# ارزیابی خطاهای دانش‌آموزان پایه چهارم بر اساس مدل تحلیل خطای نیومن در حل مسائل ریاضی

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی دانشگاه تربیت دبیرشهید رجایی

چکیده

پژوهش‌حاضر به بررسی توانایی حل مسائل کلامی ریاضی دانش‌آموزان پایه چهارم ابتدایی بر مبنای مدل تحلیل خطای نیومن به کمک روش توصیفی-پیمایشی از نوع مقطعی پرداخته است. از میان دانش‌آموزان پایه چهارم منطقه 12 شهر تهران، تعداد 399 دانش‌آموز دختر و پسر به روش تصادفی خوشه‌ای انتخاب گردیدند. به منظور جمع‌آوری داده‌ها از آزمونی محقق‌ساخته‌ که تلفیقی از چهار سؤال تشریحی و پرسش‌های نیومن بود، بهره گرفته شد. برای بررسی روایی ابزار پژوهش از روایی صوری و محتوایی و برای پایایی از آلفای کرونباخ استفاده شد که میزان آن 82/0 بدست آمد. تجزیه و تحلیل داده‌ها با استفاده از روش‌های آمار توصیفی و استنباطی (تحلیل واریانس چند متغیری) انجام گرفت. براساس یافته‌ها، دانش‌آموزان در فرایند دستیابی به پاسخ درست مسائل، بیشترین خطا را در مرحله تبدیل و کمترین آن را در مرحله کدگذاری از سطوح سلسله‌مراتبی خطای نیومن به خود اختصاص داده‌اند. نتایج آزمون خی‌دو نیز نشان داد که بین هر یک از سطوح خطای نیومن با عملکرد دانش‌آموزان در حل مسائل کلامی ریاضی، رابطه معنی‌داری وجود دارد. همچنین، نتایج حاکی از وجود تفاوت معنی‌دار در عملکرد دو گروه دختران و پسران بوده است و به‌طور کلی پسران مرتکب خطای کمتری در مقایسه با دختران شده‌اند. یافته‏های این پژوهش می‏تواند در بازبینی فرایند آموزش حل مسئله کلامی و تنظیم مواد آموزشی برای کتب درسی ریاضی مورد استفاده قرار گیرد.

کلیدواژه‌ها 20.1001.1.24765686.1399.8.4.4.5

عنوان مقاله [English]

### The evaluation of 4th grade students’ Errors based on the Newman's Error Analysis model in problem solving

چکیده [English]

Word problems, despite their difficulties, are of great importance in mathematics. Many students' ability to solve word problems is lower than their ability to solve computational problems (Burns, 2000; Miller et al., 2017). It can be argued that understanding these kinds of problems requires an active interaction between linguistic knowledge and mathematical knowledge. If these difficulties are not solved in the early stages of learning math, these difficulties will become more widespread over the years and reach the academic level. Therefore, initial action is essential for students' success in such problems in elementary school (Clements and Sarama, 2011). Most elementary school students, in the face of these problems, after reading the problem without realizing it, simply try to find the keywords and as soon as they find them, they start solving the problem, unaware that this method does not always lead them to the correct answer. Therefore, since elementary schools are the keystone of learning mathematics for future levels, conducting research to find students' difficulties in solving word problems as well as examining and recognizing their errors in solving such problems and eliminating them. They are very important in all grades of in elementary schools, especially the fourth grade; because this is the first grade to be addressed in the TIMSS international Study.
There are several ways to analyze student errors. One of these methods is the Newman error analysis method, which includes a systematic method for analyzing the errors that students make while answering word mathematical problems. This method is hierarchical and based on the assumption that students follow orderly mental patterns in problem solving that can be divided into specific stages. Other models ignore students' specific and individual methods, which are quite vital (Clarkson, 1991). According to Newman, in order to reach the correct answer in solving word problems, one must go through five hierarchies: read the problem; understand what he/she has read; to be able to choose an appropriate mathematical strategy, make a mental transformation of the words used in the problem; depending on the strategy chosen, use the required process skills and finally present the answer in an acceptable written form. These five hierarchies are abbreviated as: 1) reading, 2) comprehension, 3) transformation, 4) process skills, and 5) coding. Newman used the term "hierarchy" because failure at each level prevents the problem solver from advancing properly in the problem-solving process. In solving word problems, students go through five stages, in each of which, an error may occur that prevents the student from reaching the correct answer (Clements and Ellerton, 1996).
Newman's hierarchical model of error analysis enables teachers to identify five obvious difficulties students have when solving word problems, to recognize students' errors before solving problems, and to use appropriate strategies (Watson, 1980; White, 2005). Therefore, conducting research in this field will be useful. In this regard, the present study examines the types of students' errors in solving word problems using Newman analysis.
The study aimed to investigate the ability to solve word mathematical problems of 4th-grade students based on the Newman error analysis model using descriptive-survey method of cross-sectional type. Among the all 4th-grade primary school students from district 12th of of Tehran, 399 students were selected by using cluster random sampling. To collect data, a researcher-made test which composed of four questions as well as Newman questions was applied. To examine the validity of the research instrument, face and content validity was used and Cronbach's alpha (α=0.82) was used for reliability. The paper and pencil tests were corrected by two raters, and the inter-rater reliability was computed. Data analysis was done using descriptive and inferential statistics (MANOVA).
Based on the results, among the errors of reading, comprehension, transformation, process skills and coding, students in the process of achieving the correct answer to the word problems have the most error in the transformation (24.9%) and the least in coding (0.5%).of the Newman hierarchy stages. The results of Chi -square test at the level of 0.05 showed that there is a significant relationship between the rate of reading error and students' performance in solving math word problems (P <0.05, 2χ = 71.637). The results of Chi-square test showed that there is a significant relationship between the rate of comprehension error and students' performance in solving math word problems (P <0.05, 2χ = 61/984). The results of Chi -square test showed that there is a significant relationship between the rate of transformation error and students' performance in solving math word problems (P <0.05, 2χ = 33.543). The results of Chi-square test showed that there is a significant relationship between the rate of error of process skills and students' performance in solving math word problems (P <0.05, 2χ = 63.262). The results of Chi-square test showed that there is a significant relationship between the rate of coding error and students' performance in solving mathematical word problems (P <0.05, 2χ = 44.645).
Also, the results showed a significant difference in the performance of the two groups of boys and girls, while boys generally made fewer errors than girls. In fact, the results of Wilks' Lambda statistic showed that there was a significant difference between the total problem solving error in the Newman analysis model in comparison between the two groups of girls and boys (ƞ2 = 0.135, P = 0.002, 4.365, F (4, 394)= 4.394). The findings of this research can be used to review the word problem solving teaching process and to set up educational materials for mathematical textbooks.

کلیدواژه‌ها [English]

• Error
• the Newman method of Error Analysis

#### مراجع

Abdullah, A. H., Abidin, N. L. Z., & Ali, M. (2015). Analysis of Students' Errors in Solving Higher Order Thinking Skills (HOTS) Problems for the Topic of Fraction. Asian Social Science, 11(21), 133.
Bakhshalizādeh, S. (2013). Identifying the primary school fourth grade students’ common misconceptions in content area of math. Research Institute for Education, Tehran. (In Persian).
Bakhshalizādeh, S. & Broojerdiān, N. (2017). Identifying the primary school fourth grade students’ common misconceptions in content area of geometry and measurement: A comparison of their performance with the mean performance at international level. Educational Innovations, 16(4), 101-126. (In Persian).
Bottle, G. (2005). Teaching mathematics in the primary school: The essential guide. A&C Black. (Translated by Shahrnaz Bakhshalizadeh, 2012). (In Persian).
Burns, M. (2000). About teaching mathematics: A K-8 resource. Math Solutions Publications, Marilyn Burns Education Associates, 150 Gate 5 Road, Suite 101, Sausalito, CA 94965.
Charles, R. (2004). Solving Word Problems: Developing Students’ Quantitative Reasoning Abilities. Retrieved from pearsonschool. com/elementaryproducts. Pearson Education, Inc. Mat07289.
Clarkson, P. C. (1991). Language comprehension errors: A further investigation. Mathematics Education Research Journal, 3(2), 24-33.
Clarkson,  P.  (1983).  Types  of  errors  made  by  Papua  New  Guinean students.  Educational Studies in  Mathematics,  14(4),  355-367.
Clements,  M.  K.  (1980).  Analyzing  children's  errors  on  written  mathematical tasks.  Educational studies in  mathematics,11(1),  1-21.
Clements,  M.  A.,  &  Ellerton,  N.  F.  (1996).  Mathematics  Education  Research:  Past, Present and  Future.  Bangkok,  Thailand: UNESCO.
Clements,  D.  H.,  &  Sarama,  J.  (2011).  Early  childhood  mathematics intervention.  Science,  333(6045),  968-970.
Delisio,  L.  A.,  Bukaty,  C.  A.,  &  Taylor,  M.  (2018).  Effects  of  a  Graphic  Organizer Intervention  Package  on  the  Mathematics  Word  Problem  Solving  Abilities  of  Students with  Autism  Spectrum  Disorders.  Journal of  Special Education  Apprenticeship,  7(2),  n2.
Esmaeili,  M.  &  Rafiepour,  A.  (2014)    Analyzing  the  error  of  fifth  grade  Students  in solving  word  problems  using  Newman's  method.    The  13th  Conference  on  Mathematics Education,  Tehran,  Shahid  Rajaee  Teacher  Training  University.  (In  Persian).
Fitriani,  H.  N.,  Turmudi,  T.,  &  Prabawanto,  S.  (2018,).  Analysis  of  students  error  in mathematical  problem  solving  based  on  Newman’s  error  analysis.  In  International Conference  on  Mathematics  and  Science  Education  of  Universitas  Pendidikan Indonesia  (Vol.  3,  pp.  791-796).
Hesam,  B.  &  Pandi,  Z.  (2019).  Math  Kangaroo  Grade  3  and  4.  Fatemi  Publishing, Tehran.  (In  Persian).
Jitendra,  A.  K.,  Dupuis,  D.  N.,  &  Rodriguez,  M.  C.  (2012).  Effectiveness  of  SmallGroup  Tutoring  Interventions  for  Improving  the  Mathematical  Problem-Solving Performance  of  Third-Grade  Students  with  Mathematics  Difficulties:  A  Randomized Experiment.  Society  for  Research  on  Educational Effectiveness.
Miller,  A.,  Tobias,  J.,  Safak,  E.,  Kirwan,  J.  V.,  Enzinger,  N.,  Wickstrom,  M.,  &  Baek, J.  (2017).  Preservice  teachers’  algebraic  reasoning  and  symbol  use  on  a  multistep  fraction word  problem.
Mukunthan,  T.  (2013).  A  study  on  students'errors  on  word  problem.  International Journal of Management,  IT and  Engineering,  3(10),  205.
National  Council  of  Teachers  of  Mathematics.  (1980).  An  agenda  for  action: recommendations  for  school  mathematics  of the  l980s.  Reston,  VA:  Author.
Rahman,  T.  F.  A.  (2019).  Exploring  Students’  Error  in  Quadratic  Word-Problem Using  Newman  Procedure.  Academic  Journal  of  Business  and  Social  Sciences,  3,  1-13.
Rohmah,  M.,  &  Sutiarso,  S.  (2018).  Analysis  Problem  Solving  in  Mathematical Using  Theory  Newman.  EURASIA  Journal  of  Mathematics,  Science  and  Technology Education,  14(2),  671-681.
Singh,  P.,  Rahman,  A.  A.,  &  Hoon,  T.  S.  (2010).  The  Newman  Procedure  for Analyzing  Primary  Four  Pupils  Errors  on  Written  Mathematical  Tasks:  A  Malaysian Perspective.  Procedia-Social  and  Behavioral Sciences,  8,  264-271.
Soltani, S . & Momeni, N. (2013). Investigating the errors of fifth grade elementary school girls in solving math verbal problems based on Newman's error analysis model. (In Persian).
Tayeb, T., Angriani, A. D., Humaerah, S. R., Sulasteri, S., & Rasyid, M. R. (2018). The Students’ Errors in Answering Geometric Tests with Newman Procedures. In Journal of Physics: Conference Series (Vol. 1114, No. 1, p. 012048). IOP Publishing.
Trance, N. J. C. (2013). Process Inquiry: Analysis of Oral Problem-Solving Skills in Mathematics of Engineering Students. Online Submission, 3(2), 73-82.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands.
Watson, I. (1980). Investigating errors of beginning mathematicians. Educational Studies in Mathematics, 11(3), 319-329.
White, A. L. (2005). Active mathematics In classrooms: Finding out why children make mistakes-and then doing something to help them. Square one,15(4), 15-19.
White, A. L. (2010). Numeracy, Literacy and Newman’s Error Analysis. Journal of Science and Mathematics Education in Southeast Asia, 33(2), 129-148.
White, J. (2017). Using Children’s Literature to Teach Problem Solving in Math: Addressing the Standards for Mathematical Practice in K–5. Routledge.
Wijaya, A., Van Den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students' errors. The Mathematics Enthusiast, 11(3), 555.
Yunus, J., Zaura, B., & Yuhasriati, Y. (2019). Analysis of students error according to newman in solving mathematics problems of algebra in the form of story in second grade of smpn 1 banda aceh. Jurnal Geuthèë: Penelitian Multidisiplin, 2(2), 308-313.