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Paper Abstract: Proposes project to determine factors & conditions conducive to rich mathematics problem-solving environment & to develop a curriculum project to develop math skills. Paper Introduction: Problem-Solving in the Primary Grades Statement of the Problem In response to unacceptable levels of mathematics achievement in the United States many groups with an interest in the teaching of mathematics have called for reform (Niemi, 1996). The calls for reform are based on recent advances in cognitive theory that call for a more constructivist view of learning (Wood & Sellers, 1996). Traditionally, mathematics instruction in the primary grades has consisted of teaching computational skills, drills, and simple Text of the Paper: The entire text of the paper is shown below. However, the text is somewhat scrambled. We want to give you as much information as we possibly can about our papers and essays, but we cannot give them away for free. In the text below you will find that while disordered, many of the phrases are essentially intact. From this text you will be able to get a solid sense of the writing style, the concepts addressed, and the sources used in the research paper. Last the foundsolution should be checked against the original question to see if it isreasonable and accurate. Problem solving: The linkbetween social studies and mathematics [database]. The primaryfocus of mathematics instruction is shifting from simple computationalskills to problem-solving applications in all grade levels. M. Assessing conceptual understanding in mathematics:Representations, problem solutions, justifications, and explanations.Journal of Educational Research, 89, 351-364. These types ofproblems are useful for teaching primary students numeration,classification, and seriation which are all taught in the primary grades(Micklo, 1997). Their drawback is thatthey take more time to utilize. In addition, collaborative learning is oftenfavorable to improved science and math understanding. If the activity is deemedsuccessful and repeatable, the group leader will disseminate a copy of thefinal report to interested teachers within the school and to other schoolsas requested.Conclusions and Implications of Findings In looking at theory and research on the new constructivist,contextual, or problem-solving mathematics education, it is apparent thatit is designed to accomplish several important purposes. Thisutilizes the capacity of the brain to solve problems and to assimilateknowledge in ways that make it usable in later, new situations. The types of problems didnot changesignificantly, but the level of complexity within the created problem didincrease. I remember my own school experience and how dull andunimportant mathematics can seem when it is simply rote memorizationwithout any obvious relevance to the world of a small child. Thus, he emphasizes that effective learning forany individual has two important prerequisites: it must be clearlyperceivable as organized patterns and it must have autobiographicalreferences. Dept. Studentstend to misinterpret key words in the problem to mean the oppositemathematical operation. Changes in how a childthinks and refines his concepts of what mathematics is and how it is bestused are documented in the child's own hand and with real examples of thestudent's best and significant work (Micklo, 1999). Theteacher is a coach, or facilitator to the student (Bay, B. & Schuncke, G. Science is not entirely separate from math, nor is Englishentirely separate from math. Assessment of a problem-centeredmathematics program: Third grade. Make time for tune-ups. She shouldrequire all students treat each other with respect and encourage openmindedness during discussion. First, there is the problem of defining the desired outcome of anelementary school education. Wood and Sellers have demonstratedthat children placed in a problem-centered curriculum have significantlyhigher achievement in mathematics than those in traditional textbook basedinstruction. What problems were encountered? American Association for the Advancement of Science. Transforming ideas for teaching and learningscience. Portfolios and journal serve the purpose of documenting a child'sprogress and at the same time they give the opportunity to fulfill anothergoal of the California framework and of the NCTM standards--that childrenbe given the opportunity to explain their thinking to other students and tothe teacher. For example: Sue has seven cookies. Other opportunities for real-life problems come from socialstudies--map reading, calculating distance, travel time, populations, andcontrived economic situations (Richstad, 1998). Cerebral context. Assessments which place more importance onthe how and why of a child's solution are available. Vocational Education Journal,March 1,1-6. Teachers who volunteer to teach problem-centeredmathematics classes have a more constructivist view of learning than otherteachers before they are exposed to problem-centered instruction. (1999). For example, Wood and Sellers(1997) reported that students' beliefs about mathematics changed during thecourse of the problem-centered approach. San Francisco, CA: Jossey-Bass Publishers. Second, this connectivityis designed to extend outside the classroom and into the student's dailylife. School budgets being nonexistent,administrative support should be obtainable.Project Goals and Objectives The project goals are to raise money for the field trip and to enrichthe children's problem-solving environment. How many students areeatinghot lunch or cold lunch each day. The primary consideration is theteacher's attitude and willingness to take time to see and solve problemsas they arise in daily classroom activities. Aninitial budget for the trip can be made. There are a number of assumptions throughout the literature thatthe constructivist and problem-solving approach will lead to students withgreater knowledge of mathematics, better ability to apply knowledge intheir daily lives, and the capacity to grow into adults able to solveimportant social problems. Creating a constructivist classroomatmosphere. DeVries, R. (1997). Journal for Research inMathematics Education, 29, 436-443. Washington, D.C.: AAAS. Theimportance of collaboration was second only to administrative support whenteachers ranked the elements necessary to successfully implement astandards based curriculum. Throughout the year,journals can be kept by the students to record weekly progress toward theirgoal. Problem-Solving in the Primary GradesStatement of the Problem In response to unacceptable levels of mathematics achievement in theUnited States many groups with an interest in the teaching of mathematicshave called for reform (Niemi, 1996). J. The Clearing House, 72, 51-55.[Infotrack: General Reference Center]. The need now is to bring thosefields together in order to deal more effectively with human problems. However, these were not always adopted by school districts andthey did not make use of the new understandings in cognitive science(Sivertsen, 1993). (1994). Although he is specifically concerned with teaching usinginformation technology, or computer-assisted learning, much of what he saysapplies to all teaching. After ayear, teachers shift their beliefs, in how children learn about mathematicsand how to teach mathematics, in the direction proposed by the standards(Woods & Sellers, 1997). She has five more cookiesthan Jan. Students with higher levels ofrepresentational knowledge are able to produce better justifications,explanations and were able to use mathematical representations moreeffectively in problem-solving tasks (Niemi, 1996). At the weekly meeting, these journalentries will be shared and discussed to increase each teachers' resource ofproblem-solving situations, to gain ideas, and to support each other. Possible solutions includerecycling projects, bake sales, car washes, candy sales, and other creativemoney-makers. When teachers teach in such a way as to point outconnectedness, then they are working in tandem with brain function, ratherthan in opposition to it. As opportunities present themselves the teacher should promotethe use of mathematical problem solving across the disciplines. In much of contemporary education, however, there is a disjunctionbetween the second and third stages. (1999). Part of thedifficulty children have in posing a variety of types of word problemssituations may lie in the lack of exposure to many different types ofproblems in the classroom environment. In the above problem, children will be predisposedto understand the word "more" to mean addition (English, 1998). Teachersrespect the developing minds of students, and encourage active, inquiring,creative pursuits. Reston Va.: NCTM. A monthly report will be given to the principal on student activitiesand the money raised to date.Timeline Before school ends in June, second and or third grade teachers willbe approached to determine interest in a joint project. (1998). The standardsbased curriculum places more responsibility on the student to learn. First, it isdesigned to connect subjects that have frequently been disconnected in theprimary grades. The CaliforniaMathematicsFramework lists five strategies to help students develop attitudes andlearning strategies useful to problem solving. During August teacher in-service an initial meeting will be held with interested teachers and theprincipal. These same studentsdid not believe that they would succeed in mathematics by being quiet orcompleting their work neatly. There are many ways to create a classroom environment which is richwith problem-solving opportunities. I propose a problem-solving venture toallow the students to raise money to go on a field trip (a real-lifeproblem). From these finalevaluations from the teachers, the group leader will prepare a groupproject report for the principal. In other words, pedagogically, constructivism isconcerned with learning what is important to the student in order to followthe direction of the student's interests in understanding his or her worldand solving problems within it. In this type of problem there is an unknown reference set. Burns, M. The teacher is responsible forbeing open to alternative approaches and encouraging them. Rose, T. What allows students to participate in an enriched problem-solving environment? Constructivism, and constructivist classrooms, provide the means todo this. This last step fulfills the goal of havingstudents reflect on their learning. That is the significance of this study for education. Washington, D.C.: U.S. Copies of this and the teachers formalevaluations shall be given to the principal. This knowledge then can be applied to new situations thatthey encounter, hopefully with positive results. Funds needed oralready acquired can be added, graphed, and tabulated. H. I think the problem-solving approach ismuch more likely to gain their interest, and also much more likely to betaken outside of the classroom into their daily activities and applied toproblems they meet there.Design of the Study The first part of the study is a review of the relevant literature.The intent is to explore some of the recent literature about constructivistprinciples and the development of techniques for enhancing problem-solvingwithin the classroom setting. Contextual teaching is teaching that emphasizes the connectionbetween the content of knowledge and the context of application. After school begins in September, students will be informed of theneed to raise funds for a school field trip. These students are the hope of thefuture. G. The teacher should: (1) Model problem solving behavior whenever possible, exploring andexperimenting along with students. For many years, the focus was on providingstudents with a body of information that was thought essential to a basiceducation. [Infotrack: General ReferenceCenter]. Information is transmitted to thelearner, but not in a form, or in a manner, that enables the learner totransform the information into usable, personal knowledge. Mother brings out two glasses of lemonade. However, learning does not take place until the thirdstage in which the learner hopefully transforms the obtained publicinformation into usable, personal knowledge. Teachers will meet weekly to discuss problem-solving activities related to trip planning and funding activities. References Adams, D. Data can be graphed, percentagescalculated, estimates made for each day, which menus are most favored, andleast favored (Waite-Stupiansky & Stupiansky, 1998). What about some of the characteristics of the constructivistclassroom? Parnell (1996) noted that recent brain research has proven thatmaking connections is rooted in brain mechanisms themselves and thatlearning is completely ineffective without allowing for those connectionsto be made. Third, a long-term impactof problem-solving in mathematics education is its extension into the realworld of the students as adults. So, in the long-term, mathematics education using a problem-solvingapproach is designed to help students grow up into citizens who are able tobe effective in helping society deal with intractable social andtechnological problems. The developmental nature ofability to solve one-step word problems. What do students need to becomeeffective problem solvers? (1996). The shift from computation skills to applying mathematical conceptsto problem-solving situations requires changes in teacher philosophy,teaching methods, the skills taught (the scope and sequence), andassessment strategies. (1997). In 1989, the National Council of Teachersof Mathematics (NCTM) began emphasizing the teaching of mathematicalconcepts and problem solving at all grade levels. Deepening the Analysis: Longitudinalassessment of a problem-centered mathematics program. It will also state ifthe project was viable. Reys, 1999). 25. The five strategies in the CaliforniaMathematics framework seem particularly helpful for this since they allowfor teacher modeling and experimentation, student experimentation, andmultiple strategies in approaching problem-solving.Project design Encouraging mathematical problem solving in the classroom willincrease the learning of mathematical concepts by students and increasetheir test scores. Constructivist pedagogyfollows certain principles for good problem-solving situations, includingrequirements that the solution be testable, require inexpensive equipment,be complex, and benefits from group efforts (Brooks and Brooks, 1993). For my project I propose that three primary gradeteachers who share the same lunch period meet weekly to discuss andcoordinate classroom activities on problem solving. New design for teaching and learningin mathematics. Concepts now included inmathematics curricula arebeing changed to stress problem-solving skills, but the resources andteaching methods available to primary grade teachers are not keepingcurrent with the new standards. The California Mathematics framework echoes the NCTM standards. Educated candies: a classroom business plannedand managed by students [database]. Reys & R. Do theteachers wish to repeat the project in future years? Teachersshould be open to seeing and solving problems mathematically when they arefound regardless of the subject matter.Analysis of Data There are two things that are striking to me in looking at theliterature. J., Reys, & R.E. Attendance and lunch countsare opportunities for real-life problem solving. Traditional paper and pencil mathematics teststest primarily for computational skills. In other words, it must somehow connect to the individual'slife. An example event: There are threechildren outside. The plan should carried out and a solution found. Furthermore, effective teaching is based on certain principles thatare now more clearly understood. These principles are more oriented tohands-on activities, problem-solving, and the use of student's naturalcuriosity and creativity. It was assumed that students then would be able to utilize thisinformation in additional study, in their daily lives, and in their worklives. Learning is improvedby providing students with many different kinds of experiences, and theopportunity to experiment and indulge in multisensory activities (Adams andHamm, 1994). The ability ofchildren to correctly translate a problem into mathematical terms dependson their level of mathematical development and their fluency withmathematical terminology (Niemi, 1996). In other words, teaching can be designed to becongruent with brain function, or it can be designed to work in oppositionto it. What benefit did theteachers gain from collaborating? Christou, C. (1993). The intent is to help students gain knowledge, rather than memorizeinformation. M., Reys, B. Reys, & R. Also, students experience a disconnection between what theyperceive as school mathematics and the mathematics they use in informal,non-school situations. Richstad, B. Part of the problem, in other words, is not that there is alack of problem-solving in mathematics education, but that problem-solvingitself is a difficult achievement. As this statement makes clear, the boundaries between science, math,and technology, and other areas of human endeavor have been too rigidlydrawn in school and in academic life. Laidlaw Educational Publishing. Teachers who use the teaching concepts outlined bythe standards come to the conclusion that these methods used to teachmathematics are better and more effective than the methods used in thetraditional textbook approach.Assessment The shifting emphasis to problem solving in the mathematicscurriculum means that strategies for assessing the work of an individualstudent must be altered. The other thing that is striking to me is the need for outcomestudies. D. Finding multiple ways to solve a problem.(mathematics teaching) [database]. (1998). The use of a mathematics portfolio and journalare especially useful because they give evidence of the child'smathematical development over a larger time frame. Finally, the third part of this study includes aproject design to be carried out in my own classroom, using principleslearned from the research.Review of the Related Literature In order to provide background for understanding the problem-solvingapproach to mathematics instruction, several sections are included here.The beginning is an overview of constructivist principles, which are thefoundation of new approaches to math and science teaching. Math portfolios in the primary grades[database]. (4) Allow for the fact that more than one strategy may be needed tosolve a given problem and that problems may require original approaches. [Infotrack: General Reference Center]. Bay, J. Of Education. There is usually morethan one method which could be useful in solving a problem. Wood, T., & Sellers, P. Information can be transmitted but knowledge mustbe induced. English, L. Students withless than two years experience in problem-centered mathematics instructionbelieve that mathematics is about solving problems the teacher's way.Textbook instruction in mathematics leads students to believe that there isonly one method used to solve problems. The teachers will be meeting and reportingto the principal on the groups progress and activities.Evaluation The teachers will provide the principal or his representative with awritten weekly report on the project's status and the classrooms'activities. [Infotrack:General Reference Center]. Krech, B. (5) Present problem situations that closely resemble real situationsin their richness and complexity so that the experience that students gainin the classroom will be transferable. The purpose of this project is twofold (a) todetermine what factors and conditions contribute to, and are necessary forthe development of a rich mathematics problem-solving environment in theprimary grade classroom, (b) to develop a curriculum project which willinclude all elements necessary for primary students to develop a richrepertory of problem-solving skills.Rationale for Choice of Problem The beginning of the reform project for both science and math was theexperience of seeing the Soviet Union launch Sputnik, beating the UnitedStates into space. It is not necessarily aboutcompetence, but about a particular way to be competent in mathematics. First the problem must beidentified and understood. Journal of Researchin Mathematics Education, 28, 163-186. This does not mean that the students totally control the curriculum.Instead, the teacher is involved with guiding the students to locaterelevant topics and formulate good problems. Certainly one of the foci - on collaborativelearning - assists in that endeavor. In contrast, problems which do not have clearmapping, between the problem situation and the mathematical operationneeded, are found to be difficult; these problems include comparison typeproblems. There is an emphasison knowledge construction, rather than on memorization, and an acceptanceof mistakes or partial understandings as part of the process of learning.This is a significant shift and I am not certain that the public, as awhole, or school boards, are reallycognizant of that shift and in accord with it. Were the students able to successfully raise enough money tofund their field trip or were school funds needed to supplement the classraised moneys? The standard for grades kindergarten through fourthgrade states that; The study of mathematics should emphasize problem solving so thatstudents can: use problem-solving approaches to investigate and understandmathematical content; formulate problems from everyday and mathematical situations; develop and apply strategies to solve a wide variety of problems; verify and interpret results with respect to the original problem; acquire confidence in using mathematics meaningfully. Some of the literature alsoseems to inadequate that children have difficulties with a problem-solvingapproach, or at least with a problem-solving approach based on currentmathematical problems (Christou & Philippou, 1998; English, 1997, 1998).It is not clear how this would be remedied by a problem-solving centeredcurriculum. This began a reform period in the 196 s and 197 s inwhich new materials were developed and new approaches utilized to teachstudents. (1997). In realitythe mathematical operation called for is subtraction. Following that,there is an exploration of new mathematics standards, examination of theliterature on the effects of the problem-solving approach, review of newassessment ideas, and a focus on teacher strategies for enriching theproblem-solving environment.Constructivist principles One of the clearest statements of the difference between learningfacts and learning concepts that can be applied to one's life is SteenLarsen's (1991) discussion of the difference between information andknowledge. Students all are motivated by field trips so creativity andmotivation should be high with students. With training in posing problems, the children's ability topose problems from informal contexts increased. (1995). [Infotrack: General ReferenceCenter]. J. According to Larsen, information can easily be transmitted tothe student, but knowledge mustbe induced. These changes seem to be most difficult to achievein the primary grades where students are least familiar with mathematicalconcepts and skills. The second part of the study is a briefanalysis of the literature, with a focus on limitations and recommendationsfor further study. If a recyclingproject is chosen, objects can be sorted, weighed, and value calculated. M. Yet, it isrelevant, and important, and it is not difficult to structure the teachingsituation in order to show that relevance to students and help them gainthe knowledge to solve some of the problems in their own lives. The mathematical model: 3 children = 3 glasses of lemonade are needed 3 glasses - 2 glasses = 1 more glass of lemonade is needed Mathematics is studied in school so that we can resolve real-lifeproblems(Krech, 1999). My project isdesigned to help them apply mathematical principles in a way that isrewarding to them. There is also a problem with values. How many more cookies does Jan have? Teachers often informally meet and discuss problems and classprojects over lunch. Top 1 elements thatmust be in place to implement standards-based mathematics curricula[database]. If they can learn conceptually, if they can gain the knowledge toapply information to problems in the world, they may be able to developsolutions to important current problems, such as environmental degradation. One of the most important aspects of the constructivistenvironment is the teacher's respect for the students' errors and theability of the teacher to encourage students to develop incorrect orpartially correct ideas in a process that ultimately leads to new knowledge(DeVries and Zan, 1995).New Standards In 1991, the NCTM gave the community of mathematics teachers a newset of standards. The problems teachers design for their studentsshould follow these parameters: (a) the problem should be mathematicallysignificant, (b) the problem should occur in real-life, include realobjects, or be an obvious simulation of a real occurrence, (c) thesituation should capture the interest of the child, (d) the students shouldbe able to solve the problem and know when he has the solution. (practicing mathematicsproblem-solving skills). The American Association for the Advancement of Science (1989) statedthe need very well in a statement about curriculum change. p. Niemi, D. My interest is inimproving my ability to engage my student's in learning important conceptsand applying those concepts in ways that make mathematics a significant andhelpful part of their daily lives. The teacher and the textbook determine whatthe problems are and how they are to be solved. The number of multi-step, operationally complex problems wasgreater than structurally complex problems where the child must identifyand relate part-to-part, and part-to-whole (English, 1998). J. These gains in concept understanding are seen after two yearsof instruction with problem-centered mathematics instruction; computationskills were equivalent to children in the traditional textbook curriculum.Further, these gains in mathematics concepts, computation, and motivationto learn, continue to be evident for at least one year after the studenthas returned to traditional textbook instruction (Wood & Sellers 1997).Problem-solving approach A problem-centered curriculum in mathematics also influences thestudents' belief system about mathematics (Wood & Sellers, 1997). Atthe end of the project, after the field trip is taken, each teacher willsubmit to the group leader a formal evaluation on whether the field triplearning activity has met its goal and objectives. Instructor (199 ),1 7, 72. Young Children, November, 4-13. By allowing the child to place work into the portfolio orrecord entries into a journal, the child can see his own progress inmathematics, which will help him to develop confidence in his own abilitiesto solve problems mathematically.Teaching strategies The teacher's job in the classroom is to facilitate the learningprocess in mathematics. The problem-solving approach makes use of our bestunderstanding of how students can be engaged in learning. She can do this most effectively by designing aclassroom rich with opportunities in problem solving and by encouraging herstudents to use a variety of techniques to solve problems. TeachingChildren Mathematics, 4(3), 172-18 . Teachers will coordinate a fund-raising activity for the children andsuccessfully raise money to fund a field trip, estimated cost total forthree classes, 3 dollars. PLET 23(4), 331-335. Students may learn from each other as well asthe teacher. In other words,teachers must treat students respectfully, and students must treat eachother respectfully. Are these accurate assumptions? Create a climate forproblem solving. E. (p. Parnell (1996)indicated that public schoolsoften fail to help students make the connections between knowing and doing,school and life experience, knowledge and the application of knowledge.They treat students brains as if they were freezers to store information,rather than processing systems. My project goal is toincrease problem-solving opportunities in the primary grade classrooms bycreating in these classrooms a rich problem-solving and problem-posingenvironment. Both sets of objectives state the value of cooperative learning inlearning methods of problem solving. (2) Create a classroom atmosphere in which all students feelcomfortable trying out ideas, (3) Invite students to explain their thinking at all stages ofproblem solving. (1996). Laidlaw Mathematics, Series 2 (pp.2-5).Riverforest Ill.: Thatcher and Madison. In terms of my own educational goals, problem-solving approaches inmath allow me to work with my students to make mathematics meaningful tothem, not only in the classroom, but in their daily lives. A better overall picture of the child's developmentand learning is constructed. The intent of problem-solving education is toconnect all forms of knowledge for the student. Finally, personally the problem-solving approach makes much moresense to me. E Reys, 1999; Micklo, 1994).These types of assessments allow teachers to focus on the child'sindividual development of mathematical concepts instead of justcomputational ability. Constructivist teaching depends on creating a space inwhich eachindividual student is valued and allowed to develop fully. They did not believe that it wasimportant to be quiet to succeed, nor to complete their work neatly.Again, this is a shift from older values. She needs time to learn tolearn to use scoring guides to grade projects, to interview her students,to help students develop a portfolio of their work, and to grademathematics journals (Bay, J. The standard algorithms aretaught and used. Reys, 1999; Wood & Sellers, 1996). Promoting a problem-posing classroom. It seems that there isstill an emphasis on achievement on standardized tests. Parnell, D. Solutions to weekly problems can be recorded with the children'sreflections on their activities. 25). Likewise, teachers who taught a problem-centeredmathematics class, for at least one year, also changed their views onmathematics instruction. This reform seeks to incorporate the understandings of cognitivescience, using constructivist philosophy and techniques in order to helpstudents learn how tothink for themselves, gain better conceptual understanding, and be able touse both concepts and facts in order to solve real-world problems. Rose and Schuncke (1997) show howsimilar processes are used to solve problems in social studies andmathematics. The ability of students to give multiple meanings to formalmathematics symbols increases their understanding of concepts and theirability to pose different types of word problems (English, 1998; Niemi,1996). D. Itis not clear here that it is actually necessary to be noisy or create messywork in order to be competent in mathematics. The students who received instruction in classrooms which usedproblem-centered instruction methods gained a greater fluency withmathematical concepts, their representation, and changed their ideas aboutwhat mathematics was like. The teacher'sattitude affects the students' acceptability of multiple approaches andsolutions.Allowing for different approaches to solving a problem, the teacher mustallow each group of students or individual the opportunity to explain whythey used their method to solve the problem. Each teacher will keep a journal of activities and problemssolved with their classes' solutions. An initial approvalwill be solicited from the principal at this time. The value of collaboration between teachers when theyare striving to implement and improve the problem-solving environment intheir classrooms is proven (Bay, B. English, L. Even withtraining in posing problems, the types of word problems given for anynumber sentence was limited, although the children could change the contextof the problem. Next a plan must be devised to solve theproblem. Childhood Education, 73, 194-2 . There are a number of principles promoted byconstructivists thinkers, and each has a slightly different perspective.However, one of the more interestingconcepts is that the constructivist environment must be a sociomoral one inwhich respect for others is continually practiced. The calls for reform are based onrecent advances in cognitive theory that call for a more constructivistview of learning (Wood & Sellers, 1996). Traditionally, mathematicsinstruction in the primary grades has consisted of teaching computationalskills, drills, and simple word problems. This was at least partly addressed in the literature aboutconstructivist techniques. Wood, T., & Sellers, P. In the years following,the NCTM have strengthened their stance on the inclusion of problem solvingwithin mathematics curricula. Again, thefocus is on problem-solving as the more effective means for studentlearning, both in the classroom and in daily life. There iscertainly some support in the literature reported here for believing thatstudents are better able to understand and apply mathematical concepts(Wood and Sellers, 1996, 1997), but there are no long-range studies of theeffect of a problem-solving approach. The teacher andthe textbook are the authority. These skills are of secondaryimportance in a mathematics curriculum rich with problems solving ideas andmethods where the main goal is to teach mathematical logic and reasoning.The how and why of a child's solution is more important than the arithmeticused to compute the solution. Sivertsen, M.L. Micklo, S. Traditional mathematics classes donot utilize varied types of word problems in their textbooks(English,1998). Studentsin problem-centered classrooms were motivated by a belief in the importanceof finding their own solutions to problems and believed that to besuccessful in mathematics they must be able to explain their logic andreasoning to other people (Wood & Sellers, 1997, 171). Parent volunteers will be recruited to assist the children. & Stupiansky, N. The California Mathematics Framework alsoincludes problem-solving instruction beginning in kindergarten. National Council of Teachers of Mathematics, Curriculum and EvaluationStandards for Mathematics. & Reys, R. Journal for Research in Mathematics Education, 29, 83-97. Children'sinterpretations of standard formal number sentences appears to be limited.The diversity of types of word problems generated from an informal contextwas greater thanwith a formal number sentence where children tried to match the wordproblem's syntax to the operation in the number sentence. Sciencefor all Americans. The Clearing House, 7 ,137-141.[Infotrack: General Reference Center]. And Hamm, M. He describes the process of teaching as involving three stages.First, the knowledgeable person transforms his or her personal information(of mathematics, for example) into public. A teacher using a standards basedcurriculum needs time to observe her students. For me, thesignificance is very similar, although more personal. Instructor (199 ), 1 8, 11-13. They emphasizedthe need to: weaken or eliminate rigid subject-matter boundaries; to pay more attention to the connections among science, mathematics, and technology; to present the scientific endeavor as a social enterprise that strongly influences - and is influenced by - human thought and action; and to foster scientific ways of thinking (AAAS, 1989). Now, there is a re-focus on making education immediately relevantby working on problems in the student's daily lives. (1996). Thus, there needs to be a focus ontechniques designed to help students formulate, understand, and work withproblems. This project report will outline theyear's problem solving and fund-raising activities. (1997). TheNCTM standards also state that children should develop strategies to solvea variety of problems, check their solutions against the original problem,and become confident in their abilities (NCTM, 1991). The amount of money necessaryfor the proposed trip will be discussed. (1991). (1989). The first standard calls for mathematics as problemsolving(NCTM, 1991). The logical steps to solving problems do not vary across thedifferent subjects learned in school. Traditional textbook instruction is teacher centered. As a consequence, yet another reform period is underway during the199 s. (1998). At the end of the projectchildren will be able to (a) add and subtract amounts of money, (b)complete a bar graph, (c) weigh and measure, (d) classify and compareobjects, (e) calculate distance, (f) add and subtract units of time, (g)explain how they have solved a problem using mathematical terminology. Students who spent two years in problem-centered mathematics instruction tended to be task oriented. A student who is capable of solving problems in one subjectcan generalize the knowledge to other subjects. Journal for Research in MathematicsEducation, 27, 337-353. How many moreglasses of lemonade does Mother need to bring outside if all children willhave one glass of lemonade? Larsen, S. Waite-Stupiansky, S. A child's ability to pose or solve a problem mathematically islinked directly to the child's ability to form a representation of theproblem with mathematics symbols. Literature can be a sourceof material for formulating problems (Burns, 1997; English, 1998). Should the project be repeated? Inadequacies have been found in students' abilities to solve and posemathematical problems (Christou & Philippou, 1998; English, 1997, 1998).Problems posed in a linear fashion, when the mathematical equation can bemapped directly from the word structure of the problem, are fairly easy formost children to solve. And any otherquestions or further thoughts, comments or modifications which might betaken in future projects. The focus of constructivism, or its first principle according toBrooks and Brooks (1993), is the posing of problems that are of emergingrelevance to students. When given a formal mathematical sentence and asked to create aproblem to go with it, students will likely create a problem with the samestructure as the mathematical sentence (English, 1998). A joint classroom project will be designed to promote problem-solving skills for the full year. There is a definite relationship betweena student's representational fluency and success in problem solving,justification and explanation. (1998. And Zan, B. Were the all of the goals and objectives of theproject met? (teaching mathematical problems to children) [database].Instructor (199 ), 1 8, 54. This differs from a class which is using a standards basedcurriculum (a curriculum based on the standards of the NCTM). The purpose of teaching problem solving in the primary grades is toenable the student to understand the relationships between an event and themathematical model of that event. As the date of the trip approaches in spring, the distance, timeneeded for travel, and return time can be calculated. Strategies for teachers to use to promote a variety of problem-solving techniques to students include: (a) having students act the problemout, (b) making a diagram, (c) looking for a pattern, (d) constructing atable (e) systematic listing, (f) guess and check, (g) working backwards,(h) sorting relevant and irrelevant information, (i) solving a similar butsimpler problem, (j) changing your point of view, (k) choosing anoperation, (l) using logic, (m) using a model, (n) using a formula (LaidlawEducational Publishing, 1996, pp. This does not fitwith constructivist education methods. Phi Delta Kappan, 8 , 5 3. This, then, is transmitted inthe second stage. In October, the children will begin to raise funds. 2-3). D. The atmosphere of the classroom mustbe open to multiple ideas of how to solve a problem. & Philippou, G. The value of the new standards, calling for the inclusion of problemsolving in mathematics curricula, written by the NCTM is shown by researchstudies (Wood & Sellers, 1996, 1997). E. Children's problem posing within formal andinformal contexts. If this paper is not what you are looking for, you can search again: Search for: or Click here to request an essay written just for you.