Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors

Vlastimil Chytry; Milan Kubiatko

doi:10.29333/ejmste/11112

Full Text (PDF)

Vlastimil Chytry ¹ , Milan Kubiatko ¹ ^*

More Detail

¹ J. E. Purkyne University, Faculty of Education, Department of Preschool & Primary Education, CZECH REPUBLIC^* Corresponding Author

Abstract

School assessment is a determining factor for a pupil in all functions. The aim of the research was to determine correlation between pupils’ logical thinking and their school assessment and between pupils’ mathematics skills and their school assessment. The sample size was created by 252 high school students (117 boys and 135 girls). As research tools were used reasoning mathematical, logical thinking and mathematical skills tests. Kruskal-Wallis test was used as statistical method. A significant effect was found at the 1% significance level between these factors and school assessment, where the greatest differences are caused mainly by evaluations in mathematics that were perceived either as the best or the worst. The research also monitored the use of the newly-developed GTOLT (Group Test of Logical Thinking), which is based on the GALT (Group Assessment of Logical Thinking) and TOLT (Test of Logical Thinking) tests, rooted in standardized tools.

Keywords

logical thinking
mathematics skills
motivation
summative assessment

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2021, Volume 17, Issue 8, Article No: em1995

https://doi.org/10.29333/ejmste/11112

Publication date: 23 Jul 2021

Article Views: 1813

Article Downloads: 2374

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Albrecht, K. (1984). Brain building: Easy games to develop your problem-solving skills. Prentice-Hall Press.
Ali, A. Z. A. R. (2010). The effect of critical thinking dispositions on students’ achievement in selection and placement exam for university in Turkey. Journal of Turkish Science Education, 7(1), 61-73.
Boud, D., & Soler, R. (2016). Sustainable assessment revisited. Assessment & Evaluation in Higher Education, 41(3), 400-413. https://doi.org/10.1080/02602938.2015.1018133
Bronkhorst, H., Roorda, G., Suhre, C., & Goedhart, M. (2020). Logical reasoning in formal and everyday reasoning tasks. International Journal of Science and Mathematics Education, 18, 1673-1694. https://doi.org/10.1007/s10763-019-10039-8
Brookhart, S. M. (2013). The Use of Teacher Judgement for Summative Assessment in the USA. Assessment in Education: Principles, Policy & Practice, 20(1), 69-90. https://doi.org/10.1080/0969594X.2012.703170
Brophy, J. (1999). Toward a model of the value aspects of motivation in education: developing appreciation for. Educational Psychologist, 34(2), 75-85. https://doi.org/10.1207/s15326985ep3402_1
Brown, K., & Lally, V. (2018). Rhetorical relationships with students: A higher education case study of perceptions of online assessment in mathematics. Research in Comparative and International Education, 13(1), 7-26. https://doi.org/10.1177/1745499918761938
Chuechote, S., Nokkaew, A., Phongsasithorn, A., & Laosinchai, P. (2020). A neo-piagetian analysis of algorithmic thinking development through the “sorted” digital game. Contemporary Educational Technology, 12(1), ep261. https://doi.org/10.30935/cet.685959
Chytry, V. (2015). Logika, hry a myšlení [Logic, games and thinking]. Usti nad Labem: Univerzita J.E. Purkyne v Usti nad Labem.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Lawrence Erlbaum Associates.
Cresswell, C., & Speelman, C. P. (2020). Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors. PloS One, 15(7), e0236153. https://doi.org/10.1371/journal.pone.0236153
DeCarcer, I. A., Gabel, D. L., & Staver, J. R. (1978). Implications of Piagetian research for high school science teaching: A review of literature. Science Education, 62, 571-583. https://doi.org/10.1002/sce.3730620417
Eckstein, S. G., & Shemesh, M. (1989). Development of children’s ideas on motion: Intuition vs. logical thinking. International Journal of Science Education, 11(3), 327-336. https://doi.org/10.1080/0950069890110309
Fadiana, M., Amin, S. M., Lukito, A., Wardhono, A., & Aishah, S. (2019). Assessment of seventh grade students’ capacity of logical thinking. Indonesian Journal of Science Education, 8(1), 75-80. https://doi.org/10.15294/jpii.v0i0.11644
Finn, A. S., Kraft, M. A., West, M. R., Leonard, J. A., Bish, C. E., Martin, R. E., Sheridan, M. A., Gabrieli, C. F. O., & Gabrieli, J. D. E. (2014). Cognitive skills, student achievement tests, and schools. Psychological Science, 25(3), 736-744. https://doi.org/10.1177/0956797613516008
Firdaus, F., Kailani, I., Bakar, M. N. B., & Bakry, B. (2015). Developing critical thinking skills of students in mathematics learning. Journal of Education and Learning, 9(3), 226-236. https://doi.org/10.11591/edulearn.v9i3.1830
Garrison, C., & Ehringhaus, M. (2007). Formative and summative assessments in the classroom. Association for Middle Level Education.
Gonda, D., & Tirpakova, A (2021) An alternative approach to pupils’ acquiring a concept parameter in solving inequalities in school mathematics. International Journal of Mathematical Education in Science and Technology, 52(2), 178-193. https://doi.org/10.1080/0020739X.2019.1670365
Gonda, D., & Tirpakova, A. (2018). A new teaching method aimed at eliminating the causes of students’ unsuccessful algorithmic problem solving with parameter. Problems of Education in the 21st Century, 76(4), 499-519. https://doi.org/10.33225/pec/18.76.499
Greenstein, L. (2010). What teachers really need to know about formative assessment. ASCD.
Guo, W. Y., & Yan, Z. (2019). Formative and summative assessment in HongKong primary schools: students’ attitudes matter. Assessment in Education: Principles, Policy & Practice, 26(6), 675-699. https://doi.org/10.1080/0969594X.2019.1571993
Hartini, S., Misbah, M., Dewantara, D., Oktovian, R. A., & Aisyah, N. (2017). Developing learning media using online prezi into materials about optical equipment. Indonesian Journal of Science Education, 6(2), 313-317. https://doi.org/10.15294/jpii.v6i2.10102
Hoover, N. R., & Abrams, L. M. (2013). Teachers’ instructional use of summative student assessment data. Applied Measurement in Education, 26(3), 219-231. https://doi.org/10.1080/08957347.2013.793187
Insorio, A. O., & Librada, A. R. P. (2021). Enhancing mathematical critical thinking and problem-solving skills through emergenetics® as a grouping mechanism. Contemporary Mathematics and Science Education, 2(1), ep21002. https://doi.org/10.30935/conmaths /9289
Jawad, H. Q., Majwall, M., & Hussien, A. (2019). The effect of teaching on the skills of logical thinking in the achievement of student’s achievement in biology. Indian Journal of Public Health Research & Development, 10(6), 1125-1129. https://doi.org/10.5958/0976-5506.2019.01440.2
Jeon, S., & Park, J. H. (2014). Analysis of relationships of scientific communication skills, science process skills, logical thinking skills, and academic achievement level of elementary school students. Journal of the Korean Association for Science Education, 34(7), 647-655. https://doi.org/10.14697/jkase.2014.34.7.0647
King, D., Varsavsky, C., Belward, S., & Matthews, K. (2017). Investigating students’ perceptions of graduate learning outcomes in mathematics. International Journal of Mathematical Education in Science and Technology, 48(1), 67-80. https://doi.org/10.1080/0020739X.2017.1352044
Klieme, E., Avenarius, H., Blum, W., & Döbrich, P. (2004). The development of national educational standards: An expertise. Federal Ministry of Education and Research.
Klinger, D. A., McDivitt, P. R., Howard, B. B., Munoz, M. A., Rogers, W. T., & Wylie, E. C. (2015). The classroom assessment standards for Prek-12 teachers. Kindle Direct Press.
Korsun, I. (2019). The forming of learners’ interest towards science using inventive tasks in physics teaching. Physics Education, 54(2), 025014. https://doi.org/10.1088/1361-6552/aaff91
Kuh, G., Jankowski, N., Ikenberry, S., & Kinzie, J. (2014). Knowing what students know and can do: The current state of student learning outcomes assessment in us colleges and universities. University of Illinois; Indiana University: National Institute for Learning Outcomes Assessment (NILOA).
Labouvie, G. (1992). A neo-piagetian perspective on adult cognitive development. In R. J. Sternberg & C.A Berg (Eds.), Intellectual development. Cambridge University Press.
Lawson, A. E. (1978). The development and validation of a classroom test of formal reasoning. Journal of Research in Science Teaching, 15(1), 11-24.
Lawson, A. E. (1982). Formal reasoning, achievement, and intelligence: An issue of importance. Science Education, 66(1), 77-83.
Liu, H., Ludu, M., & Holton, D. (2015). Can K-12 math teachers train students to make valid logical reasoning? Emerging Technologies for STEAM Education, 331–353. https://doi.org/10.1007/978-3-319-02573-5_18
Marinho, P., Leite, C., & Fernandes, P. (2017). Mathematics summative assessment practices in schools at opposite ends of performance rankings in Portugal. Research in Mathematics Education, 19(2), 184-198. https://doi.org/10.1080/14794802.2017.1318085
Martinovic, D., & Manizade, A. G. (2018). The challenges in the assessment for knowledge for teaching geometry. ZDM Mathematics Education, 50(4), 613-629. https://doi.org/10.1007/s11858-018-0934-4
Mohamadi, Z. (2018). Comparative effect of online summative and formative assessment on EFL student writing ability. Studies in Educational Evaluation, 59, 29-40. https://doi.org/10.1016/j.stueduc.2018.02.003
National Council of Teachers of Mathematics (NCTM). (2014). Principles to action: Ensuring mathematical success for all. National Council of Teachers of Mathematics.
Nortvedt, G. A., & Buchholtz, N. (2018). Assessment in mathematics education: Responding to issues regarding methodology, policy, and equity. ZDM Mathematics Education, 50(4), 555-570. https://doi.org/10.1007/s11858-018-0963-z
Parke, C., Lane, S., Silver, E. A., & Magone, M. (2003). Using assessment to improve mathematics teaching and learning: Suggested activities using quasar tasks, scoring criteria, and student work. National Council of Teachers of Mathematics.
Pellegrino, J. W., Chudowsky, N., & Glaser, R. (Eds.). (2001). Knowing what students know: The science of design and educational assessment. National Academy Press.
Piaget, J., & Inhelder, B. (1955). De la logique de l´enfant á la logique de l´adolescent [From the logic of the child to the logic of the adolescent]. Presses Universitaires de France.
Pitchford, N. J., Papini, C., Outhwaite, L. A., & Gulliford, A. (2016). Fine motor skills predict maths ability better than they predict reading ability in the early primary school years. Frontiers in Psychology, 7, 783. https://doi.org/10.3389/fpsyg.2016.00783
Popham, W. J. (2014). Classroom Assessment: What Teachers Need to Know (7th ed.). Pearson Education.
Potvin, P., Hasni, A., Ayotte-Beaudet, J. P., & Sy, O. (2020). Does individual interest still predict achievement in science and technology when controlling for self-concept? A longitudinal study conducted in Canadian schools. Eurasia Journal of Mathematics Science and Technology Education, 16(12), em1904. https://doi.org/10.29333/ejmste/8938
Puddy, R. W., Boles, R. E., Dreyer, M. L., Maikranz, J., Roberts, M. C., & Vernberg, E. M. (2007). Demonstrating support for the formative and summative assessment paradigm in a school-based intensive mental health program. Journal of Child and Family Studies, 17(2), 253–263. https://doi.org/10.1007/s10826-007-9164-z
Rakoczy, K., Pinger, P., Hochweber, J., Klieme, E., Schütze, B., & Besser, M. (2019). Formative assessment in mathematics: Mediated by feedback’s perceived usefulness and students’ self-efficacy. Learning and Instruction, 60, 154-165. https://doi.org/10.1016/j.learninstruc.2018.01.004
Ramdani, R., Syamsuddin, A., & Sirajuddin, S. (2019). Development of mathematical module-problem solving approach to train student’s reflective thinking. Pedagogical Research, 4(4), em0040. https://doi.org/10.29333/pr/5861
Robinson, D., H., & Levin, J. R. (1997). Reflections on statistical and substantive significance with a slice of replication. Educational Researcher, 26(5), 21-27. https://doi.org/10.3102/0013189X026005021
Rokos, L., Lišková, J., Váchová, L., Cihlářová, M., Chadová, M., & Strapková, J. (2019). Pohled žáků vybraných základních škol a gymnázií na hodnocení při hodinách přírodopisu a biologie s akcentem na formativní hodnocení [The view of pupils of selected elementary schools and grammar schools on the evaluation during the lessons of natural history and biology with an accent on the format evaluation]. Scientia in Educatione, 10(1), 90-112. https://doi.org/10.14712/18047106.1234
Rosenthal, R., Rosnow, R.L., & Rubin, D.B. (2000). Contrasts and effect sizes in behavioral research: a correlational approach. Cambridge University Press.
Rosli, R., Goldsby, D., & Capraro, M. M. (2013). Assessing students’ mathematical problem-solving and problem-posing skills. Asian Social Science, 9(16), 54-60. https://doi.org/10.5539/ass.v9n16p54
Sartika, I., & Fatmanissa, N. (2020). Analysis of students’ error in solving trigonometric function problems which assess higher order thinking skills. Contemporary Mathematics and Science Education, 1(1), ep20002. https://doi.org/10.30935/conmaths/8437
Sewall, T., & Santaga, M. (1986). A reference guide to program evaluation in adult education. Wisconsin Assessment Centre, University of Wisconsin-Green Bay.
Sheskin, D. J. (2003). Handbook of parametric and nonparametric statistical procedures. Chapman and Hall/CRC.
Simonton, D. K. (1992). The social context of career success and course for 2,026 scientists and inventors. Personality and Social Psychology Bulletin, 18(4), 452-463. https://doi.org/10.1177/0146167292184009
Smetáčková, I. (2018). Obliba školní matematiky a její souvislost s externím hodnocením a sebehodnocením [The popularity of school mathematics and its connection with external evaluation and self-evaluation]. Scientia in Educatione, 9(2), 44-56. https://doi.org/10.14712/18047106.1049
Thomas, J. R., & Nelson, J. K. (2001). Research methods in physical activity (4th ed.). Human Kinetics.
Tobin, K. G., & Capie, W. (1980). The test of logical thinking, development and application [Paper presentation]. National Association for Research in Science Teaching, Boston, MA.
Ubuz, B., & Aydın, U. (2018). Geometry knowledge test about triangles: Evidence on validity and reliability. ZDM Mathematics Education, 50(4), 659-673. https://doi.org/10.1007/s11858-018-0964-y
Watts, T. W., Duncan, G. J., Siegler, R. S., & Davis-Kean, P. E. (2014). What’s past is prologue: Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43(7), 352-360. https://doi.org/10.3102/0013189X14553660
Weber, K., Inglis, M., & Mejia-Ramos, J. P. (2014). How mathematicians obtain conviction: implications for mathematics instruction and research on epistemic cognition. Educational Psychologist, 49(1), 36-58. https://doi.org/10.1080/00461520.2013.865527
Wei, W. (2014). Using summative and formative assessments to evaluate EFL teachers’ teaching performance. Assessment & Evaluation in Higher Education, 40(4), 611-623. https://doi.org/10.1080/02602938.2014.939609
Weurlander, M., Söderberg, M., Scheja, M., Hult, H., & Wernerson, A. (2012). Exploring formative assessment as a tool for learning: Students’ experiences of different methods of formative assessment. Assessment & Evaluation in Higher Education, 37(6), 747-760. https://doi.org/10.1080/02602938.2011.572153
Wholey, J. S. (1996). Formative and summative evaluation: Related issues in performance measurement. Evaluation Practice, 17(2), 145–149. https://doi.org/10.1016/s0886-1633(96)90019-7
Widana, I. W., Parwata, I., Parmithi, N. N., Jayantika, I. G. A. T., Sukendra, I. K., & Sumandya, I. W. (2018). Higher order thinking skills assessment towards critical thinking on mathematics lesson. International Journal of Social Sciences and Humanities, 2(1), 24-32. https://doi.org/10.29332/ijssh.v2n1.74
Yang, Y. T. C., & Chang, C. H. (2013). Empowering students through digital game authorship: Enhancing concentration, critical thinking, and academic achievement. Computers & Education, 68, 334-344. https://doi.org/10.1016/j.compedu.2013.05.023
Zaman, A., Jumani, N. B., Ali, A., & Hussain, M. A. (2011). Predictive validity of scores in mathematics for reasoning ability in mathematics for grade 9 students in Khyber Pakhtunkhwa based on curriculum of mathematics. Procedia-Social and Behavioral Sciences, 12, 588-594. https://doi.org/10.1016/j.sbspro.2011.02.072

How to cite this article

APA

Chytry, V., & Kubiatko, M. (2021). Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1995. https://doi.org/10.29333/ejmste/11112

Vancouver

Chytry V, Kubiatko M. Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors. EURASIA J Math Sci Tech Ed. 2021;17(8):em1995. https://doi.org/10.29333/ejmste/11112

AMA

Chytry V, Kubiatko M. Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors. EURASIA J Math Sci Tech Ed. 2021;17(8), em1995. https://doi.org/10.29333/ejmste/11112

Chicago

Chytry, Vlastimil, and Milan Kubiatko. "Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 8 (2021): em1995. https://doi.org/10.29333/ejmste/11112

Harvard

Chytry, V., and Kubiatko, M. (2021). Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1995. https://doi.org/10.29333/ejmste/11112

MLA

Chytry, Vlastimil et al. "Pupils’ Summative Assessments in Mathematics as Dependent on Selected Factors". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 8, 2021, em1995. https://doi.org/10.29333/ejmste/11112