Aemilia Hotel, Bologna, Italy August 6-10, 2024
Band 13 der Reihe Conference Proceedings in Mathematics Education
Münster 2024, ca. 380 S. DIN A5
978-3-95987-287-4 Print 45,90 €
978-3-95987-288-1 E-Book 41,90 €
https://doi.org/10.37626/GA9783959872881.0
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Abstract
This volume contains the papers presented at the Third International Symposium on New Ways of Teaching & Learning held from August 6-10, 2024, at the Aemilia Hotel, Bologna, Italy. The Conference was organized by The Mathematics Education for the Future Project – an international educational project founded in 1986 and dedicated to innovation in mathematics, statistics, science and computer education world wide.
Papers
Fouze Abu Qouder & Miriam Amit: Ethnomathematics in the Bedouin Culture
First Page: 1
Last Page: 6
https://doi.org/10.37626/GA9783959872881.0.01
Abstract
Ethnomathematics asserts that in addition to the formal, academic mathematics there are other forms of mathematics, Ethnic-mathematics, which has been developed in other societies and cultures around the world. Research and educational experience has shown that combining ethnomathematics with formal mathematics in classroom teaching improves the achievements of students from various ethnic and cultural groups; it strengthens their self-image and reinforces their motivation to learn and succeed in this mathematics. This paper aims mainly to offer an ethnomathematical analysis of embroidery samples taken from traditional dresses made by Bedouin tribal women who live in the desert. It also aims to describe how ethnomathematical elements are incorporated in the formal teaching of mathematics for Bedouin students and how this contributes to their learning of mathematics. Keywords: Ethnomathematics, Bedouin Society, Teaching experiment.
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Kehinde Emmanuel Adenegan: New Ways of Teaching and Learning Mathematics with Innovative Online and Offline Apps
First Page: 7
Last Page: 14
https://doi.org/10.37626/GA9783959872881.0.02
Abstract
This paper explores the latest trends in Mathematics education, focusing on innovative online and offline applications that enhance teaching and learning experiences. The use of technology in Mathematics education with numerous tools and platforms are now designed to engage students and facilitate deeper understanding of mathematical concepts. Applications such as GeoGebra, autograph, cabri3D, plotagon, with offline apps such as Cuisenaire rods, and base ten blocks were carefully considered and explored. This paper highlights the potential of various online and offline applications in transforming Mathematics education. By leveraging these tools to engage students in interactive learning experiences, teachers can foster deeper understanding of mathematical concepts and promote lifelong learning. Keywords: Apps, Mathematics, Technology, Online, Offline, Teaching-learning.
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Pahel Agarwal & Kashish Agarwal: Navigating Time’s Labyrinth through Mathematical Lens: The Math behind Videography of Slow Motion
First Page: 15
Last Page: 17
https://doi.org/10.37626/GA9783959872881.0.03
Abstract
In our three dimensional world, the directions of left-right, backward-forward and up-down dictate everything that we see and experience. Time, the fourth dimension, can be navigated through math. This endeavor seeks to unveil the enchanting mathematics behind the creation of timeless monuments in films, as we delve into the physics of motion, leveraging calculus to depict the intricate calculus of objects as they glide through space and time. The shutter speed, frame rate, and object velocity become the dancers in the mathematical ballet, orchestrating a delicate balance between real and surreal. In this research, we will use conversions, different rates at which events occur in real time and slow motion, prior knowledge to model a linear equation, and graphing to invites readers into the captivating realm where mathematics and cinematography intertwines, molding time itself into a tapestry of visual artistry.
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Melina Alexander, Sheryl Rushton, Shirley Dawson & Shernavaz Vakil: AI to AIE: Artificial Intelligence to Access, Inclusion and Equity
First Page: 18
Last Page: 22
https://doi.org/10.37626/GA9783959872881.0.04
Abstract
The adoption of Generative Artificial Intelligence (AI) in education has spurred discourse in mathematics instruction and assessment (Baidoo-Anoo & Ansah, 2023). This debate has cast AI in mathematics education under various lights, with some drawing parallels to the introduction of calculators in mathematical instruction. AI can be seen as a potential detriment to instructional quality, while others perceive it as a pivotal tool for cultivating critical thinking skills (Wardat et al., 2023). This paper explores the transformative potential of AI to improve access, inclusion, and equity for students negatively impacted due to dyscalculia, resource limitations, or instructional deficits. AI-integrated mathematics instruction not only streamlines problem-solving, reducing time spent on calculations but also catalyzes improvements in critical thinking and overall student outcomes, fostering greater success.
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Maria Emilia Alfaro, John Hicks, Anant Godbole & Ryan Nivens: A Research-Based Dual Enrollment Statistics Textbook
First Page: 23
Last Page: 26
https://doi.org/10.37626/GA9783959872881.0.05
Abstract
A new text titled Statistics with Technology for High School has been written and is being used for a dual enrollment high school course taught at ETSU. It is based on the analysis of data sets, small and large, in the context of key introductory statistical methods. Though there do exist Statistics books at the US high school level, ours features adherence to the Tennessee Mathematics Standards, an incorporation of Open-Source software, and a focus on key concepts. Even though Python has been implemented in schools across the globe, our approach has been to use the more appropriate R in the course. We aim to answer the following two questions: (i) Can Statistics be taught successfully in high school using open-source software that is commonly used in college and (ii) Can we move beyond TI-83’s in US high schools?
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Miriam Amit: Challenging Non-routine, Problem-Solving: A Hands-on Experience
First Page: 27
Last Page: 28
https://doi.org/10.37626/GA9783959872881.0.06
Abstract
This workshop, structured in four parts, introduction, hands-on experience, solution presentations and a concluding session, addresses problem-solving in mathematics. It distinguishes between routine and non-routine problems, as defined by Polya (1957), focusing on the latter. These problems, demanding creativity and uncharted solution paths, will be the center of our exploration. Participants will solve these problems and engage in group discussions to reflect on their approaches and the implications for educational practices. The workshop aims to enhance mathematics education for students, teachers, and researchers, embodying Hilbert’s ethos of embracing the challenge of problem-solving in mathematics. Key words: problem solving, non-routine problems.
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Takako Aoki & Shin Watanabe: Find out Mathematics on the Rhombic Dodecahedron
First Page: 29
Last Page: 31
https://doi.org/10.37626/GA9783959872881.0.07
Abstract
We are aiming for a workshop method as a way to teach mathematics in future school education. It is important to cooperate with each other and understand mathematics. In this workshop, we aim to discover the mathematics hidden in the rhombic dodecahedron. As an aid to thinking, I would like to make rhombic dodecahedron first and learn mathematics while looking at concrete things. You need 12 rhombuses with paper. We use the method the origami of Japanese culture. For example, in a rhombic dodecahedron, it is easy to count the number of vertices, edges and faces. And more we can see the cubic and the regular octahedron which are made by the diagonals of a rhombus. We are looking forward to holding a workshop to see what kind of mathematical problems are in the rhombic dodecahedron.
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Elena Arabini & Daniela Dallari: The Math-Chemistry Notebook as a Result of an Interdisciplinary Activity in the Italian High School
First Page: 32
Last Page: 37
https://doi.org/10.37626/GA9783959872881.0.08
Abstract
This paper describes an interdisciplinary activity developed through the whole school year in a first-year class in a Technical High School in Italy. More in detail, the Math and Chemistry curricula have been analyzed and the common topics and terms highlighted. Consequently, the sequences of the topics to be explained in the two subjects have been reorganized to match in time, and the classes presented using agreed keywords and highlighting the common terms. The students have been guided to build a three sections notebook containing Math, Chemistry, and common topics, to be used to study both subjects. As a result, a speed up in the introduction of both the curricula has been noticed together with an improvement in the students’ performances.
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Claudia Baiata & Ryan Andrew Nivens: Unplugged Computational Thinking
First Page: 38
Last Page: 43
https://doi.org/10.37626/GA9783959872881.0.09
Abstract
The education world cannot overlook the fact that, in our technologically advanced society, nine out of ten professions will require strong digital competencies in the future. Nonetheless, research demonstrates the degree to which abuse of digital devices impairs school performance, sustained attention, and interpersonal skills. Although children are currently surrounded by technology, do they truly understand how to use it and avoid being used by it? Are they actually digital natives? The aim of this study is to incorporate art, geometry, proprioception, and coding into the elementary school curriculum while providing preschool and elementary school teachers with alternative perspectives and creative, entertaining ways to teach computational thinking concepts to their students – all without the need for digital devices.
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Patti Blanton: Algebraic Reasoning and Modeling: Meaningful Curriculum for Non-STEM Majors
First Page: 44
Last Page: 48
https://doi.org/10.37626/GA9783959872881.0.10
Abstract
The times of the trivium, quadrivium and practical arts are far in our past. Universities now offer a wide array of courses and degree programs from which a broader population of students may select. A welcomed mandate from the Missouri state government was to create courses in all state public colleges and universities that followed outlined “pathways” allowing students to easily transfer credits between state institutions. One pathway is Mathematical Reasoning and Modeling. The MSU Mathematics Department chose to develop a new course in that pathway with an emphasis on algebraic functions. The course is geared toward students applying to the College of Business and students pursuing majors in Humanities or Nursing. The result is a course that is in its sixth year of implementation with higher success rates and increased student satisfaction.
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Simone Brasili: Moving from Concrete to Abstract Mathematical Thinking: The Role of Algebra Tiles
First Page: 49
Last Page: 54
https://doi.org/10.37626/GA9783959872881.0.11
Abstract
This article addresses the challenges of moving from concrete to abstract mathematical thinking. It emphasizes the importance of making a clear connection between geometry and mathematics to facilitate this transition. Algebra tiles, represented by squares and rectangles symbolizing monomials, are central to bridging this gap and providing tangible insights for students. They enable various mathematical processes, including polynomial operations and solving equations. The study shows how algebra tiles enrich mathematics education and facilitate the transition to abstract mathematical thinking. Through an in-depth investigation, the study reveals their historical, epistemological, and interdisciplinary significance and sheds light on their important role in mathematics education.
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Aarnout Brombacher: When Double 38 Is Equal To 616
First Page: 55
Last Page: 61
https://doi.org/10.37626/GA9783959872881.0.12
Abstract
Supposed learner errors in mathematics should instead be considered to be misconstructions by the learner of what they have experienced. Knowledge that lacks understanding results in the inability to apply that knowledge in unfamiliar situations. This, together with an incapacity to articulate what has been done throughout the solving of a problem, is learning that is of little use. This paper examines a range of mathematics classroom instances within the early school years. In it, the author will attempt to explain the learners’ actions by considering the learning opportunities they have been exposed to, the influence of curriculum (syllabus) sequencing and design, and the role of the teacher’s understanding of what it means to do mathematics. The fundamental assumption is that learners are inherently driven by the need to make sense. However, when placed in impoverished learning environments, misconstructions can take root.
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Gail Burrill: Engaging Students in Worthwhile Tasks in this Ever Changing World
First Page: 62
Last Page: 67
https://doi.org/10.37626/GA9783959872881.0.13
Abstract
We are living and teaching in a new world, a world drenched in data and a world in which artificial intelligence can answer nearly every question we pose to students. However, not all data are “good,” and not all answers from an AI such as ChatGPT can be accepted as accurate. This presents a dual dilemma for educators – how do we frame tasks that will promote student thinking and reasoning about mathematics and statistics and how do we address the potential use of AI by our students. The focus of this paper is on exploring possible answers to those questions building from what we know about the interaction between tasks students are given and their mathematical learning and on reframing our vision of what mathematics is important to learn.
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Kathleen Cotter Clayton: New Ways of Teaching and Learning Basic Arithmetic Using Visualizable Strategies
First Page: 68
Last Page: 73
https://doi.org/10.37626/GA9783959872881.0.14
Abstract
Confusion with number sense is often due to a vague understanding of what numbers mean and how they relate to each other. Attempts have been made to solve this by focusing on rote memorization. Yet, children who have memorized without understanding struggle to apply their skills. So often the student is taught to recognize the numeral 7 and the numeral 6 then memorize the answer as a 1 and a 3. Later in the year, the numeral 7 and the numeral 6 has a memorized answer of 1, and a year later, an answer of a 4 and a 2. This often results in frustration, confusion, and an aversion to math. There is a solution for success in learning the facts: subitizing, visualizing, and using strategies. Subitizing is the base on which to build; then, strategies help organize the numbers. Visualization gives the results in a format that can be easily recalled.
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Kathleen Cotter Clayton & Teresa Foltin: Mastering Multiplication and Division Facts: New Ways of Learning the Factswith Card Games and the Short Multiplication Table
First Page: 74
Last Page: 79
https://doi.org/10.37626/GA9783959872881.0.15
Abstract
Most students get overwhelmed with math worksheets. Students who do not understanding a concept will not benefit from additional worksheets. Flashcards merely reinforce what a student does not know and can become another source of frustration, creating feelings of failure. Rather than worksheets or flashcards, games are a successful method to learn, to apply, and to master the facts. When a student learns to read, they can apply the new skills by reading for pleasure. In the same way, math card games combine practice with pleasure. Although learning math requires hard work, it can be enjoyable. The Short Multiplication table is a derivative of the complete multiplication table. It utilizes the commutative property to remove duplicate facts; also, it is shaded into groups of fives to assist finding products and quotients.
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Klila Copperman, Anatoli Kouropatov & Ivy Kidron: Analogical Models, Intuition, and Knowledge Construction: The Case of a System of Algebraic Equations
First Page: 80
Last Page: 86
https://doi.org/10.37626/GA9783959872881.0.16
Abstract
Constructing mathematical knowledge is a critical aspect of mathematics education. An important question is the role of intuition in this process. We propose a novel methodology for analyzing students‘ work in the context of a system of equations that focuses on the role of intuition in knowledge construction and includes analysis methods.
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Teresa Foltin: Place Value: The Nucleus of Arithmetic
First Page: 87
Last Page: 92
https://doi.org/10.37626/GA9783959872881.0.17
Abstract
Place value allows numbers to be categorized into tidy components rather than an unending jumble of words. It was considered so important that Treviso Arithmetic, written in 1478, referred to place value as one of the basic arithmetic operations. Primary children speaking Eastern Asian languages understand place value years earlier than English-speaking children because the names of the numbers make place value transparent: 26 is two-ten six and 49 is four-ten nine. Thinking of 14 as 14 ones rather than one 10 and four ones interferes with carrying when adding multi-digit numbers. In order to appreciate the pattern that 10 ones equal 10, 10 tens equal 100, 10 hundreds equal 1000, and so forth, students must be allowed to work with numbers into the thousands. Place value is indeed the foundation of arithmetic.
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Courtney Fox: Self-Efficacy in Mathematics: How K-5 Teachers’ Perceptions Change Over Time and Experience
First Page: 93
Last Page: 97
https://doi.org/10.37626/GA9783959872881.0.18
Abstract
Primary teachers are expected to teach all relevant material in all areas of the curriculum to their students. Even after completing excellent teacher preparation programs, these teachers often have little confidence teaching mathematics and this impacts the way teachers present mathematics lessons to their students. Studies show that when teachers are given positive experiences in mathematics, they are more confident and better prepared to teach mathematics to their students. This work offers a possible way to rectify primary teachers’ low self-efficacy in mathematics by offering effective professional development. Using teachers’ prior experiences to design and implement a professional development opportunity, this three-phase study shows that teachers can increase their self-efficacy in mathematics so that they feel prepared to teach students in a primary classroom.
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Kathy Fox, Shelby Morge & Tracy Hargrove: Family Math in the Post-COVID-19 Setting: New and Traditional Practical Math Applications to Sponsor Conversations about Math
First Page: 98
Last Page: 103
https://doi.org/10.37626/GA9783959872881.0.19
Abstract
Family math refers to activities in the home and community that use math in practical ways. When purposefully planned, these activities create a bridge between home and school mathematics. The need for this bridge became obvious during the COVID-19 pandemic when students joined math class from home using platforms such as Zoom and Google Classroom. Technology has relevant family math applications that may be less visible when normalized in the home. This paper examines traditional and non-traditional forms of family math, ranging from an online food order app for middle school students to an electronic game for preschoolers. Connecting home and school practices encourages stakeholders to hold conversations about math in various settings. Implications include the positive effects of school-to-home communication that recognize the bi-directional importance of intentional family math practices.
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Joanne Goodell: Teaching Mathematics in the Age of Generative Artificial Intelligence
First Page: 104
Last Page: 109
https://doi.org/10.37626/GA9783959872881.0.20
Abstract
In this workshop, we will investigate some of the most common uses of Gerative Artificial Intelligence (Gen AI) tools in mathematics education, including acting as a teaching assistant to generate a range of varied examples, provide multiple explanations of concepts and procedures, generate assessments and rubrics, assess student feedback, and generate lesson plans. Suggested prompts are provided. Participants will need to bring their own devices and ensure that they have access to either ChatGPT through OpenAI, Microsoft’s BingChat, or other similar chatbot artificial intelligence models prior to attending this workshop.
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Christopher Gordon, Alisa Wickliff, Gregory Wickliff & David Pugalee: Computational Thinking in Students’ Research Projects
First Page: 110
Last Page: 116
https://doi.org/10.37626/GA9783959872881.0.21
Abstract
Computational thinking is increasingly important in the secondary curriculum beyond the computer science classroom, especially in technology heavy STEM fields. We applied the Computational Thinking in Mathematics and Science Taxonomy (Weintrop et al., 2016) to explore how secondary students demonstrated computational thinking in research projects from a month-long STEM enrichment summer program. The preliminary data show that the papers and posters of four students, one from each area of the summer curricula, demonstrate all four of the practices: Data Practices, Modeling and Simulation Practices, Computational Problem Solving Practices, and Systems Thinking Practices. These results indicate that computational thinking provides a useful framework for planning and assessing secondary students’ STEM independent research projects. Key words: computational thinking, research.
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John Gordon : Experiments in Teaching Advanced Calculus: An Early Introduction to Double Integrals
First Page: 117
Last Page: 119
https://doi.org/10.37626/GA9783959872881.0.22
Abstract
Traditionally, in the United States undergraduate education system, the concept of double integrals is presented after single variable integration theory is introduced through a first course in calculus (Calculus I) which is then followed by several applications of the theory in another sequential course, (Calculus II), followed by double (and triple integration) over rectangular and other regions in a Calculus III course. This paper outlines strategies for experimentation with a much earlier introduction to double integrals over rectangular regions which allows practitioners of mathematical modeling with no prior experience in advanced mathematics to quickly come up to speed.
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Aneta Grodzicka: Experiences in Working with Children in the Scientific Method at a Technical University
First Page: 120
Last Page: 123
https://doi.org/10.37626/GA9783959872881.0.23
Abstract
The article presents the experience of working with children using the scientific method, presenting selected characteristics of the teaching carried out at the Faculty of Mining, Safety and Industrial Automation of the Silesian University of Technology in Gliwice. The introduction contains arguments in favour of using this teaching strategy to make science teaching effective and to stimulate children’s cognitive curiosity. The next section describes the course of the project, including the stages of creating the so-called learning environment, i.e. the ‚Experience Mine‘ and the ‚Experience Factory‘. The main part of the text deals with the analysis of the achieved didactic results in terms of supporting the development of the cognitive processes of the participating children and their ability to choose appropriate behaviour in accordance with the principles of safe action. The final part contains conclusions and recommendations. Key words: out-of-school education, scientific method
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Raisa Gulati: Chaos Theory and Fractals in Finance
First Page: 124
Last Page: 129
https://doi.org/10.37626/GA9783959872881.0.24
Abstract
This research paper delves into the application of chaos theory in finance, specifically focusing on the Fractal Market Hypothesis (FMH), within the evolving landscape of finance. It delves into the interconnectedness between seemingly unrelated events, referred as the butterfly effect, and how such interplays have significant repercussions on financial markets. Additionally, the research encompasses a case study of the 2008 financial crisis and the emergence of cryptocurrencies and their contemporary relevance within the framework of chaos theory and fractals. The study also includes the usage of fractal indicator along with a comparative analysis of the Efficient Market Hypothesis (EMH) and Fractal Market Hypothesis (FMH), shedding light on their respective strengths and limitations.
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Clinton Hayes, Nadine Adams & Antony Dekkers: Using MCQs for Formative and Summative Mathematics Assessment
First Page: 130
Last Page: 135
https://doi.org/10.37626/GA9783959872881.0.25
Abstract
The use of Multiple-Choice Questionnaires (MCQs) in universities has increased due to larger student enrolments, limited resources and the increasing use of technology, as well as their ability to save marking time for staff. Electronically marked MCQs for large cohorts provide effective marking and an efficient assessment method for student knowledge. When writing mathematical-based MCQs, careful consideration must be taken to include answers containing the most common student errors, allowing feedback to pinpoint errors and correct misconceptions. Although they are relatively easy to set up, writing well-written MCQs is a skill many academics lack. MCQs are time-consuming to construct correctly, and staff require training. A review of techniques to construct MCQs is given, with a case study for formative and summative assessment.
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Nader Hilf & Avi Berman: Hints for Challenging Problems
First Page: 136
Last Page: 140
https://doi.org/10.37626/GA9783959872881.0.26
Abstract
We asked 20 middle school mathematics teachers what they think about problem solving, how they manage problem solving in their class, and how they pose hints as scaffolds to help the students to solve non-routine problems. We also asked them to suggest interesting problems combined with hints. For some problems one hint may not be sufficient and a sequence of hints is needed. This suggests the importance of teaching teachers and pre service teachers how to plan the use of hints in problem solving. Key words: problem solving, problem posing, hint posing
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Gregory Hine: Exploring Secondary Mathematics Teachers’ Reasons for Attending Voluntary Professional Learning
First Page: 141
Last Page: 146
https://doi.org/10.37626/GA9783959872881.0.27
Abstract
A problematic issue in Australian schools is the supply of secondary school mathematics teachers (SSMTs). To address this issue, one approach conducted at scale provides professional learning (PL) courses for teachers of Years 7-10 mathematics. Research was conducted with PL participants to identify their reasons for undertaking courses voluntarily, through the exercise of pre- and post-course surveys and a post-course interview. Reported in this paper are predominantly the findings from qualitative survey items. For the most part, participants expressed a need to develop their knowledge in mathematics content and pedagogy, and to feel prepared, confident and qualified. While post-course claims were generally accompanied by assertions of increased confidence in these knowledge domains, they were also underpinned by a need to practice and consolidate certain topics before teaching the course.
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Charity Jones & Kathryn Van Wagoner: A Holistic Teaching Approach to Intermediate Algebra
First Page: 147
Last Page: 152
https://doi.org/10.37626/GA9783959872881.0.28
Abstract
With greater accessibility to college in the United States, thousands of prospective graduates come to colleges and universities with low math skills and a low opinion of their ability to learn and do mathematics. Developmental mathematics programs have long been tasked with remediating student math skills, however “developmental” implies more than remediation. It implies a holistic approach to mathematics education. This requires inclusive and equitable teaching practices that utilize research-based pedagogy and curriculum as well as address students’ sense of belonging and other psychological aspects of learning. This workshop will demonstrate and explain the combination of effective and inclusive teaching practices used in Intermediate Algebra courses at an open enrollment university. Student and faculty feedback will be shared.
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Anna Khalemsky & Yelena Stukalin: Adapting Learning Methodologies in a Changing World: The Transition from Face-to-Face to Distance and Hybrid Learning via Active Learning
First Page: 153
Last Page: 159
https://doi.org/10.37626/GA9783959872881.0.29
Abstract
The challenge of distance learning during the Covid-19 pandemic has set a new standard for undergraduate statistics courses and become a trigger for intensive utilization of a wide range of modern pedagogical methods. A combination of traditional statistics teaching together with contemporary methods, such as active learning, can greatly help in creating an efficient learning experience and a positive interaction between the lecturer and the students. Hybrid internet-based instruction constitutes the basis for the development of effective teaching methods in statistics education. Problem based learning methods can help students to understand their own strengths and weaknesses. Project-based learning methods can be very practical and beneficial for achieving the internalization of a theory and the use of statistics in practice. Keywords: Teaching statistics, Distance learning, Active learning, Hybrid learning, Alternative assessment
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Ok-Kyeong Kim: Support for Preservice Teachers to Use Curriculum Resources Productively
First Page: 160
Last Page: 166
https://doi.org/10.37626/GA9783959872881.0.30
Abstract
This study investigates ways to support preservice teachers’ (PSTs’) learning to use resources productively in a mathematics methods course setting. The five components of productive resource use previously identified were applied in designing the course activities in which PSTs analyzed curriculum resources and used them to plan and teach lessons in local elementary school classrooms. Data were gathered for two semesters. The data from the first semester confirmed the usefulness of the five components for designing the course to support PSTs’ learning of productive resource use and revealed a clearer relationship among the five components. New data collected from PSTs in the second semester were examined to refine the framework as a practical and theoretical tool for systematic support for PSTs’ learning of resource use.
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Sergiy Klymchuk: A Novel Approach to Teaching and Assessing Students’ Critical Thinking in University Mathematics
First Page: 167
Last Page: 172
https://doi.org/10.37626/GA9783959872881.0.31
Abstract
This paper extends my previous study presented at the 16th conference of The Mathematics Education for the Future Project held in Cambridge in 2022 to the university level. It investigates the attitudes of the university mathematics lecturers towards the use of deliberately misleading mathematics questions in teaching and assessment as a pedagogical strategy with their students. The intention of using such questions is to enhance students’ critical thinking. Critical thinking is understood here as “examining, questioning, evaluating, and challenging taken-for-granted assumptions about issues and practices” as defined by the New Zealand Ministry of Education. The study is based on a survey of university lecturers who have been introduced to the suggested pedagogical strategy. Their attitudes are analysed in the paper and compared with the attitudes of secondary school mathematics teachers. Key words: critical thinking, assessment, university mathematics.
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Sebastian Kuntze & Jens Krummenauer: Promoting Discourse and Argumentation in Mathematics Classroom Interaction as a Challenge for Pre-Service Teachers – Vignette-Based Learning Opportunities as a Possible Solution Pathway
First Page: 173
Last Page: 181
https://doi.org/10.37626/GA9783959872881.0.32
Abstract
When it comes to noticing and analysing potential springboards into rich discourse and argumentation in interaction processes in the mathematics classroom, pre-service teachers can be expected to encounter challenges. However, such noticing and analysing is a key for teachers when they have to support a culture of mathematics-related discourse and argumentation in their classrooms. Vignette-based learning opportunities can be a solution in this context: pre-service teachers can reflect on representations of classroom situations, so that their progress in analysing the discourse and argumentation potential of teacher reactions can be monitored and corresponding learning opportunities can be provided. We present specific developments of classroom cartoon vignettes. The vignettes are implemented using the digital DIVER tool, which has been developed in the project coReflect@maths (www.coreflect.eu).
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Barbara H. Leitherer, Pankaj R. Dwarka, Entela K. Xhane & Jignasa R. Rami: Conceptualization and Challenges from a Global Undergraduate Research Study
First Page: 182
Last Page: 188
https://doi.org/10.37626/GA9783959872881.0.33
Abstract
Students in the first two years of college are normally not involved in peer review research, but voices are getting louder that they should be to address the alarming shortage in the global STEM workforce. Exposing students to rich undergraduate research experience can potentially empower them to pursue a STEM career. This paper tries to reflect on the journey of four faculty advisors who guided community college students in the US through the process of research. Special focus will be on the challenges students encountered with conceptualization, the faculty interventions to overcome those obstacles, conceptual teaching, and highlighting how abstract concepts apply to the students’ research. Additionally, the findings include examples of scientists’ feedback on student papers, and insights about students’ cultural understanding from a global perspective.
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Sigal Levy, Yelena Stukalin & Nili Guttmann-Beck: Using Practical Programming Tasks to Enhance Combinatorial Understanding
First Page: 189
Last Page: 194
https://doi.org/10.37626/GA9783959872881.0.34
Abstract
Probability theory has extensive applications across various domains, such as statistics, computer science, and finance. In probability education, students are introduced to fundamental principles such as combinatorics and symmetric sample spaces. Students pursuing degrees in computer science possess a robust foundation in programming, software engineering, and algorithmic thinking. Hence, they enter probability courses with a unique perspective and learning potential. Despite that, these students encounter challenges in grasping combinatorial concepts. In this experiment, we challenged first-year computer science students to program a simulation of a practical combinatorics problem. Students commented on if and how this task helped them internalise the basic concepts of combinatorics. We aim to show how utilising programming tasks may empower students with a deeper grasp of combinatorics. The results presented in this paper are based on a recent paper by the authors: „Using Practical Programming Tasks to Enhance Combinatorial Understanding“
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Michail Lousis: Logic as a ‘Medium’ for Paradigm Shifts in Mathematics, Psychology of Reasoning, Informatics, and Education
First Page: 195
Last Page: 206
https://doi.org/10.37626/GA9783959872881.0.35
Abstract
This study brings in serious evidence from the history of the development and evolution of the science of logic and its impact on mathematics through the use of “media”. Collectives of humans-with-media (Borba & Villarreal, 2005) produce this knowledge. The study pondered upon and identified that the media are epistemological, cognitive tools and components of the epistemic subject of mathematics, being an essential, necessary, constitutive part of it. The way, which the science of logic has historically been rendered an ‘organon’ according to Aristotle or an ‘instrument’ (medium) in a nowadays concept for leveraging the foundation of mathematics, informatics, psychology of reasoning, and scientific research by, is clarified. Furthermore, the investigation stresses that the science of logic is a conducive factor (medium) for paradigm shifts in mathematics, psychology of reasoning, informatics, scientific research, and through these in mathematics education.
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Victor Mack, Joyce Dunlap & David Pugalee: STEM Pre-College Program: How an Out-of-School Program Is Contributing to In-School Success
First Page: 207
Last Page: 211
https://doi.org/10.37626/GA9783959872881.0.36
Abstract
With an unstable economy and predominantly homogenous populations in STEM-related majors and careers, the United States of America faces unprecedented obstacles in achieving the growing expectations of a digital world. The lack of diversity in STEM-related fields suggests there are untapped human resources for addressing many of society’s challenges (Lathifa, 2023). Inclusivity in the workforce provides different perspectives, methods, and cognitive abilities for meeting many challenges in today’s global world. This study aims to examine the influence of an out-of-school program on social capital and student achievement as precollege scholars prepare for college. This study will investigate if there is a relationship between program satisfaction, social capital, and student achievement. Results linking program satisfaction, social capital, and student achievement will be reported if significant.
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Ahlam Mahagna & Avi Berman: Problem Solving and Posing – from University to Primary School
First Page: 212
Last Page: 217
https://doi.org/10.37626/GA9783959872881.0.37
Abstract
Problem solving and problem posing are very important at all stages of mathematics education. We will give examples from (1) A graduate course on matrix theory conducted using the pedagogy of problem solving before instruction, (2) A course, problem solving, problem posing, and problem choosing, given to primary school teachers in a M.Ed program. The examples will include challenging problems given to the teachers to upgrade their mathematical thinking and their mathematical knowledge and problems that the teachers posed, by adapting the challenging problems for use in their teaching, (3) Problem solving by excellent high school students, and (4) An enrichment course, based on problem solving, for middle school students.
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Jahnavi Mahana: Effect of Change of Shape on Time Period of a Pendulum
First Page: 218
Last Page: 222
https://doi.org/10.37626/GA9783959872881.0.38
Abstract
The research paper delves into the realm of simple harmonic motion (SHM) through the lens of applied mathematics, offering a comprehensive exploration of its underlying principles, mathematical representations, and real-world applications. The paper begins by establishing a foundation on the time-period taken by the pendulum, with its varying shapes. This includes a detailed analysis of the equations governing displacement, velocity, and acceleration, fostering an understanding of the interplay between differentiating structure and constant physical behaviour of the pendulum. By employing applied mathematics as a tool, the paper fundamentally offers a comprehensive perspective on SHM’s intricate mathematical representations and its wide ranging fields of research.
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Radley K. Mahlobo, Bonani Sibanda & Ramoshweu S. Lebelo: Analysing Marking Memorandum as an Aspect of Assessment in Mathematics Performance of South African High Schools
First Page: 223
Last Page: 229
https://doi.org/10.37626/GA9783959872881.0.39
Abstract
The question asked here is whether the formulation of a marking memorandum may have a possible impact on the mathematics performance of the tested learners. 2021-2022 South African National Senior Certificate grade 12 mathematics Paper 2 marking memoranda were scrutinized to establish the impact on learner performance. The results of the scrutiny gave credence to the possibility of the impact. On one hand, it was found that only one answer out of a few possible solutions was given, potentially disadvantaging learners with the alternative solutions. It was also found that the examiner’s arbitrarily assigned value to a geometric side led to a wrong answer. The paper concluded that indeed the marking memorandum can have an impact on learner performance. Key words: Assessment standard setting, performance in mathematics, marking memorandum, Euclidean Geometry.
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Günter Maresch & Eleni Lagoudaki: Do Girls and Boys have Equally Good Spatial Thinking Skills?
First Page: 230
Last Page: 235
https://doi.org/10.37626/GA9783959872881.0.40
Abstract
The online spatial thinking platform RIF has collected anonymous results from more than 2.8 million individual tasks completed by students from 36 countries around the world. This large quantity of data allows analyses, and various interpretations of students’ spatial thinking skills. The data were examined regarding age- and gender-specific differences and performance in the different areas of spatial thinking. The results of the analyses show clear trends: (1) Girls and boys have (with one exception) equally good spatial thinking skills. (2) Boys (just) have a clear advantage in the domain of mental rotation. (3) The spatial ability of adolescents hardly improves at all during puberty (between the ages of 12 and 16), (4) With increasing age, the average probability of solving the tasks correctly increases for all students in all domains of spatial thinking.
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Frank S. Marfai, Robin Cotter, Rosalind Cook, Anna Marti-Subirana & Elena Ortiz: Enhancing Equity with Course-Based Undergraduate Research Experiences at the Community College Level
First Page: 236
Last Page: 242
https://doi.org/10.37626/GA9783959872881.0.41
Abstract
Course-based undergraduate research experiences (CUREs) are an equity minded practice in which all students in class have the opportunity to engage in original research. While researchers have studied the implementation and impact of CUREs in science education at four-year colleges and universities (Auchincloss, et al., 2014), CUREs represent a new direction in STEM education at the community college level, and especially in mathematics and statistics education. Lessons learned from CUREs in partnership with industry partners spanning face-to-face, live online, and asynchronous online modalities of an introductory statistics course from a community college serving traditionally underrepresented populations in the United States will be shared. Benefits to students, findings from data collected, and future directions will also be discussed.
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Johannes Memling: Data Science and the Future of Mathematics
First Page: 243
Last Page: 248
https://doi.org/10.37626/GA9783959872881.0.42
Abstract
The progression of the nature of mathematics and mathematical problems into the future is a widely debated topic. Mathematicians are motivated by a desire to set a research agenda to direct efforts to specific problems, or a wish to extrapolate the way that subdisciplines relate to mathematics and its possibilities. It seems that the history of mathematics and mathematicians is tied to future prospectives. We would like to discuss the possible future of mathematics and how it will develop or transform into a perhaps different, and unknown to us now, science. We would like to discuss solutions of algebraic and analytic problems achieved by iterative methods inside adaptive intelligent systems that mix and match and combine algorithms as required, and the merging of classical mathematics with Data Science and Artificial Intelligence. Key words: intelligent systems, data, iterations, prospectives
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Miranda Moodley, Jacob Jaftha & Duncan Mhakure: Meta-Analysis on the use of Mathematical Modelling to Teach Mathematical Concepts in Higher Education in South Africa
First Page: 249
Last Page: 254
https://doi.org/10.37626/GA9783959872881.0.43
Abstract
Mathematical modelling (MM) is not widely used in South African higher education currently, but has the potential to improve students‘ conceptual understanding and ability to apply mathematics. Various measures are used to teach MM however, there is no consensus on an ideal model. Therefore, this meta-analysis examines and synthesizes methods used to teach MM in higher education in South Africa. The main findings show that a variety of methods are used, both standardized and non-standardized, to teach MM and often results in improved mathematical understanding. However, more research on mathematical modelling as a teaching strategy using standardized measures is needed in higher education. Keywords: Mathematical Modelling; Education; South Africa; Critical Thinking; Problem-Solving; Real-World Applications; Pedagogy
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Shelby Morge & Christopher Gordon: Integrating Mathematics and Computer Science in the classroom
First Page: 255
Last Page: 260
https://doi.org/10.37626/GA9783959872881.0.44
Abstract
Effective mathematics instruction engages students in making connections among representations. When integrating mathematics and computer science, teachers may address standards in both subjects while supporting students in making connections, thus deepening understanding. Teachers participating in a professional development workshop on strategies for meaningful and authentic computer science and mathematics integration were asked to share examples of how they integrate other subjects in mathematics. In this paper, we will share the teachers’ thinking about such integration before and after participating in the workshop. Additionally, we provide an overview of workshop activities that supported teachers’ thinking about integration. Finally, we will discuss the challenges and opportunities related to integrating computer science in the mathematics classroom.
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Caty Morris: ‘Closing the Gap’: Culturally Responsive Mathematics Education in Australia
First Page: 261
Last Page: 266
https://doi.org/10.37626/GA9783959872881.0.45
Abstract
In Australia, mathematics education continues to fail most Indigenous students, closing doors to many career and lifestyle opportunities. The Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA) is collaborating with Indigenous Communities, schools and education systems to transform mathematics education so that Indigenous students are successful in mathematics. Prof. Chris Matthews’ Goompi Model, a framework for culturally responsive teaching and learning, is central to ATSIMA’s work in the professional learning of educators. Further to this, during 2019-2021, I worked with Chris to develop over 90 pieces of content in Indigenous histories and cultures for the latest version of the Australian Curriculum: Mathematics (ACM).From these standpoints, this paper discusses our work with educators in connecting mathematics with culture for a diversity of Indigenous communities.
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Estela Navarro Robles: Building an Application with AI to Learn First Degree Equations that Recognize Specific Mistakes of the Users
First Page: 267
Last Page: 271
https://doi.org/10.37626/GA9783959872881.0.46
Abstract
In Mexico for several years, many students do not learn basic operations beyond algorithms. And when they need to learn basic algebra, in most cases they cannot do it, because they do not understand basic operations. It is important that each student has their own learning process, so if we just explain the same thing in the same way many times, most students do not understand what they are doing wrong. We have seen that students almost always have some logic to perform their results, even if their answers are incorrect. In this paper we will present a first classification of mistakes with its own logic in first degree equations built through Marton’s variation theory, based on the responses of more than a thousand high school and first year university students. It will be the basis for designing an AI Application. Key Words: AI Application, First Degree Equations, Mistakes.
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Beata Pituła: Co-teaching in the Theory and Practice of Academic Education
First Page: 272
Last Page: 276
https://doi.org/10.37626/GA9783959872881.0.47
Abstract
The aim of this paper is to present the results of the author’s own research into the various forms of using the didactic strategy called co-teaching in the practice of teaching students at universities and in selected countries of the world. The introduction presents arguments in favour of introducing coteaching more widely into academic education. The second part synthesises the conventional and unconventional forms of co-teaching described in the literature and verified through own research. The third part of the text presents a conceptualisation of the research approach. The final section presents the results of the research, together with a discussion of the findings and an indication of areas requiring further in-depth exploration. Key words: university education, co-teaching
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Raja Climax: The Twelve-Points Circle Theorem
First Page: 277
Last Page: 280
https://doi.org/10.37626/GA9783959872881.0.48
Abstract
The Nine-points Circle passes through the following nine points viz the feet of the three Altitudes(3 points),the feet of the three Medians(3 points), the midpoints of the line joining the vertex and the Orthocentre(3 points). Now, three more special points are added to this list to make it 12 points. Key words: Nine-Points Circle.
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Ann-Sofi Röj-Lindberg: Cross-curricular Teaching and Learning in Mathematics Education
First Page: 281
Last Page: 286
https://doi.org/10.37626/GA9783959872881.0.49
Abstract
In the paper I discuss cross-curricular teaching and learning in mathematics education in relation to both theoretical perspectives and empirical evidence. The main question addressed is why school mathematics is frequently conceived as difficult to integrate with other subjects, sometimes even consciously left out when teachers plan for cross-curricular activities. One proposed reason is the dominance of an instrumental view on mathematics and its learning. If mathematics education is instead viewed from a complementary perspective, from a relational view, I argue that a crosscurricular educational context could provide a meaningful, realistic setting in which to engage in doing mathematics and making learners’ mathematical knowledge less inert. Keywords: cross-curricular mathematics education, instrumental view, relational view.
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Ildar Safuanov: The Guided Reinvention in the Teaching of Linear Algebra
First Page: 287
Last Page: 290
https://doi.org/10.37626/GA9783959872881.0.50
Abstract
The paper describes how “the guided reinvention” (a technique introduced by G. Freudenthal and close to the genetic approach) can be applied in the teaching of linear algebra. The principles of constructing the course, the sequence of the study, as well as the design of the process of the teaching of linear dependence are considered. This paper is about the use of “the guided reinvention” in the teaching of some topics of linear algebra. We consider the designing the process of studying educational material using the example of studying a linear dependence. The experience of implementation of the described approach in the teaching of first year mathematic majors demonstrated the increased interest in the subject, the successful mastering of the meaning and applications of the concept of linear dependence.
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İpek Saralar-Aras & Sümeyra Tütüncü: Utilization of Technology for Assessment Purposes Among Mathematics Teachers
First Page: 291
Last Page: 296
https://doi.org/10.37626/GA9783959872881.0.51
Abstract
The integration of technology into educational settings holds profound implications for pedagogical transformation. While extant research has extensively explored the incorporation of technology within technology-rich learning environments, there exists a notable dearth of scholarly inquiry directed toward the utilization of readily accessible technology tools by teachers. This research endeavors to address this lacuna by delving into the inventive application of accessible technology resources among proficient middle school mathematics teachers in the Republic of Türkiye, with a specific focus on their evaluative practices. This paper aims to illuminate the substantive significance of our proposed research project by locating it within the existing literature.
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Marco Scipioni: Learning Statistics through Ethical Data Science
First Page: 297
Last Page: 300
https://doi.org/10.37626/GA9783959872881.0.52
Abstract
Data science represents a unique opportunity to motivate students from different academic backgrounds to learn statistics and apply it to ethical issues. Evidence of the benefits of teaching statistics through the lens of data science was found during the recent Ethical Data Science summer course at the University of North Carolina Charlotte during the Summer Ventures in Science and Math (SVSM) program. The course provided high school students with a comprehensive understanding of data science concepts while emphasizing the ethical considerations surrounding data use and its impact on society. The students engaged in analyzing datasets related to important social issues. This article reports the insights collected from the course and describes the impact of using data science to teach statistics.
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Dennis Showers: War and Peace in Math Teaching: Preparing U.S. Pre-service Teachers for a Balanced Approach in PK-6 Classrooms
First Page: 301
Last Page: 305
https://doi.org/10.37626/GA9783959872881.0.53
Abstract
As the third of the three R’s (reading, [w]riting, and ‘rithmetic) math teaching can learn from the ongoing reading wars. Although the “best” method to teach reading goes back at least to the 1920s, the conflict came into focus in the early 1970s. Although still unsettled, some common ground has been found by proponents of “balanced literacy.” Recent surveys show a similar conflict in math teaching between proponents of explicit instruction and those of inquiry approaches. This author has found that most student’s backgrounds include familiarity with explicit instruction but not experience in inquiry approaches. This workshop proposes to generate a discussion of curricula and activities that can give future teachers sufficient experience with the model to be able to incorporate it into their teaching. Keywords: Inquiry math teaching, preservice math teachers
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Vali Siadat: Mathematical Fallacies and Scandals
First Page: 306
Last Page: 310
https://doi.org/10.37626/GA9783959872881.0.54
Abstract
Mathematics is a human endeavor and mathematicians, as practitioners of this field, exhibit their creativities and innovations as well as rivalries, and at times jealousies, even enmities, towards one another. Interestingly, though, society often thinks of mathematics as an esoteric subject and mathematicians as a group of super smart but weird people who congregate in closed-door meetings and conferences and engage in gentle and peaceful discourse in their exclusive elite clubs. The history of mathematics, as it is written today, deals mostly with innovations of mathematicians, but often ignores to present the behind the scenes work of those who create it. My aim in this short presentation is to show the other side of the general societal impression of mathematicians by presenting the real-life stories of some of the great minds in mathematics and how they have handled competitions, intense peer pressure and rivalries.
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Panagiotis Stefanides: Logarithm Spiroid Definition: A Novel Theory of the Meaning of “Logarithm” via use of Specially Drawn “Spiral Forms- Spiralogarithms” and Relationship, via Proposed Plato’s Timaeus “Most Beautiful Triangle”, with the Recently Discovered Invention of the “Generator Polyhedron”
First Page: 311
Last Page: 316
https://doi.org/10.37626/GA9783959872881.0.55
Abstract
Logarithmus was coined (in Latin) by John Napier(1550-1617) and appears in1614 in his Mirifici Logarithmorum Canonis description. According to the OED, “Napier does not explain his view of the literal meaning of logarithmus. It is commonly taken to mean ‚ratio-number‘ (…). Perhaps, however, Napier may have used logos merely in the sense of ‚reckoning‘, ‚calculation’”. Here, in this work, a New Thesis of a “General Definition of Logarithm” is proposed, having been presented and disseminated to National and International Conferences, since its Deposit to the National Library of Greece [07/03/2002].The work involves specially drawn Spirals, including a “Nautilus” one, interrelating “The Golden Root Triangle–Plato’s Proposed one” by which the “Generator Polyhedron, a Non-Regular Icosahedron, is based on this. The Theory here DEFINES LOGARITHM [Λογάριθμος] as the RATIO of 2 NUMBERES [Θx/Θb], to “Etymologically” give an answer to the question: “WHY LOGARITHM?”
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Patrick Sullivan: Advancing Fraction Conceptions as Part of a Whole Comprehensive Course Redesign to Improve Student Success and Self-Efficacy in Developmental Mathematics
First Page: 317
Last Page: 323
https://doi.org/10.37626/GA9783959872881.0.56
Abstract
Low success rates in developmental mathematics (DM) courses are common across university settings. To address this issue we have implemented a comprehensive course redesign that has included shifting the nature of the content to meet students where they are. After one iteration of this course redesign the success rate increased to over 70%, from below 60%, without decline in the success rates in the next mathematics course. A significant part of this course redesign has involved understanding students’ conceptions of foundational concepts (e.g. fractions) and using what we learn to move their thinking forward. In this workshop I will share what we learned about DM students’ initial conceptions of fractions, an intervention we implemented to advance those conceptions, and what we learned about advancements in a subset of DM students’ conceptions of fractions.
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Allan Tarp: Decolonizing Math by Demodeling Essence as Existence, Teach that 1+1 = 1, while 1s+1s = 2s; a Workshop
First Page: 324
Last Page: 330
https://doi.org/10.37626/GA9783959872881.0.57
Abstract
Collapsing a V-sign, one 1s plus one 1s gives one 2s and not two. One and two is inside essence to de-model as the outside existence 1s and 2s adding to 3s where one and two only add with like units. 8 push-away 2s, 8/2, recounts 8 in 2s, and ‘demodels’ division as a broom. 4times push-back 2s, 4×2, unites 2s into a stack, and demodels multiplication as a lift. The recountformula 8 = (8/2)x2, or T = (T/B)xB, solves STEM proportionality equations as ‘ux2 = 8’ by recounting 8 in 2s, u = 8/2. Subtraction demodels as a rope to pullaway the stack so the unbundled becomes negatives, decimals, or fractions: 7 = 4B-1 = 3B1 = 3 . 2s. 4 is a BundleBundle-square solving quadratics. On a ten-by ten Bundle-Bundle ‘BBBoard’, bundle-numbers with units as 2 3s and 4 5s add next-to as 8s (integral calculus), or on-top as 3s or 5s or tens. Recounting physical units gives per-numbers or fractions, 3m/5s or 3m/5m, also adding by integral calculus.
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Hilluf Reddu Tegegne: Real Life Mathematics in Traditional Everyday Settings of the Agew and Tigray Peoples of Ethiopia: Implications for Classroom Mathematics
First Page: 331
Last Page: 337
https://doi.org/10.37626/GA9783959872881.0.58
Abstract
This paper reports the findings of a qualitative investigation of purposively selected practitioners of workplaces and traditional games with the purpose of identifying culturally embedded real-life mathematics. Data obtained from interviews, field notes and observations were analyzed through thematic methods. The results demonstrated that number sense, geometry, and algorithms surpass mathematical concepts practiced in the selected settings. This implies that educators and school leaders can get at least two lessons from real life mathematical practices. First, the mathematics used in real life settings is purposeful and geared towards achieving a specific goal. Second, the mathematics used in real life activities is manipulated with concrete objects. Keywords: Games; Real-life mathematics; Workplaces.
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Eleni Tsami, Dimitra Kouloumpou, Andreas Rokopanos, Dimitris Anastasopoulos & Anastasia Anastasopoulou: Distance Learning in Statistics and Mathematics: The Case of the Greek Universities
First Page: 338
Last Page: 343
https://doi.org/10.37626/GA9783959872881.0.59
Abstract
Distance education was introduced in the first quarter of 2020, to control the COVID-19 spread in Greek schools and universities. The present survey compares face-to-face with distance education in statistics and mathematics. We consider an electronic questionnaire consisting of 29 questions, addressed to the students of the Department of Statistics and Insurance Science at the University of Piraeus. These questions address the learning experiences, the level of satisfaction with the distance learning mode, its psychological effects, and the preferences between the two modes. Our sample comprises 494 responses and the results highlight that (i) dedicated software provides comparative advantages in work life, (ii) face-to-face and theoretical courses do not lead to better outcomes, and (iii) electronic means are considered more effective than traditional classes in terms of learning objectives by the students.
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Kamoru Olayiwola Usman & Kamoru Abiodun Sabitu: Activity–Based Learning Strategies and Mathematics Education in Nigeria
First Page: 344
Last Page: 350
https://doi.org/10.37626/GA9783959872881.0.60
Abstract
Many students in primary and secondary schools around the world experience difficulties with the learning of some aspects of the mathematics curriculum. That is, students and mathematics teachers face difficulties in mathematics teaching-learning process, especially in Nigeria. This has also created challenges for stakeholders in education. This study, therefore, examined various Activity-Based Learning Strategies (ABLS) in the mathematics classroom. The mathematics teachers’ knowledge and ability to apply these (ABLS) to mathematics class were equally investigated. It was recommended that the training of mathematics teachers should include the use of (ABLS) in the classroom. This may assist mathematics teachers to move away from the “Story-telling method” and adopt strategies that promote active learning in the classroom. Also, in-service training is recommended for the serving mathematics teachers for effective use of (ABLS).
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Vivian Libeth Uzuriaga López & Luz Elena Palacio Loaiza: Linear function for environmental managers
First Page: 351
Last Page: 357
https://doi.org/10.37626/GA9783959872881.0.61
Abstract
Research results of a Master’s thesis in Mathematics Education of the Universidad Tecnológica de Pereira, Colombia, are shown. It was a qualitative research of descriptive type, with a group of 18 students of the Environmental Administration program, who made a joint construction of the concept of function, linear, quadratic and exponential function, from situations that they will face in their professional life. The teaching and learning of the real variable function through didactic situations promoted changes both in the role of the teacher, by guiding the process, and in the student, by getting productively involved with their learning, modeling concepts through problematic situations faced by environmental administrators; allowing them to improve their academic performance and change their attitude towards mathematics.
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Deepti Verma: Teaching The Process Of Mathematical Investigation
First Page: 358
Last Page: 362
https://doi.org/10.37626/GA9783959872881.0.62
Abstract
The paper focuses on how to develop and handle concepts through mathematical investigation which would in turn develops and helps the student to arrive at more generalized abstract science concepts. Visualization is another key area to understand the shapes, many people finish school without being able to draw a picture of a solid object on a piece of paper. Hence, if we follow the idea of perspective intuitiveness, it will allow the students to visualize the shapes and can further generalize in more complex forms of it.
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Shin Watanabe & Takako Aoki: Mathematics Education and Lifelong Learning with the Future in Mind
First Page: 363
Last Page: 368
https://doi.org/10.37626/GA9783959872881.0.63
Abstract
The most important thing to increase high school students‘ motivation in mathematics education is to aim for lifelong learning. In current mathematics education in Japan, the biggest goal of mathematics education for high school students is to pass university entrance exams. In recent years, Japan’s declining population has become a serious problem for mathematics education. Anyone can now enter the university of their choice without taking any entrance exams. At this stage, there is no motivation to learn mathematics. This is an opportunity to change the purpose of learning mathematics from university entrance exams to a new purpose. The goal of mathematics education is to develop people who enjoy mathematics throughout their lives. We believe that mathematics education is a lifelong learning experience, not a short-term goal. This requires creative exploration and activity.
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Laura Watkins: Experimenting with Active Learning in Multivariable Calculus
First Page: 369
Last Page: 375
https://doi.org/10.37626/GA9783959872881.0.64
Abstract
Multivariable calculus is a course that builds upon the foundation laid differential and integral calculus courses but the nuances of transitioning from two-dimensional plane to three-dimensional space can make the course challenging. Relying on research about active learning I share changes made in my multivariable calculus course to incorporate active learning strategies along with my observations of the impact on student persistence and performance.
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Alan Zollman: Learning Beyond the Textbook: Intrinsic and Extrinsic Skills Needed for Students’ Mathematical Success
First Page: 376
Last Page: 379
https://doi.org/10.37626/GA9783959872881.0.65
Abstract
This research paper explores the dimensions of learning that extend beyond traditional textbooks, focusing on the intrinsic self-regulating abilities and extrinsic interpersonal skills crucial for students‘ success in mathematics. Investigating the symbiotic dynamics between individual aptitude and social competencies, the paper illuminates how a combination of internal cognitive abilities and effective interpersonal skills contributes to mathematical proficiency. We delineate the intrinsic self-regulating abilities, such as problem solving and persistence, alongside the importance of interpersonal skills like collaboration and communication in mathematical achievement. Findings offer valuable insights for educators, emphasizing the significance of fostering a holistic learning environment to enhance students‘ mathematical success.