Constructivism in Mathematics:
One major goal of constructivism in mathematics is to move from teacher-centred to student-centred instruction. The teacher continues to play a critical role in the construction of knowledge, but learning should occur “against the background of the learner’s current concepts” (Posner et al., 1982, p. 212). Teachers must identify and use students’ prior-knowledge to design instruction that promotes the development and creation of new concepts. According to Alsup (2004) the goal of a constructivist mathematics classroom is to actively involve children in the learning process and to present situations that students find problematic and are motivated to solve. The lesson plan outlined in this project promotes the goals of constructivism as it ensures that students’ prior-knowledge is the starting point for the lesson. The students are actively involved in the process and take ownership of their learning by presenting their work. The lesson is also designed so that teachers have several opportunities throughout the learning process to formatively assess students’ understanding as it develops. These formative assessments should result in the development of future lessons that address the class needs and explore areas that are either of interest to students or are in need of further exploration. Lesson design that is flexible and adapts to student needs is key to constructivist theory.
Collaborative:
Collaboration and cooperation are integral to the learning process and are a key element of constructivist lesson design. Inglis and Miller’s (2011) action research project found that when students are encouraged to co-create, explain their work in groups and compare problem solving methods they are more successful when asked to complete individual tasks. This measurement lesson encourages the development of cooperation and collaboration skills through a variety of teaching strategies and gives students experience working and sharing in groups. Developing collaboration skills is valuable for students in all subjects and grades and should begin in the early primary years. The measuring height lesson is age appropriate for early primary students as it develops students thinking skills and problem solving abilities. The lesson includes several thinking routines such as, see-think-wonder, think-pair-share and think boards that students can use as tools to solve problems not only in mathematics but also across subjects.
Authentic:
This lesson is authentic as students are required to determine the height of group members, which is an activity that students find engaging and relevant. According to Schmittau (2003) students often develop an inaccurate understanding of number due to the overemphasis on counting small collections in many primary classrooms. To overcome this problem, a Vygotskian cultural-historical approach to number recommends that an understanding of number “is developed out of the action of measurement rather than counting” (Schmittau, 2003, p. 229). Similarly, Yun (2000) advocates for a project approach to learning so that students can make connections between their own lives and what is learned in school. Often when students are presented with mathematics concepts outside of any real-life context they cannot transfer understanding to new situations. Hiebert et al. (1996) recognize that throughout school, students often learn a version of mathematics that does not transfer well to the actual profession of mathematics. Although this lesson is designed for early primary students, they are encouraged to think like mathematicians by designing their own way to measure height, explain their thinking and use authentic mathematical language that the teacher records on the word wall.
Concluding Ideas:
Although constructivist theory is evident in many curriculum documents, much of the literature concerning the application of constructivism in the classroom suggests that in practice, a more teacher-directed approach to mathematics is common in early primary classrooms. Allen (2011) posits that there are deeply held beliefs surrounding the teaching of mathematics in K-12 classrooms that directly limits the “implementation of innovative practices and the climate for mathematics learning” (p. 2). Proponents of constructivist teaching in mathematics recommend that teachers critically reflect on their own beliefs about teaching and learning mathematics. Educators may need to be willing to fundamentally shift traditional power dynamics, alter the classroom environment and abandon some instructional methods in order to incorporate constructivist strategies. Blumenfeld, Krajcik, Mark and Soloway (1994) recommend that through reflective practices, teachers should work collaboratively to introduce, design and redefine constructivist practices. Effectively implementing constructivism in the classroom may take, time, patience, collaboration and reflective practices but will result in a more rewarding educational experience for both educators and students.
References
Allen, K. C. (2011). Mathematics as thinking. A response to “Democracy and school math”. Democracy & Education, 19(2).
Alsup, J. (2004). A comparison of constructivist and traditional instruction in mathematics. Educational Research Quarterly, 28(4), 3-17.
Blumenfeld, P.C., Krajcik, J.S., Marx, R.W. & Soloway, E. (1994). Lessons learned: How collaboration helped middle grade science teachers learn project-based instruction. The Elementary School Journal, 94(5).
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher, 25(4),12-21.
Inglis, L., & Miller, N. (2011). Problem based instruction: Getting at the big ideas and developing learners. Canadian Journal Of Action Research, 12(3), 6-12.
Posner, G.J, Strike, K.A, Hewson, P. W & Gertzog, W.A (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education. 66(2), 211-227.
Schmittau, J. (2003). Cultural-historical theory and mathematics education. In A. Kozulin, B. Gindis, V. Ageyev, & S. Miller (Eds.), Vygotsky’s educational theory in cultural context (pp. 225-244). Cambridge, UK: Cambridge University Press.
Yun, E (2000). The project approach as a way of making life meaningful in the classroom.Clearinghouse on Early education and Parenting http://ceep.crc.uiuc.edu/pubs/katzsym/yun.html