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1. Harnessing Asynchronous Digital Simulations of Problem-based Lessons to Support Mathematics Teachers’ Professional Development: A Design-based Approach

   https://doi.org/10.1007/s10763-024-10514-x  

   Schwarts, Gil; Herbst, Patricio; Brown, Amanda M (October 2024, International Journal of Science and Mathematics Education)

   Abstract The complexity of mathematics teaching is especially evident in lessons where teachers build on students’ genuine ideas, such as problem-based lessons. To enhance teachers’ capacity for rich discussions in problem-based instruction, we have developed a unique approximation of practice: digital asynchronous simulations where teachers make subject-specific decisions for a virtual teacher avatar. The simulations are based on materials and principles from a practice-based professional development (PD) program, implemented with small groups of teachers. The self-paced simulation model offers flexibility and scalability, allowing more teachers to participate on their own schedules, but it lacks key affordances of collaborative PD. To examine how to leverage the affordances of collaborative, practice-based PD, this paper uses a design-based research approach to explicate the mechanisms in which digital simulations can support mathematics teachers’ learning about problem-based lessons. We focus on two cycles of design, implementation, analysis, and revisions of the simulation model, drawing on data from focus groups with mathematics teacher educators, prospective teachers’ performance, and teachers’ reflective assignments. The analysis illustrates how two design principles –Authenticity to the teacher’s work, andNuanced feedback– were transformed to better reflect aspects of practice-based teacher learning. We argue that self-paced, asynchronous simulations with indirect feedback can effectively emulate aspects of collaborative, practice-based PD in supporting teachers’ growth. The paper also contributes to the literature on mathematics teachers’ noticing and decision-making, examining how the two interact in simulated environments. We suggest implications for designing practice-based asynchronous digital simulations, drawing on emerging technologies. 

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2. Design principles for the development of professional noticing of students’ technological mathematical practices.

   McCulloch, A. W.; Lovett, J. N.; Cayton, C.; Dick, L. K.; Lee, H. (October 2018, Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   In support of standards for the learning and teaching of mathematics and statistics that advocate for the use of technology to promote reasoning and sense making, and to elicit student thinking, we draw on the use of authentic student work in the form of video case instruction to develop prospective secondary mathematics teachers’ [PSMTs] knowledge of students’ understanding, thinking, and learning with technology in mathematics. Specifically, we draw on the extant literature related to TPACK, video cases as learning objects, and noticing to propose a set of design principles intended to guide the development of materials to support PSMTs’ acquisition of TPACK. Here we explicate six design principles situated in the literature, provide an example of a module designed based on these principles, and share findings from pilot studies utilizing the module. 

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3. Problem posing and creativity in elementary-school mathematics

   Goldenberg, E.Paul (January 2019, Constructivist Foundations)

   > Context • In 1972, Papert emphasized that “[t]he important difference between the work of a child in an elementary mathematics class and […]a mathematician” is “not in the subject matter […]but in the fact that the mathematician is creatively engaged […]” Along with creative, Papert kept saying children should be engaged in projects rather than problems. A project is not just a large problem, but involves sustained, active engagement, like children’s play. For Papert, in 1972, computer programming suggested a flexible construction medium, ideal for a research-lab/playground tuned to mathematics for children. In 1964, without computers, Sawyer also articulated research-playgrounds for children, rooted in conventional content, in which children would learn to act and think like mathematicians. > Problem • This target article addresses the issue of designing a formal curriculum that helps children develop the mathematical habits of mind of creative tinkering, puzzling through, and perseverance. I connect the two mathematicians/educators – Papert and Sawyer – tackling three questions: How do genuine puzzles differ from school problems? What is useful about children creating puzzles? How might puzzles, problem-posing and programming-centric playgrounds enhance mathematical learning? > Method • This analysis is based on forty years of curriculum analysis, comparison and construction, and on research with children. > Results • In physical playgrounds most children choose challenge. Papert’s ideas tapped that try-something-new and puzzle-it-out-for-yourself spirit, the drive for challenge. Children can learn a lot in such an environment, but what (and how much) they learn is left to chance. Formal educational systems set standards and structures to ensure some common learning and some equity across students. For a curriculum to tap curiosity and the drive for challenge, it needs both the playful looseness that invites exploration and the structure that organizes content. > Implications • My aim is to provide support for mathematics teachers and curriculum designers to design or teach in accord with their constructivist thinking. > Constructivist content • This article enriches Papert’s constructionism with curricular ideas from Sawyer and from the work that I and my colleagues have done 

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4. Adding Family Math to the Equation: Promoting Head Start preschoolers’ mathematics learning at home and school

   https://doi.org/10.1016/j.ecresq.2022.11.002  

   Young, J. M. (January 2023, Early childhood research quarterly)

   Differences in children’s mathematics knowledge are evident at kindergarten entry, favoring children who have greater access to economic resources. Fostering preschoolers’ mathematics learning at home and in classroom settings, through games and other developmentally appropriate activities, is of great interest to educators, early childhood leaders, and policymakers. This cluster randomized trial examined the ef- fects of a naturalistic, game-based mathematics intervention implemented in Head Start classrooms and examined whether including a family math component added value. A total of 573 children (64% His- panic; 60% multilingual) were included from 66 classrooms which were randomly assigned to Classroom Math (CM), Classroom Math + Family Math (CM+FM), or business-as-usual (BAU). Results indicated that the family math component did add value to the classroom-based intervention as CM+FM resulted in a significant positive impact on children’s mathematics knowledge relative to BAU, but CM alone did not. For preschoolers age 50+ months, both interventions had significant effects on children’s mathemat- ics knowledge relative to BAU, but CM+FM had a stronger effect (d = .36). The number of math games played was significantly associated with higher mathematics scores and the number of family math mini- books returned had a significant impact on children’s spring scores, over and above the number of games played. The CM+FM intervention also had a significant effect on teachers’ instructional practice (d =.79). Adding a family math component to a game-based classroom intervention resulted in positive impacts for preschoolers and seems to be an effective, ecologically valid intervention that fosters early mathematical competencies. 

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5. Co-Constructing and Sharing STEAM Knowledge through a Culturally Relevant Literacy-Based Early Childhood School-University Partnership

   Caudle, Lori; Harper, Frances K.; Quinn, Margaret; Greene, Darelene (January 2021, Proceedings of the 2nd International Conference of the Journal Scuola Democratica)

   null (Ed.)

   Through school-university partnerships that situate learning within culturally relevant educational experiences, faculty, preservice teachers, and school-based educators are able to co-construct and share scientific knowledge. This knowledge consists of pedagogical content knowledge and funds of knowledge that include both knowledge and skills developed in cultural context that have evolved historically. In early childhood education, culturally relevant Science, Technology, Engineering, Arts, and Mathematics (STEAM) learning experiences are particularly important for young children's cognitive and social emotional development. This paper describes how intentional co-planning and collaboration to celebrate the US Read across America Day provided over 100 preschool children in eight classrooms with access to STEAM lessons virtually led by university preservice teachers in partnership with educators in the school. These activities engaged children in exploring art, computer science, physical science, engineering, and mathematics within the context of a culturally relevant version of the fairy tale Goldilocks and the Three Bears. Lessons implemented as part of school-university partnerships support Black and Latinx children's development of a sense of belonging in STEAM. Further, these experiences enhance teacher candidates' abilities to engage in culturally responsive STEAM teaching while receiving ongoing guidance and education from university faculty and school-based educators. Teacher education programs within higher education institutions should embrace school- university partnerships as contexts for the development of shared scientific knowledge and discourse since the benefits are twofold. First, children and teachers gain access to, and engage with, innovative STEAM experiences. Second, preservice teachers learn culturally relevant research-based instructional strategies through university coursework situated in authentic learning experiences; thus, their learning as teacher candidates is enhanced through planning, implementation, evaluation, and critical reflection. 

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