Jessica F. Shumway

Este artigo discute a centralidade da reflexão docente no planejamento da Atividade de Ensino de Matemática Esse processo é mediado por professores que, coletivamente, elaboram tarefas de estudo, utilizando a robótica educacional como instrumento cultural na interação professor-estudante. À luz da Teoria Histórico-Cultural, argumenta-se que a formação docente requer uma compreensão de como a prática pedagógica se constitui por processos sociais e mediados. Exploramos a Teoria da Atividade, de Leontiev, destacando a ação humana como um sistema hierárquico impulsionado por motivos e objetivos, e como suas contradições estimulam a reflexão. A Atividade de Ensino na perspectiva de Davydov é apresentada, destacando o papel fundamental do professor na elaboração de tarefas de estudo que visam o desenvolvimento do pensamento teórico matemático. A reflexão docente é analisada como função psicológica superior, ligada à interação social e mediação por instrumentos. Um episódio de planejamento entre professoras ilustra como o desencontro entre a programação esperada e a ação do robô Botley, mediada pelo diálogo, impulsionou a organização das ações e aprofundou a compreensão sobre o uso da robótica educacional no processo de ensino-aprendizagem da Matemática. Conclui-se que a reflexão é o cerne de uma formação docente que visa promover o desenvolvimento integral e o pensamento teórico matemático dos estudantes.

This paper explores the design of computational toys and kits for young children (ages 4-7) as tools for learning integrated mathematical, spatial, and computational thinking concepts. Specifically, we examine how the design features of the toys and kits represent the concepts of rotation on a point and spatial orientation of the agent. We examine toys and kits sold commercially, developed through research, and used in early childhood classrooms. Our findings indicate that the mathematical and spatial concepts are overlooked in some designs. Prior research examined toys for their affordances related to computational thinking, the present study contributes to understanding of how these toys and kits have the potential to foster foundational mathematics and spatial skills. We discuss implications for design of toys and kits as well as recommendations for future research.

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students’ long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact interdisciplinary mathematics and computer science (CS) tasks with a team of elementary school educators and school district personnel. The unit focuses on the concepts of exponents in mathematics and repeat loops as a control structure in computer science. Using a narrative approach, we describe what occurred during the collaborative planning of lessons and subsequent enactments in two fifth-grade classrooms and one computer lab and provide a practitioner‑oriented account of our experience.

Fifth-grader Noelle had an aha moment during a class discussion about Ways to Make Two-Tenths (see Figure 6.1). She mistakenly thought that 2 divided by 10 was 5, but came to understand that the solution 5 did not make sense. I asked Noelle, “How were you convinced that 2 divided by 10 is https://www.w3.org/1998/Math/MathML"> 2 10 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781032681924/37ad5977-a09c-412b-bb65-209b0375487d/content/inline210_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ?” She replied, It was just Austin explaining that 2 is smaller than 5 so that answer does not make sense. If you did 2 divided by 10 and you thought it was 5 then that wouldn’t work because 2 is smaller than 5. For 2 divided by 10, the pieces are going to be really small, they are not going to be 5. https://www.w3.org/1998/Math/MathML"> 2 10 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781032681924/37ad5977-a09c-412b-bb65-209b0375487d/content/inline210_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> makes more sense. Those are small pieces. When we talk about it, we learn more, and we figure it out. We sometimes need to argue about it to make it make sense.

Following up her' best-selling book, Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, Jessica Shumway turns her focus to upper elementary classrooms. Number Sense Routines: Developing Mathematical Understanding Every Day in Grades 3-5 is about tapping into every child' s innate number sense and providing daily, connected experiences that are responsive to children's learning needs. Consistent, Daily Routines Work:' Adaptable to any curriculum, Shumway' s 5, 10, or 15 minute warm-up routines are an easy and effective way to build and solidify students' number sense foundations as a supplement to any program Planning and Facilitating Your Classroom:' No matter how familiar the routine, Shumway provides insight on how to keep daily warm-ups fresh. She reveals careful thinking and planning that goes into each routine and offers detailed vignettes and dialogues of how they unfold in real classrooms Assessment Strategies:' As students engage in the process, each routine becomes an exciting opportunity to gain insight into where they are in their understanding and help students articulate their mathematical thinking Identify Big Ideas: Not only will these math routines help develop students' mathematical understanding as they move towards using standard algorithms, but teachers will learn to better recognize the big ideas that emerge in discussions, how to encourage important strategies based in number sense, and how to facilitate conversations on key mathematical concepts. ' 'These routines may appear in other places, [but] I have never seen them written in such detail and with so many variations.. . .. Although she makes what she does sound easy, we all know that teaching math well is anything but easy. It is challenging and complex. Unpacking what students are saying, helping them make connections not only to the math but to each other's ideas, while simultaneously recording their ideas using mathematical models, visuals, or equations is no easy task. Jessica provides wonderful visuals, examples of student work, and so much more to help educators develop the tools they need to improve their practice and in so doing improve student learning. ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' – From the Foreword by math coach and consultant Lucy West

Solve this problem: 0.38 + 0.02 =

What’s the best way to build number sense in upper elementary grades, especially for students who struggle with math? Some have memorized procedures and some are still using primary strategies to solve problems. In both cases, I’m not really sure they are making sense of the mathematics.

In September, some fourth graders and I engaged in word problems at the kidneyshaped table while the rest of the class worked in small group math stations. I posed the following problem as an informal preassessment: On our field trip to the Great Salt Lake, we collected brine shrimp. There are 9 brine shrimp in each test tube. If there are 12 test tubes, how many brine shrimp were collected from the Great Salt Lake?

Fourth-grade teacher Jeff James was planning his next unit on multiplication. The Houghton Mifflin Harcourt GO Math! textbook lessons coming up in this unit focused on using area models and partial products to multiply two-digit numbers (e.g., see Figure 7.1).