Held at The Queen’s College Oxford University, UK August 14-18, 2023
Band 9 der Reihe Conference Proceedings in Mathematics Education
Münster 2023, ca. 275 S.
Print: 978-3-95987-249-2 39,90 €
E-Book: 978-3-95987-250-8 36,90 €
https://doi.org/10.37626/GA9783959872508.0
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Abstract of Book
This volume contains the papers presented at the International Symposium: Innovative Teaching Practices held on August 14-18 2023 in The Queen’s College, Oxford University. The Symposium was organized by The Mathematics Education for the Future Project – an international philanthropic project founded in 1986 and dedicated to innovation in mathematics, science, computer and statistics education.
https://doi.org/10.37626/GA9783959872508.0
Contents List
Fouze Abu Qouder & Miriam Amit
Ethnomathematics of Bedouin Culture (Geometry in Bedouin Embroidery)
First page: 1
Last page: 6
Abstract
In this essay we will present the ethnomathematics of the Bedouin society inthe south of Israel, and in particular the ethnomathematics manifested in thefolkloric embroidery of Bedouin women. The purpose of this essay is to showhow Bedouin women knew mathematics intuitively and used unique culturalvalues and elements, which contain and reflect a variety of didacticalmathematical aspects, concepts, and attributes. Also, we will show howBedouin women knew mathematics through their embroidery work. The datapresented based on research we conducted among the Bedouin population,with the aim of searching for collecting ethnomathematics knowledge inBedouin society. This goal was derived from our need to make the subjecteasier and more accessible to our students, and to increase their desire tostudy it.
Keywords: Bedouin embroidery, Geometry, Ethnomathematics.
https://doi.org/10.37626/GA9783959872508.0.01
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Jogymol Kalariparampil Alex
Mathematics Education for the Future: Evidence from Mathematics Education and Research Centre in a Rural University
First page: 7
Last page: 12
Abstract
South African rural mathematics education is confronted by poor learnerperformance in all phases of schooling. To address this, a MathematicsEducation and Research Centre was established in a rural university.Numerous innovative and developmental activities designed for theadvancement of teaching and learning of mathematics are conducted throughthe centre for pre-service and in-service teachers. Research was conductedon the effectiveness of these programs in the centre. The qualitative data from all the stakeholders indicated that the innovative activities created a positive impact and made mathematics more accessible. The successes of the different programs suggest that such innovative and developmental activities are needed to make mathematics more accessible, which in turn can address the poor learner performance.
https://doi.org/10.37626/GA9783959872508.0.02
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Anita N. Alexander
Cultivating Inquiry in Advanced Mathematics with the Next Generation of Mathematics Professors
First page: 13
Last page: 18
Abstract
How can we shift the culture of lecture in university mathematics? The purpose of this study was to provide an intervention for mathematics majors on effective practice in teaching advanced mathematics, inspiring the next generation of mathematics professors to engage in inquiry and discourse so their future students can internalize critical concepts. This workshop will reflect those weekly seminars, beginning with puzzles to motivate topics, followed by exploring Introduction to Analysis, Number Theory, and Topology through the 5E Model. Participants completed weekly exit tickets, providing positive feedback regarding the Think-Pair-Share approach, and the Engage, Explore, and Explain aspects of the 5E Model. Survey responses indicated a strong belief in providing students with opportunities in class to collaborate and engage in discourse.
https://doi.org/10.37626/GA9783959872508.0.03
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Nurten Alpaslan & Emre Alpaslan
Mathematics for Everybody
First page: 19
Last page: 20
Abstract
It is a big mistake to think like someone who is not good at mathematics, more precisely school mathematics, has a problem with his perception. Regardless of their academic success, every individual with a developed mathematical thinking system is successful in her/his job and is happy that her/his problem solving skills have also improved. It is a prejudice to think that mathematics is difficult. In childhood, each speech and behavior that emphasize the importance of mathematics in the environment send a message to the subconscious. Doing mathematics in art, music and physical education classes in primary education, also strengthens the subconscious mathematics anxiety. Avoiding mathematics in choosing subjects in secondary education, not being able to choose the right profession in the future, and doing a job that one does not like cause the individual to be unhappy and unproductive.
https://doi.org/10.37626/GA9783959872508.0.04
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Drishana Bachhawat
Introducing the History of Mathematics in the School Curriculum
First page: 21
Last page: 23
Abstract
This paper is an attempt to introduce the history of mathematics in school curriculum. Reasons behind this thought, pros, cons, and methods written down below will give you a clear idea behind this motive. Furthermore, eachreal-life idea, flowchart, diagram, etc will help you understand the roots of this subject. This idea has the potential of giving rise to an all-rounder development to students in the mathematical field.
https://doi.org/10.37626/GA9783959872508.0.05
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Dawnette Blackwood-Rhoomes &John Gordon
Developing Abstract Mathematical Thinkers Part 2- Implementing Viable Strategies
First page: 24
Last page: 30
Abstract
Abstract mathematical thinkers in the fields of pure mathematics and theoretical computer science have contributed significantly to the body of knowledge that has fundamentally altered the course of human civilization and technological advances. Halpern and Butler [1] have stated that “our future depends on our ability to think critically in a world that is growing more complex day by day”, and that critical thinking skills “should be a priority.” They concluded that “the ability of our students to think critically and abstractly is amatter of national importance.” This paper concerns itself with the implementation of viable strategies which can result in the development of the abstract mathematical thinker.
https://doi.org/10.37626/GA9783959872508.0.06
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Simone Brasili
Online Teacher Training for K-12 Schools on Conceptual Change in Symmetry and Invariance in the Classroom during Pandemic Covid 19.
First page: 31
Last page: 37
Abstract
A paradigm shift in symmetry in K12 schooling requires a significant change inthe teaching and learning process. Teachers play a critical role in enforcing this innovation based on the link between symmetry and invariance. Providing them with scientific and interdisciplinary knowledge about symmetry and invariance can help them develop effective teaching practices. The last three year cycle of the educational research project was adapted to online instruction for teacher training because of Covid-19. The design of the teacher training program and the steps taken to implement the instruction are described, using mixed methods and various instruments to collect, analyze, and evaluate data. The study highlights the potential of online instruction to promote a paradigm shift in symmetry education.
https://doi.org/10.37626/GA9783959872508.0.07
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Gail Burrill
Preparing Students for Tomorrow: The Role of Technology
First page: 38
Last page: 44
Abstract
Research suggests technology can make a difference in mathematics teaching and learning, enabling students to build conceptual understanding and engaging them in problems of real interest. Interactive dynamic technology enables more students to have access to more mathematics, allows students to visualize mathematical ideas, and gives students agency to choose solution pathways that make sense to them. However, research also suggests many teachers allow students to use technology only after they have learned “by hand.” The increasing power of technology is a call to rethink what is important to learn in secondary mathematics, recognizing that much traditional content can be left to technology, shifting the focus to understanding and interpreting mathematical results. This paper describes ways to make such avision a reality, where we teach mathematics to prepare students for tomorrow instead of for a world that no longer exists.
https://doi.org/10.37626/GA9783959872508.0.08
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Ann Dowker
The Numbers Count Intervention: Do the Benefits Persist
through Key Stage 2?
First page: 45
Last page: 50
Abstract
Starting in 2008, Edge Hill University developed a new intensive mathematics Intervention, termed Numbers Count, for Year 2 pupils considered to be in the lowest 5% for mathematics attainment. Children receive half an hour of individualised, or very small-group intervention per day. Children, who received this intervention, performed much better than controls on Key Stage 1assessments and on standardized tests (Torgerson et al., 2011). 6359 children who underwent Numbers Count intervention in 2010-2011 or in 2011-2012were followed up at the end of Key Stage 2, using information from the National Pupil Database. The children were compared with a group, whose Key Stage 1 results had placed them in the bottom 5% in mathematics. Their performance on Key Stage 2 tests was significantly better than that of the other initially low attainers. This suggests persistent effects of the programme.
https://doi.org/10.37626/GA9783959872508.0.09
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Angeline Duma, Magdeline Stephen & Emmanuel Mushayikwa
Cumulative Knowledge Building in a Grade 12 Semiconductors Lesson: A Comparative Study between Online and Contact Mode of Teaching
First page: 51
Last page: 59
Abstract
As a consequence of the COVID-19 pandemic, most institutions in 2020 were forced to shift to online teaching. This paper seeks to understand whether the planned online sessions provided equivalent cumulative knowledge building experiences as the traditional contact sessions, particularly in Technical sciences. The study used a qualitative case study and data was collected in the form of pre-recorded observations for the online lesson and classroom observations for the contact lesson. To map the strengths of semantic gravity in both lessons, a translational device from the Legitimation Code Theory(LCT) was used. The study revealed that, while both lessons created conditions for cumulative knowledge building, contact sessions offered better opportunities because of the extended semantic gravity range and the teachers’ ability to explicitly define what constitutes knowing science. These findings suggest that online teachers could deliver effective lessons if they incorporated activities that include learner – teacher engagements to expand the semantic gravity range of their lessons.
Key words: Online sessions,
Contact sessions, Semantic gravity (SG), Legitimation Code Theory (LCT),
Cumulative knowledge building
https://doi.org/10.37626/GA9783959872508.0.10
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Courtney Fox
Exponential Growth and the Metric System: Using Stem to
Create an Active Learning Environment
First page: 60
Last page: 63
Abstract
The integration of mathematics and the sciences has long been a topic of conversation among educators. But true integration rarely happens within theclassroom for a variety of reasons – teacher preparedness, school support, and teacher beliefs. However, we can change this with engaging lessons where students are challenged in an active learning environment. This lesson uses an integrated approach to introduce students to exponential growth. By anchoring the material in the metric system, the science is highlighted throughout. Students learn both mathematics and science through an active learning experience that integrates exponential growth and the conversion of metric units from 10-15 to 1015.
https://doi.org/10.37626/GA9783959872508.0.11
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Grant A. Fraser
Teaching Online Courses for Undergraduate University
Students: Challenges and Opportunities
First page: 64
Last page: 66
Abstract
The author taught several courses using online learning during 2020 and2021. These were mathematics courses at the undergraduate University level. They were given at California State University, Los Angeles. During this experience, the author encountered many challenges and obstacles. Some oft these can be attributed to the nature of the online process itself, but in other cases, idiosyncratic policies adopted by the University proved to be counterproductive to fundamental aspects of the teaching process. Such policies must be modified to improve the effectiveness of this type of teaching. In this paper, the author summarizes his experiences, with particular attention to the difficulties that were encountered. He also proposes alternative techniques that could be employed to make the learning experience more rewarding and satisfying for both the instructor and the students.
https://doi.org/10.37626/GA9783959872508.0.12
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Gerald A. Goldin
Foundational Pillars of Mathematics: Implications for aHolistic Philosophy of Mathematics Education
First page: 67
Last page: 72
Abstract
Drawing on some well-studied ideas, I characterize three sources of human mathematical knowledge as foundational pillars: empirical observation, rational thought, and value. Together, these support the essential concept of truth in mathematics. All three are necessary to a sound, holistic philosophy of mathematics education. Empirical observation underlies learners’ sensory, exploratory processes of discovery, verification, and understanding, prerequisite to mathematical abstraction. Rational thought, informal and formal, underlies definition, axiomatization, and deduction enabled by conventional symbol systems. Value underlies more than learning about applications and practical uses. It is fundamental to experiences of beauty, social purpose, and meaning in mathematics – satisfying fundamental needs of the human psyche. Such a holistic perspective envisions a universally accessible world of mathematics.
https://doi.org/10.37626/GA9783959872508.0.13
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Christopher Gordon & David Pugalee
Publishing Secondary Students’ Research Projects
First page: 73
Last page: 78
Abstract
This paper reviews the literature on and process of publishing secondary student research by reflecting on the authors’ experiences working with four secondary students to publish their manuscripts in a peer-reviewed scientific journal. We propose two essential elements to improve student researchers’ability to publish their manuscripts. These elements include effecti ve mentoring of the entire research process and selecting a journal that provides guidance and mentoring for secondary students and their mentors in the publication process. Additional areas to consider when working with secondary studentsinclude using data analysis tools similar to those used by academic researchers.
Key words: secondary student research, Journal
https://doi.org/10.37626/GA9783959872508.0.14
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John Gordon
Developing Abstract Mathematical Thinkers Part 1 –
Identifying the Challenges
First page: 79
Last page: 82
Abstract
Abstract mathematical thinkers in the fields of pure mathematics andtheoretical computer science have contributed significantly to the body ofknowledge that has fundamentally altered the course of human civilization and technological advances. Halpern and Butler [1] have stated that “our future depends on our ability to think critically in a world that is growing more complex day by day”, and that critical thinking skills “should be a priority.” They concluded that “the ability of our students to think critically and abstractly is a matter of national importance.”
https://doi.org/10.37626/GA9783959872508.0.15
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Ivona Grzegorczyk
From 2D to 3D Symmetries
First page: 83
Last page: 89
Abstract
We study student understanding of symmetry in artistic designs. After participants mastered drawing and classifying two-dimensional designs, they moved to much more complicated three- dimensional solids and surfaces generated by graphic tools. We analyze learners’ ability to find all symmetries of three-dimensional surfaces and their classification methods.
https://doi.org/10.37626/GA9783959872508.0.16
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Ruhani Gulati & Saumya Gupta
ISOTHETIC POLYGONS: Application of Fisk’s Proof and
Fortress Theorem
First page: 90
Last page: 94
Abstract
This research paper delves into the practical application of the Art Gallery Theorem in determining the optimal guard placement for the Mayo College Girls School main building. The study explores the significance of Chvátal’s Art Gallery Theorem and Fisk’s Proof in minimizing the number of guards required to cover the interior of the polygonal structure. Moreover, the research examines the properties of isothetic polygons, performs triangulation, and applies vertex coloring techniques to achieve effective guard placement. The findings contribute to enhancing the security measures of educational institutions and provide avenues for future research in this domain.
https://doi.org/10.37626/GA9783959872508.0.17
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Pam Harris
Developing Mathematical Reasoning: The Trap of Algorithms
First page: 95
Last page: 98
Abstract
The role of mathematics education is to mentor students to reason like mathematicians, not parrot like robots. To this end, algorithms are incredible historical achievements, but are not helpful teaching tools. Traditional digitbased procedures limit student growth by allowing less sophisticated reasoning, which will not be sufficient for students to progress to more advanced mathematical concepts. This presentation illuminates the trap of teaching students to simply mimic steps and instead emphasizes logical deduction through mathematical relationships. Participants will engage in an instructional routine called “Problem Strings” to elucidate the way a mathematician might solve a problem. To inform effective curriculum design, they will also learn a nested hierarchy of reasoning domains that increase in sophistication, with each level featuring more advanced thinking.
https://doi.org/10.37626/GA9783959872508.0.18
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Marc Husband, Evan Throop-Robinson, Allison Tucker & Carolyn Clarke
Co-teaching in an Elementary Mathematics Education Methods Course: Growing Awarenesses
First page: 99
Last page: 106
Abstract
Many prospective teachers (PTs) come to elementary mathematics teacher education classes reporting poor previous learning experiences. They often expect mathematics teacher educators (MTEs) will lecture them about how to teach mathematics differently and better. Subsequently, MTEs face challenges to respond to the expectations of their students and to cultivate experiences that support envisioning teaching and learning mathematics anew. One view of co-teaching involves MTEs interacting with students fluidly and responding in the-moment to their needs (Marzocchi et al., 2021). In this paper, we describe how we invited PTs to co-teach with us while their peers worked on mathematics tasks. Using Mason’s (1998) notion of awareness, co-teaching supports PTs’ and MTEs’ growing awareness of teaching moves that provide “sensitivities which enable [them] to be distanced” (p. 260) from the showing and-telling mathematics.
https://doi.org/10.37626/GA9783959872508.0.19
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Gibbs Y.Kanyongo
Introduction to Confirmatory Factor Analysis (CFA)) using Lavaan in R Statistical Programming Language
First page: 107
Last page: 108
Abstract
This workshop will cover how to perform a confirmatory factor analysis(CFA)using Lavaan. Lavaan, which stands for latent variable analysis is a free open-source commercial package in R, and it is developed and maintained by Yves Rosseel (Rosseel, 2012). It is used to fit a variety of latent variable models, including confirmatory factor analysis, structural equation modelling and latent growth curve models. CFA allows the researcher to test the hypothesis that a relationship between observed variables and their underlying latent constructs exists. CFA falls under the broad concept of factor analysis is divided broadly into two types, exploratory and confirmatory. Exploratory factor analysis (EFA), is used to understand the underlying dimensions or constructs of an unknown scale, while confirmatory factor analysis (CFA) is used to test hypothesis of a pre-determined factor structure of a previously developed
scale.
https://doi.org/10.37626/GA9783959872508.0.20
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Kathryn Kozak
Active Learning Activities: Finding and Developing
First page: 109
Last page: 112
Abstract
Active learning is a teaching method that engages students in the learning process. Research shows that this teaching method increases student success. One of the challenges with this instructional approach is to find teaching material to use in the classroom. The Internet is one location; however, finding specific learning activities may be daunting and difficult. Thus, this paper presents a scholarship that advocates for active learning. The paper then outlines where to find some related activities for instruction, as well as explore how to develop such activities.
https://doi.org/10.37626/GA9783959872508.0.21
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Ishikka Ladia & Mrigshira Mehra
Scutoids
First page: 113
Last page: 116
Abstract
Recent studies in the field of medical science revealed a new type of cell which has more or less a geometric shape. Biologists discovered these cells in the epithelial tissues. This new shape closely resembles Prismatoids with some differences and is called Scutoid. In this paper, we will be looking at various properties of a Scutoid, benefits offered by its unique shape, and the gateways it may open to for further research.
https://doi.org/10.37626/GA9783959872508.0.22
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Barbara H. Leitherer, Pankaj R. Dwarka, Entela K. Xhane & Jignasa R. Rami
Global Learning and Climate Change: Undergraduate Research Reflections from Student Scholars and Faculty Advisors at a Two-Year College
First page: 117
Last page: 122
Abstract
Undergraduate research is considered a high-impact learning practice by the American Association of Colleges and Universities (Bowen, 2023). When the opportunity arose, a group of faculty advisors accompanied students in a two year college in the US through an independent study analyzing real-world global climate change data supplied by the World Wildlife Fund (WWF). In this collaborative work students and faculty reflect on undergraduate research as an innovative venue to develop students’ global mindsets in the 21st century. The proposal findings share candid insights about the development of student research skills, scholarly engagement, student testimonials, and future life impact. Furthermore, findings emphasize faculty experiences observing the challenging aspects of undergraduate research, analyzing student exit surveys, and recognizing the need for continuous professional development.
https://doi.org/10.37626/GA9783959872508.0.23
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Michail Lousis
Media as Constitutive Factors for Paradigm Shifts in Mathematics
First page: 123
Last page: 130
Abstract
This study brings in serious evidence from the history of the development of the science of mathematics that knowledge is not an individual enterprise but rather social/collective in nature and is produced by collectives of humans with-media (Borba & Villarreal, 2005), which has not been presented by the conceivers of the notion. The study pinpointed that the media are components of the epistemic subject of mathematics, being neither auxiliary nor supplementary, but an essential, necessary, constitutive part of it. They are so pertinent that in the case of their absence, different knowledge is produced. Further, different media in use produce different knowledge. The media that are employed in the work alter, transform, redefine, and reorganize the practices, the contents, and the ways of knowing. Thus, media are epistemological, cognitive tools. Furthermore, the investigation stresses that the media are constitutive factors for paradigm shifts in mathematics.
Keywords: mathematical cognition, humans-with-media, collective (social)
nature of mathematics, paradigm shift.
https://doi.org/10.37626/GA9783959872508.0.24
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Günter Maresch, Natalia Segura Caballero, Julia Köck & Eleni Lagoudaki
The New Online Platform RIF for Training Spatial Ability
First page: 131
Last page: 136
Abstract
Spatial ability plays a critical role in developing expertise in Mathema tics and STEM fields in general. Therefore, we (15 geometry researchers and 15students in Austria) developed the online platform RIF (https://adi3d.at/rif30/en/)where students from the age of 7 to adulthood can train their spatial thinking skills with the help of more than 1.500 interactive tasks. All the tasks are designed in such a way that they can directly be integrated into school lessons and university lectures. The platform, which is free to use for everybody, was launched in 2019 and today more than 60.000 students from 28 countries all over the world use the platform. The large amount of data allows to do a lot of research. In the talk results regarding gender differences and the correlation of spatial ability and mathematics will be presented. The analyses of the data show that girls perform better than boys in nearly all areas of spatial ability and that there is a strong correlation between spatial thinking skills and the math grade of primary and secondary students.
https://doi.org/10.37626/GA9783959872508.0.25
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Johannes Memling
From the Fundamental Theorem of Algebra to Monstrous Moonshine
First page: 137
Last page: 142
Abstract
With the use of artificial intelligence and machine learning that can solve and explain problems and can be integrated into existing workflows to support mathematical research, the focus of future courses in mathematics will be shifted towards a search for potential patterns and relations between mathematical objects and an effort to make sense of them. The AI uses the observations to guide the intuition towards solutions of potential conjectures. Future courses in mathematics will have higher levels of cognitive demand vs current technical problem-solving skills. As an example, we discuss how the Fundamental Theorem of Algebra within a small number of steps, reaches the monstrous moonshine, or moonshine theory, the unexpected connection between the monster group M and the modular j function. This connection is underlain by a vertex operator algebra, allowing physics to form a bridge between two (and more) mathematical areas.
https://doi.org/10.37626/GA9783959872508.0.26
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Shelby Morge & Christopher Gordon
Integrating Mathematics and Computer Science Using Squeak Etoys
First page: 143
Last page: 148
Abstract
To innovate means to make changes or do something in a new way (Merriam-Webster, 2023). As a follow up to our Cambridge workshop, we will share howa technology tool, Squeak Etoys, can be used to engage primary students (ages 8-10 years old) in discovering the relationship between a fractional amount and angle measure using a circle model. Innovation in education involves creativity, adaptability, and accessibility (Kaltura, 2023). Squeak Etoys is a dynamic, accessible tool that allows students to develop computer models of various topics. When teachers integrate computer science within mathematics instruction, all students have access to computer science topics and are able to make connections, which leads to deeper understanding. In this paper, we describe a problem-based lesson and engage participants in the development of a Squeak Etoys computer model.
https://doi.org/10.37626/GA9783959872508.0.27
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Diva Moriani & Nishika Shah
Non-Routine Problem-Solving Strategies for Children Making Mathematics Formula Free
First page: 149
Last page: 155
Abstract
The aim of this paper is to talk about non-routine problem-solving strategies and how they are useful for children. With respect to non-routine problemsolving strategies, I would like to discuss the following:
- Various types of non-routine problem-solving strategies
- Comparison between solving ‘using formula without thinking’ and ‘using logical reasoning and non-routine problem-solving strategies’ by solving 3-5 problems
https://doi.org/10.37626/GA9783959872508.0.28
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Janina Morska
The Teacher’s Job after the Pandemic
First page: 156
Last page: 159
Abstract
In this paper I would like to share my experience of how to use the modern computer and information technologies during the lessons with students after the pandemic. I will present tools such as applications, websites and computer programs used to explain new material, conduct exercises with students and test their knowledge and skills. I will discuss how to prepare notes for children, useful in the event of absence or problems in class. I will also present my mathematical blog called “mathematical impressions” where I post links and materials.
Keywords: mathematics, teaching, applications, computer programs, didactic
materials, didactic games, angles, fractions, integers.
https://doi.org/10.37626/GA9783959872508.0.29
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Ildikó Nagy Pomuczné
Content and Teaching of the Topic of Number Theory in the 11th Grade of High School in Hungary
First page 160
Last page 163
Abstract
The National Curriculum (NAT 2020) dedicates an entire chapter to the topic of number theory in the 11th grade of the high school curriculum. The number theory is the topic of IV. chapter of the centrally published textbook, and contains 12 lessons. This is considered a novelty compared to the previous 11th grade teaching materials that date back several decades. In my presentation, I will present the course material included in the centrally published textbook, and I would also like to touch on the antecedents of the topic in the lower grades. I highlight the knowledge and problem-solving methods that are new in the new curriculum, and look back at older curricula from the point of view of teaching number theory. In my presentation, I would like also to present the documentation created on my mathematics lessons for the 11th grade group I am currently teaching.
https://doi.org/10.37626/GA9783959872508.0.30
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Maria de Natividade
AMU Commission for Mathematics Education in Africa: A Contribution to Improving the Quality of Mathematics Teaching and Learning in Africa
First page: 164
Last page: 167
Abstract
The African Mathematical Union Commission for Mathematic Education in Africa (AMUCMEA) is one of the 5 African Mathematical Union Commissions whose principal objectives is to contribute to the production and improvement of Mathematics teachers in all education System in the African continent. In this talk we will give a brief history of the commission, the activities developed since its creation and a plan of actions for the next 4 years, with the purpose of establishing relationships with other organizations that pursue the same objectives.
https://doi.org/10.37626/GA9783959872508.0.31
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Reinhard Oldenburg
A Technology-oriented Algebra Curriculum
First page: 168
Last page: 173
Abstract
The traditional algebra curriculum of (lower) secondary schools is (at least in Germany) plagued by several severe deficits: 1) Students are hardly interested and motivated to learn algebra. 2) The semantics of algebra as discussed in didactics is unnecessary complex and partially incompatible with algebra in upper secondary schools and at the university level. 3) The algebra taught is partly incompatible with the algebra of programming languages and computer algebra systems. This paper gives a short overview of a technology-oriented curriculum that shall overcome these issues and it presents some of the technological tools that have been developed to provide a consistent and motivating learning experience of algebra. An essential feature is that technology is not just a medium, but a tool and benchmark for consistency.
https://doi.org/10.37626/GA9783959872508.0.32
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Elizabeth Oldham & Aibhín Bray
Innovative Experiential Practice(s) in Teacher Education: A Case Study in an Irish University
First page: 174
Last page: 180
Abstract
On the premise that experience of innovative practices is a key factor helping teachers and student-teachers to adopt them, this paper examines work done with serving, preservice and prospective teachers in Trinity College Dublin. For teachers and student-teachers, it focuses on use of the Bridge21 (Bridge to 21st Century Teaching and Learning) model of professional development, with participants experiencing constructivist, team-based, technology-mediated and project-based teaching and learning. Also, at a time of unprecedented teacher shortage, ways of attracting good candidates into teaching must be considered; hence, a module for undergraduate mathematics students allows prospective teacher education candidates to spend time experiencing school classrooms as assistants to teachers. Research indicating positive outcomes from these practices is reported, and possible developments are outlined.
https://doi.org/10.37626/GA9783959872508.0.33
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Andrea Peter-Koop
The Impact of a Long-Term In-service Program for Early Years Teachers
on Students’ Achievements in Early Mathematics
First page: 181
Last page: 186
Abstract
This paper reports the findings of an evaluation study in the context of a longterm professional development program aiming at kindergarten and Grade 1 teachers, enabling them to assist children with the transition to school in terms of their mathematics learning. The program especially focused on children potentially at risk with respect to their school mathematics learning. Pre- and post-test data indicate considerable improvement in early number understanding for most of the children.
https://doi.org/10.37626/GA9783959872508.0.34
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Sarah Quebec Fuentes
S3D Approach: Strategies and Tools for Fostering Equitable
Small-Group, Student-to-Student Discourse
First page: 187
Last page: 193
Abstract
Placing students in small groups does not automatically imply that the students will be able to productively interact with each other about the mathematics. The S3D Approach is a two-phase process through which educators can progress to improve small-group, student-to-student discussions in their mathematics classes. In the first phase, educators evaluate existing smallgroup discourse via three lenses (group dynamics, discourse quality, and teacher support). In the second phase, educators use what they learned in Phase 1 to enhance the small-group discourse through purposeful teacher actions. Tools are associated with each lens of Phase 1 as well as Phase 2 to assist educators in recording their observations. The S3D Approach helps establish norms of a safe classroom where students contribute their thinking, through which a shared understanding of mathematical justification is built.
https://doi.org/10.37626/GA9783959872508.0.35
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Ann-Sofi Röj-Lindberg
Reflections on the Links between Innovative Practices in
Mathematics Education and Democracy
First page: 194
Last page: 199
Abstract
Mathematics education can promote democratic competences and values, but also inhibit them, and create inequalities. A basic idea behind the promotion of democratic competences and attitudes is proposed by Vithal (1999): within a mathematics classroom where it is possible for students to experience democratic life students can learn to listen to others’ ideas, argue, take decisions, and critically analyse arguments made by authorities, e.g., the teacher. Aguilar and Zavaleta (2012) found three facets of mathematics education linked to democracy: a provider of critical mathematical skills, a source of values and attitudes, and a social gatekeeper. In this paper I discuss how mathematics teachers through innovative practices can foster a democratic competence in their students.
https://doi.org/10.37626/GA9783959872508.0.36
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İpek Saralar Aras & Bengi Birgili
In the Pursuit of a Course Design: A TPACK-based Geometry for Preservice Mathematics Teachers
First page: 200
Last page: 205
Abstract
Preservice mathematics teachers seem to need professional support regarding the use of educational technologies to teach geometry topics. Particularly, our previous study showed that when it comes to their technopedagogical content knowledge (TPACK), they self-report to need guidance to teach with technology. The purpose of this study was to develop a 14-week course to increase their TPACK in hopes of bridging the knowledge gap identified in earlier studies. This paper summarized the course content with a humble expectation to get valuable feedback from an international audience. The developed course included lessons on components of TPACK, which were found to require improvement to best meet future students’ needs in teaching geometry with technology. We hope that preservice teachers’ TPACK levels will be improved after the course.
Keywords: Course design, design-based research, preservice mathematics
teachers, technology, TPACK.
https://doi.org/10.37626/GA9783959872508.0.37
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Nishika Shah and Diva Moriani
Using Technology to Learn Mathematics
First page: 206
Last page: 208
Abstract
This paper is an attempt to introduce using technology to learn mathematics. Reasons behind this thought, pros, cons, and methods written down below will give you a clear idea behind this motive. Furthermore, each real-life idea, flowchart, diagram, etc. will help you understand the roots of this subject. This idea has the potential of giving rise to all-rounder students in the mathematical field.
https://doi.org/10.37626/GA9783959872508.0.38
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Pari Shah
Non-routine Problem-solving Strategies
First page: 209
Last page: 212
Abstract
Students constantly confront new problems both at school and in their daily lives. Therefore, they need to be flexible beyond knowing and applying various strategies. Because the strategy they use in one problem may not work in another, the ability to switch to another strategy is crucial. The problems with the greatest potential to improve flexibility are non-routine problems since they are challenging and require higher-order thinking skills. Non-routine problems compel students to think creatively and rationally and foster communication skills as students document and explain the strategies to others as well. It also helps them gain confidence as, they soon realise that they can independently determine appropriate strategies and successfully apply them. These problem solving skills are necessary as students these days are used to being told to follow a learned algorithm, which is basically spoon-feeding.
https://doi.org/10.37626/GA9783959872508.0.39
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Atara Shriki & Ilana Lavy
Mathematics Teachers Using ChatGPT for Designing Lessons Plans
First page: 213
First page: 218
Abstract
In November 2022, a kind of „revolution“ took place. The prototype of the ChatGPT was launched and immediately hit the headlines. Soon the interest in the software reached our elementary school prospective mathematics teachers‘ (ESPMTs) classrooms, and they began to wonder whether artificial intelligence models will shortly replace teachers. So we initiated an experiment in which the ESPMTs „chatted“ with ChatGPT about mathematics education and used it for designing lesson plans (LPs). Reflecting on their experience, the ESPMTs found that interacting with ChatGPT for designing LPs produced higher-quality LPs in a much shorter time. Nonetheless, they realized that lacking the human-like understanding and empathy that human teachers possess, as of today, artificial intelligence models cannot replace them. This paper presents examples from the chats and the ESPMTs‘ reflections.
https://doi.org/10.37626/GA9783959872508.0.40
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M. Vali Siadat
An Innovative Model of Teaching and Learning in Mathematics
First page: 219
Last page: 224
Introduction
We present the theory and practice of a research-based model of teaching and learning of mathematics at the college, coined the Keystone model. This is a model of dynamically assessing student learning and adjusting teaching practices. Keystone’s philosophy is grounded on the belief that all students can learn mathematics provided they are engaged in the learning process. This system views classroom as a learning community where through peer-topeer interaction and cooperation, all students achieve. Contrary to other programs that put the students in competition with one another, essentially pitting them against each other for grades, our program challenges students to cooperate so that all attain the standards of excellence. Keystone is an alternative model to traditional educational practices and its basic principles should be applicable to all disciplines.
https://doi.org/10.37626/GA9783959872508.0.41
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Clifford Singer
Geometric Constructions: Understanding Constructing Irrational Numbers on the Number Line with Compass and Ruler in the Middle School.
First page: 225
Last page: 229
Abstract
The technology is a compass and ruler with pencil and paper. The scope of this mathematics section is to develop step by step construction with visual hands-on skills which I have been teaching since 1992. Drawing accurate diagrams as demonstrations of geometry instruction is an essential goal. Starting the lesson, students practice the use of the compass and ruler to build geometric figures. The lesson is designed to represent the square root of a number on a number line and locate precisely. We are going to learn the steps for representation of irrational numbers on a number line and solve a few examples to understand the concept better. In terms of a visual representation we are going to use a horizontal number line. One must understand the definition of irrational numbers a history of irrational numbers. Irrational numbers have decimals that neither terminate nor become periodic.
https://doi.org/10.37626/GA9783959872508.0.42
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Panagiotis Stefanides
Dissemination Methods Employed in Presenting the Discrete Geometries of the Discovered Invention of a Non-Regular Icosahedron: “The Generator Polyhedron”
First page: 230
Last page: 236
Abstract
The New Polyhedral Form [ beyond the Five Regular Platonic Polyhedral], resulted from a polychronous work, while searching [mainly] Plato’s Timaeus Philosophy and Geometries involved in the Building of the World’s Structures[ mainly by Tetrahedral Forms] based on his “ Most Beautiful Triangle” [the Magirus/ Kepler one is a Constituent part of this Triangle, similar to it , but not the same and not as beautiful as it ] proposed Diachronically to Conferences by the Author. The Theories Developed in this work, presented, via various methods [Papers, Posters, “3D Models” etc.], to Live and Virtual National and International Conferences, to Mathematical, Engineering and Physics Societies, Art Exhibitions, to The Math Forum, to Institutions and Universities’ Libraries [ and to one of them this Novel Solid Model for Exhibition]. Also similarly to the Social Mass Media such as LinkedIn, ResearchGate, Academia, by Paper Deposits.
https://doi.org/10.37626/GA9783959872508.0.43
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Aynalem Tesfaye
The Effect of Gender and School Location on Early-Grade Children’s Mathematics Achievement in Halaba, Ethiopia
First page: 237
Last page: 244
Abstract
Mathematics education plays a vital role in equipping individuals with the necessary knowledge and skills that are useful for individual life. This study investigated early-grade (grade 1-4) children’s achievement in mathematics in relation to school location and gender. Data were collected from 423 earlygrade children and 9 principals at 9 primary schools in the Halaba zone in Ethiopia, through semi-structured interviews and the Early Grade Mathematics Assessment (EGMA) test. The findings of this study revealed that early-grade children’s achievement in mathematics as measured by EGMA is average (51.5%). There is a statistically significant difference between male and female students’ mean scores and the difference in the urban area showed a large gap however, the difference in relation to school location is not significant. There is a statistically significant effect for gender on students’ achievement with a large effect size (η 2 = .055) however, the effect of school location and the interaction effect of gender and school location were not statistically significant.
https://doi.org/10.37626/GA9783959872508.0.44
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Eleni Tsami, Dimitra Kouloumpou, Andreas Rokopanos & Dimitrios Anastasopoulos
Shapes and Geometric Aptitude
First page: 245
Last page: 250
Abstract
The PISA results with regards to Mathematics and Science for the Greek students have been alarming in multiple consecutive reports. Drawing from this experience, we focus on cultivating the basic geometric understanding of the individual and create a series of constructive and discovery-learning exercises, in order to facilitate the learning process. In this context, we develop an exercise intended for students between ten and twelve years of age. The exercise guides the students to identify geometrical shapes in a background and subsequently to observe and conceptualize basic properties of the triangle (e.g., the sum of the angles of a triangle). The exercise is in digital format and is implemented through educational platforms, thus allowing students to practice in an engaging environment.
https://doi.org/10.37626/GA9783959872508.0.45
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Vivian Libeth Uzuriaga López, Héctor Gerardo Sánchez Bedoya & Walter F. Castro Gordillo
Problem situations for the teaching of school mathematics
First page: 251
Last page: 254
Abstract
The problem situations built from the needs and interests of the students are adequate for teaching and learning mathematics. The situations encourage both students to abandon their passive role and commit to the construction of knowledge and teachers to give up their leading role and assume to be learning guides through intentional questions that promote the development of mathematical thinking. The situations are part of didactic units built within the framework of the postgraduate training in Education in la Universidad Tecnológica de Pereira-Colombia- of professors who teach mathematics. The research is qualitative and of a descriptive nature, which reports on the transformation of the teaching and learning processes of mathematics at different levels of schooling.
https://doi.org/10.37626/GA9783959872508.0.46
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Ariana-Stanca Văcăreţu
Visible Maths
First page: 255
Last page:260
Abstract
The starting point of the Visible Maths series of workshops was the realisation that students have difficulties understanding mathematical concepts. I hypothesised that creating real objects that show mathematical concepts or ideas might support students’ understanding. The students involved in this project were 9th graders (14-15 years old). I worked with a professional designer for designing and implementing the workshops. During the first workshop we launched the task: “Choose a mathematical concept (e.g. radian, cone sections, trigonometric circle, function, number, Pascal’s triangle, etc.), design and make an object to illustrate the concept.” After five months, in the eighth workshop, the students presented the prototypes and the work process. This paper presents my experience with the Visual Maths workshops, and some of the implementation results.
https://doi.org/10.37626/GA9783959872508.0.47
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Alan Zollman
Wellness Pedagogical Knowledge: Professional Development to Address STEM Teachers’ Needs
First page: 261
Last page: 265
Abstract
Covid-19 demonstrated to us that the traditional professional development was not enough to assist our teachers (Maher & Zollman, 2021). They needed intra-personal and inter-personal support beyond subject content knowledge, pedagogy content knowledge, and technological pedagogical knowledge. To meet their needs, we shifted our approach to included “Wellness Pedagogical Knowledge” in our workshops with teachers. These addressed teacher’s wellbeing, emotional support, and interests. We added topics for internal, selfregulating skills such as time management, setting priorities and stress management. We also included external, interpersonal skills such as empathy, patience, active listening, and teamwork. Lastly, we added teacher interests such as personal finance and how to separate scientific information from opinions and beliefs. Teachers accepted these ideas as a positive impact onthem and their students.