scholarly journals Computational Thinking Concepts for Grade School

2016 ◽  
Vol 9 (1) ◽  
pp. 23-32 ◽  
Author(s):  
John F. Sanford ◽  
Jaideep T. Naidu
Keyword(s):  
Recent Literature ◽  
Early Education ◽  
Computational Thinking ◽  
Grade School ◽  
Mathematical Concepts ◽  
Core Ability ◽  
Core Areas ◽  
And Mathematics

Early education has classically introduced reading, writing, and mathematics. Recent literature discusses the importance of adding “computational thinking” as a core ability that every child must learn. The goal is to develop students by making them equally comfortable with computational thinking as they are with other core areas of early education. Computational thinking does not come naturally and requires training and guidance. This paper argues for the inclusion of computational thinking in tandem with mathematics. As an example, the paper demonstrates spreadsheet applications that can be utilized concurrently with early mathematical concepts. It demonstrates that at this time, spreadsheets are the best medium for inculcating computational thinking but recognizes that advances in technology may favor other digital approaches in time.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

scholarly journals You can count on your fingers: The role of fingers in early mathematical development

2018 ◽  
Vol 4 (1) ◽  
pp. 107-135 ◽  
Author(s):  
Firat Soylu ◽  
Frank K. Lester ◽  
Sharlene D. Newman
Keyword(s):  
Mathematics Education ◽  
Human Cognition ◽  
Diagnostic Tools ◽  
Mathematical Concepts ◽  
Simple Arithmetic ◽  
Road Map ◽  
Mathematics Ability ◽  
Finger Counting ◽  
Bodily Activity ◽  
And Mathematics

Even though mathematics is considered one of the most abstract domains of human cognition, recent work on embodiment of mathematics has shown that we make sense of mathematical concepts by using insights and skills acquired through bodily activity. Fingers play a significant role in many of these bodily interactions. Finger-based interactions provide the preliminary access to foundational mathematical constructs, such as one-to-one correspondence and whole-part relations in early development. In addition, children across cultures use their fingers to count and do simple arithmetic. There is also some evidence for an association between children’s ability to individuate fingers (finger gnosis) and mathematics ability. Paralleling these behavioral findings, there is accumulating evidence for overlapping neural correlates and functional associations between fingers and number processing. In this paper, we synthesize mathematics education and neurocognitive research on the relevance of fingers for early mathematics development. We delve into issues such as how the early multimodal (tactile, motor, visuospatial) experiences with fingers might be the gateway for later numerical skills, how finger gnosis, finger counting habits, and numerical abilities are associated at the behavioral and neural levels, and implications for mathematics education. We argue that, taken together, the two bodies of research can better inform how different finger skills support the development of numerical competencies, and we provide a road map for future interdisciplinary research that can yield to development of diagnostic tools and interventions for preschool and primary grade classrooms.

scholarly journals CULTURAL HISTORICAL ANALYSIS OF IRANIAN SCHOOL MATHEMATICS CURRICULUM: THE ROLE OF COMPUTATIONAL THINKING

2021 ◽  
Vol 12 (3) ◽  
pp. 411-426
Author(s):  
Abolfazl Rafiepour ◽  
Danyal Farsani
Keyword(s):  
Curriculum Reform ◽  
Curriculum Design ◽  
Mathematics Curriculum ◽  
Historical Analysis ◽  
Computational Thinking ◽  
School Mathematics ◽  
Curriculum Changes ◽  
International Comparative ◽  
And Mathematics ◽  
School Mathematics Curriculum

In this paper, six mathematics curriculum changes in Iran will be reviewed, spanning from 1900 until the present time. At first, change forces, barriers, and the main features of each curriculum reform will be represented. The first five curriculum changes are described briefly and the sixth and most recent curriculum reform will be elaborated. In this paper, we call the last reform as contemporary school mathematics curriculum change. This recent (contemporary) curriculum reform will be explained in more detail, followed by a discussion of the effect of globalization and research finding in the field of mathematics and mathematics education (in the Iranian mathematics curriculum). In total, three key ideas are distinguished as an effect of globalization which is “New Math”, “International Comparative Studies”, and “Computational Thinking”. Finally, the paper comments on the necessity of paying more attention to information and communication technology as part of globalization; in particular, recall policy-makers to consider “Computational Thinking” as an important component of future curriculum design.

Computational Thinking and Participatory Teaching as Pathways to Personalized Learning

2018 ◽  
pp. 212-228 ◽  
Author(s):  
Eric Hamilton ◽  
Aileen M. Owens
Keyword(s):  
Learning Strategy ◽  
Computational Thinking ◽  
Personalized Learning ◽  
Collaborative Problem Solving ◽  
Video Production ◽  
Historical Trends ◽  
International Group ◽  
Collaborative Problem ◽  
And Mathematics

This chapter discusses personalized learning by briefly outlining historical trends and deficiencies associated with what can be referred to as production style or assembly line approaches to education before contrasting personalized learning definitions. The chapter extends those definitions. It discusses participatory teaching as a personalized learning strategy by which students take on roles of co-teaching, co-designing lessons, or co-designing curriculum with adult teachers. One participatory teaching example involves an international group of students who help one another learn science and mathematics through shared video production. This example involves a US school involved in a larger districtwide effort comprehensively designed to involve each student. Organized around computational thinking, multidisciplinary innovation, arts integration, and collaborative problem-solving, the district may be viewed as a case study in implementing personalized learning. The chapter furnishes several examples that blend participatory teaching and computational thinking.

Integrating Computational Thinking and Mathematics

2022 ◽  
pp. 175-196
Author(s):  
Marja Bertrand ◽  
Immaculate Kizito Namukasa
Keyword(s):  
Education Reform ◽  
Creative Thinking ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Non Profit ◽  
The Arts ◽  
Learning Mathematics ◽  
Steam Education ◽  
Context Of Learning ◽  
And Mathematics

Globally, computational thinking and coding in schools has become more popular as well as a growing area of interest in education reform. Coupling coding with creative thinking promises to meaningfully engage students in their learning and to improve their coding and computational thinking skills. This prompts discussions about STEAM (Science, Technology, Engineering, Arts, and Mathematics), which promotes creativity and innovation through the integration of the arts in STEM subjects. This study addresses the following question: What mathematics and computational thinking do students learn through different models of STEAM education in non-profit and in-school contexts? A small sample was taken of four different STEAM programs in Ontario, Canada. We carried out a qualitative case study with 103 participants, 19 adults and 84 students. The findings from this study have implications for designing, implementing and researching K-8 STEAM programs that promote coding and computational thinking skills in the context of learning mathematics.

Building a Design-Centered STEAM Course

2021 ◽  
pp. 416-427
Author(s):  
Antonios Karampelas
Keyword(s):  
Computer Aided Design ◽  
Industrial Revolution ◽  
Design Thinking ◽  
Computational Thinking ◽  
Community Schools ◽  
Learning Goals ◽  
Architectural Engineering ◽  
Online Setting ◽  
And Mathematics ◽  
Aided Design

This chapter presents the blended-learning, project-based high school STEAM (science, technology, engineering, art, and mathematics) course that has been developed and delivered at the American Community Schools (ACS) Athens. The STEAM course fosters data literacy; critical, creative, and computational thinking; and problem-solving. The topics range from the internet of things, artificial intelligence, and data-based investigations to an introduction to aerospace, electrical, and architectural engineering, in the context of the Fourth Industrial Revolution. Computer-aided design software and the design thinking methodology are the major creative tools students use to experience immersive STEAM learning. The content of the course is described in terms of learning goals, instruction, and assessments, accompanied by instructional material. The transition of the STEAM course to an online setting is also discussed, and the author's reflections are shared.

Computational Expression

2021 ◽  
pp. 134-156
Author(s):  
Amanda L. Strawhacker ◽  
Amanda A. Sullivan
Keyword(s):  
Stem Education ◽  
Visual Arts ◽  
21St Century ◽  
Fine Arts ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Pedagogical Approach ◽  
The Past ◽  
Science Technology ◽  
And Mathematics

In the past two decades, STEM education has been slowly replaced by “STEAM,” which refers to learning that integrates science, technology, engineering, arts, and mathematics. The added “Arts” portion of this pedagogical approach, although an important step towards integrated 21st century learning, has long confused policymakers, with definitions ranging from visual arts to humanities to art education and more. The authors take the position that Arts can be broadly interpreted to mean any approach that brings interpretive and expressive perspectives to STEM activities. In this chapter, they present illustrative cases inspired by work in real learning settings that showcase how STEAM concepts and computational thinking skills can support children's engagement in cultural, performing, and fine arts, including painting, sculpture, architecture, poetry, music, dance, and drama.

Computational Thinking and Mathematics

2016 ◽  
pp. 853-865
Author(s):  
Thiago Schumacher Barcelos ◽  
Ismar Frango Silveira
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Basic Education ◽  
National Curriculum ◽  
Computational Thinking ◽  
Thinking Skills ◽  
Educational Systems ◽  
Curriculum Guidelines ◽  
And Mathematics ◽  
The One

On the one hand, ensuring that students archive adequate levels of Mathematical knowledge by the time they finish basic education is a challenge for the educational systems in several countries. On the other hand, the pervasiveness of computer-based devices in everyday situations poses a fundamental question about Computer Science being part of those known as basic sciences. The development of Computer Science (CS) is historically related to Mathematics; however, CS is said to have singular reasoning mechanics for problem solving, whose applications go beyond the frontiers of Computing itself. These problem-solving skills have been defined as Computational Thinking skills. In this chapter, the possible relationships between Math and Computational Thinking skills are discussed in the perspective of national curriculum guidelines for Mathematics of Brazil, Chile, and United States. Three skills that can be jointly developed by both areas are identified in a literature review. Some challenges and implications for educational research and practice are also discussed.

Semantic Realism

1998 ◽  
pp. 6-12 ◽  
Author(s):  
Elaine Landry
Keyword(s):  
Category Theory ◽  
Linguistic Analysis ◽  
Philosophical Study ◽  
Physical Sciences ◽  
Mathematical Concepts ◽  
Ontological Realism ◽  
Semantic Realism ◽  
And Mathematics

I argue that if we distinguish between ontological realism and semantic realism, then we no longer have to choose between platonism and formalism. If we take category theory as the language of mathematics, then a linguistic analysis of the content and structure of what we say in and about mathematical theories allows us to justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study. Insofar as this analysis relies on a distinction between ontological and semantic realism, it relies also on an implicit distinction between mathematics as a descriptive science and mathematics as a descriptive discourse. It is this latter distinction which gives rise to the tension between the mathematician qua philosopher. In conclusion, I argue that the tensions between formalism and platonism, indeed between mathematician and philosopher, arise because of an assumption that there is an analogy between mathematical talk and talk in the physical sciences.

A Framework for Computational Thinking Dispositions in Mathematics Education

2018 ◽  
Vol 49 (4) ◽  
pp. 424-461 ◽  
Author(s):  
Arnulfo Pérez
Keyword(s):  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Relevant Literature ◽  
Computational Thinking ◽  
Secondary Mathematics ◽  
Mathematical Concepts ◽  
Thinking Dispositions ◽  
Secondary Mathematics Teachers ◽  
Tolerance For Ambiguity ◽  
Epistemic Frame

This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions—tolerance for ambiguity, persistence, and collaboration—and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices useful in computer science, helps students understand mathematical concepts as outward oriented. The article conceptualizes the characteristics of CT dispositions through a review of relevant literature and examples from a study that explored secondary mathematics teachers' engagement with CT. Discussion of the CT framework highlights the complementary relationship between CT and mathematical thinking, the relevance of mathematics to 21st-century professions, and the merit of CT to support learners in experiencing these connections.

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