Transitioning to the NCTM Principles/CCSS Practices
Was Nancy’s approach bad? No. There might have been some educational gains for some students. Learners construct their own knowledge at all times and in all types of situations, but different instructional approaches may influence the quality and content accuracy of the construction. The fact that students faced one another in small groups rather than in rows looking at one another’s backs may have promoted some worthwhile discussion among students. Although the tiles were not applied in the best way for making connections between multiple representations, they still provided an alternative representation for algebraic terms and for the distributive property, so they may have helped some students better understand the mathematics. Nancy also had students present their answers, thus opening an opportunity for students to share their thinking and summarize ideas.
We surmise that Nancy’s perception of teaching mathematics is one that relies on teacher control or is rule-driven. She probably has had little experience using various tools, such as manipulatives, to guide exploratory activities. However, the fact that she has elements that are conducive to reform activities in her class indicates that she is trying to embrace different approaches to teaching. Her instruction and choice of activities are those of a teacher in transition to a Standards-based teaching approach supported by NCTM and CCSS. What is lacking is implementation of the principles and practices, together with the mathematics content in her instruction. A clearer vision of what the principles and practices entail is key to her success in moving forward with the transition.
The two examples show that labeling an activity or class as Standards-based or not requires close scrutiny of the tasks students are doing, how they are instructed to do it, and whether a single
teaching method is used exclusively. Let’s consider the revisions made to Nancy’s lesson and ask one final question: Is it now aligned to best practices? Some would say, “Yes, somewhat,” but also, “What about a real-life challenging application out of which the need to multiply binomials arises? (SMP1). Why not have students do individual explorations first, before going into groups?” (SMP2),
My point is that many of us are teachers in transition, with various levels of understanding of what the Standards imply Furthermore, we all come to the table with different experiences, expertise, and expectations. “Opportunities to reflect on and refine instructional practice—during class and outside of class, alone and with others” will be instrumental to helping us move closer to a common vision for teaching and learning (NCTM, 2000, p. 19).