Developing Critical Thinking Skills from Dispositions to Abilities: Mathematics Education from Early Childhood to High School

ABSTRACT

In light of the importance of developing critical thinking, and given the scarcity of research on critical thinking in mathematics education in the broader context of higher order thinking skills, we have carried out a research that examined how teaching strategies oriented towards developing higher-order thinking skills influenced students’ critical thinking abilities. The guiding rationale of the work was that such teaching can foster the students’ skills of and dispositions towards critical thinking. In this article, we discuss ways in which critical thinking can be incorporated in mathematics instruction. In particular, we highlight how content taught in the probability strand can intentionally be focused on the development of students’ critical thinking. We report results of a study demonstrating improvement in secondary mathematics students’ dispositions towards critical thinking and abilities to think critically.

In light of the importance of developing critical thinking, and given the scarcity of research on critical thinking in mathematics education in the broader context of higher order thinking skills, we have carried out a research that examined how teaching strategies oriented towards developing higher-order thinking skills influenced students’ critical thinking abilities. The guiding rationale of the work was that such teaching can foster the students’ skills of and dispositions towards critical thinking. In this article, we discuss ways in which critical thinking can be incorporated in mathematics instruction. In particular, we highlight how content taught in the probability strand can intentionally be focused on the development of students’ critical thinking. We report results of a study demonstrating improvement in secondary mathematics students’ dispositions towards critical thinking and abilities to think critically.

Cite this paper

Aizikovitsh-Udi, E. and Cheng, D. (2015) Developing Critical Thinking Skills from Dispositions to Abilities: Mathematics Education from Early Childhood to High School.*Creative Education*, **6**, 455-462. doi: 10.4236/ce.2015.64045.

Aizikovitsh-Udi, E. and Cheng, D. (2015) Developing Critical Thinking Skills from Dispositions to Abilities: Mathematics Education from Early Childhood to High School.

References

[1] Aizikovitsh-Udi, E. (2012). Developing Critical Thinking through Probability Models, Intuitive Judgments and Decision- Making under Uncertainty. Published Doctoral Dissertation, Saarbrucken: LAP Lambert Academic Publishing, ISBN 978- 3-8383-7240-2.

[2] Aizikovitsh-Udi, E., & Amit, M. (2008). Developing Critical Thinking in Probability Lesson. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 9-13). Morelia: Universidad Michoacana de San Nicolás de Hidalgo, Centro de Investigación y de Estudios Avanzados del IPN.

[3] Ben-Chaim, D., Ron, S., & Zoller, U. (2000). The Disposition of Eleventh-Grade Science Students toward Critical Thinking. Journal of Science Education and Technology, 9, 149-159.

http://dx.doi.org/10.1023/A:1009474023364

[4] Beyer, B. (1987). Practical Strategies for the Teaching of Thinking. Boston: Allyn & Bacon.

[5] Bryan, M. (1987). The Great Philosophers. New-York: BBC Books.

[6] Costa, A. L. (1991). The School as a Home for the Mind: A Collection of Articles. Palatine, IL: SkyLight.

[7] Costa, A. L., & Marzano, R. (1991). Teaching the Language of Thinking. In A. L. Costa (Ed.), Developing Minds: A Resource Book for Teaching Thinking (pp. 251-254). Alexandria, VA: Association for Supervision and Curriculum Development.

[8] Ennis, R. H. (1962). A Concept of Critical Thinking. Harvard Educational Review, 32, 81-111.

[9] Ennis, R. H. (1963). Needed: Research in Critical Thinking. Educational Leadership, 21, 17-20, 39.

[10] Ennis, R. H. (1985). The Logical Basis for Measuring CT Skills. Educational Leadership, 43, 44-48.

[11] Ennis, R. H. (1987a). A Conception of Critical Thinking—With Some Curriculum Suggestions. American Philosophical Association Newsletter on Teaching Philosophy, 1-5.

[12] Ennis, R. H. (1987b). A Taxonomy of Critical Thinking Dispositions and Abilities. In J. B. Baron, & R. J. Sternberg (Eds.), Teaching Thinking Skills: Theory and Practice (pp. 9-26). New York: Freeman.

[13] Ennis, R. H. (1989). Critical Thinking and Subject Specificity: Clarification and Needed Research. Educational Researcher, 18, 4-10.

http://dx.doi.org/10.3102/0013189X018003004

[14] Ennis, R. H. (2002). Goals for a Critical Thinking Curriculum and Its Assessment. In A. L. Costa (Ed.), Developing Minds (3rd ed., pp. 44-46). Alexandria, VA: Association for Supervision and Curriculum Development.

[15] Ennis, R. H., & Millman, J. (2005a). Cornell Critical Thinking Test, Level X (5th ed.). Seaside, CA: The Critical Thinking Company.

[16] Ennis, R. H., & Millman, J. (2005b). Cornell Critical Thinking Test, Level Z (5th ed.). Seaside, CA: The Critical Thinking Company.

[17] Facione, P. A., & Facione, N. C. (1992). The California Critical Thinking Disposition Inventory. Millbrae, CA: California Academic Press.

[18] Facione, P. A., Facione, N. C., & Giancarlo, C. A. (1996). The California Critical Disposition Inventory: Test Manual. Millbrae, CA: California Academic Press.

[19] Forman, E., Larreamendy-Joerns, J., Steinc, M. K., & Brown, C. A. (1998). “You’re Going to Want to Find out Which and Prove It”: Collective Argumentation in a Mathematics Classroom. Learning and Instruction, 8, 527-548.

http://dx.doi.org/10.1016/S0959-4752(98)00033-4

[20] Harpaz, Y. (Ed.). (1996). Education for Critical Thinking. Jerusalem: The Ministry of Education and Culture. (In Hebrew)

[21] Innabi, H., & Sheikh, O. (2007). The Change in Mathematics Teachers’ Perceptions of Critical Thinking after 15 Years of Educational Reform in Jordan. Educational Studies in Mathematics, 64, 45-68.

http://dx.doi.org/10.1007/s10649-005-9017-x

[22] Lieberman, V., & Tversky, A. (1996). Critical Thinking: Statistical Considerations and Intuitive Judgments. Tel Aviv: Open University. (In Hebrew)

[23] Lieberman, V., & Tversky, A. (2002). Probability Thinking in Daily Life. Tel Aviv: Open University. (In Hebrew)

[24] Lipman, M. (1991). Thinking in Education. New York: Cambridge University Press.

[25] McPeck, J. E. (1981). Critical Thinking and Education. New York: St. Martin’s Press.

[26] Perkins, D. N. (1992). Smart Schools: From Training Memories to Training Minds. New York: Free Press.

[27] Regev, Y. (1997). Socrates and the Internet. Computers in Education, 43, 1-13.

[28] Sternberg, R. (1984). How Can We Teach Intelligence? Educational Leadership, 39, 38-48.

[29] Swartz, R. J. (1992). Critical Thinking, the Curriculum, and the Problem of Transfer. In D. N. Perkins, J. Lochhead, & J. Bishop (Eds.), Thinking: The Second International Conference (pp. 261-284). Hillsdale, NJ: Erlbaum.

[30] Swartz, R. J., & Parks, S. (1994). Infusing the Teaching of Critical and Creative Thinking into Content Instruction. Pacific Grove, CA: Critical Thinking & Software.

[31] Zohar, A. (1996). To Learn, to Think, and to Learn to Think. Jerusalem: Branco Weiss Institute for Fostering Critical Thinking. (In Hebrew)

[32] Zohar, A., & Dori, Y. J. (2003). Higher Order Thinking Skills and Low Achieving Students: Are They Mutually Exclusive? Journal of the Learning Sciences, 12, 145-181.

http://dx.doi.org/10.1207/S15327809JLS1202_1

[1] Aizikovitsh-Udi, E. (2012). Developing Critical Thinking through Probability Models, Intuitive Judgments and Decision- Making under Uncertainty. Published Doctoral Dissertation, Saarbrucken: LAP Lambert Academic Publishing, ISBN 978- 3-8383-7240-2.

[2] Aizikovitsh-Udi, E., & Amit, M. (2008). Developing Critical Thinking in Probability Lesson. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 9-13). Morelia: Universidad Michoacana de San Nicolás de Hidalgo, Centro de Investigación y de Estudios Avanzados del IPN.

[3] Ben-Chaim, D., Ron, S., & Zoller, U. (2000). The Disposition of Eleventh-Grade Science Students toward Critical Thinking. Journal of Science Education and Technology, 9, 149-159.

http://dx.doi.org/10.1023/A:1009474023364

[4] Beyer, B. (1987). Practical Strategies for the Teaching of Thinking. Boston: Allyn & Bacon.

[5] Bryan, M. (1987). The Great Philosophers. New-York: BBC Books.

[6] Costa, A. L. (1991). The School as a Home for the Mind: A Collection of Articles. Palatine, IL: SkyLight.

[7] Costa, A. L., & Marzano, R. (1991). Teaching the Language of Thinking. In A. L. Costa (Ed.), Developing Minds: A Resource Book for Teaching Thinking (pp. 251-254). Alexandria, VA: Association for Supervision and Curriculum Development.

[8] Ennis, R. H. (1962). A Concept of Critical Thinking. Harvard Educational Review, 32, 81-111.

[9] Ennis, R. H. (1963). Needed: Research in Critical Thinking. Educational Leadership, 21, 17-20, 39.

[10] Ennis, R. H. (1985). The Logical Basis for Measuring CT Skills. Educational Leadership, 43, 44-48.

[11] Ennis, R. H. (1987a). A Conception of Critical Thinking—With Some Curriculum Suggestions. American Philosophical Association Newsletter on Teaching Philosophy, 1-5.

[12] Ennis, R. H. (1987b). A Taxonomy of Critical Thinking Dispositions and Abilities. In J. B. Baron, & R. J. Sternberg (Eds.), Teaching Thinking Skills: Theory and Practice (pp. 9-26). New York: Freeman.

[13] Ennis, R. H. (1989). Critical Thinking and Subject Specificity: Clarification and Needed Research. Educational Researcher, 18, 4-10.

http://dx.doi.org/10.3102/0013189X018003004

[14] Ennis, R. H. (2002). Goals for a Critical Thinking Curriculum and Its Assessment. In A. L. Costa (Ed.), Developing Minds (3rd ed., pp. 44-46). Alexandria, VA: Association for Supervision and Curriculum Development.

[15] Ennis, R. H., & Millman, J. (2005a). Cornell Critical Thinking Test, Level X (5th ed.). Seaside, CA: The Critical Thinking Company.

[16] Ennis, R. H., & Millman, J. (2005b). Cornell Critical Thinking Test, Level Z (5th ed.). Seaside, CA: The Critical Thinking Company.

[17] Facione, P. A., & Facione, N. C. (1992). The California Critical Thinking Disposition Inventory. Millbrae, CA: California Academic Press.

[18] Facione, P. A., Facione, N. C., & Giancarlo, C. A. (1996). The California Critical Disposition Inventory: Test Manual. Millbrae, CA: California Academic Press.

[19] Forman, E., Larreamendy-Joerns, J., Steinc, M. K., & Brown, C. A. (1998). “You’re Going to Want to Find out Which and Prove It”: Collective Argumentation in a Mathematics Classroom. Learning and Instruction, 8, 527-548.

http://dx.doi.org/10.1016/S0959-4752(98)00033-4

[20] Harpaz, Y. (Ed.). (1996). Education for Critical Thinking. Jerusalem: The Ministry of Education and Culture. (In Hebrew)

[21] Innabi, H., & Sheikh, O. (2007). The Change in Mathematics Teachers’ Perceptions of Critical Thinking after 15 Years of Educational Reform in Jordan. Educational Studies in Mathematics, 64, 45-68.

http://dx.doi.org/10.1007/s10649-005-9017-x

[22] Lieberman, V., & Tversky, A. (1996). Critical Thinking: Statistical Considerations and Intuitive Judgments. Tel Aviv: Open University. (In Hebrew)

[23] Lieberman, V., & Tversky, A. (2002). Probability Thinking in Daily Life. Tel Aviv: Open University. (In Hebrew)

[24] Lipman, M. (1991). Thinking in Education. New York: Cambridge University Press.

[25] McPeck, J. E. (1981). Critical Thinking and Education. New York: St. Martin’s Press.

[26] Perkins, D. N. (1992). Smart Schools: From Training Memories to Training Minds. New York: Free Press.

[27] Regev, Y. (1997). Socrates and the Internet. Computers in Education, 43, 1-13.

[28] Sternberg, R. (1984). How Can We Teach Intelligence? Educational Leadership, 39, 38-48.

[29] Swartz, R. J. (1992). Critical Thinking, the Curriculum, and the Problem of Transfer. In D. N. Perkins, J. Lochhead, & J. Bishop (Eds.), Thinking: The Second International Conference (pp. 261-284). Hillsdale, NJ: Erlbaum.

[30] Swartz, R. J., & Parks, S. (1994). Infusing the Teaching of Critical and Creative Thinking into Content Instruction. Pacific Grove, CA: Critical Thinking & Software.

[31] Zohar, A. (1996). To Learn, to Think, and to Learn to Think. Jerusalem: Branco Weiss Institute for Fostering Critical Thinking. (In Hebrew)

[32] Zohar, A., & Dori, Y. J. (2003). Higher Order Thinking Skills and Low Achieving Students: Are They Mutually Exclusive? Journal of the Learning Sciences, 12, 145-181.

http://dx.doi.org/10.1207/S15327809JLS1202_1