Abstract
The following article provides an analysis of the skills that enable a primary school learner to process mathematical information. The author studies students’ performance on particular tasks from the mathematics tests developing for primary school learners, presented in the regional research (20142016), and from the TIMSS international research test (2011, 2015). The author describes the two categories of information processing skills – subjectrelated (mathematics specific) and interdisciplinary learning skills – and illustrates them with corresponding quiz items, designed to test one’s ability to handle information. The author also singles out the two groups of challenges: students may lack, on the one hand, subject skills, on the other hand, universal learning skills. The results of the research reveal the difficulties related to mathematical education and show that when the learner has to process mathematical information, he/she demonstrates sufficient awareness of how to apply mathematical information in order to accomplish various tasks. Therefore, the increase of informational literacy should be considered as one of the learning outcomes of the primary education.
Keywords: Information processinglearning processlearning skillTIMSS researchmathematicsmonitoring
Introduction
Nowadays the term information can be interpreted in a few different ways. The main ones would be, as follows: a set of valuable data in an object under consideration; coded knowledge; “the semantics of signals, symbolic messages, numbers, notes, images” (Gubarev, 2011, p.11); schematic models (tables, schemes, diagrams, and others). The student develops the ability to handle information both in the learning environment and in daily situations.
According to the Russian approach to primary education, information processing stands for the number of the learner’s achievements in a particular subject as well as the fourth grader’s overall performance at school. In the first case, the Federal State Educational Standard of Primary General Education (FSES PGE) considers such universal learning skills as “the application of various methods of search…, collection, comprehension, analysis, compilation, transmission, and interpretation of information in compliance with communicative and cognitive purposes…” (Ministerstvo obrazovanija i nauki Rossiyskoy Federatsii, 2015, p.9) to be the teaching priorities. Such skills let one regard informational literacy as “an integral feature” (after Vinogradova) of learner’s functional literacy in the primary school.
Research Questions
How can the TIMSS international research tests and results of regional research be taken into account in the development of the learning tasks connected with information processing.
Purpose of the Study
This study was designed to analyse learners’ ability to handle information in the Russian primary schools. Thereupon, I distinguish between two categories of information processing skills (subject and interdisciplinary learning skills) and describe the peculiarities of the development of some subject and universal learning skills, which demonstrate the child’s ability to handle mathematical information.
The objectives of the study were, as follows: to illustrate how primary school learners’ informational skills manifest themselves in course of writing monitoring papers, to single out the main challenges and their possible causes, and suggest ways of their prevention and elimination.
Research Methods
This study is based on the Data Analysis type of tasks accomplished by Russian learners in the frames of the international TIMSS (TIMSS – Trends in Mathematics and Science Study) test in 2011 and 2015 (Rezul'taty mezhdunarodnogo issledovanija TIMSS, 4 klass, 2015), as well as the Information Processing type of tasks that were included in the regional monitoring and assessment tests (Primernaja osnovnaja obrazovatel'naja programma nachal'nogo obshhego obrazovanija, 2015). The tasks for the regional monitoring were designed by Kuznetsova, Krasnyanskaya, and Rydze in the Centre for Educational Quality Assessment (Kovaleva, Director), the Federal State Budgetary Scientific Institution (FSBSI) Institute for Strategy of Education Development of the Russian Academy of Education, and Moscow Education Quality Centre (Soldatov, Director), the Academy of Public Administration in Moscow Oblast. I analysed the subject and interdisciplinary content of the TIMSS test (Foy, 2013; Martin, Mullis, 2009; Mullis et al., 2016; Mullis, Martin, Goh, Cotter, 2016; Mullis et al., 2015) and the Sample Main Syllabus (Primernaja osnovnaja obrazovatel'naja programma nachal'nogo obshhego obrazovanija, 2015). I systematised the skills of interest and analysed them in different papers (tests).
Findings
As the study of the specifically chosen type of mathematics tasks, Information Processing, shows, among the main subject skills one may list (Primernaja osnovnaja obrazovatel'naja programma nachal'nogo obshhego obrazovanija, 2015) the ability to comprehend and complete tables as well as read diagrams. Moreover, the student has an opportunity to learn to “comprehend simple mathematical expressions, including linking words (‘…and…’, ‘if…, then…’, ‘it is true/ false that…’, ‘each’, ‘every’, ‘all’, ‘some’, ‘not’); to make, take down, and follow an instruction (a simple algorithm) or a search plan; to recognize the same information in different forms (tables or diagrams); to design simple research, collect and present information obtained in tables and diagrams…” (
Processing Information. Subject Skills
The present group includes subjectrelated skills and competences that learners develop since the first grade. The majority of students, finishing primary school, can easily “read” a table or a diagram, select necessary data, and fill in table cells. According to the results of both regional and international studies, more than 80% of children cope with this task.
Sara – green Barbara – yellow Tom – blue Christine – green Ron – brown
Juan – red Tina – red Bill – brown Mary – green Emma – red Don – blue
John – blue Sally – yellow Paul red Linda – blue Jeff – yellow
Mrs. Jones then asked the students to make a table showing these results.
Fill in the missing numbers in the table.
Subject skill – Interpreting Data (facts, information)
Task 2. (Regional Monitoring 2014/2015, 2015/2016)
Read the text and fill in the missing numbers in the Table
Pete, Dean, and Alex are taking part in a competition, consisting of two parts  a 60 metres race and a long jump. It takes Pete 10 seconds to run the distance, Dean’s result is 1 second worse, and Alex is 1 second slower than Dean. Alex stages a jump of 310 cm, Pete’s result is 295 cm. Dean’s result is 10 cm better than Alex’s.
Subject skill – Making and Verifying Statements for Particular Sets of Data
Task 3. (Regional Monitoring 2015/2016)
Mike wrote numbers 3, 9, 27, 54 on the chalkboard and said, “All these numbers are odd, and every other number is three times greater than the previous one.” What number do you need to write instead of 54 for his statement to be true?
Answer: _____ The right answer is “81”.
I also suggest paying attention to a generally accepted fact that fourth graders find it difficult to process (comprehend, present, and interpret) informational texts, nevertheless, it is the predominant text type in mathematics and daily life. They are more difficult to handle than literary texts. Both Russian and foreign scholars address this challenge in their papers (Kurovskaya, 2016; Kuznetsova, 2016; Little et al., 2007 ; Zuckerman, Kovaleva, Kuznetsova, 2013; Rydze, Pozdneva, 2014 ). As it is noted in one of them, “most problematic were the questions addressed to the basic reading skill of retrieving explicitly stated information and making straightforward inferences” (Zuckerman, Kovaleva, Kuznetsova, 2013, p. 127).
Therefore, the learner’s ability to handle mathematics information depends on such skills as reading information, represented in a graphical model (for instance, in a table), and filling it in; interpreting data (facts, information); making and checking statements for particular objects, data, as well as drawing a conclusion. While completing a task individually, apart from subject skills, the learner also demonstrates universal learning skills, such as analysis, focusing on the task, planning, and control of the process and the overall outcome.
Information Processing. Interdisciplinary Learning Skills
One may conclude that a learner is equipped to process information, when she possesses certain subject skills and when she is able to foreground the information necessary to solve the problem, to justify her solution, to focus exclusively on the suggested situation and question without trying to replace it with a simpler one, etc. I will now regard some of these skills and describe them in regard to the researches under consideration.
Interdisciplinary Learning Skill – Processing Information Provided in Different Forms
Task 4. (TIMSS2011, 2015)
In 2008, Peter paid the following amounts in the first six months for his telephone bill.
In 2009, Peter paid the following amounts in the first six months for his telephone bill.
In some months, Peter paid less for his telephone bill in 2009 than in 2008.
In which months?
Answer: _______. The right answer: “Peter paid less in 2009 than in 2008 in March and April” or “In March and April.”)
Interdisciplinary Learning Skill – Drawing Conclusions Based on Personal Selection and Choice of Data
The following task was accomplished as a part of a complex quiz entitled
Task 5. (Regional Monitoring 2014/2015, 2015/ 2016)
Exhibition Details
The exhibition takes place from 14 September to 14 October in Moscow at Pavilion 230 of the Exhibition of Achievements of National Economy (VDNH).
Opening Hours: 10.00 am – 8.00 pm (box office open until 7 pm)
Exhibition Prices: Adult  300 roubles, Pupil – 150 roubles, Preschooler – free.
Question 1. How long will the exhibition last?
1) 2 weeks 2) all summer
3) 1 year 4) 1 month (the right answer)
Question 2. How much money will a family of three people with two adults and a fiveyearold child spend? (The right answer: “600 roubles.”)
Interdisciplinary Learning Skill – Presenting the Outcome of one’s Actions in a Set Format (Way)
Task 6. (Regional Monitoring 2015/2016)
Tonny said, “One can make two different quadrangles, if one takes two of such triangles.” Was he right? Prove your answer with pictures.
Answer: _____________.
Any learner could get either 0, 1, or 2 points for the test item.
2 points were granted to the learners who gave the answer “Yes, he was”, (“Yes”) and drew two different quadrangles.
1 point was granted to the learners who gave the answer “Yes, he was”, (“Yes”), and drew one quadrangle or two identical quadrangles.
0 points were granted in any other case (for example, the answer was right, however, a triangle was depicted instead of a quadrangle, like in
40.6% of the students coped with the task (received 12 points), whereas 15% did not start doing the task at all.
Commentary
The main challenge was to give the right answer not only in words but in images as well. The fourth grader is expected to be able to draw a quadrangle, constructed out of two triangles. Thus, she possesses the subject skills necessary to accomplish the task. By the end of primary school, the learner also possesses general universal communicative skills, therefore, she may formulate a statement, justify her answer, etc. (Little et al., 2007 ; Mullis et al., 2016). In this case, the students were expected to
Discussion
The research results allow us to draw the following conclusions. Whether the learner will get the right answer or fail a subject task in information, processing relies heavily upon the inclusion of special topics and numerous types of tasks, related to tables, diagrams, and students’ abilities to read and complete tables, diagrams, and schemes, in mathematics course books. The challenges the learner may face are both of subjective and objective nature. On the one hand, there can be an insufficient amount of tasks, drilling the ability to provide statements relying on a model or instruction (for instance, “When answering, use the model If…, then…”). On the other hand, children are used neither to using mathematical terms nor to formulating statements, because they are likely to think, “this is Maths, not Russian or Literature”. When the learner faces test items of interdisciplinary character, where he/she has to handle mathematical information in contextual and practical situations; he/she gets the right answer only when the assignment type is familiar to him/her and does not require any personal approach to the solution or format.
Conclusion
The research has showed that students tend to lack the following universal learning skills – focusing on the task, generalizing data provided inconsistently or in different forms, planning and controlling the order and result of one’s actions, presenting the outcome, and justifying it. At the same time, when students write final tests (on the primary school material), they demonstrate sufficient awareness of how to apply mathematical information in order to accomplish various tasks.
One’s ability to process mathematical data and solve subject and interdisciplinary learning tasks is of crucial importance for the increase of informational literacy as an outcome of the primary school education.
Acknowledgement
The study was conducted in compliance with the State Assignment 27.7948.2017/BCh.
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21 August 2017
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Education, educational equipment, educational technology, computeraided learning (CAL), study skills, learning skills, ICT
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Rydze, O. A. (2017). Learners’ Achievements In Mathematical Information Processing At Primary School. In S. K. Lo (Ed.), Education Environment for the Information Age, vol 28. European Proceedings of Social and Behavioural Sciences (pp. 512522). Future Academy. https://doi.org/10.15405/epsbs.2017.08.60