The Reference Committee firmly shares the view that the state of the mathematical sciences and related quantitative disciplines in Australia has deteriorated to a dangerous level, and continues to deteriorate. Accordingly the author decided to structure this Report around a small number of recommendations, some long term and others to address immediate problems. In the last five years there have been many reviews analysing the mathematical sciences in Australia and elsewhere. Australia has gone...

Topics: ERIC Archive, Stakeholders, Science Education, Foreign Countries, Mathematics Education,...

This study investigated the recordings of fraction notation, when the number of fractional parts exceeded the whole study, made by 79 Year 4 students from two schools serving quite different communities. Approximately 30% of the Year 4 students changed the name of the denominator when the whole was exceeded by one unit-fraction, for example, the fraction name changed from quarters to fifths when creating 5 quarters. This practice of changing the name of the fractional part when the whole was...

Topics: ERIC Archive, Mathematics Instruction, Foreign Countries, Fractions, Elementary School Students,...

This book focuses on how to make math friendly for parents and children. The book has a companion audiotape with ideas and guidelines for the interested parent. The book's introduction also suggests some ways for parents to guide their children's reading. Part 1 of the book consists of three "Read-along Stories": "Turkey Tallies" (Lou Hamilton and Dave Coverly); "Paul Bunyan versus the Conveyor Belt" (William Hazlett Upson); and "Makanda Mahlanu (Josepha...

Topics: ERIC Archive, Bibliographies, Home Study, Mathematics, Mathematics Skills, Parent Student...

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison is a powerful tool that mathematics teachers can use to introduce students to multiple strategies. Comparison can and should play a key role in the...

Topics: ERIC Archive, Numbers, Mathematics Instruction, Problem Solving, Mathematics Skills, Mathematical...

This effort is part of a project designed to identify mathematical requirements related to Navy electronics training. The relationship between mathematics ability and electronics performance in the Navy's Basic Electricity and Electronics (BE/E), Class "A," and Class "C" schools was examined to identify the mathematics skills required to complete Navy electronics training successfully and function adequately in electronics maintenance in the fleet. School performance...

Topics: ERIC Archive, Educational Research, Electronic Technicians, Job Performance, Mathematics...

Identification and development of giftedness is a major task of mathematics teachers worldwide. An early identification of gifted children in mathematics can have a number of benefits, like, providing opportunities for the nourishment of their talent, saving them from burnout, and proper utilisation of mathematical talent in future. As creativity plays an important role in the development of gifted behavior, it could be erroneous to exclude creativity from gifted education programs. In this...

Topics: ERIC Archive, Mathematics Instruction, Academically Gifted, Talent Identification, Creativity,...

As outlined in the paper "The 20 Matchstick Triangle Challenge: An Activity to Foster Reasoning and Problem Solving" by Pat Graham and Helen Chick [EJ1093090], an incredibly useful set of information about the mathematical ability of your students will be revealed. You can look at the way your students try to solve the 20 matchsticks problem, their method of recording, their errors, and also the ramifications of the questions they ask. When your students have completed and discussed...

Topics: ERIC Archive, Mathematics Skills, Mathematical Concepts, Mathematics, Mathematics Education,...

The Georgia Criterion-referenced Tests are designed to measure a core group of essential basic skills at key points throughout the educational development of students. This monograph reports test results for grades one, four, eight, and ten. Results are presented by graphs and figures, with brief narrative summaries. Information is provided on: (1) student performances in reading and mathematics criterion-referenced tests; (2) historical comparisons of student progress; (3) demographic and...

Topics: ERIC Archive, Basic Skills, Criterion Referenced Tests, Elementary Secondary Education, Mathematics...

Examples are given of criterion-referenced test items in mathematics and reading used at the sixth grade level in Georgia. Three skill areas are identified for mathematics: concept identification, component operations, and problem solving. Tests measure students' ability to: (1) recognize whole numbers, fractions, and decimals; (2) identify relations/properties; (3) select units to measure; (4) identify sets of points; (5) determine probability; (6) apply formulas to measure; (7) compute; (8)...

Topics: ERIC Archive, Criterion Referenced Tests, Educational Objectives, Elementary Education, Grade 6,...

This is one in a series of publications designed for parents and teachers to help children acquire developmentally appropriate basic educational skills at home and in school. Topics included are: (1) "What is math?" explaining mathematical concepts such as number, measurement, space, and time; (2) "How do children learn about math?"; (3) "Why is an understanding of math important?"; (4) "How you can help your children learn math?"; and (5) "Points to...

Topics: ERIC Archive, Early Childhood Education, Mathematical Concepts, Mathematics Skills, Measurement,...

This module assumes that the information presented in previous modules is well known to the learner. Module 6 is the third of three modules (4, 5, and 6) designed to provide an in-depth look at the Standards of Mathematical Practice which are part of the Common Core State Standards for Mathematics. Module 6 focuses on strategies for implementing the practices in the classroom, determining the degree of students' progress towards meeting the practices, and using an observation tool to ensure...

Topics: ERIC Archive, Mathematics Education, Academic Standards, State Standards, Mathematics Instruction,...

Eighty-eight sets of parents who enrolled their 4- and 5-year-old children in computer classes completed a questionnaire designed to gather demographic data and information about their reasons for enrolling the children and their attitudes about the importance of computer competence. Parents could check one of three reasons for enrolling their child: (1) It was a program for 4- and 5-year-olds; (2) It was important for their child to work with computers; or (3) Other. The first option was...

Topics: ERIC Archive, Computer Literacy, Creative Development, Enrollment Influences, Mathematics Skills,...

The Commission on the Reorganization of Secondary Education finds itself confronted with problems of great difficulty in recommending a reorganization of the mathematical studies of the secondary school. Antecedent to new courses, there should be an agreement among psychologists and educators such as has not yet been reached. It seems, therefore, that the best service that the commission can at this time render is to present an analysis of the situation. This report, therefore, is submitted...

Topics: ERIC Archive, Advisory Committees, Secondary Education, Mathematics Instruction, Educational...

One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the present study was to collect empirical data concerning this type-of-multiplier effect in combination with two additional task variables which have...

Topics: ERIC Archive, Division, Elementary School Mathematics, Foreign Countries, Grade 6, Intermediate...

Not so long ago, the common response of teachers to high school use of computer algebra systems (CAS) was invariably along the lines of, "What will be left to teach if our students have access to devices which solve, factorise, do calculus and more?" and "If students use such tools, then they will never learn how to do their mathematics, and their algebra skills will deteriorate" and the classic cry, "What will be left for us to put into our examinations?". This...

Topics: ERIC Archive, Mathematics Instruction, Educational Technology, Algebra, Instructional Innovation,...

This report evaluates the degree to which the achievement level descriptions adopted by the National Assessment Governing Board (NAGB) for the 1992 National Assessment of Educational Progress (NAEP) assessment in mathematics accurately represent what students at a given achievement level can do. Three different analytical approaches were used in the investigation and resulted in the following conclusions: (1) judged in terms of actual student performance, many of the items selected as exemplars...

Topics: ERIC Archive, Elementary Secondary Education, Mathematical Concepts, Mathematics Achievement,...

The Louisiana Educational Assessment Program (LEAP) Grade 11 Test is designed to measure proficiency in four subject areas including English, mathematics, social studies, and science. This guide for mathematics is intended to provide a description of the way in which specific skill areas are assessed on the LEAP test and instructional considerations in promoting proficiency of these target skill areas. Skill areas included are: (1) fractions and operations; (2) decimal numbers and operations;...

Topics: ERIC Archive, Grade 11, High Schools, Mathematical Enrichment, Mathematics Instruction, Mathematics...

The 157 mathematics achievement tests cited in this bibliography are used to assess students' knowledge of various mathematical skills and operations. Some of the tests are part of large achievement batteries. The tests are primarily designed for grades 4 through 6. This document is one in a series of topical bibliographies from the Test Collection (TC) at Educational Testing Service (ETS) containing descriptions of more than 18,000 tests and other measurement devices prepared by commercial...

Topics: ERIC Archive, Achievement Tests, Annotated Bibliographies, Intermediate Grades, Knowledge Level,...

To better understand the nature of problems in math learning, a case study was conducted of the specific strengths and weaknesses of a child with a severe math-learning disability. The subject, Adam, was nearly 11 years old when interviews began and had been officially classified as learning disabled due to organic brain dysfunction. A semistructured clinical interview method was employed in the study: tasks or problems, often followed by flexible questioning, were posed to the subject....

Topics: ERIC Archive, Case Studies, Individualized Instruction, Interviews, Learning Disabilities, Learning...

Developmental patterns and interrelationships of various informal skills, reading and writing of numerals, and a range of base ten/place value concepts/skills were examined in a study involving 78 primary school children from four schools who were individually examined in a standardized interview. A total of 23 tasks were administered and scalogram, individual protocol, and error analyses were performed. Results indicate that the children learned to read and write numerals in a step-like...

Topics: ERIC Archive, Basic Skills, Cognitive Development, Elementary School Students, Kindergarten...

Efforts to develop a mathematics curriculum that meets the needs of a modern society are reflected in reform recommendations across the developed world. A common requirement is for students to understand the calculation procedures they are taught and to develop "number sense". This paper will analyse students' strategies for calculating in the USA, England and the Netherlands and consider the way these relate to curriculum priorities. (Contains 5 tables.) [For complete proceedings,...

Topics: ERIC Archive, Foreign Countries, Mathematics Curriculum, Problem Solving, Curriculum Development,...

This paper reports on a class assignment written by preservice teachers on the use of mathematics in different professions. The professions included licensed practical nurse, auto mechanic, research and development product manager for industrial cleaning products, dental office assistant, snack bar employee at a beach club, beauty salon owner and operator, apple orchard and fruit stand owner, secretary at a university alumni hall, bus person at a restaurant, video store clerk, professional...

Topics: ERIC Archive, Higher Education, Mathematical Applications, Mathematics, Mathematics Skills,...

This paper promotes the importance of noticing young children's mathematical strengths. It draws on the philosophical positions of children's rights and competence to propose a shift in the ways in which all involved might notice the mathematical engagement, understandings, experiences and practices of young children. Noticing children's mathematics generates the potential for educators to document learning and to respond in ways that promote ongoing engagement in areas that are of relevance...

Topics: ERIC Archive, Mathematics Instruction, Mathematics Skills, Academic Ability, Relevance (Education),...

A study examined 60 adult students' informal knowledge of percent and its relationship to their formal computational skills. The students studying in adult education programs were interviewed to ascertain the following: (1) their ideas of the meanings of three benchmark percentages--100, 50, and 25 percent--as they appear in advertising and media contexts; (2) their ability to use these numbers in everyday mental math tasks; and (3) their visual representations of these quantities. Students...

Topics: ERIC Archive, Adult Basic Education, Computation, Educational Research, Mathematical Concepts,...

This Middle School Course of Study document is designed to be user friendly. Units can be used sequentially and each unit may need a different amount of time to complete. When using this document, consider the students' prior knowledge and their understanding of the concepts. The Idaho Mathematics Achievement Standards are consistently referenced as they form the basis of this organizational document. They have been combined in the units so that students and teachers can readily see connections...

Topics: ERIC Archive, Middle Schools, Mathematics Education, State Standards, Mathematics Skills,...

The Minnesota Board of Teaching is committed to establishing and maintaining quality standards for the licensing of teachers who teach in Minnesota public schools. As part of these standards, specific and selected examinations serve as important instruments in the licensing process. The principal purpose of the examinations of basic skills is to determine objectively if prospective teachers have adequate skills in reading, writing, and mathematics to meet the needs of the learners whom they...

Topics: ERIC Archive, Teacher Effectiveness, State Standards, State Licensing Boards, Teacher...

This study investigated hearing-impaired students' understanding of the mathematical concept of fractional numbers, as measured by their ability to determine the order and equivalence of fractional numbers. Twenty-one students (ages 10-16) with hearing impairments were compared with 26 students with normal hearing. The study concluded that hearing-impaired subjects lagged behind their hearing peers in arithmetic computation and the development of the concept of fraction. The hearing-impaired...

Topics: ERIC Archive, Arithmetic, Comprehension, Elementary Secondary Education, Fractions, Hearing...

The focus of this study was on the expectations that first-grade teachers have of the mathematics skills of their incoming first-grade students. At the end of one school year and at the beginning of the next school year, first-grade teachers (n=64) in rural and urban settings completed the Mathematics Skills Expectations Survey (MSES). The MSES considers 11 basic areas of mathematical skills appropriate for the primary grade level and allows respondents to indicate agreement or disagreement...

Topics: ERIC Archive, Elementary School Teachers, Grade 1, Mathematics Instruction, Mathematics Skills,...

Study of the arts enhances young people's intellectual, personal, and social development. The arts provide a rich and engaging curriculum that develops students? abilities to think, reason, and understand the world and its cultures. A comprehensive arts education encompasses such areas as the history of the arts, the honing of critical-analysis skills, the re-creation of classic as well as contemporary works of art, and the expression of students' ideas and feelings through the creation of...

Topics: ERIC Archive, Social Development, Art, Visual Arts, Art Education, College Entrance Examinations,...

At the present time, state mandated testing is solely in mathematics and reading, so it behooves schools to provide the best mathematics curriculum. Adults who are deficient in numeracy face difficulties in the societal arena. Objectives in mathematics need to be carefully selected by the teacher. Three categories of objectives should be stressed: knowledge, skills, and attitudes. This paper discusses the following four sources of objectives for student achievement: those in the manual section...

Topics: ERIC Archive, Academic Achievement, Elementary Secondary Education, Mathematics Skills, Numeracy,...

The Louisiana mathematics standards were created by over one hundred Louisiana educators with input by thousands of parents and teachers from across the state. Educators envisioned what mathematically proficient students should know and be able to do to compete in society and focused their efforts on creating standards that would allow them to do so. The new standards provide appropriate content for all grades or courses, maintain high expectations, and create a logical connection of content...

Topics: ERIC Archive, Mathematics Instruction, State Standards, Kindergarten, Elementary Secondary...

This paper describes a study that examined parents' beliefs about children's number skill development. Twenty-seven parents of 4- and 5-year-olds were interviewed about number tasks that could be solved by children between the ages of 4 and 7 years. In addition, parents were asked a series of open-ended questions about how they would answer a child's questions about math, their own experiences with math, and their expectations for their children's performance in math. Parents predicted that...

Topics: ERIC Archive, Beliefs, Computation, Mathematics Skills, Number Concepts, Numbers, Parent Attitudes,...

The workshop that is the subject of this report, one in a series of workshops made possible through a grant to the CFE from the National Science Foundation, is the starting point for that effort. The center's mission is to promote evidence-based policy analysis that both responds to current needs and anticipates future ones. This one-day workshop was designed as an initial step in exploring the research in cognition and developmental psychology that sheds light on children's capacity to learn...

Topics: ERIC Archive, Workshops, Resource Materials, Policy Analysis, Developmental Psychology, Early...

This is the academic numeracy journey of Tania, who participated in a research study that investigated the academic numeracy skills of nursing students. Tania is a mature aged woman, and her story represents many of such mature aged students as they journey into a largely unknown university culture. The data for this research came from student assignments, surveys, interview transcripts, emails and screencasts. To see the development in Tania's numeracy, this paper utilises the micro- and...

Topics: ERIC Archive, Nursing Students, Mathematics Education, Numeracy, Foreign Countries, Nontraditional...

Graduate Exit Examination for the 21st Century (GEE 21) is an integral part of the Louisiana school and district accountability system passed by the state legislature and signed into law in 1997. The primary purposes of the accountability system are to raise expectations for achievement for all Louisiana public school students and to improve public education in the state. This document is part of a series of materials meant to promote understanding of knowledge and skills students must have and...

Topics: ERIC Archive, Accountability, Academic Achievement, Grade 10, State Standards, Test Items, Public...

There are a number of characteristics of gifted children reported by teachers and researchers. Such characteristics may include curiosity, advanced mathematical skills, large vocabulary, acute sense of humour. This paper examines the demands that humour, as a creative activity, makes on cognitive and social development. It is derived from research that includes interviews with renowned professional humorists and examination of their work. The production of humour requires a sophisticated...

Topics: ERIC Archive, Gifted, Creative Activities, Empathy, Social Development, Cognitive Development,...

Because little is presently known about changes in children's knowledge of the logical principles of arithmetic and, more specifically, about how children's developing knowledge is reflected in the use of solution procedures, two types of three-term arithmetic problems were presented for solution to 6-, 7-, 9-, 11-, and 20-year-olds. Problems were to be solved mentally. One type could be solved only by calculating sums and differences. The other type could also be solved without computation by...

Topics: ERIC Archive, Arithmetic, Children, Cognitive Ability, Foreign Countries, Individual Development,...

Teachers are often faced with the difficulty of deciding exactly what problems the students are experiencing, and the extent to which students might understand "some of it". The one-on-one approach to helping students is most common, but very time consuming, and is an approach that may only serve to fix an immediate difficulty, perhaps by addressing procedural aspects rather than the concepts. One reason for this may be the very real difficulty both parties have in identifying exactly...

Topics: ERIC Archive, Student Attitudes, Mathematics Instruction, Mathematics Skills, Teaching Methods,...

This curriculum guide lists mathematics topics and concepts, learning outcomes, and sample learning objectives (in three columns) for grades 1 to 8. Topics/concepts, in the first column, describe the major parts of the subject under consideration. They define broadly the content to be included in the study of each subject area. Learning outcomes, in the second column, describe, in general terms, the behaviors students are expected to demonstrate as a result of their learning experiences. These...

Topics: ERIC Archive, Behavioral Objectives, Elementary Education, Elementary School Mathematics,...

Three mathematics scoring methods are being used or explored in large scale assessment programs: (1) item-by-item scoring; (2) holistic scoring; and (3) "trait" scoring. This study investigated all three methods of scoring on three mathematics performance-based assessments. Mathematics assessment tasks were selected from a pool of pilot tasks because they could be scored using all three methods. Results of the study suggest that holistic scoring and item-by-item scoring methods...

Topics: ERIC Archive, Alternative Assessment, Elementary Secondary Education, Mathematical Concepts,...

The 162 mathematics achievement tests cited in this bibliography are used to assess students' knowledge of various mathematical skills and operations. Many of the tests are part of large achievement batteries. Both norm reference and criterion referenced tests are included. The tests are primarily designed for preschool through grade 3. This document is one in a series of topical bibliographies from the Test Collection (TC) at Educational Testing Service (ETS) containing descriptions of more...

Topics: ERIC Archive, Achievement Tests, Annotated Bibliographies, Knowledge Level, Mathematics Skills,...

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,...

High school students normally encounter the study and use of formal proof in the context of Euclidean geometry. Professional mathematicians typically use an informal trial-and-error approach to a problem, guided by intuition, to arrive at the truth of an idea. Formal proof is pursued only after mathematicians are intuitively convinced about the truth of an idea. Is the use of intuition to arrive at the plausibility of a mathematical truth unique to the professional mathematician? How do...

Topics: ERIC Archive, Grade 9, Intuition, Academically Gifted, Geometry, Mathematics Instruction, Geometric...

The focus of this issue of "NetNews" is dyscalculia, or math disability. Most of the attention over the years has been on reading and writing difficulties, thus leading to the belief that math difficulties are not very common or serious. However, it has been estimated that about 6% of school-age children experience significant math difficulties. Although this is far less than the estimated 20% incidence rate for reading difficulties, today's world calls for strong mathematical...

Topics: ERIC Archive, Mathematical Aptitude, Numeracy, Mathematics Education, Learning Disabilities,...

This report presents results of several extensive empirical studies. Prior to these studies it was believed that errors in procedural skills such as multi-digit subtraction could be accurately modelled with two mechanisms: bugs ("competence" phenomena reflecting mistaken beliefs about subtraction which are stable over time) and slips ("performance" phenomena loosely related to subtraction which are unstable over time). A computational descriptive framework, the...

Topics: ERIC Archive, Computer Software, Diagnostic Tests, Elementary Education, Elementary School...

This research dealt with the social constitution of learning in classroom settings, attempting to reveal Bruner's (1990, 1996) folk psychology or folk pedagogy in everyday teaching and learning processes. Specifically, it focused on how the reasons or arguments for completing activities emerge while children are attempting to solve a given mathematical problem in group work. A microethnographic study of such interactions in German elementary classrooms showed that children do not usually reveal...

Topics: ERIC Archive, Classroom Environment, Elementary Education, Elementary School Curriculum, Group...

This paper investigates which students delay taking a required developmental mathematics course and the impact of delay on student performance in introductory microeconomics. Analysis of a sample of 1462 students at a large Midwestern university revealed that, although developmental-level mathematics students did not reach the same level of performance as nondevelopmental microeconomics students, students who did take developmental mathematics performed better than students who had not yet done...

Topics: ERIC Archive, Microeconomics, Remedial Instruction, Developmental Studies Programs, Mathematics...

Mathematical practices and knowledge are often in dispute for those race and class identities at the margins of social power. This talk will describe both the ways in which mathematics can be complicit with social domination, and the ways in which it can aid in resistance and reconfiguration. It will end with a presentation of Culturally Situated Design Tools, software based on the ethnomathematics of cultural artifacts from Native American, African American, Latino, and Youth Subculture...

Topics: ERIC Archive, Racial Bias, Racial Discrimination, Socioeconomic Status, Social Bias, Social Class,...

The stories of 10 outstanding Pennsylvania men and women in this booklet illustrate the determination of educationally disadvantaged people to overcome insurmountable obstacles. They were aided in their successful struggles to enhance their reading and math skills as well as their careers by their participation in various adult basic education and literacy programs throughout Pennsylvania. The 10 people represented various counties in Pennsylvania: (1) Donna Smith, Allegheny County; (2) Donald...

Topics: ERIC Archive, Academic Achievement, Adult Basic Education, Adult Literacy, Career Development, Case...

The gateway to a successful future is not so much knowing your intended career path today but in keeping an open and curious mind about the information you are learning now in your classes and how it relates to potential career opportunities for the future--whether entering the work force after high school, college or advanced studies. This issue of "InDemand" illustrates how math and science skills are key to entering multiple career paths in most high-growth industries. These...

Topics: ERIC Archive, Demand Occupations, Science Process Skills, Mathematics Skills, Industry, Education...