Math Operational TermsMath Operational Terms

Prepared by Dr. Elva Cerda PPrepared by Dr. Elva Cerda Péérezrez

University of Texas/TSC BrownsvilleUniversity of Texas/TSC Brownsville

Mathematical Mathematical OperationalOperational

TermsTerms

PatternsPatterns

A pattern is a model to be copied or A pattern is a model to be copied or a design from which to work.a design from which to work.

Example: (Pattern)Example: (Pattern)

Source: New Concise Webster’s Dictionary, 1990 Edition

EstimationEstimation Estimation presents students with another Estimation presents students with another

dimension of mathematics; terms such as dimension of mathematics; terms such as about, near, closer to, between, and a little about, near, closer to, between, and a little less than illustrate that mathematics less than illustrate that mathematics involves more than exactness.involves more than exactness.

Example: Without counting, estimate which Example: Without counting, estimate which has less than 5 and which has more than 5.has less than 5 and which has more than 5.

5

Source: 1989 NCTM Standards: Grades K-4 Standards 5: Estimationhttp://standards.nctm.org/previous/currevstds/k4s5.htm

Drawing PicturesDrawing Pictures

Drawing pictures are natural ways that Drawing pictures are natural ways that students communicate their mathematical students communicate their mathematical investigations from early childhood through investigations from early childhood through 22ndnd grade. grade.

Example: A child’s notation for 10Example: A child’s notation for 10½.½.

Source: 1989 NCTM Standards: Grades K-2 Communicationhttp://standards.nctm.org/document/chapter4/comm.htm

Concrete Representations: ModelsConcrete Representations: Models

Representations are more powerful tools Representations are more powerful tools for thinking; they make mathematical for thinking; they make mathematical ideas more concrete and available for ideas more concrete and available for reflection. They support and extend reflection. They support and extend reasoning by helping students focus on reasoning by helping students focus on essential features of the mathematical essential features of the mathematical situation.situation.

Example: Example: 1 + 1 = 21 + 1 = 2

Source: Principles and Standards http://www/nctm.org/tcm/2001/01/p288.htm

(Using cubes)(Using cubes)

++ ==

GraphGraph

A graph is the set of all points that A graph is the set of all points that correspond to the ordered pairs that correspond to the ordered pairs that satisfy that equationsatisfy that equation

Example: Example:

Source: Math Dictionaryhttp://kidsmath.about.com/.../bldictionary.htm?terms=math+dictionary

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1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

EastWestNorth

NumbersNumbers

Numbers are the total count of Numbers are the total count of aggregated units or the symbol that aggregated units or the symbol that stands for this amount.stands for this amount.

Example: Example:

Source: New Concise Webster’s Dictionary, 1990 Edition

(3)

NumerationNumeration Numeration is the act, art, or method Numeration is the act, art, or method

of expressing or reading off numbers of expressing or reading off numbers set down in numerals, especially set down in numerals, especially those written decimally.those written decimally.

Example: Counting with an abacus.Example: Counting with an abacus.

Source: Ato Z Dictionary Wysiwyg:/44/http://www.infoplease.com/ipd/A0562528.html

Critical Thinking in MathCritical Thinking in Math Critical thinking is the central to inquiry and Critical thinking is the central to inquiry and

application and should be interwoven application and should be interwoven throughout the mathematics curriculum to throughout the mathematics curriculum to provide a context for learning and applying provide a context for learning and applying mathematical ideas.mathematical ideas.

Example: Try to make a hexagon with Example: Try to make a hexagon with different shapes of manipulatives.different shapes of manipulatives.

Source: Grades 6-8: Problem Solvinghttp://standards.nctm.org/document/chapter6/prob.htm

Guessing and CheckingGuessing and Checking

To form a judgment or estimate of (something) To form a judgment or estimate of (something) without actual knowledge or enough facts for without actual knowledge or enough facts for certainty; to investigate in order to determine the certainty; to investigate in order to determine the condition, validity, etc.condition, validity, etc.

Example: Guess how many bricks are there? Example: Guess how many bricks are there? Then, count them to check if you were right.Then, count them to check if you were right.

Source: Webster’s New World. College Dictionary. Fourth Edition. New York (1999)

ManipulativesManipulatives

Manipulatives are important tools in helping Manipulatives are important tools in helping student think and reason in more meaningful student think and reason in more meaningful ways. By giving students concrete ways to ways. By giving students concrete ways to compare and operate on quantities this compare and operate on quantities this contributes to the development of well-contributes to the development of well-grounded understandings of mathematical grounded understandings of mathematical ideas.ideas.

Example: The student will add 3 + 2 using Example: The student will add 3 + 2 using bingo chips.bingo chips.

Source: Manipulatives: One Piece of the Puzzlehttp://www.cetm.org/mtms/2001/02/p356.htm

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National Council of Teachers of Mathematics National Council of Teachers of Mathematics Curriculum and Evaluation StandardsCurriculum and Evaluation Standards

The National Council of Teachers of Mathematics The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provides guidelines Curriculum and Evaluation Standards provides guidelines for excellence in mathematics education and issue a call for excellence in mathematics education and issue a call for all students to engage in more challenging for all students to engage in more challenging mathematics. It is intended to be a resource and guide for mathematics. It is intended to be a resource and guide for all who make decisions that affect the mathematics all who make decisions that affect the mathematics education of students in prekindergarten through grade 12.education of students in prekindergarten through grade 12.

Example: Example: As teachers, we have to make sure to implement these As teachers, we have to make sure to implement these

standards in the curriculum. We have to be sure that standards in the curriculum. We have to be sure that our students are meeting the requirements that are our students are meeting the requirements that are needed to achieve the skills in math.needed to achieve the skills in math.

Source: Principles and Standards-Prefacehttp://standards.nctm.org/document/prepost/preface.htm

Mathematical TablesMathematical Tables

A systematic list of details, facts, numbers, etc. A systematic list of details, facts, numbers, etc. systematically arranged in columns or rows.systematically arranged in columns or rows.

Example: Multiplication tableExample: Multiplication table

Source: Billstein, R.et al. (1990). A Problem Solving Approach to Mathematics for Elementary School Teachers. Ed. The Benjamin/Cummings Publishing Co., Inc. 4th ed.

xx 00 11 22 33 44 55

00 00 00 00 00 00 00

11 00 11 22 33 44 55

22 00 22 44 66 88 1010

33 00 33 66 99 1212 1515

44 00 44 88 1212 1616 2020

55 00 55 1010 1515 2020 2525

Drawings in MathDrawings in Math

A picture of the study of the relationships A picture of the study of the relationships among numbers, shapes, and quantities among numbers, shapes, and quantities made with a pencil, pen, or crayon.made with a pencil, pen, or crayon.

Example: A drawings of a geometric Example: A drawings of a geometric shapes.shapes.

Source: Webster’s New World. College Dictionary. Fourth Edition. New York (1999)