{"id":10256,"date":"2021-01-12T20:40:39","date_gmt":"2021-01-12T20:40:39","guid":{"rendered":"https:\/\/citejournal.org\/\/\/"},"modified":"2021-06-04T19:53:11","modified_gmt":"2021-06-04T19:53:11","slug":"when-robots-invade-the-neighborhood-learning-to-teach-prek-5-mathematics-leveraging-both-technology-and-community-knowledge","status":"publish","type":"post","link":"https:\/\/citejournal.org\/volume-21\/issue-1-21\/mathematics\/when-robots-invade-the-neighborhood-learning-to-teach-prek-5-mathematics-leveraging-both-technology-and-community-knowledge","title":{"rendered":"When Robots Invade the Neighborhood: Learning to Teach PreK-5 Mathematics Leveraging Both Technology and Community Knowledge"},"content":{"rendered":"\n

As equity in mathematics education has garnered more attention, multiple avenues have emerged for increasing learning opportunities for students historically marginalized in mathematics. In this project, we brought together two avenues for equity-minded mathematics teaching: developing mathematics teaching among prospective teachers (PTs) that incorporated both technology<\/em> and funds of knowledge<\/em> to foster mathematics learning toward supporting broader equity goals.<\/p>\n\n\n\n

This study examined mathematics teaching that utilized digital technologies for increasing opportunities for mathematical reasoning and sense making and supporting positive dispositions toward mathematics (as recommended in Forgasz et al., 2010). Leveraging funds of knowledge means using the cultural, linguistic, and cognitive resources from home or community settings to promote learning the school mathematics curriculum (Aguirre et al., 2012; Harper et al., 2018).<\/p>\n\n\n\n

This paper reports our study of the use of robotics in mathematics teaching, which are appropriate for working with students across grades preK-12 and for supporting culturally responsive teaching (Leonard et al., 2016, 2018; Newton et al., 2020; Sullivan & Bers, 2016; Xia & Zhong, 2008). We explored PTs\u2019 development of mathematics teaching within an elementary mathematics methods course through a model that engaged them in learning about technological tools and about community-based mathematics practices. Our aim was to design and implement science, technology, engineering, and mathematics (STEM) activities that leveraged both robotics and funds of knowledge.<\/p>\n\n\n\n

Background<\/h2>\n\n\n\n

Although this study centered PTs\u2019 development, we grounded our work with PTs in separate lines of research. This research suggested that integrating digital technology and leveraging funds of knowledge in mathematics classrooms can positively impact the mathematics achievement of preK-12 students (e.g., Kisker et al., 2012; Li & Ma, 2010). Bringing these two pedagogical approaches together in a university-based elementary mathematics methods course was grounded in theories framing both mathematics and digital technologies as situated within cultural practices. This effective and equitable teaching had to address the different needs, positions, and identities of students as they engaged with mathematics through technology (Forgasz et al., 2010; Nasir, 2002). <\/p>\n\n\n\n

Teaching mathematics with technology shows potential to support differentiated instruction and student-centered practices (Thomas & Edson, 2019), but without cultural considerations can exacerbate inequities (Forgasz et al., 2010). In particular, differences across gender, race\/ethnicity, and socioeconomic groups in access to and uses of technology at both home and school may further limit mathematics learning opportunities for students from historically marginalized groups (Forgasz et al., 2010; Warschauer & Matuchniak, 2010; Wang & Moghadam, 2017).<\/p>\n\n\n\n

For example, Black students are likely to use technology in school mathematics at least once a week; however, the use of that technology often prioritizes remedial computer-drill (Kitchen & Berk, 2016; Warschauer & Matuchniak, 2010), an instructional approach that is known to perpetuate inequitable mathematics outcomes for Black students (Berry et al., 2014; Martin, 2019). Thus, educators integrating technology into mathematics teaching toward equity goals must consider the broader sociocultural and sociopolitical conditions impacting mathematics learning opportunities for students from historically marginalized groups.<\/p>\n\n\n\n

Accordingly, a funds of knowledge approach is a promising complement to teaching mathematics with technology because of the inherent emphasis on bridging cultural-, community-, and home-based practices with school practices. Leveraging funds of knowledge fosters a strengths-based approach by positioning students\u2019 diverse knowledge bases, experiences, and resources as assets for mathematics learning (Aguirre et al., 2012; Moll et al., 1992). Adopting such a strength-based approach encourages teachers to emphasize what students know and can do with available resources and tools, which may mediate challenges in the differential access and use of technology.<\/p>\n\n\n\n

This study aimed to integrate two considerations essential in the preparation of teachers of mathematics (Association of Mathematics Teacher Educators, 2017), using mathematical tools and technology and drawing on students\u2019 mathematical strengths, usually considered separately. In this study, we asked the following research question: How do PTs develop mathematics teaching that uses the cultural, linguistic, and cognitive resources from home and community settings to promote learning school mathematics with robotics?<\/p>\n\n\n\n

Learning to teach mathematics with technology requires a sophisticated and integrated knowledge of teaching, mathematics, and technology (Koehler & Mishra, 2009; Thomas & Edson, 2019). Likewise, learning to bridge funds of knowledge and the school mathematics curriculum requires deep knowledge of teaching, mathematics, and students\u2019 community- and home-based experiences and resources (Aguirre et al., 2012; Harper et al., 2018). Thus, bringing together these two avenues for equity in mathematics education increases the complexity of learning to teach.<\/p>\n\n\n\n

Our study aimed to open pathways for and identify challenges to preparing PTs for teaching mathematics by leveraging both technology, namely robotics, and funds of knowledge. The following sections contain a brief overview of the research on teaching and learning to teach mathematics with robotics and funds of knowledge.<\/p>\n\n\n\n

Research on Robotics in STEM Education<\/h3>\n\n\n\n

Policymakers have called for integrated content frameworks to support preK-12 STEM education that incorporates critical thinking, fundamentals of coding, and use of digital technologies (e.g., Tennessee Department of Education, 2018a). Students historically marginalized in mathematics, however, also experience marginalization when learning coding and using digital technologies.<\/p>\n\n\n\n

For example, by age six, stereotypes that boys are better than girls at robotics and computer programming lowers girls\u2019 sense of belonging in STEM and limits their access to activities such as computer games and technological toys (Master et al., 2016). Research consistently shows that cultural stereotypes and, consequently, limited opportunities to engage with coding and digital technologies maintain gender inequities (Bian et al., 2017; Funke et al., 2017; Master et al., 2016, 2017), but considerations of access and participation among Black and Latinx children remain underexplored. In fact, the experiences of Black and Latinx children have been largely ignored (Newton et al., 2020).<\/p>\n\n\n\n

Only a few studies have taken up cultural considerations (Leonard et al., 2016, 2018; Newton et al., 2020; Scott et al., 2015), but those studies show that robotics offers an authentic way for teachers and students to draw on cultural capital as they use digital technologies and engage with the fundamentals of coding. Further, robotics provides a highly engaging STEM strategy to reinforce mathematical concepts (e.g., solving equations; Grubbs, 2013).<\/p>\n\n\n\n

In addition to individual motivation, Yuen et al. (2014) found that using robotics facilitated collaborative learning experiences that encouraged students to draw on multiple strengths in design and implementation, which aligns with equitable approaches to broadening participation in mathematics education (Esmonde, 2009). Additional research suggests that student use of robotics is an impactful instructional method for students with exceptional needs (e.g., autism spectrum disorder, emotional and behavioral disorders, Down syndrome, and medically fragile students; Benitti, 2012; Knight et al., 2019; Nickels & Cullen, 2017; Taylor, Vasquez et al., 2017).<\/p>\n\n\n\n

Support for developing teachers\u2019 STEM instructional skills and pedagogical use of robotics is an ongoing area of research. Leonard et al. (2018) focused on developing practicing teachers\u2019 STEM skills in tandem with culturally responsive teaching. Findings from their study noted increased teacher efficacy, improved technical understanding, and development of equitable STEM practices for teachers.<\/p>\n\n\n\n

Research indicates a continued \u201cneed for teacher [professional development] and ongoing support as teachers integrate robotics and computational thinking in their classrooms\u201d (Chalmers, 2018, p. 99). This study contributes to the field\u2019s emerging understandings of how teachers learn to integrate robotics into mathematics instruction.<\/p>\n\n\n\n

Research on Funds of Knowledge in Mathematics Education<\/h3>\n\n\n\n

Guidance on preparing teachers of mathematics increasingly has emphasized the importance of drawing on students\u2019 mathematical strengths, particularly regarding valuing diverse mathematical, cultural, and linguistic funds of knowledge (Association of Mathematics Teacher Educators, 2017). Funds of knowledge refer to the \u201chistorically accumulated and culturally developed bodies of knowledge and skills essential for household or individual functioning and well-being\u201d (Moll et al., 1992, p. 133). Accordingly, mathematics instruction that leverages funds of knowledge uses the cultural, linguistic, and cognitive resources from home or community settings to promote learning the school mathematics curriculum (Aguirre et al., 2012; Harper et al., 2018).<\/p>\n\n\n\n

Research has shown that culturally relevant learning environments that value funds of knowledge positively affect student effort and engagement (Howard, 2001; Ladson-Billings, 2009). In addition to increasing participation, incorporating children\u2019s everyday mathematics practices into classroom instruction challenges students\u2019 expectations about mathematics, broadening ideas about who can do mathematics and what mathematics is (Civil, 2002). Consequently, situating mathematics in its community- and home-based cultural context significantly increases student performance on traditional measures of mathematics achievement (Kisker et al., 2012). <\/p>\n\n\n\n

Supporting teachers to utilize funds of knowledge for students\u2019 learning of school mathematics is not straightforward (Civil, 2007). Given the commonly held misperception that mathematics is culturally neutral, the divide between home-based and school-based mathematics remains wide. Thus, identifying and leveraging everyday mathematics practices proves more challenging than in other disciplines such as language arts or social studies (Gonz\u00e1lez et al., 2001).<\/p>\n\n\n\n

Research on PTs\u2019 development of mathematics teaching that leverages funds of knowledge shows a tendency toward only superficial connections to out-of-school experiences (e.g., changing names of locations) or only procedural mathematics (e.g., calculations with money) rather than reasoning and sense making (Aguirre et al., 2012; Harper et al., 2018). These findings indicate a continued need for research in mathematics teacher education on bridging funds of knowledge and school mathematics in meaningful ways, and this study contributes to the field\u2019s understandings of how teachers learn to leverage funds of knowledge in mathematics instruction.<\/p>\n\n\n\n

Transdisciplinary Connections as Funds of Knowledge<\/h3>\n\n\n\n

In addition to home- and community-based funds of knowledge, we also included knowledge, experiences, and ways of knowing from other disciplines in our current framing of funds of knowledge. We chose to broaden the concept of funds of knowledge in this study for several reasons.<\/p>\n\n\n\n

First, connecting mathematics to other disciplines shows promise for addressing inequities in mathematics (Jao & Radakovic, 2018). Transdisciplinary connections can enhance students\u2019 ability to leverage their home- and community-based funds of knowledge in meaningful ways in mathematics (Harper 2017, 2019). Further, the focus on using robotics in mathematics is inherently transdisciplinary, bringing together computer science and mathematics. A conceptual model that expands STEM to STEAM, by promoting cross-curricular content integration through art-related fields (e.g., social studies, literature, and visual art), fosters teachers\u2019 ability in creating authentic problem-based learning tasks (Quigley et al., 2017).<\/p>\n\n\n\n

Finally, teachers can identify and leverage everyday practices from children\u2019s lives more easily in other disciplines than in mathematics (Gonz\u00e1lez et al., 2001). Thus, we hoped that encouraging transdisciplinary connections might also enhance teachers\u2019 ability to leverage children\u2019s home- and community-based funds of knowledge in meaningful ways in mathematics instruction.<\/p>\n\n\n\n

Research Questions<\/h2>\n\n\n\n

Overall, we aimed to explore how PTs develop mathematics teaching that uses the cultural, linguistic, and cognitive resources from home and community settings to promote learning school mathematics with robotics. More specifically, we addressed the following research questions:<\/p>\n\n\n\n

  1. How do PTs connect mathematics learning and robotics?<\/li>
  2. How do PTs who use robotics for mathematics instruction leverage community funds of knowledge and transdisciplinary connections?<\/li><\/ol>\n\n\n\n

    Methods<\/h2>\n\n\n\n

    Context and Participants<\/h3>\n\n\n\n

    Research took place within initial teacher licensure programs at a public university in the southeastern United States. Across fall 2018, spring 2019, and fall 2019, groups of PTs from five sections of a master\u2019s-level elementary mathematics methods course designed, planned for, and facilitated mathematics activities at informal STEM events (henceforth, family STEM nights) hosted afterschool by nearby public elementary schools and preschools. Table 1 provides a summary of PT enrollment across the five sections of elementary mathematics methods.<\/p>\n\n\n\n

    Table 1<\/strong>   Prospective Teacher Enrollment Across Five Sections of Mathematics Methods<\/p>\n\n\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t
    Semester<\/strong><\/th>Section Focus<\/strong><\/th>Total PTs<\/strong><\/th>Enrollment by Licensure Area\/Cohort<\/strong><\/th>\n<\/tr>\n<\/thead>\n
    Fall 2018<\/td>K-5<\/td>16<\/td>8 master\u2019s candidates seeking initial licensure for K-5
    \n 6 master\u2019s candidates seeking initial licensure for special ed
    \n 2 undergraduate (seniors) seeking initial licensure in deaf ed<\/td>\n<\/tr>\n
    Fall 2018<\/td>PK-3<\/td>20<\/td>19 master\u2019s candidates seeking initial licensure for PK-3
    \n 1 undergraduate (senior) seeking initial licensure for K-5<\/td>\n<\/tr>\n
    Spring 2019<\/td>K-5<\/td>21<\/td>8 master\u2019s candidates seeking initial licensure for K-5 (urban)
    \n 9 master\u2019s candidates seeking initial licensure for K-5
    \n 4 master\u2019s candidates seeking initial licensure for special ed<\/td>\n<\/tr>\n
    Fall 2019<\/td>K-5<\/td>22<\/td>11 master\u2019s candidates seeking initial licensure for K-5
    \n 9 master\u2019s candidates seeking initial licensure for special ed
    \n 2 undergraduate (seniors) seeking initial licensure in deaf ed<\/td>\n<\/tr>\n
    Fall 2019<\/td>PK-3<\/td>24<\/td>24 master\u2019s candidates seeking initial licensure for PK-3<\/td>\n<\/tr>\n
    TOTAL<\/td>\u00a0<\/td>103<\/td>37 seeking initial licensure for K-5
    \n (28 master\u2019s candidates; 1 undergraduate; 8 master\u2019s \u2013 urban)
    \n 43 master\u2019s candidates seeking initial licensure for PK-3
    \n 19 master\u2019s candidates seeking initial licensure for special ed
    \n 4 undergraduate (seniors) seeking initial licensure in deaf ed<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n

    We did not explicitly ask PTs to self-identify race and gender; therefore, these demographics are not reported in Table 1. Based on informal conversations with students across the courses, demographics seemed typical of teacher education programs nationally (i.e., mostly young white women from middle class backgrounds).<\/p>\n\n\n\n

    Harper was the instructor for all sections of the course, and Stumbo served as a teaching assistant for all sections in spring and fall 2019. The methods course is designed for master\u2019s candidates seeking initial licensure while simultaneously completing a yearlong teaching internship; however, some undergraduate students take the course before their internship based on senior privilege. The course is a requirement for PTs across multiple licensure programs, including preK-3 licensure, K-5 licensure, K-5 licensure with a focus on urban, multicultural education, special education, and deaf education.<\/p>\n\n\n\n

    In preparation for facilitating activities at the family STEM nights, all PTs completed various activities and readings to learn about leveraging cultural and community funds of knowledge, making transdisciplinary connections, and using digital technology in mathematics teaching as part of the methods course (for more details about course readings, class and homework activities, etc., across various sections and semesters, see Harper, 2020).<\/p>\n\n\n\n

    For example, in fall 2018, several groups of PTs expressed interest in using available robotics but ultimately decided to use nondigital resources (e.g., snap cubes and geometric shape building sets) because they lacked experience using robotics. Consequently, beginning in spring 2019, we included in the methods course one 3-hour class session dedicated to using technology, transdisciplinary connections, and home- and community-based experiences in mathematics education.<\/p>\n\n\n\n

    Building on required course readings (e.g., Carpenter et al., 2017; Daml, 2017), this lesson introduced general principles for teaching mathematics with technology and making transdisciplinary and home-school connections. PTs engaged with three robotics tools and one nondigital STEM tool to identify ways of supporting mathematics and transdisciplinary learning using available resources and to identify possible home-school experiences to enrich this learning.<\/p>\n\n\n\n

    The nondigital STEM tool focused on magnetism (STEM Magnets Set by Learning Resources; https:\/\/www.learningresources.com\/stem-magnets-activity-set<\/a>). One robotics tool involved programming a pathway on a tablet using block coding (Dash by Wonder Workshop; https:\/\/www.makewonder.com\/robots\/dash\/<\/a>). Another robotics tool involved programming a pathway using directional arrows on the robot itself (Code and Go Robot Mouse by Learning Resources; https:\/\/www.learningresources.com\/code-gor-robot-mouse-activity-set<\/a>). Another involved connecting circuits to build a robot that could create artwork with one or two markers (Smart Art Circuit Cubes by Tenka; https:\/\/circuitcubes.com\/collections\/kits\/products\/circuit-cubes-smart-art-kit-lite<\/a>).<\/p>\n\n\n\n

    The family STEM night project served as the major course project and was designed to integrate various ideas from across course activities and readings (not only the 3-hour lesson described previously). The project design was adapted from the Community Exploration Module developed by the TEACH Math project (Turner et al., 2015). The project was divided into four stages in fall 2018 and spring 2019 and five stages in fall 2019. PTs completed the project in small groups of two to four. For more details about the major project, including detailed assignment descriptions and rubrics, see Harper (2020). Stages were as follows:<\/p>\n\n\n\n

    1. Community Walk. PTs visited the community surrounding the school where the family STEM night was held to identify community-based experiences and mathematics and STEM practices they could leverage in their activity design. They reflected on what they learned about mathematics in the community and proposed an idea for the family STEM night activity. This stage supported PTs to (a) describe key mathematics concepts; (b) use tools, technology, and other resources effectively to support mathematics learning; (c) leverage community-based experiences to support mathematics learning; and (d) view all people as mathematically capable.<\/p>\n\n\n\n

    2. Lesson plan. PTs developed a lesson plan for their family STEM night activity and received feedback from the instructor or teaching assistants. Revisions were made as needed. This stage was designed to address the four goals from Stage and 1 was also to support PTs to anticipate children\u2019s strategies and mathematical thinking and view students as capable of solving sophisticated, yet accessible, mathematics problems.<\/p>\n\n\n\n

    3. Lesson implementation. PTs implemented their lesson at a family STEM night.<\/p>\n\n\n\n

    4. Reflection. PTs answered eight reflection questions to demonstrate their ability to recognize children\u2019s mathematical engagement and to describe what they learned about mathematics teaching and from the lesson implementation. This activity focused on the Stage 1 and 2 goals and encouraged PTs to relate children\u2019s strategies to the mathematics concepts students are learning.<\/p>\n\n\n\n

    5. Revision and publication. Beginning in fall 2019, PTs revised their lesson plan based on their experience with implementation and their reflection. They provided a rationale for their revisions and published their final lessons to share with other teachers. This activity was added to encourage PTs to analyze and learn from their own teaching and contribute to a network of teachers who seek to improve their classroom practice.<\/p>\n\n\n\n

    Data Sources and Analysis<\/h3>\n\n\n\n

    Data sources included reflections on the community walk and initial ideas for STEM lessons (one per group of PTs; Project Stage 1), initial and final lesson plans with instructor feedback (one per group of PTs; Project Stages 1 and 5), and written reflections following the implementation of the STEM lesson (one per PT; Project Stage 4). Analysis proceeded through various rounds, which were guided by a qualitative approach that involves iterative rounds of analysis to describe, condense, and display the data in ways that allow for researchers to identify themes (Miles et al., 2014) in relation to the research question.<\/p>\n\n\n\n

    Round 1<\/em><\/h3>\n\n\n\n

    The first round of analysis sought to condense the data set by limiting it to those data relevant to the research questions (i.e., only those lessons that used robotics in mathematics instruction). Harper examined each lesson plan from all five sections of the course to identify whether planned activities incorporated robotics or other digital technologies. Only those groups who incorporated robotics were selected for the second round of analysis. Accordingly, only data from two groups in spring 2019 and two groups from fall 2019 were included in subsequent analyses.<\/p>\n\n\n\n

    Ten PTs participated as members of these four groups; all 10 PTs were master\u2019s degree candidates completing their yearlong internship. In spring 2019, both groups \u2013 a group of four special education PTs (Adam, Claire, Peyton, and Whitney; all names are pseudonyms) and a pair of K-5 urban education PTs (Hollie and Idil) \u2013 implemented their lessons at Dozier Elementary (an urban Title I, preK-5 school; 42% Black, 17% Latinx student population). In fall 2019, a pair of K-5 PTs (Brittany and Lily) implemented their lesson at Mountainside Elementary (a rural Title I, K-5 school; 90% white student population). The other pair in fall 2019 (Dallas and Hope) implemented their lesson at Moses Smith Preschool (an urban Title I, public preschool; 90% Black student population).<\/p>\n\n\n\n

    Round 2<\/em><\/h3>\n\n\n\n

    The goal of the next round of analysis was to develop a codebook to describe the contents of the data set relevant to the research questions. Harper began this process by analyzing written reflections by PTs in selected groups from spring and fall 2019. Using NVivo, analysis began with three broad themes: (a) mathematics, (b) technology, and (c) funds of knowledge. Through iterative cycles of open coding, subthemes were identified and data were coded at the sentence level. Additional themes were added until codes were exhaustive. Initial analysis focused on individual responses to three of eight reflection questions.<\/p>\n\n\n\n

    1. How did you see children and families engaging in mathematics during your task?<\/li>
    2. How did you see children and families connect your mathematics task to or align it with family or community knowledge or practices?<\/li>
    3. How did you see children and families connect your mathematics task to other content areas (e.g., STEAM or literacy)?<\/li><\/ol>\n\n\n\n

      These three questions were selected for codebook development because they elicited PTs\u2019 ability to recognize and describe children\u2019s engagement with mathematics, technology, and funds of knowledge, whereas other reflection questions asked about mathematics teaching and learning more broadly.<\/p>\n\n\n\n

      The appendix<\/a> provides definitions for all themes and subthemes, with illustrative examples for each subtheme. Subthemes for mathematics focused on identifying the specific mathematics topics engaged during the STEM night (e.g., counting, distance, or multiplication).<\/p>\n\n\n\n

      Subthemes for funds of knowledge identified sources of home or community connections (e.g., familiar locations, family, or parental involvement). Subthemes for technology noted the specific robotics and supporting digital technologies used or how the tools were used (e.g., Code and Go Robot Mouse or Dash Robot).<\/p>\n\n\n\n

      One additional theme emerged, Access, which denoted PTs\u2019 descriptions of how mathematics was accessible for or inclusive of every student. Subthemes in this category identified specific features of an activity that broadened access to mathematics (e.g., multiple entry points or student input). Stumbo and Kim reviewed the initial coded excerpts using the codebook to confirm that themes and subthemes were exhaustive for responses to the three reflection questions and helped refine definitions in the final version of the codebook. <\/p>\n\n\n\n

      Round 3<\/em><\/h3>\n\n\n\n

      Harper used the established codebook (appendix<\/a>) to analyze remaining data. Namely, the codebook was used to analyze data from the community walk (Project Stage 1), group lesson plans (Project Stages 2 and 5), and individual written responses to the remaining five reflection questions (Project Stage 4):<\/p>\n\n\n\n