The Development of the Components of the Length Measurement Concept in the Procedure of Measurement Using a Ruler
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The research related to testing pupils’ achievement in the field of Measurement and Measure in initial teaching of geometry points to an insufficient adoption of the basic components of the length measurement concept among pupils. In order to discover the cause, we looked at the basic components on which the procedure of measuring length using a ruler is based, highlighted the possibilities of introducing the procedure in measuring length, and determined pupils’ achievement during the procedure of measuring length using a ruler. The research sample consisted of 145 pupils, out of which 72 were the 2nd grade pupils and 73 were the 4th grade pupils. A descriptive method was applied in the research. The technique we used was testing, and for the statistical data processing we used a χ2 test. The results of the research show that, when drawing a straight line of a given length using a ruler, there is no statistical difference in achievement between the 2nd and 4th grade pupils, nor in the pupils’ knowledge regarding drawing a ruler independently, while drawing a straight line of a given length using a “broken” ruler 4th grade pupils are statistically better. The results of the research indicate that pupils’ achievement is better in doing standard tasks than in non-standard ones, given that the latter require conceptual knowledge. The components of the concept of length measurement using ruler have not been sufficiently developed yet, and these include: zero-point, partitioning a measured object in a series of consecutive measurement units and their iteration. We shed more light on the critical stage in the procedure of length measurement – the transition from non-standard to standard units and the formation of the length measurement scale. For further research, we propose to look at the formation of the concept of length measurement using the ruler through all its components and their inclusion in the mathematics curriculum, as well as examining the correlation of pupils’ achievement in the procedure of measuring length with their achievement in measuring area (and volume).
Abstract
The research related to testing pupils’ achievement in the field of Measurement and Measure in initial teaching of geometry points to an insufficient adoption of the basic components of the length measurement concept among pupils. In order to discover the cause, we looked at the basic components on which the procedure of measuring length using a ruler is based, highlighted the possibilities of introducing the procedure in measuring length, and determined pupils’ achievement during the procedure of measuring length using a ruler. The research sample consisted of 145 pupils, out of which 72 were the 2nd grade pupils and 73 were the 4th grade pupils. A descriptive method was applied in the research. The technique we used was testing, and for the statistical data processing we used a χ2 test. The results of the research show that, when drawing a straight line of a given length using a ruler, there is no statistical difference in achievement between the 2nd and 4th grade pupils, nor in the pupils’ knowledge regarding drawing a ruler independently, while drawing a straight line of a given length using a “broken” ruler 4th grade pupils are statistically better. The results of the research indicate that pupils’ achievement is better in doing standard tasks than in non-standard ones, given that the latter require conceptual knowledge. The components of the concept of length measurement using ruler have not been sufficiently developed yet, and these include: zero-point, partitioning a measured object in a series of consecutive measurement units and their iteration. We shed more light on the critical stage in the procedure of length measurement – the transition from non-standard to standard units and the formation of the length measurement scale. For further research, we propose to look at the formation of the concept of length measurement using the ruler through all its components and their inclusion in the mathematics curriculum, as well as examining the correlation of pupils’ achievement in the procedure of measuring length with their achievement in measuring area (and volume).
참고문헌 (44)
- Antić, M., "The Development of the Components of the Linear Measurement Concept among the Pupils of the First Grade of Primary School", Teaching Innovations, 31(1), pp.58~74 (2018)[DOI]
- Baroody, A. J., "An alternative reconceptualization of procedural and conceptual knowledge", Journal for Research in Mathematics Education, 38(2), pp.115~131 (2007)[DOI]
- Barrett, Ј. Е., "Learning and teaching measurement", pp.17~30 (2003), National Council of Teachers of Mathematics
- Battista, M. T., "Understanding the development of students' thinking about length", Teaching Children Mathematics, 13(3), pp.140~146 (2006)
- Božin, A., "Leksikon obrazovnih termina", pp.326~327 (2014), Učiteljski fakultet
- Bragg, P., "What is taught versus what is learnt: The case of linear measurement", Proceedings of the 23rd Annual Conference of the MERGA ˗ Mathematics Education Beyond 2000, 1, pp.112~118 (2000), MERGA
- Bragg, P., "A measure of rulers: The importance of units in a measure", Proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education, 2, pp.159~166 (2004), Bergen University College
- Buys, K., "Young children learn measurement and geometry", pp.15~36 (2008), Sense Publishers
- Carpenter, T. P., "The development of the concept of a standard unit of measure in young children", Journal for Research in Mathematics Education, 7(1), pp.53~58 (1976)[DOI]
- Clements, D., "Quantifying path length : Fourth-grade children's developing abstractions for linear measurement", Cognition and Instruction, 21(4), pp.475~520 (2003)[DOI]
- Coolican, H., "Research methods and statistics in psychology" (1999), Hodder and Stoughton
- Đokić, O., "Theoretical and methodological basis of quality education", pp.79~95 (2013), University of Belgrade ̶ Teachers` Training Faculty and State Higher Vocational School in Nowy Sacz
- Đokić, O, "Leksikon obrazovnih termina", pp.388~389 (2014), Učiteljski fakultet
- Đokić, O., "Realno okruženje u početnoj nastavi geometrije", Teaching Innovations, 27(2), pp.7~21 (2014)[DOI]
- Freudenthal, H., "Didactical phenomenology of mathematical structures" (2002), Kluwer Academic Publishers
- Gomezescobar, A., "Numbers and space intervals in length measurements in the Spanish context : Proposals for the transition to measuring with the ruler", International Journal of Science and Mathematics Education, 16(7), pp.1375~1386 (2018)[DOI]
- Henning, P. H., "Handbook of research on dducational communications and technology", pp.143~168 (2004), Lawrence Erlbaum Associates
- Hiebert, J., "Cognitive development and learning linear measurement", Journal for Research in Mathematics Education, 12(3), pp.197~211 (1981)[DOI]
- Kamii, C., "Measurement of length : The need for a better approach to teaching", School Science and Mathematics, 97(3), pp.116~121 (1997)[DOI]
- Kamii, C., "Measurement of length : How can we teach it better", Teaching Children Mathematics, 13(3), pp.154~158 (2006)
- Lehrer, R., "A research companion to principles and standards for school mathematics", pp.179~192 (2003), National Council of Teachers of Mathematics
- Levine, S. C., "Children’s understanding of ruler measurement and units of measure: A training study", Proceedings of the 31st Annual Conference of the Cognitive Science Society, pp.2391~2395 (2009), Cognitive Science Society
- Mitchell, A., "Fractions: Teaching for understanding", pp.52~62 (2011), The Australian Association of Mathematics Teachers (AAMT) Inc
- Nührenbörger, M., "Children’s measurement thinking in the context of length, In Developments in mathematics education in German-speaking countries", Selected Papers from the Annual Conference on Didactics of Mathematics, pp.95~106 (2001), Gesellschaft für Didaktik der Mathematik
- Nunes, T., "Tools for thought : The measurement of length and area", Learning and Instruction, 3(1), pp.39~54 (1993)[DOI]
- Pijaže J., "Intelektualni razvoj deteta – izabrani radovi" (1996), Zavod za udžbenike i nastavna sredstva
- Pravilnik o nastavnom planu i programu za prvi i drugi razred osnovnog obrazovanja i vaspitanja, "Službeni glasnik Republike Srbije – Prosvetni glasnik, br. 10", 04, 2004
- Pravilnik o nastavnom planu i programu za četvrti razred osnovnog obrazovanja i vaspitanja, "Službeni glasnik Republike Srbije – Prosvetni glasnik, br.03", 06, 2006
- Pravilnik o programu nastave i učenja za drugi razred osnovnog obrazovanja i vaspitanja, "Službeni glasnik Republike Srbije – Prosvetni glasnik, br. 16", ~ (2018)
- Ryan, J., "Children's mathematics 4 – 15: Learning from errors and misconceptions", pp.2007, McGraw Hill
- Sarama, J., "Early childhood mathematics education research : Learning trajectories for young children" (2009), Routledge
- Schneider, M., "The nature of learning: Using research to inspire practice", pp.69~90 (2010), OECD
- Skemp, R. R., "The psychology of learning mathematics" (1993), Penguin Books
- Smith III, J. P., "Curricular treatments of length measurement in the United States : Do they address known learning challenges", Cognition and Instruction, 31(4), pp.388~433 (2013)[DOI]
- Smith, J. P., "Compendium for research in mathematics education", pp.355~385 (2017), National Council of Teachers of Mathematics
- Standardi postignuća – obrazovni standardi za kraj prvog ciklusa obaveznog obrazovanja i vaspitanja, "Nacionalni prosvetni savet, Zavod za vrednovanje kvaliteta obrazovanja i vaspitanja", Srbija, ~ (2011)
- Stephan, M., "Learning and teaching measurement, 2003 Yearbook", pp.3~16 (2003), National Council of Teachers of Mathematics
- Stephan, M., "The roles of representation in school mathematics, 2001 Yearbook", pp.63~76 (2001), National Council of Teachers of Mat
- Tan Sisman, G., "The length measurement in the Turkish mathematics curriculum : It’s potential to contribute to students learning", International Journal of Science and Mathematics Education, 10(2), pp.363~385 (2012)[DOI]
- Tan Sisman, G., "A study on sixth grade students’ misconceptions and errors in spatial measurement : length, area and volume", International Journal of Science and Mathematics Education, 14(7), pp.1293~1319 (2015)[DOI]
- Van de Walle, J. A., "Elementary and middle school mathematics: Teaching developmentally" (2018), Pearson Education
- Zeljić, M., "Odnos proceduralnog i konceptualnog znanja učenika u procesu ovladavanja postupcima računanja u početnoj nastavi matematike", Nastava i vaspitanje, 63(4), pp.653~668 (2014)
- Zöllner, J., "How four to six year old children compare length indirectly", Paper presented at the Cerme8 (2013)
- Zöllner, J., "“I spy with my little eye“: Different components of a concept of the length, In Mathematics education in the early years", Results from the POEM2 Conference, pp.359~370 (2016)