Resume_Larina (1136637), страница 2
Текст из файла (страница 2)
Analysis of the use of real-life context in teaching mathematics in Russia from aninternational perspectiveTheoretical framework of the study consists of next theories and concepts:situated learning (J. Lave, E. Wenger, Greeno, Smith, & Moore, J.R. Anderson); role ofusing context in education (R.A. Engle, D. Hammer, O. Chapman, B. Cooper,A.V.Harries, OECD); real-life context in teaching math (H. Freudenthal, А. Treffers,V.V.
Firsov, N.A. Tereshin, I.M. Shapiro, M.V. Egupova); word problems (L.M.Fridman, B. Greer, L. Verschaffel, S. Gerofsky, R. Watanabe, B. Ischinger, W. Blum, M.Niss, T. Palm, D.H. Jonassen, Y.A. Tyumeneva, M.V. Egupova); teachers’ beliefs (A.G.Thompson, L.R. Van Zoest, J.V. Bohl, D. Stipek, R. Mosvold).Research Questions1. Research questions about math teaching practices and its connections with students’results in math:a. Which math teachers’ approaches towards real-life context are popular inRussia and what is the difference between them in Russian and other countries?b.
What is the relationship between math teachers’ practices towards real-lifecontext and the students’ results in TIMSS and PISA?2. Research questions about math teachers’ approaches towards real-life context inmathematics lessons:a. What type of real-life word problems do teacher use in math lessons?b. What are the teaching practices and strategies towards real-life context in mathlessons?c. What is the difference in the use of real-life context between math teaching inRussia and other countries?3. Research questions about the math teachers’ beliefs about using real-life context inmath learning at secondary level:a.
What are the math teachers’ beliefs about role of real-life context in mathlearning in Russia?b. What is the difference in teachers’ beliefs about using real-life context betweenmath teachers in Russian and other countries?5MethodologyThe mixed-method design was chose to conduct that research.In order to answer the first group of research questions there were employeddatasets of two large-scale assessment TIMSS and PISA, and one panel from alongitudinal survey TrEC3:1. Math teacher questionnaires from TIMSS 2011 and student questionnaire from thePISA 2012: representative and randomized samples from Russia and 16 othercountries (Australia, Israel, Jordan, Italy, Kazakhstan, Republic of Korea, Malaysia,Norway, United Arab Emirates, Singapore, Thailand, Tunisia, Turkey, Finland,Sweden, Japan) were employed.2.
The panel of math teacher questionnaire of TrEC 2014 in Russia (representativerandomized sample, N=192).3. Achievement datasets of TIMSS 2011 и PISA 2012, that were conducted on thesame sample within the framework of TrEC. TIMSS 2011 sample consisted of the8th grade students and PISA 2012 sample consisted of the 9th grade students. Thetotal sample consisted of 4778 from 210 classrooms.Descriptive statistics, chi-square and linear regression analysis were used.In order to answer the second and third groups of research questions there wereemployed qualitative data. In 2014-2016 the additional data was collected in 30 schoolsfrom 9 regions in Russia.
The sample was non-random and consisted teachers who haveparticipated in TrEC study in 2012. In every school:1. There was conducted a semi-structured interview with math teacher (N=28).2. A math lesson in 8th or 9th grade was videotaped (N=25).The collected data was transcribed and coded. Transcripts of interviews wereanalyzed with open and axial coding within the framework of the grounded theoryanalysis. Next, there were analyzed word problems, which teachers used at thevideotaped lessons (N=90). In addition, word problem from demo versions of the BasicState Exam 2015 and the Unified State Exam 2015 were considered.
Coding schemeswere developed in order to code word problems and teachers’ approaches towards reallife in math lesson. Descriptive statistics, chi-square analysis, regression and clusteranalysis were used.Main resultsIn order to answer the first group of research questions the datasets of TIMSS 2011,PISA 2012 and TrEC were analyzed. First, according to TIMSS 2011 data, it was shownthat mathematics teachers in Russia and in foreign countries devote a comparable amountof time to many math teaching practices, including working with real-life context.However, in Russia, students at the 8th grades are much less likely to meet a task thatrequire more independent problem-solving activity (solving complex and unfamiliarproblems that do not have an obvious method of solution) compare to peers in othercountries. And, at the same time, they are much more likely to perform tasks on3Trajectories in Education and Careers, https://trec.hse.ru/en/6reproductive activity (apply facts, concepts and procedures to solve routine problems).
Asfor math test, Russian students more often needs to solve problems on memorizing rules,procedures and facts than their peers in foreign countries. It is important to note, that thereal-life word problems tasks were presented in math tests in Russia with the samefrequency as in foreign countries. Thus, in many cases, teachers in Russia use real-lifecontext in teaching mathematics to the same extent as teachers in other countries.However, the number of math problems requiring more independent activity from astudent is used less frequently in math lessons in Russia.However, the results of the international study of PISA 2012 revealed quite oppositeresults: students in Russia are more familiar with the tasks and concepts that can beattributed to formal mathematics, rather than to applied mathematics.
For example, the 9thstudents in Russia noted that they more often work in math lessons with concepts fromalgebra (quadratic and exponential functions) and geometry (vectors, polygons), solveequations, than with real-life word problems. Compare to other countries the frequencyof formal math problems is one the highest among them.Finally, the results of the comparison math teaching practices in classes withdifferent TIMSS 2011 or PISA 2012 were ambiguous and contradict to the statedhypothesis. First, the frequency of the using teaching methods in these classes wassignificantly different only in several cases.
But, secondly, teachers' responses about thefrequency of using these methods varied significantly in different databases. Thus, basedon the results of the analysis, no unequivocal and significant connection between theteaching methods and the students’ math achievements has been showed.Next, the answers for the second group of research questions were obtained.
At thefirst step of the videotaped lesson analysis it was shown that the word problem is themost popular way of real-life connection in math lesson in Russia and other countries. Inmost cases these word problems involved context structural or interior design, shoppingand banking.
But, unlike math teachers in other countries, teachers in Russian useintegrated problems in math classroom as a demonstration of math application in otherschool subjects. In addition, the views of mathematics teachers about what tasks shouldbe used in the lessons to demonstrate the applicability of the content of the lesson ineveryday life differed. So, in most cases the word problems in math lessons could besolved with mathematical modeling, but they have a cliché formulations and their contextwere not significant and relevant to the students.
In other words, most often in theclassroom, students encountered word problems that were not a correct reflection ofeveryday life.The analysis of the teachers’ approaches towards real-life context in math lessonshowed, that in most cases teachers avoided the elaborating the context of the problem(narrative approach) and paid more attention to the overall structure of the problem, itstype and the use of the known method of solutions (paradigmatic approach).
In general,teaching interventions towards word problems of Russian math teachers are correspondto teaching practices in other countries. In addition, math teachers both in Russia andother countries are more focused on the modeling phase of problem solving than on the7interpretation phase. However, unlike foreign colleagues, Russian teachers do not payattention to distinguishing relevant and irrelevant information in word problem.Finally, the interventions towards word problems varied significantly by the type ofthe word problem.
If the word problem’ context was significant to a student life and hadnon-routine formulation, then the teachers were more likely to elaborate the real-lifecontext of that problems. Conversely, if the word problem had to be solved just withmodeling the situation, then math teachers devoted more time to the structure of such aproblem.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
