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GOALS IN MATH EDUCATION.
Term Paper ID:24260
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Essay Subject:
Examines five goals of National Council of Teachers of Mathematics & ways to achieve them.... More...
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5 Pages / 1125 Words
6 sources, 5 Citations,
APA Format
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Paper Abstract:
Examines five goals of National Council of Teachers of Mathematics & ways to achieve them.
Paper Introduction:
The National Council of Teachers of Mathematics has produced a list of five goals which students in a well-taught classroom should achieve. This paper will outline how these five goals can be attained by students in a fourth-grade classroom using the Saxon text, Math 54: An Incremental Development (Hake & Saxon, 1996). Examples of how to incorporate each goal individually into the class's lessons will follow.
A good mathematics curriculum will help a teacher instill these goals in students. The best method of disseminating these goals to students is within the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught in isolation from one another or from other subjects.
The five goals can be summarized as follows:
Text of the Paper:
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Thewords are defined in terms of one another, but students often need to seeand feel to grasp a concept fully. Likewise,students will not be able to use mathematical concepts and ideas to solveproblems if they have not learned the language and vocabulary associatedwith the mathematical model and the arithmetic skills necessary. Given this difficulty in testing whether a student values mathematics, ateacher can present students with multiple and varied uses of mathematicalconcepts which are not limited to the segment of the day labeled mathstudy. References Andrews, A. Teaching Children Mathematics, 3, 236-239. Students will learn to value mathematics.2. This is an area where the Saxon text isweaker. To meet this goal, a teacher needsto allow students to explain how they arrived at an answer, not justevaluate the student's answer. Math 54: An incremental development(2nd ed.). In the science unit on the geology of the earth, students canbrainstorm ideas on how to build a model of the earth. Apartial understanding and assessment of a student's level of mathematicalreasoning can be gained by having all students show all their work whensolving word problems. An example of supplementary activity for liquid measures isgiven. This constant drilland review of skills increases the competency level of each student andhelps students retain previously learned math skills. The Saxon text presents newvocabulary clearly. Saxon practice sets usually request that studentsdefine the type of problem being worked before beginning the solution.This step helps both the student and the teacher determine if the childlogically understands the problem. Teaching K-8, 27(1), 78-81.----------------------- 1 Cross-curricular teaching alsoemphasizes the first goal of having students realize that mathematicsconcepts are used everywhere; mathematics is valuable for the power itgives users to understand the real world. Students can be encouraged to compete with themselves on theseassessments by charting their progress on bar graphs showing the number ofproblems solved correctly. (1996). Hake, S., & Saxon, J. Students will be able to solve problems using mathematical concepts andsolutions.4. (1991). Computers supportalgebraic thinking. It does not supply real-life situations where mathematics can beused, except for the word problems given in the practice sets.Enterprising teachers may use cross-curriculum studies to supply theseproblems. Programming skills help students tomathematize problems and use symbolic logic on familiar processes (Clements& Sarama, 1997, p. The goals of the NCTM are intended to increase students' ability toparticipate in their own education. Applying the mathematical label givesstudents an ideal of how to figure out a solution. Different types of containersand measurement devises can be brought to the playground or field, andtests can be run to find the relationships among the measures. G. Phi Delta Kappan, 78, 361-367. It does not give enough time to have students practiceand use the vocabulary orally or in written work. 32 ). (1997, February). If the teacher is lucky enough to have access to computers with LOGO,problem solving can become an extension of learning to program the turtleto do what the student wishes. The resultscan be hypothesized, tested, documented, and presented to the other groupsin the class by oral presentation and visual aids consisting of graphs. Specialized terminology (for example: some somemore, some some went away, and equal groups) used by Saxon to showrelationships between word problems does seem to help students recognizepatterns in real-life problems. The five goals can be summarized as follows:1. The best method of disseminating these goals to students iswithin the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught inisolation from one another or from other subjects. In the unit on liquid measure, students seeing how much water is inan ounce, pint, quart, gallon, liter, and milliliter would be helpful. Astudent will not be able to reason mathematically if that student is unableto think or communicate using mathematical terms and ideas. In the above example, the goal of students learning to reasonmathematically was also incorporated. (1996, September).Writing to learn math and science. The relationship between animals in anecosystem (4th grade science) can be shown on a line graph, or as anequation saying that for every X caribou there is one wolf. Professional standards forteaching mathematics. Practicing representation:Learning with and about representational forms. G., & Hall, R. Successfully findingsolutions to their own problems gives students confidence in their ownabilities in mathematics and increases their self-esteem. Reston, VA: Author. The lessonis on liquid measurement and is a unit which teachers might choose tosupplement so that students gain mastery of the vocabulary and can practiceother skills. 237). The timed drillincreases students' speed with simple arithmetic functions; this in turnincreases a students competency. This goal isattainable through the use of the textbook to provide practice andcontrolled new situations for students to test their mathematical knowledgeand abilities. Mathematical reasoning is an importantfirst step to continuing to higher mathematics and mathematical proof. X*caribou = 1wolf. Commission on TeachingStandards for School Mathematics. Measurement is a concrete concept whichcan be practiced beyond paper and pencil. The five goals build on one another in a non-linear fashion. The National Council of Teachers of Mathematics has produced a listof five goals which students in a well-taught classroom should achieve.This paper will outline how these five goals can be attained by students ina fourth-grade classroom using the Saxon text, Math 54: An IncrementalDevelopment (Hake & Saxon, 1996). Greeno, J. When students are able to mathematize problems, they can explain whyand how they arrived at their solutions. Ryan, J., Rillero, P., Cleland, J., & Zambo, R. Norman, OK: Saxon Publishers. Examples of how to incorporate each goalindividually into the class's lessons will follow. This is an important part ofmeeting the goal of having students be able to communicate mathematically.Children naturally use language to define and focus on causal and dependentrelationships (Andrews, 1997, p. Clements, D., & Sarama, J. As students experience being competent inmathematical skills and concepts, they apply these to the problems thatthey encounter in their own lives. The language of mathematics must be employed in the classroomwhenever it is applicable. This gives the students concrete experience with the measuring ofliquid and the size differentials of the units of measure; it also providesa chance to practice mathematical reasoning (goal number 5) and forces thestudents to use mathematical vocabulary and terms in their presentations.Having the students put their answers in writing reinforces the use ofvocabulary and makes the students articulate their thinking and gives thema chance to correct their logic, as well as their mechanics and grammarbefore their presentations (Ryan, Rillero, Cleland, & Zambo, 1996, p. That each student will become confident in using mathematics is thesecond goal of a mathematics education as stated by the NCTM. Math concepts which will probably be involved are scale,measurement, volume, vocabulary, and different modes of symbolicrepresentation. P. This implies cross-curricular teaching in orderfor students to be exposed to the flexibility of mathematical terminologyand to understand how problems in other subjects can be made simpler by theway that they are framed or presented. The goal of having students learn to value mathematics is difficultto objectify because it involves placing an intrinsic value on subjectmatter without an easy method of verifying if a student values the subject. Students need to be ableto use mathematical terms actively instead of just comprehending them.This owning of the vocabulary comes only from repeated usage. (1997, January). The third goal is that students will become mathematical problemsolvers is building on the same tools used to increase students' confidencein their own abilities. (1997). National Council of Teachers of Mathematics. Doing what comes naturally:Talking about mathematics. The groups can then build their best idea and presentit to the class. Students will become confident in their own ability to use mathematicalconcepts in their daily life.3. Students will learn to reason mathematically (National, 1991). A good curriculum, ingenuity, andaccess to ideas will enable an elementary school teacher to meet and exceedeach of the mathematics goals. Teaching Children Mathematics, 3, 32 -323. Mathematics uses several forms of representation which are taughtor reviewed during the fourth grade: arithmetic expressions, tables,graphs, and equations (Hale & Saxon, 1996; Greeno & Hall, 1997, p. 78).The hands-on activity supplements the text in this unit, motivates thestudents, meets several of the goals outlined by the NCTM. Different solutionscan all be correct. Programming skills can be very helpful inlearning to break down problems into smaller pieces for which math skillsand logic are able to supply answers. The Saxon text provides daily practice in math skillspreviously covered and in the new skills being taught. 361).Information from other areas of study can be and often is presented usingthese forms of representation. Teachers know the importance of student participation in learning tomaximize student interest and learning retention (Greeno & Hall, 1997, p.362). A good mathematics curriculum will help a teacher instill these goalsin students. Students will learn to communicate mathematically.5.
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