The Effect of Activity-Based Teaching on Remedying the Probability-Related Misconceptions: A Cross-Age Comparison

Affiliation(s)

Department of Elementary Mathematics Education, Faculty of Education, Ad?yaman University, Ad?yaman, Turkey.

epartment of Computer Education and Instructional Technology, Faculty of Education, Ad?yaman University, Ad?yaman, Turkey.

Department of Elementary Mathematics Education, Faculty of Education, Ad?yaman University, Ad?yaman, Turkey.

epartment of Computer Education and Instructional Technology, Faculty of Education, Ad?yaman University, Ad?yaman, Turkey.

ABSTRACT

The aim of this paper is to compare the effect of activity-based
teaching on remedying probability-related misconceptions of students at
different grades. Thus, a cross-sectional/age
study was conducted with a total of 74 students in 6th-8th grades. Experimental instructions
were given to all the groups three times/ week, 40 min/session, for 2 weeks. Students’ progress was examined by pre-test and
post-test measurements. The
results of the analysis showed that, as a result of the intervention, all graders’ post-test
scores regarding all the concepts (PC: *Probability
Comparison*, E: *Equiprobability* and R: *Representa**tiveness*) showed a significant increase when compared to pre-test
scores. It was found out that this increase did not create a significant
difference based on age in PC concept, but that in 8th grade students, it showed a significant
difference in E and R concepts compared to 6th graders. On the other hand, it
was also assessed that the increases observed between 7th and 8th graders with
regard to E and R concepts were not significant. In summary, the implemented intervention can be
suggested to have different effects depending on age and the concept.

Cite this paper

Gürbüz, R. , Erdem, E. & Fırat, S. (2014). The Effect of Activity-Based Teaching on Remedying the Probability-Related Misconceptions: A Cross-Age Comparison.*Creative Education, 5,* 18-30. doi: 10.4236/ce.2014.51006.

Gürbüz, R. , Erdem, E. & Fırat, S. (2014). The Effect of Activity-Based Teaching on Remedying the Probability-Related Misconceptions: A Cross-Age Comparison.

References

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http://dx.doi.org/10.1016/j.jmathb.2009.03.002

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http://dx.doi.org/10.1080/00207391003675158

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http://dx.doi.org/10.1016/j.compedu.2011.11.005

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http://dx.doi.org/10.1119/1.18376

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http://dx.doi.org/10.1016/0010-0285(72)90016-3

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http://dx.doi.org/10.1007/s10649-006-9032-6

[30] Keren, G. (1984). On the importance of identifying the correct sample space. Cognition, 16, 121-128.

http://dx.doi.org/10.1016/0010-0277(84)90002-7

[31] Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students’ reasoning about probability. Journal for Research in Mathematics Education, 24, 392-414.

http://dx.doi.org/10.2307/749150

[32] Konold, C. (1989). Informal conceptions of probability. Journal of Cognition and Instruction, 6, 59-98.

http://dx.doi.org/10.1207/s1532690xci0601_3

[33] Lamprianou, I., & Lamprianou, T. A. (2003). The nature of pupils’ probabilistic thinking in primary schools in Cyprus. International Group for the Psychology of Mathematics Education, 3, 173-180.

[34] Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557568. http://dx.doi.org/10.1007/BF00540060

[35] Memnun, D. S. (2008). Olasilik kavramlarinin ogrenilmesinde karsilasilan zorluklar, bu kavramlarin ogrenilememe nedenleri ve cozüm onerileri. Inonü üniversitesi Egitim Fakültesi Dergisi, 9, 89-101.

[36] Mevarech, Z. R. (1983). A deep structure model of students’ statistical misconceptions. Educational Studies in Mathematics, 14, 415-429.

http://dx.doi.org/10.1007/BF00368237

[37] Morsanyi, K., Primi, C., Chiesi, F., & Handley, S. (2009). The effects and side-effects of statistics education: Psychology students’ (mis)conceptions of probability. Contemporary Educational Psychology, 34, 210-220.

http://dx.doi.org/10.1016/j.cedpsych.2009.05.001

[38] Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8, 372-377.

[39] Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66, 293-315.

http://dx.doi.org/10.1007/s10649-006-9062-0

[40] Nilsson, P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247-261.

http://dx.doi.org/10.1016/j.jmathb.2009.10.003

[41] Offenbach, S. I. (1964). Studies of children’s probability learning behavior: I. Effect of reward and punishment at two age levels. Child Development, 35, 709-715.

[42] Offenbach, S. I. (1965). Studies of children’s probability learning behavior: II. Effect of method event frequency at two age levels. Child Development, 36, 951-962. http://dx.doi.org/10.2307/1126936

[43] Olson, J. (2007). Developing students’ mathematical reasoning through games. Teaching Children Mathematics, 13, 464-471.

[44] Piaget, J. (1952). The child’s conception of number. New York: Humanities Press.

[45] Polaki, M. V. (2002). Using instruction to identify key features of basotho elementary students’ growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285-313.

http://dx.doi.org/10.1207/S15327833MTL0404_01

[46] Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602-625.

http://dx.doi.org/10.2307/749889

[47] Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say? For the Learning of Mathematics, 18, 41-51.

[48] Sharma, S. (2006). How do Pasifika Students reason about probability? Some findings from fiji. Waikato Journal of Education, 12, 87-100.

[49] Shaughnessy, J. M. (1993). Probability and statistics. Mathematics Teacher, 86, 244-248.

[50] Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 295-316.

http://dx.doi.org/10.1007/BF00385927

[51] Shaw, D. (1999). Active teaching for active learners. Curriculum Administrator, 35, 37-45.

[52] Tatsis, K., Kafoussi, S., & Skoumpourdi, C. (2008). Kindergarten children discussing the fairness of probabilistic games: The creation of a primary discursive community. Early Chilhood Education Journal, 36, 221-226. http://dx.doi.org/10.1007/s10643-008-0283-y

[53] Thompson, P. W. (1992). Notations, principles, and constraints: Contributions to the effective use of concrete manipulatives in elementary mathematics. Journal for Research in Mathematics Education, 23, 123-147.

[54] Tversky, A., & Kahneman, D. (2003). Preference, belief, and similarity: Selected writings by Amos Tversky/edited by Eldar Shafir. Judgment under uncertainty: Heuristics and biases (p. 207). Cambridge: The MIT Press.

[55] Watson, J. M., & Moritz, J. B. (2002). School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology, 33, 59-84.

http://dx.doi.org/10.1080/00207390110087615

[56] Watson, J. M., & Kelly, B. A. (2004). Statistical variation in a chance setting: A two-year study. Educational Studies in Mathematics, 57, 121-144.

http://dx.doi.org/10.1023/B:EDUC.0000047053.96987.5f

[57] Way, J. (2003). The development of young children’s notions of probability. Proceedings of CERME3, Bellaria.

http://www.dm.unipi.it/cluster-pages/didattica/

[58] Weir, M. W. (1962). Effects of age and instructions on children’s probability learning. Child Development, 33, 729-735.

[59] Zembat, I. O. (2008). Kavram Yanilgisi Nedir? In M. F. Ozmantar, E. Bingolbali, & H. Akkoc (Eds.), Matematiksel Kavram Yanilgilari ve Cozüm Onerileri (pp. 1-8). Ankara: PegemA Yayincilik.

[1] Abraham, M. R., Williamson, V. M., & Westbrook, S. L. (1994). A cross-age study of the understanding five concepts. Journal of Research in Science Teaching, 31, 147-165.

http://dx.doi.org/10.1002/tea.3660310206

[2] Amir, G., & Williams, J. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18, 85-107.

http://dx.doi.org/10.1016/S0732-3123(99)00018-8

[3] Aspinwall, L., & Shaw, K. L. (2000). Enriching students’ matematical intuitions with probability games and tree diagrams. Mathematics Teaching in the Middle School, 6, 214-220.

[4] Baker, M., & Chick, H. L. (2007). Making the most of chance. Australian Primary Mathematics Classroom, 12, 8-13.

[5] Barnes, M. (1998). Dealing with misconceptions about probability. Australian Mathematics Teacher, 54, 17-20.

[6] Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30, 558-567. http://dx.doi.org/10.2307/749774

[7] Bezzina F. (2004). Pupils’ Understanding of Probabilistic & Statistics (14-15+) Difficulties and Insights For Instruction. Journal of Maltese Education Research, 2, 53-67.

[8] Chernoff, E. J. (2009). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28, 19-29.

http://dx.doi.org/10.1016/j.jmathb.2009.03.002

[9] Dooren, W. V., Bock, D. D., Depaepe, F., Janssens, D., & Verschaffel, L. (2003). The illusion of linearity: Expanding the evidence towards probabilistic reasoning. Educational Studies in Mathematics, 53, 113138. http://dx.doi.org/10.1023/A:1025516816886

[10] Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills. M.A. Thesis, Adiyaman: Adiyaman University.

[11] Fast, G. (1997). Using analogies to overcome student teachers’ probability misconceptions. Journal of Mathematical Behavior, 16, 325344. http://dx.doi.org/10.1016/S0732-3123(97)90011-0

[12] Fast, G. (2001). The stability of analogically reconstructed probability knowledge among secondary mathematics students. Canadian Journal of Science, Mathematics and Technology Education, 1, 193-210.

http://dx.doi.org/10.1080/14926150109556461

[13] Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Reidel, Dordrecht, The Netherlands.

http://dx.doi.org/10.1007/978-94-010-1858-6

[14] Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal of Research in Science Teaching, 28, 96-105.

[15] Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523-549.

http://dx.doi.org/10.1007/BF00312714

[16] Ford, M. I., & Kuhs, T. (1991). The act of investigating: Learning mathematics in the primary grades. Childhood Education, 67, 313-316.

http://dx.doi.org/10.1080/00094056.1991.10520819

[17] Garfield, J., & Ahlgren, A. (1988). Difficulties in Learning Basic Concepts in Probability and Statistics: Imlications for Research. Journal for Research in Mathematics Education, 19, 44-63.

http://dx.doi.org/10.2307/749110

[18] Gibbs, W., & Orton, J. (1994). Language and mathematics. In A. Orton, & G. Wain, (Eds.), Issues in teaching mathematics (pp. 95-116), London: Cassell.

[19] Greer, B. (2001). Understanding probabilistic thinking: The legacy of Efrahim Fischbein. Educational Studies in Mathematics, 45, 15-33.

http://dx.doi.org/10.1023/A:1013801623755

[20] Gürbüz, R. (2007). The effects of computer aided instruction on students’ conceptual development: A case of probability subject. Eurasion Journal of Educational Research, 28, 75-87.

[21] Gürbüz, R., Catlioglu, H., Birgin, O., & Erdem E. (2010). An investigation of fifth grade students’ conceptual development of probability through activity based instruction: A quasi-experimental study. Educational Sciences: Theory & Practice, 10, 1021-1069.

[22] Gürbüz, R. (2010). The effect of activity based instruction on conceptual development of seventh grade students in probability. International Journal of Mathematical Education in Science and Technology, 41, 743-767.

http://dx.doi.org/10.1080/00207391003675158

[23] Gürbüz, R., & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers and Education, 58, 931-941.

http://dx.doi.org/10.1016/j.compedu.2011.11.005

[24] Gürbüz, R., Birgin, O., & Catlioglu, H. (2012). Comparing the probability-related misconceptions of pupils at different education levels. Croatian Journal of Education, 14, 307-357.

[25] Hammer, D. (1996). More than misconceptions: Multiple perspectives on student knowledge and reasoning, and an appropriate role for education research. American Journal of Physics, 64, 1316-1325.

http://dx.doi.org/10.1119/1.18376

[26] Jones, G. A., Langrall, C. W., Thornton, C. A., & Timothy Mogill, A. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101125.

[27] Jun, L. (2000). Chinese students’ understanding of probability. Unpublished Doctoral Dissertartion. Singapore: National Institue of Education, Nanyang Technological University.

[28] Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454.

http://dx.doi.org/10.1016/0010-0285(72)90016-3

[29] Kazima, M. (2006). Malawian students’ meanings for probability vocabulary. Educational Studies in Mathematics, 64, 169-189.

http://dx.doi.org/10.1007/s10649-006-9032-6

[30] Keren, G. (1984). On the importance of identifying the correct sample space. Cognition, 16, 121-128.

http://dx.doi.org/10.1016/0010-0277(84)90002-7

[31] Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students’ reasoning about probability. Journal for Research in Mathematics Education, 24, 392-414.

http://dx.doi.org/10.2307/749150

[32] Konold, C. (1989). Informal conceptions of probability. Journal of Cognition and Instruction, 6, 59-98.

http://dx.doi.org/10.1207/s1532690xci0601_3

[33] Lamprianou, I., & Lamprianou, T. A. (2003). The nature of pupils’ probabilistic thinking in primary schools in Cyprus. International Group for the Psychology of Mathematics Education, 3, 173-180.

[34] Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23, 557568. http://dx.doi.org/10.1007/BF00540060

[35] Memnun, D. S. (2008). Olasilik kavramlarinin ogrenilmesinde karsilasilan zorluklar, bu kavramlarin ogrenilememe nedenleri ve cozüm onerileri. Inonü üniversitesi Egitim Fakültesi Dergisi, 9, 89-101.

[36] Mevarech, Z. R. (1983). A deep structure model of students’ statistical misconceptions. Educational Studies in Mathematics, 14, 415-429.

http://dx.doi.org/10.1007/BF00368237

[37] Morsanyi, K., Primi, C., Chiesi, F., & Handley, S. (2009). The effects and side-effects of statistics education: Psychology students’ (mis)conceptions of probability. Contemporary Educational Psychology, 34, 210-220.

http://dx.doi.org/10.1016/j.cedpsych.2009.05.001

[38] Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8, 372-377.

[39] Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66, 293-315.

http://dx.doi.org/10.1007/s10649-006-9062-0

[40] Nilsson, P. (2009). Conceptual variation and coordination in probability reasoning. Journal of Mathematical Behavior, 28, 247-261.

http://dx.doi.org/10.1016/j.jmathb.2009.10.003

[41] Offenbach, S. I. (1964). Studies of children’s probability learning behavior: I. Effect of reward and punishment at two age levels. Child Development, 35, 709-715.

[42] Offenbach, S. I. (1965). Studies of children’s probability learning behavior: II. Effect of method event frequency at two age levels. Child Development, 36, 951-962. http://dx.doi.org/10.2307/1126936

[43] Olson, J. (2007). Developing students’ mathematical reasoning through games. Teaching Children Mathematics, 13, 464-471.

[44] Piaget, J. (1952). The child’s conception of number. New York: Humanities Press.

[45] Polaki, M. V. (2002). Using instruction to identify key features of basotho elementary students’ growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285-313.

http://dx.doi.org/10.1207/S15327833MTL0404_01

[46] Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602-625.

http://dx.doi.org/10.2307/749889

[47] Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say? For the Learning of Mathematics, 18, 41-51.

[48] Sharma, S. (2006). How do Pasifika Students reason about probability? Some findings from fiji. Waikato Journal of Education, 12, 87-100.

[49] Shaughnessy, J. M. (1993). Probability and statistics. Mathematics Teacher, 86, 244-248.

[50] Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 295-316.

http://dx.doi.org/10.1007/BF00385927

[51] Shaw, D. (1999). Active teaching for active learners. Curriculum Administrator, 35, 37-45.

[52] Tatsis, K., Kafoussi, S., & Skoumpourdi, C. (2008). Kindergarten children discussing the fairness of probabilistic games: The creation of a primary discursive community. Early Chilhood Education Journal, 36, 221-226. http://dx.doi.org/10.1007/s10643-008-0283-y

[53] Thompson, P. W. (1992). Notations, principles, and constraints: Contributions to the effective use of concrete manipulatives in elementary mathematics. Journal for Research in Mathematics Education, 23, 123-147.

[54] Tversky, A., & Kahneman, D. (2003). Preference, belief, and similarity: Selected writings by Amos Tversky/edited by Eldar Shafir. Judgment under uncertainty: Heuristics and biases (p. 207). Cambridge: The MIT Press.

[55] Watson, J. M., & Moritz, J. B. (2002). School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology, 33, 59-84.

http://dx.doi.org/10.1080/00207390110087615

[56] Watson, J. M., & Kelly, B. A. (2004). Statistical variation in a chance setting: A two-year study. Educational Studies in Mathematics, 57, 121-144.

http://dx.doi.org/10.1023/B:EDUC.0000047053.96987.5f

[57] Way, J. (2003). The development of young children’s notions of probability. Proceedings of CERME3, Bellaria.

http://www.dm.unipi.it/cluster-pages/didattica/

[58] Weir, M. W. (1962). Effects of age and instructions on children’s probability learning. Child Development, 33, 729-735.

[59] Zembat, I. O. (2008). Kavram Yanilgisi Nedir? In M. F. Ozmantar, E. Bingolbali, & H. Akkoc (Eds.), Matematiksel Kavram Yanilgilari ve Cozüm Onerileri (pp. 1-8). Ankara: PegemA Yayincilik.