This document presents content standards tables for math. [CASAS content standards tables are designed for educators at national, state and local levels to inform the alignment of content standards, instruction and assessment. The Content Standards along with the CASAS Competencies form the basis of the CASAS integrated assessment and curriculum management system. For "Aligning CASAS Competencies and Assessments to Basic Skills Content Standards. Second Edition", Content Standards for...

Topics: ERIC Archive, Adult Education, Mathematics Skills, Basic Skills, Academic Standards

The problem considered in this paper demonstrates that quite profound and inherently fascinating mathematics is accessible to students who have a sound number sense and deep conceptual understanding of very basic mathematics. This is one of many reasons why we should teach mathematics in ways that promote these attributes in students.

Topics: ERIC Archive, Numbers, Mathematical Concepts, Mathematics Skills, Mathematics Instruction,...

"Kumon Math," published by Kumon North America, Inc., is a supplemental mathematics curriculum for students in preschool through secondary school. The curriculum is not structured by age or grade level, but by a student's own pace, and is composed of hundreds of short assignments that progress through increasingly difficult mathematics skills. Students complete one assignment every weekday and attend a Kumon center for two sessions per week. Every assignment is timed and graded....

Topics: ERIC Archive, Enrichment Activities, Meta Analysis, Mathematics Curriculum, Mathematics Skills,...

Using mathematical gossip in the classroom allows teachers to expand their students' horizons, and provide pathways to improvement of understanding. The expansion of a simple idea into another mathematical context can enrich a student's learning. In particular it may help to bridge the gap between purely procedural approaches and a conceptual understanding of the underlying mathematics. Having both procedural and conceptual understanding provides a springboard for strategic use of mathematics...

Topics: ERIC Archive, Mathematics Instruction, Teaching Methods, Concept Formation, Mathematics Skills,...

This module assumes that the information presented in previous modules is well known to the learner. Module 5 is the second 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 5 focuses on how the practices connect to the content standards using tasks as examples. Additionally, there is a short section on the interrelatedness of the Math Practices which provides...

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

This module assumes that the information presented in previous modules is well known to the learner. Module 4 is the first 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 4 focuses on developing an initial understanding of the Standards by Mathematical Practices by closely examining the wording of the descriptions for each practice and viewing instructional...

Topics: ERIC Archive, Mathematics Education, Academic Standards, State Standards, Teacher Role, Student...

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever possible, to ensure that they regularly question those things that they take for granted. In this article we consider some more favourite problems:...

Topics: ERIC Archive, Calculus, Mathematics Instruction, Mathematical Logic, Mathematics Skills, Problem...

The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology that treats person-in-activity as an integral whole. Laves approach was used as the researcher conducted 70 hours of ethnographic observation of...

Topics: ERIC Archive, Civil Engineering, Engineers, Mathematics Activities, Mathematics Skills, Research...

Examined were preschoolers' spontaneous use of correspondence strategies. A total of 40 children 4 and 5 years of age were asked to divide a pile of cookies into two equal groups. The cookies were two sizes, halves and wholes, so even though there were trials with an odd number of cookies, it was possible to divide the cookies evenly. When children's division strategies and accuracy in dividing the cookies were examined, data indicated that subjects frequently used correspondence strategies to...

Topics: ERIC Archive, Age Differences, Cognitive Ability, Difficulty Level, Division, Mathematics Skills,...

Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is the idea that they are parts of a whole. The fact that one whole object can be divided into many equal parts, with each part having a name relative to...

Topics: ERIC Archive, Numbers, Mathematics Instruction, Mathematics Skills, Teaching Methods, Human Body,...

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...

According to this author, the solution to the "phonics versus whole language" debate over the teaching of reading is balance and a focus on the needs of all students. There is similarly a need, in developing numerate young people, to focus on the teaching and learning of mathematics and mathematics skills some of the time, and on application and tasks some of the time (not necessarily at discrete times). Clearly the balance needs to be flexible and dependent on the particular needs of...

Topics: ERIC Archive, Numeracy, Mathematics Instruction, Mathematics Teachers, Foreign Countries, Learning...

Founded in 2006 by Jonathan Osler, Math and Community Organizing teacher at El Puente Academy for Peace and Justice, a public CES high school in Brooklyn, New York, Radical Math is an organization for educators working to integrate issues of political, economic, and social justice into math education. In April 2007, Radical Math cosponsored "Creating Balance in an Unjust World" a conference on math education and social justice. With the urgent need for mathematical literacy and the...

Topics: ERIC Archive, Social Justice, Numeracy, Mathematics Skills, High Schools, Public Schools,...

This report discusses the place of numeracy in adult education, examines conceptions of what numeracy and numeracy provision might include, and explores links between literacy and numeracy provision. Section A takes a critical look at how much attention is being paid to mathematics education in adult education/adult literacy programs and addresses issues related to the place of numeracy in adult literacy education. Section B discusses numeracy from the perspectives of employers, mathematics and...

Topics: ERIC Archive, Adult Basic Education, Adult Literacy, Adult Programs, Basic Skills, Literacy...

Everyday, people face situations that call for adding, subtracting, multiplying, or dividing, and at least half of the time, these calculations are accomplished without the use of pen, paper, or calculators. Because figuring "in your head" is such an important life skill, it should have a regular role in classroom math teaching. This article describes an approach to teaching mental math skills using an exercise called "hands-on-the-table-math." To be sure this is a learning...

Topics: ERIC Archive, Mathematics Skills, Teaching Methods, Mathematics Instruction, Arithmetic, Problem...

The Brookings Institution report questions the efficacy of increasing the number of students who take algebra in eighth grade. Although this policy has resulted in more equitable access to advanced math study, the report argues that a subgroup of students enrolled lack the basic mathematical skills needed to succeed. The report further argues that the presence of lower achievers may weaken the instructional opportunities of highly proficient students. The report recommends that algebra...

Topics: ERIC Archive, Low Achievement, Grade 8, Algebra, Mathematics Instruction, Mathematics Achievement,...

In the area of cognitive skills, the actual differences between males and females are relatively small. Females score slightly higher on verbal tasks and males score slightly higher on mathematical tasks. According to the cognitive approach to stereotypes, people should perceive these differences to be quite large. To determine whether subjects would estimate large differences between females and males in verbal and mathematical performance, 101 college students estimated the average scores for...

Topics: ERIC Archive, Cognitive Ability, College Students, Higher Education, Mathematics Skills, Sex...

The National Assessment of Educational Progress (NAEP) is a congressionally mandated project of the U.S. Department of Education's National Center for Education Statistics. It assesses what students in the United States should know and be able to do in geography, reading, writing, mathematics, science, U.S. history, the arts, civics, and other academic subjects. This document presents a framework and recommendations for the 1996 NAEP mathematics assessment that are intended to reflect recent...

Topics: ERIC Archive, Academic Achievement, Elementary Secondary Education, Evaluation, Mathematical...

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,...

This module examines Rigor, the third of the three shifts required for implementation of the Common Core State Standards for Mathematics (CCSSM). This module is based on the premise that the information from Modules 1 and 2 is well understood. Course Objectives: By the end of the module, the learner will be able to: (1) identify the components of rigor and give examples of each; (2) describe the relationship among the components; (3) determine if a standard is written to align with one of the...

Topics: ERIC Archive, Academic Standards, State Standards, Mathematics, Mathematics Skills, Comprehension,...

Research shows that a child's goals for and beliefs about learning are related to his or her performance in mathematics. This pamphlet includes suggestions for parents to help ensure that their children develop positive learning attitudes and succeed in mathematics, including: (1) Introducing babies and toddlers to numbers, counting and shapes; (2) Helping pre-kindergartners explore basic mathematic language such as "more than," "less than," "equal to,"...

Topics: ERIC Archive, Mathematics Education, Caregivers, Parents, Childhood Attitudes, Young Children,...

No student who hopes to compete in today's rapidly evolving global economy and job market can afford to graduate from high school with weak mathematical skills, which include the ability to use logic, reason, and solve problems. The benefits associated with improving the math performance of American students also extend to the larger U.S. economy. Highlights of this paper include: (1) American students lag far behind other industrialized nations in math skills; and (2) Requiring more students...

Topics: ERIC Archive, Mathematics Skills, Education Work Relationship, Global Approach, Mathematics...

Preschool children's problem-solving strategies on structured and unstructured number tasks were compared in this study. Participants were 20 four-years-olds and 20 five-year-olds. Each child was administered a number conservation, addition and subtraction, and division task. The addition and subtraction task contained trials which were designed to classify children into one of three levels of addition and subtraction understanding: primitive, qualitative, and quantitative. In the division...

Topics: ERIC Archive, Addition, Division, Individual Differences, Mathematics Skills, Performance Factors,...

This study assessed estimation skills on both static and transformation (conservation) tasks on numerosities ranging from 3 to 16, and included addition and subtraction trials to control for response bias. A total of 148 four- and five-year-old children estimated the number of balls of yarn sewn on elastic straps, and participated in 1 addition, 1 subtraction, and 2 conservation trials at each numerosity of the transformation task. The children were classified into three groups based on their...

Topics: ERIC Archive, Arithmetic, Conservation (Concept), Estimation (Mathematics), Individual Differences,...

"Saxon Math" focuses on fundamental mathematics skills, targeting children from kindergarten through grade 12. This report focuses on middle school math, defined as grades 6 through 9. The 6th grade curriculum covers simplifying expressions containing parentheses, graphing functions, and understanding ratios and proportions. The 7th grade curriculum covers pre-algebra topics such as rate, powers, roots, and geometric proofs. The 8th grade curriculum covers all topics usually taught in...

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

The purpose of this study was to examine the division procedures of preschool children to determine whether such procedures involved one-to-one correspondence. Large and small numerosity trials were included so that the amount of effort and ease of using other procedures would vary. Odd and even number trials were included to determine whether children actually knew what the procedures they used implied about relative numerosity. Subjects were 20 four-year-olds and 20 five-year-olds, with equal...

Topics: ERIC Archive, Age Differences, Cognitive Ability, Difficulty Level, Division, Error Patterns,...

What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity theoretic model of abstraction in context. Selected protocol data are presented. The initial state of the abstractions and changes that were observed during the consolidation process are discussed. Features of consolidation noted are: reconstruction of...

Topics: ERIC Archive, Abstract Reasoning, Mathematics Skills, Task Analysis, Protocol Analysis, Cognitive...

Nonroutine problem-solving, too, involves elements of routine. Often, elementary routines such as solving for a variable are not carried out without error. In this paper, we use new findings from neuroscientific research to explain why even excellent students make mistakes in elementary routines. [For complete proceedings, see ED489597.]

Topics: ERIC Archive, Problem Solving, Mathematics Education, Mathematics Skills, Error Patterns,...

The University of Wollongong's first locally developed and hosted Massive Open Online Course (MOOC) "The Reluctant Mathematician" was run in the last four weeks of our summer holiday, prior to Autumn session in 2014. It was developed to lift maths skills at our university and also in the community--where maths skills continue to be a challenge and in some cases a source of stress. Internally the MOOC provided an alternative online way to support students who struggle with mathematics...

Topics: ERIC Archive, Online Courses, Mathematics Instruction, Scaffolding (Teaching Technique), College...

All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).

Topics: ERIC Archive, Arithmetic, Computation, Mathematics Instruction, Calculators, Teaching Methods,...

In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete representations. This study presents a finite abelian group of inversions of two letter symbols with vertical and horizontal axes of symmetry and whose...

Topics: ERIC Archive, Algebra, Symbols (Mathematics), Mathematics Instruction, Multiplication, Mathematical...

Hispanic students are notably behind their white counterparts in the core academic skills. Although the precise size of the gap depends on the subject area, age or grade, and the assessment, by all measures, a significant gap in mathematics, reading skills and science exists between Hispanic and white students. Educational achievement, or knowledge learned in school, matters. Persons with the same academic diploma often have vastly different levels of math knowledge, reading abilities or...

Topics: ERIC Archive, White Students, Reading Skills, Academic Achievement, Hispanic American Students,...

This paper provides a brief literature review on the use of building blocks in the elementary school classroom and discusses classroom activities using blocks as they influence other subject areas. The paper includes work activities that develop mathematics and science skills, language arts and reading, and social sciences. Comments on these activities from experienced elementary school teachers are included. (JPB)

Topics: ERIC Archive, Class Activities, Cognitive Development, Early Childhood Education, Kindergarten,...

This guide provides illustrated examples of classroom learning centers designed for use with migrant students. Designating learning centers in the classroom is an effective way to introduce, develop, and reinforce skills in an enjoyable way. The learning centers described in this guide can be made from: (1) fabric boards (large); (2) fabric boards (small); (3) heavy corrugated cardboard, wood, or form board; and (4) real life objects. Spaces can be divided into mini centers, and can be...

Topics: ERIC Archive, Curriculum Guides, Elementary Secondary Education, Learning Activities, Learning...

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 different parts of mathematical thinking can be either enabled or hindered by aspects of human nature. This novel theoretical framework can...

Topics: ERIC Archive, Mathematics Skills, Mathematics Instruction, Thinking Skills, Case Studies,...

Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a structure-preserving mapping from a base or source to the target. Although concrete aids can provide valuable assistance to concept acquisition, their...

Topics: ERIC Archive, Abstract Reasoning, Analogy, Elementary Education, Elementary School Mathematics,...

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 methods for making valid inferences. A knowledge of mathematics is essential for a well-educated citizenry. However, the need for and use of...

Topics: ERIC Archive, At Risk Persons, Course Descriptions, Foreign Countries, Mathematical Concepts,...

The University of Wisconsin-Madison is using a novel assessment process to find whether rising juniors have the quantitative skills needed for success in their chosen upper-division courses. Sampling from departments across the campus, information is gathered about quantitative skills used in specific courses and the extent to which students can show these important skills at the start of the semester. Instructors play a key role in helping to design free-response tests reflecting capabilities...

Topics: ERIC Archive, College Students, Demonstration Programs, Higher Education, Mathematics Skills,...

Noting that parental involvement is an important factor in student success, this study examined differences in student learning in reading and mathematics related to levels of parental volunteerism in kindergarten, after controlling for differences in testing scores at the beginning of the school year. The study drew on data from the National Center for Education Statistics Early Childhood Longitudinal Study (kindergarten class of 1998-1999). The results of multivariate analysis of covariance...

Topics: ERIC Archive, Academic Achievement, Kindergarten, Mathematics Skills, Parent Participation,...

Noticing young children's mathematics can involve talking to them and watching as they undertake mathematical tasks or answer questions. Interviews are a key methodology for researchers who focus on young children's mathematical learning, providing opportunities to notice what children are doing and gain insights into their thinking. This paper focuses on one-to-one task based interviews as a tool for noticing young children's mathematics and particularly the use of flexible, semi-structured...

Topics: ERIC Archive, Mathematics Skills, Young Children, Semi Structured Interviews, Down Syndrome,...

If the ability to reason proportionally seems to be a good indication of likely success in further mathematical pursuits (Lamon, 1999), how do children develop this ability, and how can teachers facilitate this? In this present study, six ratio/rates task-based assessment questions were trialled on ten students from Grades 5 to 9 in an attempt to describe the developing understanding of students within this construct of rational number. Tentative points of growth (or stages of understanding)...

Topics: ERIC Archive, Mathematics Instruction, Numbers, Foreign Countries, Mathematical Concepts,...

To ensure all students have every opportunity to succeed, Indiana adopted world-class academic standards in English-language arts, mathematics, science, and social studies and an assessment system to measure student progress. These standards clearly outline what students should know and be able to do in each subject, at each grade level. This booklet clearly spells out what students should know and be able to do in Integrated Mathematics I. Examples are given to provide an understanding of what...

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

In this study, the teaching experiment methodology is used to observe firsthand a gifted student's mathematical learning and reasoning. A series of teaching experiments was conducted with 1 gifted and 1 average 7th-grade student to investigate how the gifted student's mathematical concepts and operation constructions differed from those of the average student. The teaching experiment approach provides opportunities for gifted and average students to be challenged by immersion in various...

Topics: ERIC Archive, Grade 7, Mathematics Skills, Problem Solving, Teaching Methods, Thinking Skills,...

These excerpts from the National Council of Teachers of Mathematics (NCTM) Standards support the Third International Mathematics and Science Study (TIMSS) Resource Kit by offering some context for discussing the teaching of algebra and geometry seen in the videotapes that are also part of the kit. The Standards describe the mathematics content that all students should know and be able to do. This document is divided into grade levels K-4, 5-8, and 9-12 with each level having 12 to 14 standards....

Topics: ERIC Archive, Algebra, Elementary Secondary Education, Geometry, Mathematics Achievement,...

The evidence on the failure of American high schools to educate and graduate their students is widespread. The release of the latest National Assessment of Educational Progress (NAEP) long-term trends (LTT) assessment data in April adds another data point to this sad compendium. In this Outlook, I focus on trends in high school math, an area of critical national need, and one that has been a focus of national policy for decades. I present data that show a disconnect between the rigor of the...

Topics: ERIC Archive, High Schools, Mathematics Instruction, Educational Trends, Mathematics Skills,...

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...

This paper reports on a study that investigated the interpretation of media graphs developed by student teachers. The analyses of interviews indicate that cognitive, affective and contextual, aspects might constitute important components of the interpretation of graph such as those that we can find in print media. Particularly we discuss Critical Sense in graphing which is a skill that people can use to read the data, building an interpretation that balances these different aspects. The...

Topics: ERIC Archive, Student Teachers, Graphs, Cognitive Processes, Mathematics Instruction, Interviews,...

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 equals a stronger economy. (Contains 13 endnotes.)

Topics: ERIC Archive, Mathematics Skills, Educational Needs, Mathematics Achievement, Mathematical...

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry representatives to find out what mathematical skills were needed in the workplace, estimation was identified as an essential skill. In this article,...

Topics: ERIC Archive, Computation, Mathematics Skills, Mathematics, Mathematics Instruction, Foreign...

This summary presents the major findings of recent research carried out at the Center for Research on Elementary and Middle Schools at Johns Hopkins University and published in "Ability Grouping and Student Achievement in Elementary Schools: A Best-Evidence Synthesis." The center examined more than 100 studies of five ability-grouping plans commonly used in elementary schools: between-class, within-class, regrouping for reading and/or mathematics, the "Joplin Plan," and...

Topics: ERIC Archive, Ability Grouping, Academic Achievement, Elementary Education, High Achievement, Low...