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5,573 results on '"área"'

1. Facilitating Adolescents with Disabilities Understanding of Area and Perimeter Concepts via Manipulative Instruction.

Author

Cass, Mike, Cates, Dennis, Jackson, Cynthia W., and Smith, Michelle

Abstract

A study examined the effect of manipulative instruction on the acquisition and maintenance of perimeter and area problem-solving skills by students with learning disabilities in math. Three rural students with learning disabilities in mathematics in grades 7-10 participated in the study. All training was conducted daily for 15-20 minutes on a one-on-one basis by a certified special education teacher using a geoboard. The procedures for teaching perimeter and area problem solving are detailed. None of the students could solve the problems presented to them during the baseline condition. With each intervention, there was a marked increase in problem-solving ability. Using the geoboard, the students reached performance criterion (at least 80 percent of problems solved correctly on 3 or more consecutive days) in the two types of problem solving after 5-7 days of practice. Maintenance checks performed in each of 3 consecutive weeks following treatment revealed that all students solved all area and perimeter problems correctly when using the geoboard. Immediately following Christmas vacation, the students were given four area and four perimeter problems and asked to solve them using only paper and pencil. They scored 90-100 percent. The findings revealed that the use of concrete manipulatives promotes the maintenance of skills. (Contains 16 references.) (TD)

Published
2002

2. Reconstructing Mathematics Pedagogy from a Constructivist Perspective.

Author

Simon, Martin A.

Abstract

Constructivist epistemologies have been instrumental in recent research on mathematics learning and have provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it offers no particular vision of how mathematics should be taught; models of teaching based on constructivism are needed. Data are presented from a whole-class teaching experiment in which constructivist perspectives encountered problems of teaching practice. The analysis of the data led to the development of a model of teacher decision making with respect to mathematical tasks. Central to this model is the creative tension between the teacher's goals for student learning and the responsibility to be sensitive and responsive to the mathematical thinking of the students. Themes represented include: (1) Students' thinking/understanding is taken seriously and given a central place in the design and implementation of instruction; (2) The teacher's knowledge evolves simultaneously with the growth in the students' knowledge; (3) Planning for instruction is seen as including the generation of a hypothetical learning trajectory; (4) The continually changing knowledge of the teacher creates continual change in the teacher's hypothetical learning trajectory. Contains 47 references. (Author/GW)

Published
1993

3. Mathematics at Work in Alberta.

Author

Alberta Dept. of Education, Edmonton., Glanfield, Florence, and Tilroe, Daryle

Abstract

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information for solving the problem, ideas to consider in the problem-solving process, and the solution. The problem topics include: (1) straightening steel rods shipped to customers in coils; (2) laying out the horizontal alignment of a highway; (3) calculating the dimensions of unusually shaped windows; (4) calculating parking capacities on city street; (5) transmitting telephone calls; (6) adjusting a parabolic satellite antenna; (7) calculating the materials required to construct a highway; (8) calculating the forces on a bridge; (9) mounting a gas heater for optimal efficiency; (10) maximizing the efficiency of a telephone network; (11) forecasting energy needs of electrical utilities; (12) calculating the terminal velocity of a metal sphere; (13) ensuring adequate visibility at a railway crossing; (14) analyzing spot speed data to determine highway speed limits; and (15) calculating minimum area requirements that metal plates must cover in the construction of wooden trusses. (MDH)

Published
1992

4. Responses to the Have a Heart Problem.

Author

Mann, Robert

Abstract

Presents solutions to the Have a Heart problem that appeared in the February 2002 issue of this journal. (Author/NB)

Published
2003

7. Measure for Measure.

Author

Farenga, Stephen J., Joyce, Beverly A., and Ness, Daniel

Abstract

Presents an activity on measurement and points out the importance of units which, in most cases, are omitted by students. Focuses on measurement in informal settings, indirect measurement, ratio and scales, and surface area to volume ratio. (YDS)

Published
2002

8. Assessing Geometric and Measurement Understanding Using Manipulatives.

Author

Strutchens, Marilyn E., Harris, Kimberly A., and Martin, W. Gary

Abstract

Assesses students' geometric thinking through an action research task that uses problems from the National Assessment of Educational Progress (NAEP). Improves students' conceptual understanding of geometric properties and measurement by exploring complex figures, perimeter, and area concepts. (YDS)

Published
2001

9. Using Representations To Explore Perimeter and Area.

Author

Moyer, Patricia S.

Abstract

Uses the book "Spaghetti and Meatballs for All! A Mathematical Story" to help children differentiate between the mathematical concepts of perimeter and area. (KHR)

Published
2001

11. Isoperimetric Quadrilaterals: Mathematical Reasoning with Technology.

Author

Foletta, Gina M. and Leep, David B.

Abstract

Presents a mathematics lesson that focuses on particular connections between geometry and measurement, how change in shape effects the area of the interior region of parallelograms with the same perimeter. (ASK)

Published
2000

12. Young Children's Intuitive Understanding of Rectangular Area Measurement.

Author

Outhred, Lynne N. and Mitchelmore, Michael C.

Abstract

Focuses on the strategies young children (N=115) use to solve rectangular covering tasks before they have been taught area measurement. Children's solution strategies were classified into five developmental levels. Emphasizes the importance of understanding the relationship between the size of a unit and the dimensions of the rectangle in learning about rectangular covering. (Contains 32 references.) (Author/ASK)

Published
2000

13. Linear Geometric Number Patterns: Middle School Students' Strategies.

Author

Bishop, Joyce

Abstract

Presents the results of (n=23) seventh- and eighth-grade students' interviews as they solve problems related to four linear geometric patterns involving perimeter and area. Students' responses suggest four levels of thinking about linear geometric number patterns. (Contains 33 references.) (Author/ASK)

Published
2000

14. The Analysis of Leaf Shape Using Fractal Geometry.

Author

Hartvigsen, Gregg

Abstract

Describes ways to examine leaf structure and shape using fractal geometry. Students can test hypotheses using the leaves of replicated plants to look for non-linear trends in leaf shape along the stems of plants, across species, and under different environmental growth conditions. (SAH)

Published
2000

16. Teacher Intervention in Small-Group Work.

Author

Brodie, Karin

Abstract

Describes a study which took place in a grade 9 classroom that consisted of five groups with 3-5 pupils in a group. Pupils were required to calculate the areas of a number of shapes on a geoboard. Concludes that a teacher working with pupils in small groups brings new challenges for mathematics teachers. (Contains 11 references.) (ASK)

Published
2000

17. Don't Teach Technology, Teach with Technology.

Author

Cyrus, Vivian Flora and Flora, Ben V.

Abstract

Uses a discovery lesson for determining the area of an equilateral triangle given a side length as an illustration of how to introduce features of the TI-92 graphing calculator geometry package within a mathematical context. (KHR)

Published
2000

18. A Triangle Divided: Investigating Equal Areas.

Author

Scher, Daniel

Abstract

Explores a variety of approaches to solving one geometry problem illustrating the work of teachers, the flow of their ideas, and the diverse areas of mathematics they applied. (KHR)

Published
2000

19. Modeling Soft-Drink Packaging.

Author

Froelich, Gary

Abstract

Describes the process of mathematical modeling, an extensive teacher's guide, and a student modeling activity to improve the efficiency of soft-drink packaging. (KHR)

Published
2000

20. Investigations in Mathematics Education. Volume 17, Number 1.

Author

Ohio State Univ., Columbus. Center for Science and Mathematics Education., ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., Suydam, Marilyn N., and Kasten, Margaret L.

Abstract

This issue contains abstracts and critical comments on 11 articles, plus an editorial comment entitled "A Teacher Shortage?". Studies included concern solution processes on addition and subtraction examples; numerical rule induction; individual differences in performance on manipulative, pictorial, and symbolic tasks; the effect of a calculator curriculum; proportionality rules in judgments of area; van Hiele levels of geometric thought; interaction patterns and attitudes; word problems with ratios; incremental development in algebra; instruction with two types of calculators; and errors in translation from sentence to equation. Research studies reported in "Resources in Education" from July to September 1983 are listed. (MNS)

Published
1984

21. Quincy Market. [A Product of] the Regional Math Network: A Teacher Invigoration and Curriculum Development Project.

Author

Harvard Univ., Cambridge, MA. Graduate School of Education.

Abstract

In this middle school mathematics unit two imaginary characters, Horatio and Portia, decide to make their fortune in Quincy Market (Boston, Massachusetts) running a Bull Market cart. In order to solve the problems that they encounter, they need to learn ratio and proportion, map reading, estimation, area and perimeter, population sampling, problem solving, and the collecting and processing of data. Teacher notes at the beginning of each section indicate the math objectives, materials, and whether the activity is a reinforcement or an extension of a math skill. The unit is divided into seven modules that can be used either independently or sequentially. These are: (1) an introduction to Quincy Market; (2) the use of the ruler; (3) map exploration; (4) ratio and proportion; (5) scale drawing; (6) perimeter and area; and (7) a simulation (in which the students run their business using the Bull Market Game or a computer simulation). Each module consists of two or three class activities and additional activities which can be used as extensions. The unit contains student worksheets, teacher notes, transparency masters, Bull Market Game cards, and a diskette to be used with the computer portion of the "simulation" module. (TW)

Published
1987

22. When 'Big' Does Not Refer to Overall Size: Dimensional Adjectives in Context.

Author

Gelman, Susan A.

Abstract

Two experiments examining adults' use of dimensional adjectives focused specifically on the distinction made between height and overall size as determiners of "bigness." The subjects in both experiments were college students. In the first, the hypothesis that the meaning of "big" shifts as a function of the object being described was tested. The subjects were asked to judge the size of symmetrical and tall rectangles and line drawings of people. It was predicted that they would be more likely to emphasize height in people but area in rectangles. The results were clear and in accord with the prediction. In the second experiment, subjects were asked to judge either the bigness or the area of figures of people. It was predicted that, if height bias in the first experiment was due to a perceptual problem, the subjects would answer alike in the two conditions ("big" and "area"). However, if "big" does not refer to area, the subjects would show more of a height bias when judging bigness than when judging area. The results again suggested that the adjective "big" as applied to figures does not refer to overall area. Theories of semantic development must deal with the variability of meanings across contexts. (MSE)

Published
1985

23. Gingerbread-House Geometry.

Author

Emenaker, Charles E.

Abstract

Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

Published
1999

24. Hands-On Method for Teaching the Concept of the Ratio between Surface Area and Volume.

Author

Cohen, Annette, Moreh, Anat Ben, and Chayoth, Reuben

Abstract

Explores the difficulties students have in understanding the relationship between surface area and volume. Examines four cases where the ratio of surface area to volume varies, and makes recommendations for demonstrating each with models. (Contains 15 references.) (WRM)

Published
1999

25. Perimeter or Area? Which Measure Is It?

Author

Chappell, Michaele F. and Thompson, Denisse R.

Abstract

Explores middle school students' understanding of area and perimeter. Concludes that students need to construct visual representations of figures with given areas and perimeters, generate related word problems, and justify properties to grasp the concepts of area and perimeter. (ASK)

Published
1999

26. Beginning Pre-Service Teachers' Approaches to Teaching the Area Concept: Identifying Tendencies Towards Realistic, Structuralist, Mechanist, or Empiricist Mathematics Education.

Author

Oldham, Elizabeth, Van Der Valk, Ton, Broekman, Harrie, and Berenson, Sarah

Abstract

Examined frameworks that might be robust across different cultures and educational systems in describing teachers' approaches to teaching mathematics, discussing their application in teacher education courses. Examination of lesson plans (related to teaching the concept of area) from Irish and Dutch preservice teachers produced a two-dimensional framework relating preservice teachers' ideas to archetypal realistic, structuralist, mechanist, or empiricist approaches. (SM)

Published
1999

27. The Lesson Preparation Method: A Way of Investigating Pre-Service Teachers' Pedagogical Content Knowledge.

Author

Van Der Valk, Ton A. E. and Broekman, Harrie H. G. B.

Abstract

An international team of mathematics and science educators developed a method of investigating the pedagogical content parts of preservice teachers' knowledge bases. They asked preservice teachers to prepare a lesson plan about a topic (area) as if they had to teach it, then they later interviewed them. The method produced significant, rich information about preservice teachers' knowledge base. (SM)

Published
1999

29. In Search of Perfect Triangles.

Author

Bonsangue, Martin Vern, Gannon, Gerald E., and Buchman,

Abstract

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)

Published
1999

30. Area of Spherical Triangles.

Author

Davis, Elwyn H.

Abstract

Provides a set of classroom activities or steps that can be used to determine the area of a triangle on a sphere. (ASK)

Published
1999

31. A Slice of the Pie.

Author

Schuman, Raymond A.

Abstract

Presents a mathematics activity in which equal areas and volumes are focused upon when sharing a circular pie. (ASK)

Published
1998

33. The Predominance of the Linear Model in Secondary School Students' Solutions of Word Problems Involving Length and Area of Similar Plane Figures.

Author

De Bock, Dirk, Verschaffel, Lieven, and Janssens, Dirk

Abstract

Reports on two closely related studies on students' tendency to use linear models in situations in which they are not applicable. Results provide a convincing demonstration of the predominance of the linear model in secondary students' solutions to this kind of mensurational problem. Contains 25 references. (Author/ASK)

Published
1998

34. Modeling Mathematics Concepts: Using Physical, Calculator, and Computer Models To Teach Area and Perimeter.

Author

Widmer, Connie and Sheffield, Linda

Abstract

U.S. mathematics education has been criticized for being too broad. This article examines ways middle school students use simple problems and situations to foster a deeper understanding of underlying concepts. Presents a sample area and perimeter problem, describes extending the problem using tiles to determine minimum perimeter, and discusses using spreadsheets, graphs, and graphing calculators. (PEN)

Published
1998

35. Investigating Polygonal Areas: Making Conjectures and Proving Theorems.

Author

Naraine, Bishnu and Hoosain, Emam

Abstract

Presents an activity for eighth-grade students and beyond to explore relationships between and among the areas of various polygons. Emphasizes that students should be given the opportunity to design their own examples. (ASK)

Published
1998

36. Mathematical Investigations--Powerful Learning Situations.

Author

Chapin, Suzanne H.

Abstract

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for students to explore a topic in depth and to make connections among representations. (ASK)

Published
1998

37. Covering Shapes with Tiles: Primary Students' Visualisation and Drawing.

Author

Owens, Kay and Outhred, Lynne

Abstract

Investigates students' early concepts of area by analyzing responses to a worksheet of items that involved visualizing the tiling of given figures. Concludes that half of the students had difficulty visualizing the tiling of shapes, but those students who participated in spatial activities were generally more successful in determining the number of tiles that would cover a shape. Contains 18 references. (Author/ASK)

Published
1998

38. Preservice Teachers' Understanding of Perimeter and Area.

Author

Menon, Ramakrishnan

Abstract

Presents a study in which postgraduate elementary school preservice teachers (n=44) were given four tasks, two to assess their understanding of perimeter and two to assess their understanding of area. Concludes that teachers have a procedural understanding of perimeter and area rather than a conceptual and relational understanding. Contains 15 references. (Author/ASK)

Published
1998

39. A Learning Environment for the Conservation of Area and Its Measurement: A Computer Microworld.

Author

Kordaki, Maria and Potari, Despina

Abstract

Describes a computer microworld for learning the concept of conservation of area and its measurement; analyzes its main features (drawing segments and polygons, manipulation of areas using simulations of children's sensory-motor actions, measuring areas, transforming areas into equivalent ones, and measuring lengths and angles); and presents the results of a pilot study evaluating the microworld. (Author/PEN)

Published
1998

40. Using ROOTine Problems for Group Work in Geometry.

Author

Panasuk, Regina M. and Greenleaf, Yvonne

Abstract

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Published
1998

41. Area Judgment from Width and Height Information: The Case of the Rectangle.

Author

Mullet, Etienne and Rulence-Paques, Patricia

Abstract

Adults, 9-year olds, and 5-year olds were shown horizontal and vertical lines of various sizes, presented on same wall or different walls, and asked to estimate corresponding area. Responses indicated that when width and height were separated, children gave same weight to both dimensions while adults gave greater weight to larger dimensions; when joined, 9-year olds gave greater weight to larger dimension. (EV)

Published
1998

42. Investigating Mathematics with PentaBlocks.

Author

Berman, Sheldon, Plummer, Gary A., Scheuer, Don, Berman, Sheldon, Plummer, Gary A., and Scheuer, Don

Abstract

These classic pattern blocks were introduced in the early 1960s as part of the Elementary Science Study materials developed by the Educational Development Center (EDC). The six classic shapes share one common characteristic: all of the angle measurements are multiplies of 30 degrees. Shapes include the regular triangle, square, and hexagon; the isosceles trapezoid or "half-hexagon"; the 60-degree and 120-degree rhombus; and the 30-degree and 150-degree rhombus. This book contains 20 sequential activities which involve perimeter and area, angles and similarity, and symmetry operations and tiling. (ASK)

Published
1998

43. The Impact of Model-Centered Instruction on Student Learning: The Area and Volume Units.

Author

Raghavan, Kalyani, Sartoris, Mary L., and Glaser, Robert

Abstract

Examines the impact of the first two units of a sixth-grade curriculum module implemented in a public school during the 1993-94 school year. Describes the underlying rationale and content of the entire nine-unit module and focuses on units on area and volume. Concludes with a discussion of implications and suggestions for curriculum refinement. Contains 48 references. (Author/ASK)

Published
1997

44. The Great Calculus II Conundrum.

Author

Revak, Marie, Pendergraft, Dave, and Brown, Cynthia

Abstract

Presents a murder mystery in the form of six Calculus II review problems. Students must solve the six problems to determine the murderer, murder weapon, and time and location of the murder. (AIM)

Published
1997

45. Fibonacci Numbers and an Area Puzzle: Connecting Geometry and Algebra in the Mathematics Classroom.

Author

Sullivan, Mary M. and Panasuk, Regina M.

Abstract

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and geometry. (Author/ASK)

Published
1997

46. Packing Them In.

Author

Carter, Claudia

Abstract

This activity involves students investigating the mathematics of packaging and exploring various concepts in geometry, including area and the Pythagorean theorem. Mathematics comes out of the discussion of packaging cans into six-packs and focuses on the cost-effectiveness of the horizontal storage area used. Students learn how knowledge of mathematics allows exact answers that lead to generalizations and formulas. Includes activity sheets. (PVD)

Published
1997

47. That's Gross (Tonnage).

Author

Hopkins, Martha H.

Abstract

This activity for grades three through six determines how to identify the gross tonnage of a ship by measuring volume in cubic feet. During the problem-solving process, students construct and use a tool for measuring volume, derive a formula based on data collected, and compare their data with a given set of statistics. (AIM)

Published
1997

48. More Functions of a Toy Balloon.

Author

Coes, Loring, III

Abstract

Presents activities that use toy balloons to offer students interesting opportunities to connect algebra and geometry. Involves students measuring the speed of a released balloon and investigating the subtle relationship between the volume of a sphere and its surface area. Prompts a rich and revealing discussion about why the experimental results are not the same as those expected theoretically. (JRH)

Published
1997

49. Development of Students' Spatial Thinking in a Unit on Geometric Motions and Area.

Author

Clements, Douglas H., Battista, Michael T., and Sarama, Julie

Abstract

Studied the development of third graders' spatial thinking during an instructional unit on area and motion. Found strong positive effects on the transformation of internalized images. Found initial gender differences in spatial thinking, but both boys and girls made substantial gains during instruction. Students applied a unitizing operation to construct spatial and numerical units and "units of units." (Author/KB)

Published
1997

50. Exploring Area with Geoboards.

Author

Trafton, Patricia A. and Hartman, Christina

Abstract

Presents an activity for students to investigate equal parts and area and the connection between area and fractions. Highlights the importance of such a lesson in which children explore rich mathematical ideas, share their thinking and their work with one another, and make connections to other mathematical ideas. (ASK)

Published
1997

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