that prompted this article (the "Two Spinners Game") came from such a resource. The authors observed two teachers using this activity in their Grade 5...
Topics: ERIC Archive, Textbooks, Grade 5, Probability, Foreign Countries, Educational Games, Educational...
The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a deep understanding of decimals because of their prior knowledge of decimals through real life associations. Germany, like Australia, operates around a...
Topics: ERIC Archive, Prior Learning, Foreign Countries, Arithmetic, Primary Education, Mathematics...
About fifteen years ago, the author discovered an interesting activity in some materials that Malcolm Swan from the Shell Centre (University of Nottingham, UK) had developed for the English National Curriculum Council in 1991. The activity, one which has been used by several presenters in professional development workshops in Australia in recent years, involves sharing chocolate in a problem solving context. In this article, the author describes one way that he uses this exercise with teachers...
Topics: ERIC Archive, National Curriculum, Middle School Students, Foreign Countries, Middle Schools,...
Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the calculator is broken? This article describes the mathematics that children learned and a teacher's awareness of children's mathematical understanding,...
Topics: ERIC Archive, Calculators, Number Concepts, Computation, Primary Education, Educational Technology,...
In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process, they have described the way in which Polya's four step heuristic for problem solving, now popularly known as the "See, Plan, Do, Check...
Topics: ERIC Archive, Elementary School Mathematics, Grade 4, Grade 5, Number Concepts, Competition,...
Recently, the author has been fortunate to be a visitor in a number of classrooms in the United States, England and Europe. On one such visit to an Elementary School in Columbia, Missouri, the teachers accepted him into their normal classrooms for their normal lessons. He moved between three classes: Grade 1, Grade 2 and Grade 4. A snapshot account of what he saw and his reactions are presented. Here, the author highlights the significance of helping children make connections in mathematics via...
Topics: ERIC Archive, Grade 4, Grade 2, Grade 1, Problem Solving, Mathematics Instruction, Learning...
This article deals with the increasing academic pressure facing five-year-old children who are in kindergarten schools in the U.S. Part of the reason kindergarten is becoming more and more academic is a growing understanding of the importance of early learning and the capabilities of young children. Proponents of ramping up standards in early elementary education tend to focus on the numbers: more children learning to read or do math sooner must be good. These achievements, however, may come at...
Topics: ERIC Archive, Kindergarten, Young Children, Child Development, Academic Standards, High Risk...