Connecting Number Theory with High School Mathematics

Number theory is the study of natural numbers and one of the oldest branches of mathematics. Elementary number theory concepts are integrated into K-12 learning experience. This paper will identify ideas and methods in elementary number theory that could be connected to K-12 education and taught in high school classrooms. In fact, Common Core Standards in Mathematics include some basic concepts and skills in elementary number theory. In this study, we will focus on the greatest common divisor, Euclid\u27s algorithm, least common multiple, factorization and divisibility criteria (divisible by 2, 3, 4, 5, 6, 8, 9, and 11). We hope that learning these contents could foster students’ interests in mathematics and help them develop computational and reasoning skills

Exploring Approaches to Engage K-12 Students in Learning Computational Thinking Using Collaborative Robots

Minority students are largely underrepresented in the STEM field. The goal for this project was to develop a program which promotes the inclusion of computation skills among students and help them work collaboratively with the use of human – robot interaction. Robots are such a strong tool that can be used to enhance computational thinking and engage students towards a technical field. Through workshops and readings about computational thinking we worked on building a block-based program that introduces the uses of robots as teaching tool for computational thinking

Tinkering with Logo in an Elementary Mathematics Methods Course

With an increased push to integrate coding and computational literacy in K–12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to teach in K–5. Experiences programming in Logo to construct authentic artifacts in the form of two-dimensional geometric graphics not only supported PSTs’ understanding of core geometric and spatial concepts, but also helped them to make connections between mathematics and computational literacy. Artifacts and discourse are discussed as they relate to three core considerations: engaging learners to construct authentic artifacts, supporting a communitarian ethos, and supporting various types of rapid feedback

A Literature Review of Quantum Education in K-12 Level

Quantum computing is an emerging technology paradigm of computing and has the potential to solve computational problems intractable using today’s classical computers or digital technology. Quantum computing is expected to be disruptive for many industries. The power of quantum computing technologies is based on the fundamentals of quantum mechanics, such as quantum superposition, quantum entanglement, or the no-cloning theorem. To build a highly trained and skilled quantum workforce that meets future industry needs, there is a need to introduce quantum concepts early on in K-12 schools since the learning of quantum is a lengthy process. As fundamental quantum concepts derive from physics, students usually start to learn physics in secondary schools. Since the resources and curriculum design for quantum education in K-12 level is rare, we conducted a literature review with a focus on quantum computing education in K-12 level and filled the research gap

Board # 102 : PECASE: Implementing K-12 Engineering Standards through STEM Integration - An Executive Summary of the Products and Research

This executive summary of the grant, PECASE: Implementing K-12 Engineering Standards through STEM Integration, comes at the conclusion of the project. The purpose of the grant was to develop a definition and explore the practice of engineering in K-12 STEM classrooms. The definition was then used to assess curricula, policy documents, teacher practice, and student learning. Through this work, the definition was then used to help with the framing and development of curricula for K-5 classrooms. The resulting curricula are called the PictureSTEM units. These instructional units for K-5 classrooms utilize engineering design and picture books to teach young students about mathematics, science, engineering, technology, computational thinking, and reading in an integrated manner. Each of the modules in the PictureSTEM curriculum was developed using the curriculum design method described by Clements’ Curriculum Research Framework, which follows three stages: Stage 1: Initial Development, Stage 2: Pilot and Teaching Experiment, and Stage 3: Classroom Implementation. The theoretical framework guiding the development of the PictrueSTEM modules came from the initial work of this grant in developing a definition of engineering for K-12 environments and built upon that work to include the following four foundational components: 1) engineering design as the interdisciplinary glue, 2) realistic engineering contexts to promote student engagement, 3) high-quality literature to facilitate meaningful connections, and 4) instruction of specific STEM content within an integrated approach. The units have an overarching engineering design project that provides the scaffolding for all learning in the unit. The engineering design learning highlights problem scoping and solution generation as an iterative process that requires learning about client needs and relevant background knowledge and applying these to their solution. The context of the units revolves around having a client who has asked for the students’ help with a problem. The contexts have multiple ways the students can get interested in the problem, such as providing a challenge, helping them to making personal connections, or highlighting the realistic nature of the work that engineers do. In recognizing the large emphasis on reading in elementary classrooms, these units build upon the rich literature in STEM and reading integration to support the learning of literacy skills, as well as providing students with background knowledge and real-world contexts through the use of high-quality STEM-focused literature. Each of the units includes science, mathematics, computational thinking, picture books, and an engineering design challenge to integrate STEM+C learning. STEM+C activities throughout the unit help students develop their prototypes or make evidence-based decisions while designing. The focus on engineering and reading allows for a rich environment in which students can explore the interdisciplinary nature of learning engineering, science, mathematics, and computational thinking. This paper and poster presentation will highlight the engineering definition and the curricular units developed through this project, as well as highlights from the research results gleaned from this work

Computational Thinking Education in K–12

A guide to computational thinking education, with a focus on artificial intelligence literacy and the integration of computing and physical objects. Computing has become an essential part of today's primary and secondary school curricula. In recent years, K–12 computer education has shifted from computer science itself to the broader perspective of computational thinking (CT), which is less about technology than a way of thinking and solving problems—“a fundamental skill for everyone, not just computer scientists,” in the words of Jeanette Wing, author of a foundational article on CT. This volume introduces a variety of approaches to CT in K–12 education, offering a wide range of international perspectives that focus on artificial intelligence (AI) literacy and the integration of computing and physical objects. The book first offers an overview of CT and its importance in K–12 education, covering such topics as the rationale for teaching CT; programming as a general problem-solving skill; and the “phenomenon-based learning” approach. It then addresses the educational implications of the explosion in AI research, discussing, among other things, the importance of teaching children to be conscientious designers and consumers of AI. Finally, the book examines the increasing influence of physical devices in CT education, considering the learning opportunities offered by robotics. Contributors Harold Abelson, Cynthia Breazeal, Karen Brennan, Michael E. Caspersen, Christian Dindler, Daniella DiPaola, Nardie Fanchamps, Christina Gardner-McCune, Mark Guzdial, Kai Hakkarainen, Fredrik Heintz, Paul Hennissen, H. Ulrich Hoppe, Ole Sejer Iversen, Siu-Cheung Kong, Wai-Ying Kwok, Sven Manske, Jesús Moreno-León, Blakeley H. Payne, Sini Riikonen, Gregorio Robles, Marcos Román-González, Pirita Seitamaa-Hakkarainen, Ju-Ling Shih, Pasi Silander, Lou Slangen, Rachel Charlotte Smith, Marcus Specht, Florence R. Sullivan, David S. Touretzk

Voicing Code in STEM

An exploration of coding that investigates the interplay between computational abstractions and the fundamentally interpretive nature of human experience. The importance of coding in K–12 classrooms has been taken up by both scholars and educators. Voicing Code in STEM offers a new way to think about coding in the classroom—one that goes beyond device-level engagement to consider the interplay between computational abstractions and the fundamentally interpretive nature of human experience. Building on Mikhail Bakhtin's notions of heterogeneity and heteroglossia, the authors explain how STEM coding can be understood as voicing computational utterances, rather than a technocentric framing of building computational artifacts. Empirical chapters illustrate this theoretical stance by investigating different framings of coding as voicing. Understanding the experiential nature of coding allows us to design better tools and curricula for students, and enables us to see computing as experience beyond the mastery of symbolic power. Arguing for a critical phenomenology of coding, the authors explain that the phenomenological dimension refocuses attention on the fundamentally complex nature of human experiences that are involved in coding and learning to code. The critical dimension involves learning to recognize voices that historically have received less attention