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Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)Teachers in the elementary grades often teach all subjects and are expected to have appropriate content knowledge of a wide range of disciplines. Current recommendations suggest teachers should integrate multiple disciplines into the same lesson, for instance, when teaching integrated STEM lessons. Although there are many similarities between STEM fields, there are also epistemological differences to be understood by students and teachers. This study investigated teachers’ beliefs about teaching mathematics and science using argumentation and the epistemological and contextual factors that may have influenced these beliefs. Teachers’ beliefs about different epistemological underpinnings of mathematics and science, along with contextual constraints, led to different beliefs and intentions for practice with respect to argumentation in these disciplines. The contextual constraint of testing and the amount of curriculum the teachers perceived as essential focused more attention on the teaching of mathematics, which could be seen as benefiting student learning of mathematics. On the other hand, the perception of science as involving wonder, curiosity, and inherently positive and interesting ideas may lead to the creation of a more positive learning environment for the teaching of science. These questions remain open and need to be studied further: What are the consequences of perceiving argumentation in mathematics as limited to concepts already wellunderstood? Can integrating the teaching of mathematics and science lead to more exploratory and inquirybased teaching of mathematical ideas alongside scientific ones?more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)Collective Argumentation Learning and Coding (CALC) is a project focused on providing teachers with strategies to engage students in collective argumentation in mathematics, science, and coding. Collective argumentation can be characterized by any instance where multiple people (teachers and students) work together to establish a claim and provide evidence to support it (Conner et al., 2014b). Collective argumentation is an effective approach for promoting critical and higher order thinking and supporting students’ ability to articulate and justify claims. The goal of the CALC project is to help elementary school teachers extend the use of collective argumentation from teaching mathematics and science to teaching coding. Doing so increases the probability that teachers will integrate coding in regular classroom instruction, making it accessible to all students. This project highlighted Gloria (pseudonym), a fourthgrade teacher from Cohort 1 because of the extent to which she went from fear of coding to fluent implementation. Initially, Gloria was comfortable engaging her students in argumentation, explaining they already used it in mathematics with Cognitively Guided Instruction (CGI). However, she was “terrified” about learning to code because she didn’t view herself as proficient with technology. She was willing to overcome her fear of coding because she saw the value in providing her students with coding experiences that would help them develop the necessary skills for our increasingly technological society. In the course of three months, Gloria’s instruction progressed from using simple coding activities to more sophisticated coding platforms. This progression in her coding instruction paralleled the change in her personal feelings about coding as she moved from “terrified” to “comfortable with it”.more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; & RuizArias, P.M. (Ed.)Much of the research on the development of professional noticing expertise has focused on prospective teachers. We contend that we must investigate practicing teachers as well, and in particular practicing secondary teachers, because they bring with them years of teaching experience and are situated in unique contexts. Hence we studied the longitudinal growth of the professional noticing expertise of a group of practicing secondary teachers (N=10) as they progressed through a 5year professional development (PD) about being responsive to students’ mathematical thinking. Results indicated that the first half of the PD supported their interpreting and decidinghowto respond skills, and the second half of the PD supported their attending skills, which were already strong even before the PD. We compare these results with the activities that occurred in the PD and discuss implications for future research and PD programs.more » « less

Sacristán, A.I. ; null ; RuizArias, P.M. (Ed.)In this report, we discuss five forms of reasoning about multiple quantities that sixthgrade students exhibited as they examined mathematical relationships within the context of science. Specifically, students exhibited forms of sequential, transitive, dependent, and independent multivariational reasoning as well as relational reasoning. We use data from wholeclass design experiments with students to illustrate examples of each of these forms of reasoning.more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)

Putting the “M” back into STEM: Considering how units coordination relates to computational thinkingSacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)This theoretical commentary examines theory driven discussions in Science, Technology, Engineering, and Mathematics (STEM) fields and mathematics fields. Through this examination, the authors articulate particular parallels between spatial encoding strategy theory and units coordination theory. Finally, these parallel are considering pragmatically in the Elementary STEM Teaching Integrating Textiles and Computing Holistically (ESTITCH) curriculum where STEM and social studies topics are explored by elementary students. This commentary concludes with questions and particular directions our mathematics education field can progress when integrating mathematics in STEM fields.more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)In our project, we develop curricular materials to support prospective secondary teachers’ development of MKT and provide professional development (PD) opportunities for instructors ho will teach with these materials. In this paper, we examine the ways in which mathematics faculty engage in the teaching rehearsal debriefs included in the PD to answer the question: To what instructional interactions do instructors of mathematics content courses attend during rehearsal debriefs enacted in PD? Findings show that mathematics instructors attend to all types of interactions but attention is influenced by instructors’ mathematical knowledge.more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)

Sacristán, A.I ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)In this paper we present an integrated design approach for bridging content between science, technology, engineering, math, and computational thinking (STEM+C). We present data from a design experiment to show examples of the kinds of integrated reasoning that students exhibited while engaging with our design. We argue that covariational reasoning can provide strong scaffolding in making integrated connections between the STEM+C content areas.more » « less

Sacristán, A.I. ; CortésZavala, J.C. ; RuizArias, P.M. (Ed.)The phenomenon of the sea level rise is a pressing environmental and social issue of the present age. Starting with the assumption that mathematics can be utilized to help students explore this phenomenon, we designed a simulation in NetLogo, in which students investigated the relationships between the quantities of temperature rise, height of future sea level, and total land area. In this paper, we present the analysis of a wholeclass design experiment in a sixthgrade classroom and discuss how our design helped students to examine sea level rise as both an environmental and a social issue.more » « less