Academic journal article The Mathematics Enthusiast

Understanding Teacher Noticing of Students' Prior Knowledge: Challenges and Possibilities

Academic journal article The Mathematics Enthusiast

Understanding Teacher Noticing of Students' Prior Knowledge: Challenges and Possibilities

Article excerpt

In recent years, mathematics education researchers have adopted the construct of "teacher noticing" to denote the special ways in which teachers pay attention to specific aspects of instruction (Sherin, Jacobs, & Philipp, 2011). There are some variations in the uses of this construct. Some researchers have coined related terms, such as "noticing classroom interactions" (Sherin & van Es, 2005), "professional vision," (Sherin & van Es, 2009), "professional noticing of children's mathematical thinking" (Jacobs, Lamb, & Philipp, 2010) and "noticing of student thinking" (van Es, 2011). Overall, studying teacher noticing allows for an examination of how teachers understand students' ideas during classroom instruction and through the examination of artifacts from classrooms, such as student worksheets or classroom videos in activities outside of the classroom. Most recently, researchers' examination of teacher noticing specifies the object of teachers' attention, such as "teacher noticing of students' algebraic thinking" (Walkoe, 2015), "noticing of students' mathematical strengths" (Jilk, 2016), and "noticing of equitable practices" (McDuffie, Foote, Drake, Turner, Aguirre, Bartell, & Bolson, 2015). Researchers' expectation about adopting a more limited focus on teacher noticing is twofold. On the one hand, having a better understanding of specific aspects of teacher noticing can help to unpack teacher thinking in relation to instructional demands. On the other hand, research on teacher noticing can support the development of teacher education initiatives for increasing teacher noticing of specific aspects of instruction and thus promote teacher learning. In general, understanding teacher thinking can guide teacher education initiatives for supporting teachers' development of capabilities for attending to student thinking in the classroom.

My work centers on understanding teacher noticing of students ' prior knowledge. Research on learning shows robust evidence concerning the importance of prior knowledge (National Research Council [NRC], 2000). Prior knowledge affects learning (Dochy, Segers, & Buehl, 1999). People make sense of something new in light of what they already know. In addition, new knowledge becomes more meaningful and memorable when it is connected to what is known and past experiences (NRC, 2000). Recommendations for mathematics teachers state that making explicit connections with prior knowledge during instruction solidifies students' mathematical understanding (NRC, 2001). Teacher observation instruments identify attention to students' prior knowledge as a teaching action that can promote mathematical understanding (e.g., Boston & Smith, 2009). Maintaining a high-level cognitive engagement requires tasks that provide opportunities for students to connect with their prior knowledge (Stein & Smith, 1998). Typically, curriculum materials refer to students' prior knowledge in the teachers' edition of textbooks as mathematical content that students have already studied in school in the same course of study or in prior courses. Teachers recognize students' prior knowledge of school mathematics (Hohensee, 2016). However, my conceptualization of students' prior knowledge goes beyond school mathematics and considers students' experiences outside of school.

Various perspectives in mathematics education research have considered students' experiences in relation to mathematics. Work regarding students' funds of knowledge (González, Andrade, Civil, & Moll, 2001) and children 's mathematical knowledge bases (Turner et al., 2012) exemplify how students' experiences, including students' cultural and linguistic backgrounds, shape mathematical problem solving. Studies on ethnomathematics (e.g., Ascher, 1994) have documented how individuals engage in mathematical activities in various nontraditional spaces. Similarly, studies on out-of-school mathematics demonstrate that mathematical problem-solving is tightly connected to contextual experiences (e. …

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