The purpose of this study was to determine prospective teachers' knowledge about the concept of division. One focus of interest was whether the prospective teachers were able to represent division of fractions. The participants were introduced to an alternative model for representation of fractions based on a rate or ratio model of division involving whole numbers. A second focus of interest was whether the prospective teachers would be able to apply this model to problems of division of...

Topics: ERIC Archive, Arithmetic, Pedagogical Content Knowledge, Mathematics Skills, Preservice Teachers,...

This document is the teacher's edition of a learning module designed to help nonnative English speakers develop basic workplace mathematics skills. This module was developed by educators from the Emily Griffith Opportunity School. The math curriculum presented in how math might be taught to nonnative English speakers at a manufacturing worksite. Included in the manual are an introduction outlining the module's objectives and scope, eight session outlines, an appendix explaining basic...

Topics: ERIC Archive, Adult Basic Education, Behavioral Objectives, Cultural Differences, Learning...

This document, which was developed as a resource kit for Australian teachers of adult learners working toward a Certificate of General Education for Adults (CGEA), contains checklists for use in assessing and recording students' progress in their courses. The kit includes three types of records: assessment records (intended for detailed individual assessment of a single assessment task against all the selection criteria and preparing assessment samples for moderation); records of achievement...

Topics: ERIC Archive, Adult Basic Education, Adult Literacy, Check Lists, Foreign Countries, High School...

The purpose of the present study was to reveal the developmental pathway from third grade cognitive competencies to sixth grade conceptual and procedural fraction knowledge through the intervening whole numerical skills at fifth grade. The study used empirical data that come from 536 students in nine schools across two Delaware public school districts. Students were followed longitudinally for four years, beginning in third grade and ending in sixth grade. All students in participating schools...

Topics: ERIC Archive, Fractions, Number Concepts, Mathematics Skills, Numeracy, Cognitive Processes, Public...

Judith P. Hoyer Family Learning Centers, also known as Judy Centers, serve all children birth through kindergarten who live in designated Title I school zones. There are twenty-seven Judy Centers and three satellites throughout Maryland serving forty-four elementary school zones. The Kindergarten Readiness Assessment (KRA) is conducted in the beginning of the kindergarten year and reflects school readiness based on the new curricular standards. The KRA replaces the previous school readiness...

Topics: ERIC Archive, School Readiness, Kindergarten, Early Intervention, Language Skills, Emergent...

Two of the challenges faced by mathematics teacher educators involve the issue of preservice teachers' mathematical content knowledge and the impact this has on their PCK, and the perceived gap between the theoretical knowledge received in their teaching course and the practical knowledge gained in the classroom while on professional experience. This paper examines the use of what is essentially a teacher educator tool or strategy, designed to give pre-service teachers a realistic environment...

Topics: ERIC Archive, Mathematics Teachers, Preservice Teachers, Pedagogical Content Knowledge,...

Introduction: The present study evaluated the feasibility of using an iPad application or "app" for algebra-readiness mathematics, with accompanying braille materials and accessible graphics, when used in authentic educational settings. Methods: Twenty-nine students with visual impairments in grades 4-11 used the materials under the direction of their teachers of students with visual impairments (N = 19). Twenty percent of the mathematics problems included graphics such as maps, line...

Topics: ERIC Archive, Algebra, Assistive Technology, Braille, Computer Graphics, Courseware, Elementary...

The purpose of the current study was to examine four family context

Topics: ERIC Archive, STEM Education, Mathematics Skills, Self Concept, Family Environment, Socioeconomic...

The major idea in this paper is the formulation of a theory of three distinct but interrelated worlds of mathematical thinking each with its own sequence of development of sophistication, and its own sequence of developing warrants for truth, that in total spans the range of growth from the mathematics of new-born babies to the mathematics of research mathematicians. The title of this paper is a play on words, contrasting the act of "thinking through" several existing theories of...

Topics: ERIC Archive, Mathematics Education, Cognitive Development, Thinking Skills, Mathematical Concepts,...

In fall 2003, the Head Start Bureau began implementing the Head Start National Reporting System (NRS) to systematically assess the early literacy, language and numeracy skills of all 4- and 5-year-olds enrolled in Head Start. In addition to child progression on a designated set of outcomes during the year preceding kindergarten, the data will provide the Bureau with information that can be used to enhance its current program monitoring system and develop targeted training and technical...

Topics: ERIC Archive, Disadvantaged Youth, Program Effectiveness, Program Improvement, Mathematics Skills,...

In 1990, the National Assessment of Educational Progress (NAEP) included a Trial State Assessment (TSA); for the first time in the NAEP's history, voluntary state-by-state assessments (37 states, the District of Columbia, Guam, and the Virgin Islands) were made. The sample was designed to represent the 8th grade public school population in a state or territory. The 1990 TSA covered five mathematics content areas (numbers and operations; measurement; geometry; data analysis, statistics, and...

Topics: ERIC Archive, Academic Achievement, Calculators, Educational Assessment, Family Environment, Grade...

This study sought to examine to what extent language learners in an immersion classroom used their native language and the foreign language when performing the cognitive operations involved in math word problems. Thirty-two third- through sixth-graders in a Spanish immersion program participated in the study. Data were collected through: (1) interviews; (2) student questionnaires that covered pupils' abilities, attitudes, and preferences with regard to thinking in Spanish; (3) classroom...

Topics: ERIC Archive, Bilingualism, Cognitive Processes, Elementary Education, Elementary School Students,...

Instructional designers can embrace leadership skills to shape the culture in educational entities toward a "living" institute (Senge, 2000, p. 54). Assessment and measurability set the direction toward the design of plan, implementation and strategy to organization. Paradigm shifts must take place in education.

Topics: ERIC Archive, Instructional Design, Leadership Qualities, Instructional Leadership, Change Agents,...

Georgia has one of the few state-funded universal pre-kindergarten programs in the United States, with the aim of providing pre-k services to all 4-year-olds whose families want their children to participate in the program, regardless of family income level. In the 2011-2012 school year, Georgia's Pre-K Program served a total of over 94,000 different children throughout the year in a variety of settings across the state, including local school systems, private settings, and blended Head...

Topics: ERIC Archive, Literacy, Kindergarten, Preschool Education, Mathematics Skills, Family Income, Child...

In a meta-analysis of 164 studies, Alfieri, Brooks, Aldrich, and Tenenbaum (2010) found that assisted discovery learning was more effective than explicit instruction or unassisted discovery learning and that explicit instruction resulted in more favorable outcomes than unassisted discovery learning. In other words, "unassisted discovery does not benefit learners, whereas feedback, worked examples, scaffolding, and elicited explanations do." The primary aim of the present research was...

Topics: ERIC Archive, Discovery Learning, Reading Instruction, Feedback (Response), Beginning Reading,...

This qualitative study clarifies opinion of 32 European volunteer youth leaders on concepts of competence, fewer opportunities and enlargement strategies on competence of fewer opportunities. Leaders underline main competencies as follows: tongue, languages, mathematical, digital, learning, social, entrepreneurship, cultural. Key competences are those which all individuals need for personal fulfillment and development, active citizenship, social inclusion and employment (Figel, 2007). The key...

Topics: ERIC Archive, Competence, Skill Development, Educational Opportunities, Qualitative Research,...

This is an exploratory study into the individual problem-posing characteristics of 480 Grade 9 Singapore students who were novice problem posers working on two geometric tasks. The students were asked to pose a problem for their friends to solve. Analyses of solvable posed problems were based on the problem type, problem information, solution type and domain knowledge. With the open-ended task, the students tend to over-condition their problems and to produce more problems with implicit...

Topics: ERIC Archive, Foreign Countries, Problem Solving, Grade 9, Geometry, Geometric Concepts,...

Three studies examined the abstractness of children's mental representation of counting, and their understanding of the cardinality principle, namely, that the last number word used in a count tells how many items there are. In the first experiment, 24 toddlers of 2-3 years counted objects, actions, and sounds. Findings revealed that children counted objects best; most were also able to count actions and sounds. This finding suggests that at a very young age, children begin to develop an...

Topics: ERIC Archive, Age Differences, Comprehension, Computation, Fundamental Concepts, Individual...

This is an activity-oriented guide for general mathematics classes, grades 8-12. Mathematics used includes measurement, estimation, time, computation, ratio, and money. Students assume the role of an industrial engineering technician determining the amount of time allowed and operator pay for completing an operation on a production line. A deck of playing cards, a clipboard, a stopwatch, and graph paper are needed. The term "piece rate," related with other pay methods is explained,...

Topics: ERIC Archive, Computation, Mathematical Applications, Mathematical Enrichment, Mathematics...

Mathematical knowledge can be categorized in different ways. One commonly used way is to distinguish between procedural mathematical knowledge and conceptual mathematical knowledge. Procedural knowledge of mathematics refers to formal language, symbols, algorithms, and rules. Conceptual knowledge is essential for meaningful understanding of mathematical ideas because it is knowledge rich in relationships. Students use conceptual knowledge to develop underlying meaning for procedural knowledge,...

Topics: ERIC Archive, Mathematics Education, Symbols (Mathematics), Mathematical Applications, Mathematics...

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia tendencies and giving them relevant extra learning opportunities based on their specific difficulties are critically important for them to go with...

Topics: ERIC Archive, Mathematics Skills, Learning Disabilities, Identification, Arithmetic, Brain...

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 the experimental classroom design with a pretest-posttest control in order to increase the representation of visual thinking ability on mathematical...

Topics: ERIC Archive, Junior High School Students, Mathematics Instruction, Secondary School Mathematics,...

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and when they interpret mathematical information" (ACARA, 2012). Concept maps can be used to organise and represent the connections in knowledge...

Topics: ERIC Archive, Foreign Countries, Concept Mapping, Secondary School Mathematics, Secondary School...

Despite the importance of teacher fractional knowledge, there are several areas of teacher understanding that are not well understood. The purpose of this study was to characterise profiles of pre-service teachers' (PSTs) mathematical competence on the topic of fraction multiplication by examining PSTs' understanding of multiplication of fractions in three different contexts. Analyses of 60 PSTs' written responses revealed that there are distinct gradations of competency, ranging from the PSTs...

Topics: ERIC Archive, Preservice Teachers, Mathematics Instruction, Multiplication, Fractions, Pedagogical...

The purpose of this descriptive survey research study conducted with agriculture teachers in North Carolina was to determine their in-service training needs in order to be effective for preparing students with the 21st century skills necessary for students to be successful. This study reaffirms the need for continuation of leadership education as an important skill and integration of reading, writing, and math concepts into all agricultural education curricula for preparing students to be...

Topics: ERIC Archive, Inservice Teacher Education, Agricultural Education, Cooperative Learning, Role,...

The purpose of this study was to investigate whether gender accounts for student differences in performance and achievement in mathematics. Data for the study were drawn from the Second International Mathematics Study (SIMS) of seventh and eighth grade students from Japan, Belgium, Canada (British Columbia and Ontario), France, the United States, New Zealand, and Thailand. Students were tested on the same mathematical items and problems. Results indicated no substantial gender effects or...

Topics: ERIC Archive, Females, Foreign Countries, Global Approach, Grade 7, Grade 8, Junior High Schools,...

This paper provides information about North Carolina End-of-Course Exams. The North Carolina End-of-Course Assessments were developed for two purposes: (1) To provide accurate measurement of individual student knowledge and skills specified in the North Carolina Standard Course of Study; and (2) To provide accurate measurement of the knowledge and skills attained by groups of students for school, school system, and state accountability. [For the main report, "State High School Tests: Exit...

Topics: ERIC Archive, Exit Examinations, Academic Standards, State Standards, Academic Failure, Alignment...

Since 2007, when this technical report was originally issued, the assessment field has made considerable progress in developing valid and reliable screening measures for early mathematics difficulties. This update includes new research published since 2007. It focuses on valid and reliable screening measures for students in kindergarten and first grade. However, the authors also examined data on screening tests for second and third grades because the goal of screening is to identify students...

Topics: ERIC Archive, Mathematics Skills, Learning Problems, Screening Tests, Kindergarten, Grade 1, Grade...

The development of numerical abilities was examined in three groups of 5 year-olds: one including 13 children accomplishing a numerical training in pencil-and-paper format (EG1); another group including 21 children accomplished a homologous training in computerized format; the remaining 24 children were assigned to the control group (CG). The participants were assessed at three successive times (t0, t1 and t2) with a battery of validated tests assessing numerical abilities and fluid...

Topics: ERIC Archive, Preschool Children, Mathematics Skills, Numbers, Computer Uses in Education,...

The aim of this study is to know the differences of enhancement in mathematical problem solving ability (MPSA) between the students who received soft skill- based metacognitive learning (SSML) with the students who got conventional learning (CL). This research is a quasi experimental design with pretest-postest control group. The population in this study is the students of Junior High School in Pekanbaru city. The sample consist of 135 students, 68 of them are from the high-level school, and 67...

Topics: ERIC Archive, Mathematics Instruction, Problem Solving, Mathematics Skills, Junior High School...

This pilot study examined the efficacy of a Tier 2 first-grade mathematics intervention program targeting whole-number understanding for students at risk in mathematics. The study used a randomized block design. Students (N = 89) were randomly assigned to treatment (Fusion) or control (standard district practice) conditions. Measures of mathematics achievement were collected at pretest and posttest. Treatment and control students did not differ on mathematics assessments at pretest. A series of...

Topics: ERIC Archive, Grade 1, Elementary School Mathematics, Intervention, At Risk Students, Randomized...

This article seeks to identify and review the basic characteristics of learning disability which are specifically mentioned in the literature. In addition, the article intends to conduct a brief analysis on learning disability policy in Israel and the differentiation problems at the level of awareness among the Arab society in Israel. Despite the fact that during the past twenty years this field earned a significant progress in Israel, lags in awareness and educational policy between the Arab...

Topics: ERIC Archive, Learning Disabilities, Community Involvement, Educational Policy, Etiology, Reading...

Mathematical proficiency serves as a foundation for student success in the classroom and real world. One component of mathematical proficiency is fluency with basic facts. Frequently, students with mathematics difficulties struggle to become proficient and fluent in the four basic operations. Interventions are available to help develop and promote fluency for students. Digital-based interventions, such as programs on computers or tablet applications, are one avenue by which students are able to...

Topics: ERIC Archive, Intervention, Mathematics Instruction, Electronic Learning, Mathematics Skills,...

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis and probability, algebra, and geometry. The following are among the broad categories of occupations included in the eight occupational groups:...

Topics: ERIC Archive, Algebra, Competency Based Education, Correlation, Data Analysis, Geometry,...

A growing debate exists over the possibility that various types of external rewards may have negative effects on intrinsic motivation. Past research has produced conflicting results. The present study examines past research in light of behavioral principles and utilizes single-subject research methods to examine the potential effects of ability--and effort-based verbal praise statements on mathematics task performance and task persistence. Results of this study do not support the criticism...

Topics: ERIC Archive, Learning Motivation, Mathematics Achievement, Persistence, Criticism, Rewards, Verbal...

Home-based peer tutoring was used to teach math skills to 4 girls with deficits in mathematics and histories of abuse or neglect. Girls living in the same home formed tutoring dyads, and each participant served as both the peer tutor and the tutee during the course of the study. At the initiation of the tutoring intervention, an expert tutor provided multiple 3-min tutoring sessions to the designated peer tutor on three or four mathematics skills. The peer tutor concurrently provided 3-min...

Topics: ERIC Archive, Females, High Risk Students, Tutors, Mathematics Skills, Peer Teaching, Mathematics...

The focus of this paper is the use of National Assessment Program in Literacy and Numeracy (NAPLAN) items to develop students' competence in reading mathematical text, to promote thinking strategies including estimation, and to evaluate alternative solutions for errors and misconceptions. Showing students test items and discussing strategies for thinking about questions and responses promotes student confidence and resilience, and enables a greater sense of student control over their learning....

Topics: ERIC Archive, Test Items, Critical Thinking, Misconceptions, Thinking Skills, Educational...

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents' funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised...

Topics: ERIC Archive, Mathematics Skills, Indigenous Populations, Cultural Maintenance, Cultural Relevance,...

This study examines the trends of the U.S. states' reading and math proficiency standards before and after the adoption of the Common Core State Standards (CCSS) and explores their impact on school practices and student achievement. Drawing on the 2003-15 National Assessment of Educational Progress (NAEP) grades 4 and 8 assessment and survey datasets, the study gives new insights into the CCSS policy challenges and outcomes. The states that adopted CCSS raised the rigor of proficiency standards...

Topics: ERIC Archive, Common Core State Standards, Educational Trends, Reading Skills, Mathematics Skills,...

A quantitative observational study exploring the relationship of gender to mathematics self-efficacy and the frequency of back substitution in multiple-choice assessment sampled undergraduates at a western United States parochial university. Research questions addressed: to what extent are there gender differences in mathematics self-efficacy, as demonstrated on multiple-choice test items; and to what extent are there gender differences in the frequency of employing back substitution as an...

Topics: ERIC Archive, Test Items, Self Efficacy, Multiple Choice Tests, Algebra, Gender Differences,...

Developed from Noddings's (2002) care theory, von Glasersfeld's (1995) constructivism, and Ryan and Frederick's (1997) notion of subjective vitality, a mathematical caring relation (MCR) is a quality of interaction between a student and a mathematics teacher that conjoins affective and cognitive realms in the process of aiming for mathematical learning. In this paper I examine the challenge of establishing an MCR with one mathematically talented 11-year-old student, Deborah, during an 8-month...

Topics: ERIC Archive, Constructivism (Learning), Caring, Mathematics Teachers, Mathematics Education,...

This study was conducted on year 4 students enrolled in the Bachelor of Education program for Cycle one teacher candidates. The effect of practicing mental calculation strategies in improving students' numeracy proficiency was put under some tests to measure its effect in a scientific way. A Pre-quiz was conducted before with no prior practice done in order to check the strategies the students were using in performing calculations. After four weeks practice and implementation which focused...

Topics: ERIC Archive, Foreign Countries, Mental Computation, Learning Strategies, Preservice Teachers,...

This article summarizes the findings of research studies focusing on number sense instruction to improve mathematics competence of school going children. Twenty-three studies were located that met the inclusion criteria. Interventions gleaned from the review were categorized based on type of instruction (i.e., constructivist, explicit or a combination of the two). Treatment outcomes are discussed in relation to the various instructional approaches, student characteristics (e.g., grade, age),...

Topics: ERIC Archive, Literature Reviews, Mathematics Instruction, Numeracy, Numbers, Mathematics Skills,...

Theory-based prototype computer-video instructional modules were developed to serve as an instructional supplement for students experiencing difficulty in learning mathematics, with special consideration given to students underrepresented in mathematics (particularly women and minorities). Modules focused on concepts and operations for factors, prime numbers, and fractions. Task analysis and demand specification procedures were used to sequence instructional objectives within and across topics....

Topics: ERIC Archive, Academic Achievement, Affective Objectives, Computer Assisted Instruction, Computer...

Noting that portfolios contain the students' best efforts at writing and mathematics problem-solving skills, this pamphlet discusses issues surrounding Vermont's portfolio assessment program from the parent's point of view. The pamphlet discusses reasons to use portfolios, how portfolios differ from traditional ways of looking at students' writing and math skills, what goes into a portfolio, how portfolios are evaluated, how the results of portfolio assessment are used by various entities,...

Topics: ERIC Archive, Alternative Assessment, Elementary Secondary Education, Evaluation Methods,...

This document contains the lesson plans for a 12-week course in basic workplace pre-algebra that was developed for clothing and textile workers through the joint effort of Northeastern Illinois University's Chicago Teachers' Center and the Amalgamated Clothing and Textile Workers Union. A chart for recording students' mastery of 25 course objectives is provided. The following activities are completed in the 12 course sessions: making introductions (including beginning a placement inventory test...

Topics: ERIC Archive, Adult Education, Arithmetic, Basic Skills, Behavioral Objectives, Competency Based...

Parents in affluent communities have been following the suggestion of research and delaying kindergarten entry of their young age-eligible children in order to increase the likelihood of the child's academic success. This study examined the correlation between the chronological age of a child entering kindergarten and his or her performance on reading and math achievement tests in second grade. Gender differences in math and reading performance in second grade were also examined. The subject...

Topics: ERIC Archive, Academic Achievement, Age Differences, Age Grade Placement, Educational Research,...

This curriculum package on production percentage math is a product of the Workforce 2000 Partnership, which combined the resources of four educational partners and four industrial partners in Alabama, Georgia, and South Carolina to provide education and training in communication, computation, and critical thinking to employees in the apparel, carpet, and textile industries. After a brief overview of the Workforce 2000 Partnership, the curriculum package's contents are described. Presented next...

Topics: ERIC Archive, Adult Education, Adult Literacy, Arithmetic, Behavioral Objectives, Carpeting,...

This paper outlines the current state of knowledge about how intellectual competence is acquired. Implications resulting from recent changes in the psychology of learning and development are beginning to revitalize the science of learning and instruction. Four broad topics illustrate the links between instructional experiments, fundamental research on learning and thinking, and potential applications to the science of instruction: (1) understanding natural language; (2) learning to read; (3)...

Topics: ERIC Archive, Association (Psychology), Cognitive Ability, Cognitive Processes, Cognitive...

This article addresses the question: "What are the implications for the preparation of prospective elementary teachers of 'early algebra' in the elementary grades curriculum?" Part of the answer involves language aspects of algebra: in particular, how a change in pre-service teachers' attitudes to algebra, from instrumental to relational, is correlated with learning the conventional meaning of algebraic and other mathematical terms. (Contains 13 references.) (Author/MM)

Topics: ERIC Archive, Algebra, Elementary Education, Elementary School Teachers, Higher Education,...