Teacher Noticing: What Does it Involve?

Posted on by

James Brickwedde, Project for Elementary Mathematics

Many teachers across Minnesota have begun experimenting with the Building Thinking Classroom practices (Liljedahl, 2021). Imagine that a rich task with low floor entry points and high ceiling interest has been given to the students to work on. The students are at their vertical work surfaces. There is a buzz in the room as students work through the parts of the task. You, the teacher, are standing at a strategic vantage point observing. What are you listening for? What are you looking for? This is what is known as attending, observing and listening skills. The question always is, what are you attending to? Merely the students’ level of engagement, their noise levels? Are the strategies what you anticipated in your planning the lesson? Is there some unexpected divergent thinking? 

The quality of one’s attention makes a difference on how the lesson will ultimately unfold. It is not enough that students have high engagement levels. Attending to the details of the students’ mathematical strategies is what Building Thinking Classroom allows the teacher access to. Do the strategies appearing on the boards demonstrate a reasonable approach? Does the work contain the nugget of a good idea but represents only a partial understanding? How does the strategy used by collaborative team one compare with that used by collaborative team four? Has a group done something unexpected from what you thought might emerge? The anticipatory planning by the teacher in structuring the learning task is the in-the-moment interpreting necessary for next steps in the lesson. (Jacobs, et al. 2010; Jacobs & Empson, 2016; van Es, et al. 2021) 

Deciding how to respond in the moment is a skill that cannot be outlined in any lesson plan that a publisher can provide you. These decisions are based on what is directly in front of you and your ability to interpret the students’ work. Studies have shown that having students publicly share their thinking improves achievement levels. However, the improvement is not as significant as in those classrooms where the teacher pushes the conversation to have students elaborate on the details of their decision making and how one group’s strategies compares and contrasts with others. In addition, achievement is higher in those classrooms where errors are processed constructively and in full. (Webb, et al. 2014; Kazemi & Stipek, 2001). 

Interpreting students’ thinking is what focuses the decision-making process. This knowledge base includes the developmental frameworks and learning trajectories that students might move through as they refine their mathematical understandings. Without this knowledge base, decision-making about how to facilitate the classroom conversation around the students’ work is likely to be superficial.

Aimie Albrecht, a researcher in Australia, has written  a wonderful summary of what Teacher Noticing involves. In that summary, she draws on how Smith and Stein’s (2011) Five Practices for Orchestrating Mathematical Discussions can be viewed through the teacher noticing skill set. As Albrecht summaries the infusion of teacher noticing practices with the five practices as…

  • Anticipating possible student thinking
  • Monitoring actual student thinking – noticing within
  • Selecting a subset of student thinking to share – noticing among
  • Sequencing instances of student thinking to frame the discussion
  • Connecting different instances of student thinking to highlight key mathematical ideas

Here is where the Mathematical Teaching Practices upon which the 2022 Minnesota Mathematics Academic Standards are based, come into play. Figure one captures the eight instructional practices  articulated in Principles to Actions (NCTM, 2014). How one interprets students’ thinking influences how one enacts the eight practices. 

Figure One

It is not possible in short articles such as this to capture the various nuances of the developmental frameworks and learning trajectories for the various grade levels. That requires professional development efforts for the grade level bands and content domains one teaches. Nevertheless, to really move the needle on student achievement, first attending to the details of students’ thinking, then interpreting where along the continuum of development of the mathematical ideas that they are, allows for deciding how to respond as one’s ability to anticipate student thinking improves. Facilitating rich classroom conversations based on the range of student strategies is a skill set that is learned and grows by reflecting on one’s efforts, both the triumphs and the stumbles. There will be both! The best feedback to draw upon is if the students’ thinking has moved forward and is grounded both conceptually and procedurally. 

References

Albrecht, A. (2022, January 16). Teacher noticing. Wonder in Mathematics. https://amiealbrecht.com/2022/01/16/teacher-noticing/

Jacobs, V.R. and Empson, S.B., (2016), Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education 48:185–197.

Jacobs, V.R., Lamb, L.L.C., Phillipps, R.A. (2010) Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education. 41(2), 169–202.

Kazemi, E. & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms, The Elementary School Journal. 102 (1) pp. 59-80.

Liljedahl, P., & Zager, T. (2021). Building thinking classrooms in mathematics : 14 teaching practices for enhancing learning, grades K-12. Corwin. 

National Council of Teachers of Mathematics. (2014). Principles to actions. National Council of Teachers of Mathematics: Reston, VA.

Smith, M.S., and Stein, M.K. (2011). 5 Practices for orchestrating productive mathematics discussions. Reston, VA : Thousand Oaks, CA: National Council of Teachers of Mathematics ; Corwin.

van Es, E. A., &. Sherin., M.G. (2021). “Expanding on prior conceptualizations of teacher noticing.” ZDM – Mathematics Education 53 (1): 17–27. https://doi.org/10.1007/s11858-020-01211-4.

Webb, N.M., Franke, M.L., Ing, M., Wong, J., Fernandez, C.H.,  Shin, N., and Turrou, A.C. (2014). Engaging with others’ mathematical ideas: Interrelationships among student participation, teachers’ instructional practices, and learning, International Journal of Educational Research, 63, pp 79-93.