UC Santa Cruz

This dissertation focused on mathematics instruction in early grades (Pre-K - 3rd grade) by exploring teachers’ beliefs about mathematics teaching and the teaching practices of one teacher. I specifically examined teachers’ beliefs and one teacher’s practices that reflect asset-based views of students and support mathematics learning with understanding. This work contributes to early mathematics education research by documenting teachers’ beliefs about mathematics, documenting one accomplished teacher’s practices, and comparing that teacher’s practices when teaching in-person and online. In my analysis of teachers’ beliefs (Chapter 2), Early Grades Teachers’ Beliefs About Mathematics, Language, and Emergent Bilinguals, I explored the research question: what are early grades teachers’ professed beliefs about mathematics, language, student thinking, students’ out-of-school experiences, and students’ home and everyday language practices, in particular for EBs? I documented teachers’ professed beliefs related to mathematics and EBs through one survey and one interview. I was particularly interested in characterizing teachers’ beliefs about mathematics (Schoen & LaVenia, 2019) and their beliefs about language (Fernandes, 2020). Through analysis of teachers’ beliefs, I found that the 20 teachers in this study held varying degrees of asset-based views of EBs. All the teachers responded to the survey with at least 74% of their non-neutral responses in ways that reflect an asset-based view. I identified and sorted teachers’ total percentage of asset-based responses on the survey across four categories which include 1) some asset-based views, 2) many asset-based views, 3) most asset-based views, and 4) all asset-based views. In addition to what I found in the survey responses, the interviews clarified and provided more detailed descriptions of their beliefs. From the interviews, I found that teachers held beliefs about students’ assets and teaching mathematics with EBs related to students’ everyday and home language, students’ backgrounds and experiences, mathematics vocabulary, and supporting EBs. Teachers described their views on using students’ assets in two ways: allowing students’ assets in the classroom or drawing on students’ assets for mathematics learning. In the analysis of teaching practices during in-person instruction (Chapter 3), An Account of an Accomplished Teacher’s In-Person Mathematics Instruction in a First Grade Classroom: Drawing on Students’ Assets, I explored the nature of in-person mathematics instruction for five weeks in Ms. C’s first-grade class. The research questions that guided this analysis include: what was the nature of mathematics instruction in a first-grade classroom with an accomplished teacher? and, how did an accomplished teacher draw on students’ assets (student thinking and experiences)? This analysis provided evidence that Ms. C 1) created opportunities for students to develop conceptual understanding, 2) used teacher moves and was highly responsive to students and their thinking, 3) established norms around participating in the class, making mistakes, and efficiency, and 4) drew on students’ experiences outside of the classroom. During that period of in-person instruction, there was evidence that Ms. C’s teaching practices aligned with her professed beliefs documented through the survey and interview. In particular, her teaching practices reflected the low “transmissionist”, low “facts first”, and low “fixed instructional plan” beliefs documented in previous research (from the belief constructs, Schoen & LaVenia, 2019). The central features of Ms. C’s in-person teaching practices also aligned with research-based recommendations for effective mathematics teaching (e.g., Hiebert & Carpenter, 1992; Aguirre et al., 2012; Moschkovich, 2013; Turner et al., 2016; Wager, 2013). The vignettes in Chapter 3 provide detailed examples of her teaching practices and illustrate how Ms. C drew on students’ assets to create opportunities for mathematics learning with understanding. In the analysis comparing in-person and online teaching practices (Chapter 4), A Comparison of Mathematics Instruction In-Person and Online with First-Grade Students, I described how Ms. C adapted and facilitated mathematics instruction online with first-grade students, including one EB. I explored the research questions: 1) What were the differences between classroom routines and mathematics activities in person compared to online during COVID-19 in an early grades classroom? 2) Did Ms. C enact math instruction online that aligns with her professed beliefs? If so, how? 3) What was the nature of online math instruction for the EB in Ms. C’s classroom? My observations support the claim that most of the central features of Ms. C’s mathematics instruction documented during in person teaching (i.e., teaching for conceptual understanding, using teacher talk moves, establishing norms, and using students' experiences) were similar, even when the lessons looked different. For example, I observed Ms. C consistently eliciting student thinking and strategies while problem-solving both in-person and online. She also used a variety of teacher moves, such as revoicing and questioning, to guide students to uncover patterns and identify information that they noticed. In terms of the professed beliefs documented in Chapter 2, two of the belief constructs observed to align with her teaching practices in person (Schoen & LaVenia, 2019), Ms. C’s low “transmissionist” and low “facts first” beliefs, were also reflected in the observations of her teaching practices online. However, institutional constraints impacted her teaching practices in ways that resulted in less alignment with her low “fixed instructional plan” belief, documented in Chapter 2 and observed during in-person teaching in Chapter 3. There were structural and policy differences between the two settings. Despite those differences, this analysis showed that many of the central features of Ms. C’s mathematics teaching practices persisted even when she transitioned to online teaching during a pandemic with her first-grade students.