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Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 55404

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Prof. Dr. Jennifer M. Suh

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Mathematics Education Leadership Department, George Mason University, 4400 University Dr., MS1E8, Fairfax, VA 22030, USA
Interests: learning trajectory-based lesson study; mathematical modeling in the early grades; virtual manipulatives technology

Special Issue Information

Dear Colleagues,

This Special Issue calls for researchers to consider “Futuring Mathematics Education” with innovating teaching practices that prepare all students with critical twenty-first-century skills. Our complex world requires one to be a global citizen with creativity, critical thinking, communication, and collaboration skills in the mathematics classroom. According to PISA’s definition (OECD, 2018),

Mathematical literacy is an individual’s capacity to formulate, employ and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to recognize the role that mathematics plays in the world and to make the well-founded judgements and decisions needed by constructive, engaged and reflective citizens (p.4).

If we are serious about promoting mathematical literacy, as described above, to broaden the participation of underrepresented youth, research on equitable teaching practices for mathematics in grades K–12 is critically important. We need to capitalize on students’ funds of knowledge and the curiosities that they bring to school, as well as the knowledge they acquire from their community or local context. The real-world context from which a teacher can draw as students formulate, employ, and interpret mathematics in their immediate community may differ based on their region and culture; yet, capitalizing on this knowledge and leveraging local contexts, such as culture, environment, technology, agriculture, and other local industry, can link familiar ideas to scientific ideas for students. We invite researchers from around the world to share empirical research (e.g., case studies, teaching experiments, and design research) focused on describing the core practices (e.g., problem-based learning, mathematical modeling, collaborative problem solving, integrating technology) that promote equitable teaching in mathematics classrooms, motivating students to engage in complex instruction in mathematics. What can we learn from innovative teaching practices across international settings that advance the “futuring” of the teaching and learning of mathematics?

Prof. Dr. Jennifer M. Suh
Guest Editor

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Keywords

core practices in mathematics education
problem-based learning, mathematical modeling, and collaborative problem solving
equitable teaching and broadening participation
motivation to pursue mathematical endeavors by connecting math to personal and society issues in the real world

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Published Papers (10 papers)

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Research

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27 pages, 2855 KiB

Open AccessArticle

The Influence of the Developed Specific Multi-Paradigm Programming in Digital Logic Education

by Lukas Hapl and Hashim Habiballa

Mathematics 2021, 9(11), 1255; https://doi.org/10.3390/math9111255 - 31 May 2021

Cited by 1 | Viewed by 2729

Abstract

This article introduces the possible usage of the developed programming discourse that can be used to support training in the digital logic area. The discourse merges several programming paradigms into one solution. The intended learners are secondary school students focused on digital system programming. The main intent is to find out whether digital logic curriculum based on Digital Circuits Based Logical Programming (DCBLP) inheritance has positive impact on the students and the way they explore the digital logic itself. Students’ cognitive and affective areas are in the scope of this preliminary research and questionnaires and cognitive tests will help to support the research. Experimental and control groups were used to gather relevant records. To analyse and support the interpretation of the data gathered by questionnaires, the chi-square test (two-tailed) has been used. ANOVA has been used to evaluate data for the achievement test results. The preliminary research revealed there is a possibility of using developed programming discourse DCBLP in digital logic training. Students claim overall usefulness of the discourse in the training; the strong motivation power of the programming discourse itself has not been discovered. From the test we conclude that the performance of the students trained using new programming discourse is significantly better. It is possible to use more different programming paradigms, such as imperative and declarative, in one solution to support training in the area of digital logic. Such solutions can enhance the way the students deal with the programming languages and also supports interdisciplinary relationships. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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15 pages, 6082 KiB

Open AccessArticle

Application of Basic Graph Theory in Autonomous Motion of Robots

by Petr Coufal, Štěpán Hubálovský and Marie Hubálovská

Mathematics 2021, 9(9), 919; https://doi.org/10.3390/math9090919 - 21 Apr 2021

Cited by 8 | Viewed by 3574

Abstract

Discrete mathematics covers the field of graph theory, which solves various problems in graphs using algorithms, such as coloring graphs. Part of graph theory is focused on algorithms that solve the passage through mazes and labyrinths. This paper presents a study conducted as part of a university course focused on graph theory. The course addressed the problem of high student failure in the mazes and labyrinths chapter. Students’ theoretical knowledge and practical skills in solving algorithms in the maze were low. Therefore, the use of educational robots and their involvement in the teaching of subjects in part focused on mazes and labyrinths. This study shows an easy passage through the individual areas of teaching the science, technology, engineering, and mathematics (STEM) concept. In this article, we describe the research survey and focus on the description and examples of teaching in a university course. Part of the work is the introduction of an easy transition from the theoretical solution of algorithms to their practical implementation on a real autonomous robot. The theoretical part of the course introduced the issues of graph theory and basic algorithms for solving the passage through the labyrinth. The contribution of this study is a change in the approach to teaching graph theory and a greater interconnection of individual areas of STEM to achieve better learning outcomes for science students. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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20 pages, 2768 KiB

Open AccessArticle

Mathematical Modeling as a Catalyst for Equitable Mathematics Instruction: Preparing Teachers and Young Learners with 21st Century Skills

by Jennifer Suh, Kathleen Matson, Padmanabhan Seshaiyer, Spencer Jamieson and Holly Tate

Mathematics 2021, 9(2), 162; https://doi.org/10.3390/math9020162 - 14 Jan 2021

Cited by 15 | Viewed by 6015

Abstract

This case study focuses on a team of teachers and students in a Lesson Study, focused on using mathematical modeling (MM) to make significant decisions to design and plan for a sustainable edible garden in their community. We examined (a) how teachers develop students’ capacity to engage in mathematical modeling, while attending to equitable teaching practices; and (b) how teachers’ view of teaching through mathematics modeling changed after unit implementation. We found that teachers were deliberate in employing specific structures, routines, and tools to attend to equitable participation, when eliciting student thinking in the modeling process. We found that teachers’ view of mathematics modeling changed as they recognized how MM allowed for (a) integration of important mathematics concepts while giving students ownership of the mathematics; (b) opportunity to assess both content and 21st century process skills; and (c) positive energy that came from both students and teachers when teaching through the use of mathematical modeling. A promising strategy for preparing our youth for rigorous mathematics and skills to solve ill-structured problems is by integrating mathematical modeling in early elementary grades to develop critical 21st century skills and a productive disposition towards problem posing and problem solving. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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20 pages, 3081 KiB

Open AccessArticle

Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

by Janka Medová, Kristína Ovary Bulková and Soňa Čeretková

Mathematics 2020, 8(12), 2257; https://doi.org/10.3390/math8122257 - 21 Dec 2020

Cited by 9 | Viewed by 4315

Abstract

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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26 pages, 1047 KiB

Open AccessArticle

How Does Pedagogical Flexibility in Curriculum Use Promote Mathematical Flexibility? An Exploratory Case Study

by Kyeong-Hwa Lee, GwiSoo Na, Chang-Geun Song and Hye-Yun Jung

Mathematics 2020, 8(11), 1987; https://doi.org/10.3390/math8111987 - 7 Nov 2020

Cited by 3 | Viewed by 3838

Abstract

Flexibility has been increasingly valued in mathematics education to better prepare students for lives in the rapidly changing society of the future. Although there has been conjecture that teachers’ flexibility plays a substantial role in facilitating students’ mathematical flexibility, there has been little examination of how teachers can use a flexible curriculum to develop mathematical flexibility (MF) in authentic classroom environments. This paper elaborates the notion of flexible curriculum use, referred to as pedagogical flexibility (PF) in curriculum use, as the competence to expand pedagogical space and make alternative pedagogical decisions when planning and enacting a curriculum that differs from the routine practices provided in the intended and written curriculum. We develop a framework for PF in curriculum use to identify and characterize teachers’ curriculum use to promote MF. In an explorative case study with one middle school teacher, we analyzed what and how specific aspects of PF in curriculum use promote potential and actual MF in the learning of central tendency measures. Findings indicate that the teacher could expand his pedagogical space by carefully differentiating the pedagogical considerations of the curriculum and could find alternative approaches by making associative and reflective connections among them. This provides insight into how PF in curriculum use can promote students’ potential and actual MF. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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19 pages, 2377 KiB

Open AccessFeature PaperArticle

Complex Tasks: Potentials and Pitfalls

by Nina Bohlmann and Ralf Benölken

Mathematics 2020, 8(10), 1780; https://doi.org/10.3390/math8101780 - 14 Oct 2020

Cited by 4 | Viewed by 4151

Abstract

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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19 pages, 1951 KiB

Open AccessArticle

A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables

by José Agüero-Rubio, Javier López-Martínez, Marta Gómez-Galán and Ángel-Jesús Callejón-Ferre

Mathematics 2020, 8(9), 1468; https://doi.org/10.3390/math8091468 - 1 Sep 2020

Cited by 1 | Viewed by 2377

Abstract

Students in the electrical branch of the short-cycle tertiary education program acquire developmental and design skills for low voltage transmission power lines. Aerial power line design requires mathematical tools not covered well enough in the curricula. Designing suspension cables requires the use of a Taylor series and integral calculation to obtain the parabola’s arc length. Moreover, it requires iterative procedures, such as the Newton–Raphson method, to solve the third-order equation of the steady-static response. The aim of this work is to solve the steady-static response equation for suspended cables using simple calculation tools. For this purpose, the influence of the horizontal component of the cable tension on its curvature was decoupled from the cable’s self-weight, which was responsible for the tension’s vertical component. To this end, we analyzed the laying and operation of the suspended cables by defining three phases (i.e., stressing, lifting, and operation). The phenomena that occurred in each phase were analyzed, as was their manifestation in the cable model. Herein, we developed and validated the solution of the steady-static response equation in suspended cables using simple equations supported with intuitive graphics. The best results of the proposed calculation procedure were obtained in conditions of large temperature variations. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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18 pages, 1812 KiB

Open AccessArticle

Metacognitive Knowledge and Mathematical Intelligence—Two Significant Factors Influencing School Performance

by Vlastimil Chytrý, Jaroslav Říčan, Petr Eisenmann and Janka Medová

Mathematics 2020, 8(6), 969; https://doi.org/10.3390/math8060969 - 12 Jun 2020

Cited by 12 | Viewed by 7325

Abstract

Metacognitive knowledge and mathematical intelligence were tested in a group of 280 pupils of grade 7 age 12–13 years in the Czech Republic. Metacognitive knowledge was tested by the tool MAESTRA5-6+. Mathematical intelligence is understood as an important criterion of a learner’s ability to solve mathematical problems and defined as the specific sensitivity to the six particular phenomena: causality, patterns, existence and uniqueness of solution, geometric imagination, functional thinking, and perception of infinity. The main objective of the research is to explore relationships and links between metacognitive knowledge and mathematical intelligence of the learners and discover the scope of impacts of their metacognitive knowledge on the school success rate. Based on the collected answers and nearly zero correlation (r = 0.016) between the researched domains, a two-dimensional model considering the correlations between metacognitive knowledge and mathematical intelligence was designed. The developed model enables to describe an impact of the domains on the learner’s school performance within the selected school subjects, and concurrently, it emphasizes their importance within the educational practice as such. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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14 pages, 813 KiB

Open AccessEditor’s ChoiceArticle

Formative Transcendence of Flipped Learning in Mathematics Students of Secondary Education

by Jesús López Belmonte, Arturo Fuentes Cabrera, Juan Antonio López Núñez and Santiago Pozo Sánchez

Mathematics 2019, 7(12), 1226; https://doi.org/10.3390/math7121226 - 12 Dec 2019

Cited by 42 | Viewed by 7520

Abstract

Educational technology is achieving great potential in the formative processes of today’s society. Flipped learning is considered as a pedagogical innovation derived from the technological influence in learning spaces. The general objective of the research is to analyze the effectiveness of flipped learning on a traditional teaching and learning approach in the subject of Mathematics. To achieve this objective, an experimental design of a descriptive and correlational type has been followed through a quantitative research method. Two study groups have been set up. In the control group, the contents have been imparted from a traditional perspective, and in the experimental group, innovation has been applied through the use of flipped learning. The sample of participants has been chosen by means of intentional sampling and reached the figure of 60 students in the 4th year of Secondary Education at an educational center in Ceuta (Spain). A questionnaire has been used for data collection. The results reflect that the application of flipped learning has obtained better assessment in established attitudinal and mathematical indicators. It is concluded that with the use of flipped learning, motivation and skills are increased in the analysis and representation of graphs. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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Review

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15 pages, 2423 KiB

Open AccessReview

Benefits and Limitations of the Artificial with Respect to the Traditional Learning of Mathematics

by Michael Gr. Voskoglou and Abdel-Badeeh M. Salem

Mathematics 2020, 8(4), 611; https://doi.org/10.3390/math8040611 - 16 Apr 2020

Cited by 23 | Viewed by 12095

Abstract

The present article focuses on the role that the artificial teaching and learning of mathematics could play for education in the forthcoming era of a new industrial revolution that will be characterized by the development of an advanced Internet of things and energy, and by the cyber-physical systems controlled through it. Starting with a brief review of the traditional learning theories and methods of teaching mathematics, the article continues by studying the use of computers and of applications of artificial intelligence (AI) in mathematics education. The advantages and disadvantages of artificial with respect to traditional learning in the classroom are also discussed, and the article closes with the general conclusions and a few comments on the perspectives of future research on the subject. Full article

(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)

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