scholarly journals NONSTANDARD MATH WORD PROBLEMS AND ANALYSIS OF THE PARTIAL STAGES OF ITS SOLUTION

2021 ◽  
Vol 79 (5) ◽  
pp. 716-727
Author(s):  
Radka Dofková ◽  
Michaela Surá
Keyword(s):  
Word Problem ◽  
Prospective Teachers ◽  
Word Problems ◽  
Solution Process ◽  
Problem Solution ◽  
Mathematics Problem Solving ◽  
Cognitive Estimation ◽  
The Right ◽  
The Given ◽  
Math Problems

Choosing the right strategy is an important condition to successfully solve math problems. Research studies often present individual types of strategies more or less separately. This study aims to determine student solutions of selected word problems in the whole context of the solution process. In this context, such nonstandard word problems combine verbal formulation and the character of nonstandard problems (impossible to be solved using an algorithm). In order to get an overall picture of the stages of word problem solution, an analysis of solving a given word problem was conducted among 171 respondents aged 10-11. The analysis was conducted in compliance with partial steps of word problem processing, as the solving of the problem was viewed from a wider perspective. The student’s reaction to the problem, working with the given information, individual forms of solution, and answer formation were recorded. In order to have a more complex idea and possibility to compare, the chosen way of solving the problem was also presented to a selected sample of 26 teachers. Available solutions were analyzed, and there were sought ways how the solution was assessed by the teachers based on selected parameters. Especially their meta-cognitive estimation of the correctness of their own solution was subject to scrutiny. Despite the fact that the respondents chose different strategies of solution (graphic, arithmetical, using judgment, etc.), it appears that the success rate of solving the given nonstandard word problem was very low. Thus, it is necessary to implement such word problems into standard math lessons, also within pre-graduate teacher preparation. Keywords: mathematics teaching, primary school mathematics, problem-solving, prospective teachers, word problem

scholarly journals Analisis kesalahan siswa dalam menyelesaikan soal cerita matematika berdasarkan kriteria Watson

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Laely Mafruhah ◽  
Arif Muchyidin
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Descriptive Study ◽  
Study Data ◽  
Seventh Graders ◽  
Response Level ◽  
Qualitative Descriptive ◽  
Mathematical Word Problems ◽  
The Given ◽  
Error Types

Tujuan dari penelitian ini adalah untuk mendeskripsikan kesalahan yang dilakukan oleh siswa dalam menyelesaikan soal cerita matematika berdasarkan kriteria Watson dan faktor-faktor yang menyebabkan siswa melakukan kesalahan tersebut. Penelitian ini merupakan penelitian deskriptif kualitatif dengan melibatkan 44 siswa kelas VII MTs Yapik Sindangjawa, Cirebon sebagai subjek penelitian. Data jenis kesalahan dan faktor yang menyebabkan siswa melakukan kesalahan dalam menyelesaikan soal cerita matematika diperoleh melalui tes penyelesaian masalah berbentuk soal cerita matematika dan pedoman wawancara. Hasil penelitian menunjukkan bahwa subjek dalam penelitian ini melakukan kesalahan yang bervariasi dari delapan jenis kesalahan yang ada pada kriteria Watson. Jenis kesalahan yang sering dilakukan oleh siswa adalah Inappropriate Procedure (IP) yaitu prosedur yang digunakan tidak tepat, Omitted Conclusion (OC) yaitu tidak menuliskan kesimpulan, dan Above Other (AO) yaitu kesalahan lainnya seperti tidak mengerjakan soal. Adapun jenis kesalahan yang jarang dilakukan oleh siswa adalah Response Level Conflict (RLC) yaitu siswa berusaha menyelesaikan soal, namun menghasilkan kesimpulan yang kurang logis. Beberapa faktor penyebab siswa melakukan kesalahan dalam menyelesaikan soal cerita matematika adalah siswa tidak mengetahui rumus yang akan digunakan, kurangnya waktu dalam mengerjakan semua soal tes, dan siswa menganggap bahwa soal cerita merupakan soal yang sulit untuk diselesaikan. Analysis of students' errors in solving mathematical word problems based on Watson's criteriaAbstractThis study aimed to describe the errors made by students in solving mathematical word problems according to Watson’s criteria as well as factors that cause students to do that errors. This study was a qualitative descriptive study involved 44 seventh graders of MTs Yapik Sindangjawa, Cirebon, Indonesia as the subjects of this study. Data of error types and factors that lead students to do such errors in solving mathematical word problems were collected using the test of solving mathematical word problems and interview guidelines. The results showed that the subjects made various errors from the eight types of errors that exist in Watson's criteria. The types of errors that often made by students were Inappropriate Procedure (IP) namely using inappropriate procedures; Omitted Conclusion (OC) namely students not writing conclusions; and Above Other (AO) namely making other mistakes such as not giving a response towards the given problem. The type of error that was rarely made by students was Response Level Conflict (RLC), where students try to solve the problem but produce less logical conclusions. Some of the factors that cause students to do some errors in solving mathematical word problems namely students do not know the formula to be used to solve the given problems, lack of time to solve all problems of the test, and students think that the mathematical word problem was difficult to be solved.

Untersuchung von Schülerlösungen mit Hilfe von Lösungsniveaus bei Textaufgaben mit realitätsnahem Inhalt

2020 ◽  
pp. 63-78
Author(s):  
Gabriella Ambrus
Keyword(s):  
Problem Solving ◽  
Word Problem ◽  
Word Problems ◽  
Open Problems ◽  
Modelling Problem ◽  
Concrete Solution ◽  
The Given

In this article, some school results in connection with the solution of such word problems are discussed, which are based on realistic situa-tions. The word problems here are however special ones: they are formulated like the “conventional word problems” – where a concrete solution is expected. At the same time, the given situation of the task is open, it has solutions dependent on further conditions. A level-classifying method “solution levels” is used to evaluate the results. Classification: D50, D70, F90, M10 Keywords: word problem, open problems, reality-based problems, modelling, problem solving

scholarly journals Students’ suspension of sense making in problem solving

ZDM ◽  
2021 ◽  
Author(s):  
Gemma Carotenuto ◽  
Pietro Di Martino ◽  
Marta Lemmi
Keyword(s):  
Problem Solving ◽  
Qualitative Study ◽  
Word Problem ◽  
Word Problems ◽  
Mathematical Problem ◽  
Critical Issue ◽  
Mathematical Problem Solving ◽  
Sense Making ◽  
Mathematical Problems

AbstractResearch on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.

scholarly journals Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

2021 ◽  
Author(s):  
Yasemin Copur-Gencturk ◽  
Tenzin Doleck
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematics Learning ◽  
Mathematical Knowledge For Teaching ◽  
Important Indicator ◽  
Strategic Competence ◽  
The Usa ◽  
Valid Solution

AbstractPrior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.

A. A. Fridman. Stépéni nérazréšimosti problémy toždéstva v konéčno oprédélénnyh gruppah. Doklady Akadémii Nauk SSSR, vol. 147 (1962), pp. 805–808. - A. A. Fridman. Degrees of insolvability of the word problem in finitely defined groups. English translation of the preceding by Sue Ann Walker. Soviet mathematics, vol. 3 no. 6 (1962), pp. 1733–1737. - C. R. J. Clapham. Finitely presented groups with word problems of arbitrary degrees of insolubility. Proceedings of the London Mathematical Society, ser. 3 vol. 14 (1964), pp. 633–676. - William W. Boone. Finitely presented group whose word problem has the same degree as that of an arbitrarily given Thue system (an application of methods of Britton). Proceedings of the National Academy of Sciences, vol. 53 (1965), pp. 265–269. - William W. Boone. Word problems and recursively enumerable degrees of unsolvability. A first paper on Thue systems. Annals of mathematics, ser. 2 vol. 83 (1966), pp. 520–571. - William W. Boone. Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups. Annals of mathematics, ser. 2 vol. 84 (1966), pp. 49–84.

1968 ◽  
Vol 33 (2) ◽  
pp. 296-297
Author(s):  
J. C. Shepherdson
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Nauk Sssr ◽  
London Mathematical Society ◽  
National Academy Of Sciences ◽  
Doklady Akademii Nauk Sssr ◽  
Finitely Presented Groups ◽  
Recursively Enumerable ◽  
Finitely Presented ◽  
Degrees Of Unsolvability

Word problems related to derivatives of the displacement map

1991 ◽  
Vol 110 (3) ◽  
pp. 569-579 ◽  
Author(s):  
J. Devlin
Keyword(s):  
Periodic Solutions ◽  
Word Problem ◽  
Word Problems ◽  
Abstract Word ◽  
Local Problem ◽  
Image Position ◽  
Derivatives Of

In [6], we considered the equationwhere z ∈ ℂ and the pi are real-valued functions; abstract word-problem concepts and techniques were applied to the local problem of the bifurcation of periodic solutions out of the solution Z ≡ 0. This paper is a sequel to [6]; we present an extension of certain concepts given in that paper, and give a global version of some of our word-problem results.

Manufacturability Analysis for Solid Freeform Fabrication

1999 ◽  
Author(s):  
R. K. Arni ◽  
S. K. Gupta
Keyword(s):  
Systematic Approach ◽  
Solid Freeform Fabrication ◽  
Second Step ◽  
Freeform Fabrication ◽  
Design Tolerance ◽  
The Face ◽  
The Right ◽  
The Given ◽  
Manufacturing Problems ◽  
Case Effect

Abstract This paper describes a systematic approach to analyzing manufacturability of parts produced using Solid Freeform Fabrication (SFF) processes with flatness, parallelism and perpendicularity tolerance requirements on the planar faces of the part. SFF processes approximate objects using layers, therefore the part being produced exhibits stair-case effect. The extent of this stair-case effect depends on the angle between the build orientation and the face normal. Therefore, different faces whose direction normal is oriented differently with respect to the build direction may exhibit different values of inaccuracies. We use a two step approach to perform the manufacturability analysis. We first analyze each specified tolerance on the part and identify the set of feasible build directions that can be used to satisfy that tolerance. As a second step, we take the intersection of all sets of feasible build directions to identify the set of build directions that can simultaneously satisfy all specified tolerance requirements. If there is at least one build direction that can satisfy all tolerance requirements, then the part is considered manufacturable. Otherwise, the part is considered non-manufacturable. Our research will help SFF designers and process providers in the following ways. By evaluating design tolerances against a given process capability, it will help designers in eliminating manufacturing problems and selecting the right SFF process for the given design. It will help process providers in selecting a build direction that can meet all design tolerance requirements.

Intensive Word Problem Solving for Students With Learning Disabilities in Mathematics

2021 ◽  
pp. 105345122110475
Author(s):  
Bradley Witzel ◽  
Jonté A. Myers ◽  
Yan Ping Xin
Keyword(s):  
Learning Disabilities ◽  
Problem Solving ◽  
Word Problem ◽  
Word Problems ◽  
Mathematics Performance ◽  
Students With Learning Disabilities ◽  
Word Problem Solving ◽  
Model Based ◽  
Students With Ld

State exams frequently use word problems to measure mathematics performance making difficulties with word problem solving a barrier for many students with learning disabilities (LD) in mathematics. Based on meta-analytic data from students with LD, five empirically validated word-problem strategies are presented with components of model-based problem solving (MBPS) highlighted.

scholarly journals OSOBENNOSTI POKAZATELEY UL'TRASONOMETRII ZhENSKOGO NASELENIYa GORODA ChELYaBINSKA

2005 ◽  
Vol 8 (2) ◽  
pp. 25-28
Author(s):  
E N USOL'TsEVA ◽  
O V SAFRONOV ◽  
E V BRYuKhINA
Keyword(s):  
Characteristic Feature ◽  
Ultrasound Wave ◽  
Spongy Bone ◽  
Anatomic Structure ◽  
Lower Jaw ◽  
Tibia Diaphysis ◽  
The Right ◽  
The Given ◽  
Peripheral Skeleton ◽  
Tubular Bones

Characteristic feature of ultrasonic densitometry have been investigated in women,s population of Chelyabinsk (n=200) from 25 to 65 years old. We used domestically produced Echoosteometr-02. A basis of a body of the lower jaw became a new area for ultrasonic densitometry. We can recommend a lower jaw as a new area for ultrasonic densitometry taking into account high pithiness of data in a combination with simplicity of research. Traditional localizations have been also applied: proximal phalanges of the hand, patella, tibia diaphysis and calcaneus bones of the right and left sides. We have established a "peak" values of a speed of the ultrasound wave for the given bones. Also we have found that a tubular bones and a large spongy bone - a lower jaw - possess the highest speed of an ultrasound wave, and the speed was mach less in a small spongy bones, that is caused by their anatomic structure. Ultrasound densitometry parameters of the peripheral skeleton start to reduce from 40-50 years behind exception patella - from 55 years. The lowest values were in group of women of 60-65 years. The rates of ultrasonic densitometry received by us are possible to use for women population of Chelyabinsk.

Sign in / Sign up

Export Citation Format

Share Document