Relevant bibliographies by topics / Mathematical understanding

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematical understanding'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 July 2025

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Journal articles on the topic "Mathematical understanding"

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Pirie, S. E. B., and R. L. E. Schwarzenberger. "Mathematical discussion and mathematical understanding." Educational Studies in Mathematics 19, no. 4 (1988): 459–70. http://dx.doi.org/10.1007/bf00578694.

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Chattopadhyay, Rabindranath. "Understanding Undefined Quantities: Bridging Mathematical Concepts with Physical and Mathematical Realities." International Journal of Science and Research (IJSR) 13, no. 1 (2024): 923–24. http://dx.doi.org/10.21275/sr24111235936.

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Williams, Helen. "Understanding mathematical words." Practical Pre-School 2004, no. 45 (2004): 25. http://dx.doi.org/10.12968/prps.2004.1.45.40241.

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Bundy, Alan. "Understanding mathematical proofs." New Scientist 192, no. 2573 (2006): 27. http://dx.doi.org/10.1016/s0262-4079(06)60723-9.

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White, Allan Leslie. "Juggling Mathematical Understanding." Southeast Asian Mathematics Education Journal 4, no. 1 (2014): 57–67. http://dx.doi.org/10.46517/seamej.v4i1.29.

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This paper presents a theoretical model for the teaching for understanding of school mathematics. After describing two categories of understanding, it develops a continuum between rote and insight. In the process of describing the model, it articulates the assumptions underpinning the model and presents a process whereby a teacher can move the teaching strategies towards the development of insight within the students. It will argue that the development of insight should be the goal of all school mathematics classrooms. And that in order to achieve this goal the classroom teacher must become an
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Maclellan, Effie. "Articulating ‘understanding’: Deploying mathematical cognition." Scottish Educational Review 46, no. 2 (2014): 73–89. http://dx.doi.org/10.1163/27730840-04602006.

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Scotland's Curriculum for Excellence (CfE), constitutes the demands that teachers are supposed to meet. Its intentions for the mathematics curriculum are similar to those in many countries: that learners be sufficiently mathematically literate to use mathematics in the personal, professional and societal dimensions of their lives. But like many attempts to reform mathematical curricula elsewhere, CfE does not address the fundamental issue of mathematical understanding. Of course, learner understanding transcends the mathematical curriculum per se, but the significance of mathematical understan
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Sultanova, L. B. "Understanding in mathematical science." Rossiiskii Gumanitarnyi Zhurnal 6, no. 1 (2017): 33. http://dx.doi.org/10.15643/libartrus-2017.1.3.

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Armour-Garb, B. "Understanding and Mathematical Fictionalism." Philosophia Mathematica 19, no. 3 (2011): 335–44. http://dx.doi.org/10.1093/philmat/nkr013.

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Yoong, Wong Khoon. "Aspects of Mathematical Understanding." Singapore Journal of Education 8, no. 2 (1987): 45–55. http://dx.doi.org/10.1080/02188798708547623.

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Byers, Victor, and Stanley Erlwanger. "Memory in mathematical understanding." Educational Studies in Mathematics 16, no. 3 (1985): 259–81. http://dx.doi.org/10.1007/bf00776733.

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Dissertations / Theses on the topic "Mathematical understanding"

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Piatek-Jimenez, Katrina L. "Undergraduate mathematics students' understanding of mathematical statements and proofs." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280643.

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This dissertation takes a qualitative look at the understanding of mathematical statements and proofs held by college students enrolled in a transitional course, a course designed to teach students how to write proofs in mathematics. I address the following three research questions: (1) What are students' understandings of the structure of mathematical statements? (2) What are students' understandings of the structure of mathematical proofs? (3) What concerns with the nature of proof do students express when writing proofs? Three individual interviews were held with each of the six participant
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Lau, Kwok-yin Arthur, and 劉國賢. "Fostering mathematical understanding through collaborativeexplanation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31961769.

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Apostu, Raluca. "Understanding cyclical thrombocytopenia : a mathematical modeling approach." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101834.

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Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in the platelet count. Although first reported in 1936, the pathogenesis and an effective therapy remain to be identified. Since besides fluctuations in platelet levels the patients hematological profile have been consistently normal, a destabilization of a peripheral control mechanism might play an important role in the genesis of this disorder. In this thesis, we investigate through computer simulations the mechanisms underlying the platelet oscillations observed in CT. First, we collected t
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Bufacchi, Rory John. "Understanding defensive peripersonal space through mathematical modelling." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10054520/.

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The spatial location of environmental events with respect to one’s body largely dictates their behavioural relevance. Given that stimuli occurring near the body have a greater potential to cause harm, even the phylogenetically-old defensive hand-blink reflex (HBR) increases in magnitude with stimulus proximity. The HBR has allowed for a preliminary characterisation of a defensive peripersonal space (DPPS). The work described here provides a full spatial characterization of DPPS using formal geometrical modelling of HBR data, and highlights the functional significance of DPPS through its depend
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Gibbons, Stacie Joyce. "Manipulatives and the Growth of Mathematical Understanding." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3212.

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The purpose of this study was to describe how manipulatives facilitated the growth of one group of high school students' mathematical understanding of combinatorics and Pascal's Triangle. The role of manipulatives in mathematics education has been extensively studied, but much of the interest in manipulatives is focused on the general uses of manipulatives to support student learning. Unfortunately, there is a lack of research that explicitly defines how manipulatives can help students develop mathematical understanding. I have chosen to examine mathematical understanding through the lens of t
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Tapia, Ernesto. "Understanding mathematics: a system for the recognition of on-line handwritten mathematical expressions." [S.l. : s.n.], 2004. http://www.diss.fu-berlin.de/2005/12/index.html.

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Milton, Kenneth G. "Students' understanding of the mathematical equality and inequality relations : a developmental approach." Thesis, Curtin University, 1999. http://hdl.handle.net/20.500.11937/1006.

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The motivation for this study was the desire to make the path to learning elementary algebra as 'generalised arithmetic' more clearly defined for both students and teachers.In the initial learning of algebra, algebraic expressions are transformed to equivalent other forms and techniques are developed for solving simple equations. Both facets require students to have a thorough understanding of arithmetic equality ' properties' if the developed procedures and techniques are to be adequately understood. The same can be claimed also with respect to arithmetic inequality and the solving of inequat
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Marshall, Anne Marie 1974. "Understanding opportunities to practice what we preach mathematical experiences of mathematics education doctoral students /." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8750.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.<br>Thesis research directed by: Dept. of Curriculum and Instruction. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Thangavel, Vigneshwaran. "Mathematical models for understanding lithium sulfur batteries phenomena." Thesis, Amiens, 2019. http://www.theses.fr/2019AMIE0017.

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Les batteries Li-S ont attiré beaucoup d'attention au cours de la dernière décennie en raison de leur très haute densité d'énergie théorique de 2567 Wh.kg-1. Bien que plusieurs développements aient été réalisés pour améliorer les performances des batteries Li-S, l'évaluation de certains mécanismes et de leur limitation reste difficile. Dans le cadre de mes travaux de doctorat, nous avons mis au point de multiples modèles mathématiques qui aident à l'évaluation et à l'optimisation de certains phénomènes liés aux batteries Li-S. Nous avons développé un nouveau modèle de type Monte-Carlo cinétiqu
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Milton, Kenneth G. "Students' understanding of the mathematical equality and inequality relations : a developmental approach." Curtin University of Technology, Science and Mathematics Education Centre, 1999. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=10294.

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The motivation for this study was the desire to make the path to learning elementary algebra as 'generalised arithmetic' more clearly defined for both students and teachers.In the initial learning of algebra, algebraic expressions are transformed to equivalent other forms and techniques are developed for solving simple equations. Both facets require students to have a thorough understanding of arithmetic equality ' properties' if the developed procedures and techniques are to be adequately understood. The same can be claimed also with respect to arithmetic inequality and the solving of inequat
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Books on the topic "Mathematical understanding"

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Rowan, Garnier, ed. Understanding mathematical proof. Taylor & Francis, 2014.

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Klenk, Virginia. Understanding symbolic logic. 3rd ed. Prentice Hall, 1994.

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Klenk, Virginia. Understanding symbolic logic. 3rd ed. Prentice Hall, 1994.

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Robinson, Katherine M., Adam K. Dubé, and Donna Kotsopoulos, eds. Mathematical Cognition and Understanding. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-29195-1.

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Sokolowski, Andrzej. Understanding Physics Using Mathematical Reasoning. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80205-9.

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Dhurandhar, Sanjeev. Understanding Mathematical Concepts in Physics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-60394-5.

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Klenk, Virginia. Understanding symbolic logic. 2nd ed. Prentice Hall, 1989.

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Stefan, Ma, and Xia Yingcun, eds. Mathematical Understanding of Infectious Disease Dynamics. World Scientific Pub Co, 2009.

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Pat, Jones. Building permanent mathematical understanding: Sixth grade. Charism, CPR, LLC, 2004.

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Jones, Pat. Building permanent mathematical understanding: Fifth grade. Charism, CPR, LLC, 2004.

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Book chapters on the topic "Mathematical understanding"

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Davis, Andrew, Maria Goulding, and Jennifer Suggate. "Mathematical understanding." In Mathematical Knowledge for Primary Teachers. Routledge, 2017. http://dx.doi.org/10.4324/9781315621128-3.

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Rosini, Massimiliano Daniele. "Mathematical Preliminaries." In Understanding Complex Systems. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00155-5_2.

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Huang, Rongjin, and Yeping Li. "Promoting Mathematical Understanding." In Algebra Teaching around the World. SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-707-0_12.

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Pound, Linda, and Trisha Lee. "Building mathematical understanding." In Teaching Mathematics Creatively, 3rd ed. Routledge, 2021. http://dx.doi.org/10.4324/9781003055396-10.

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Newton, Kristie, and Sarah Sword. "Mathematical Knowledge." In Mathematical Learning and Understanding in Education. Routledge, 2018. http://dx.doi.org/10.4324/9781315537443-1.

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Damrau, Milena. "Theoretical Background of Mathematical Statements and Proof." In Understanding the Generality of Mathematical Statements. Springer Fachmedien Wiesbaden, 2023. http://dx.doi.org/10.1007/978-3-658-43763-3_2.

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AbstractIn this chapter, the theoretical basis for the conceptualization of understanding generality and proof is built. Thereby, characteristics of mathematical statements and generality are highlighted, particularly elaborating on how mathematical generality differs from generality in other sciences, it is explained how proof is shaped historically by so-called socio-mathematical norms, and different views and characteristics of proof are discussed. Further, this chapter also discusses usages and relations of the terms reasoning, argumentation, and proving, before different types of argument
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Banerjee, Santo, D. Easwaramoorthy, and A. Gowrisankar. "Mathematical Background of Deterministic Fractals." In Understanding Complex Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62672-3_1.

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Folina, Janet. "Towards a Better Understanding of Mathematical Understanding." In Boston Studies in the Philosophy and History of Science. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93342-9_8.

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Davis, Andrew, Maria Goulding, and Jennifer Suggate. "Understanding algebra." In Mathematical Knowledge for Primary Teachers. Routledge, 2017. http://dx.doi.org/10.4324/9781315621128-12.

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Greer, Brian. "13. How children, under instruction, develop mathematical understanding." In Studies on Mathematics Education and Society. Open Book Publishers, 2024. https://doi.org/10.11647/obp.0407.13.

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The relationship between the development and institutionalisation of mathematical understanding across millennia and its development for an individual child is the starting-point for this chapter. Greatly influenced by the writings of Hans Freudenthal, a position is taken in opposition to the theory propounded by Jean Piaget. The counterposition emphasises that a child can only be said to acquire any but the most elementary mathematics under more or less formal instruction and other forms of social and cultural interactions. The perennial debate about the relative weights that should be afford
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Conference papers on the topic "Mathematical understanding"

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Kuzmak, Sylvia. "Mapping knowledge for probability and statistics application: mathematical and non-mathematical." In Promoting Understanding of Statistics about Society. International Association for Statistical Education, 2016. http://dx.doi.org/10.52041/srap.16105.

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A mapping (a cognitive analysis) of knowledge used in the effective application of probability and statistics in real world situations is presented, identifying both mathematical and non- mathematical knowledge involved. The fundamental role of domain-related knowledge and expertise is emphasized, with illustrations provided using applications involving social data. Use of the knowledge mapping to support improvement of educational practice is proposed, including its use as a basis to evaluate the completeness of current curriculum and instruction in applied probability and statistics, to guid
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Raveh, Ira, Elena Trotskovsky, and Nissim Sabag. "MATHEMATICAL UNDERSTANDING AND ENGINEERING UNDERSTANDING: THE EXPERT PERCEPTIONS." In 10th annual International Conference of Education, Research and Innovation. IATED, 2017. http://dx.doi.org/10.21125/iceri.2017.0985.

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Gifford, Julian D., and Noah D. Finkelstein. "Categorizing mathematical sense making and an example of how physics understanding can support mathematical understanding." In 2019 Physics Education Research Conference. American Association of Physics Teachers, 2020. http://dx.doi.org/10.1119/perc.2019.pr.gifford.

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Guo, Y., L. Huang, C. Liu, and X. Jiang. "An Automatic Mathematical Expression Understanding System." In Ninth International Conference on Document Analysis and Recognition (ICDAR 2007) Vol 2. IEEE, 2007. http://dx.doi.org/10.1109/icdar.2007.4377009.

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RECK, ERICH H. "DEDEKIND, STRUCTURAL REASONING, AND MATHEMATICAL UNDERSTANDING." In Essays in Philosophy and History of Mathematics. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812812230_0007.

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Khurana, Meenu, Rashmi Aggarwal, Ridhima Rani, and Viney Khurana. "Understanding password vulnerabilities - A mathematical approach." In DIDACTIC TRANSFER OF PHYSICS KNOWLEDGE THROUGH DISTANCE EDUCATION: DIDFYZ 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0080658.

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Jóhannsdóttir, Bjorg, and Heather Ann Coughlin. "Folding for Fractional Understanding." In The 14th International Congress on Mathematical Education. WORLD SCIENTIFIC, 2024. http://dx.doi.org/10.1142/9789811287152_0103.

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Zhao, Kai, Zezhong Yang, and Dandan Sun. "Research on Mathematical Understanding in Mainland China." In International Conference on Management, Computer and Education Informatization. Atlantis Press, 2015. http://dx.doi.org/10.2991/mcei-15.2015.39.

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Yamada, Kuniko, Hiroshi Ueda, Harumi Murakami, and Ikuo Oka. "Presenting mathematical web pages for understanding lectures." In 2012 Joint 6th Intl. Conference on Soft Computing and Intelligent Systems (SCIS) and 13th Intl. Symposium on Advanced Intelligent Systems (ISIS). IEEE, 2012. http://dx.doi.org/10.1109/scis-isis.2012.6505066.

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Alani, Nabella, and Wahyudin. "Students’ mathematical conceptual understanding during online learning." In PROCEEDING OF INTERNATIONAL CONFERENCE ON FRONTIERS OF SCIENCE AND TECHNOLOGY 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0102776.

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Reports on the topic "Mathematical understanding"

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Sitabkhan, Yasmin, Aida Alikova, Nurgul Toktogulova, Adema Zholdoshbekova, Wendi Ralaingita, and Jonathan Stern. Understanding Primary School Teachers’ Mathematical Knowledge for Teaching. RTI Press, 2024. http://dx.doi.org/10.3768/rtipress.2024.rr.0052.2409.

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We present the results from an exploratory study that aimed to measure teachers’ specialized knowledge in early mathematics during a pilot of an educational intervention using the Foundational Mathematical Knowledge for Teaching (FMKT) survey. The survey was administered to 323 teachers in the Kyrgyz Republic in 2021. We delve into survey results at two timepoints (pre- and post-intervention) to showcase the areas in which the intervention was successful and identify ongoing challenges in teacher knowledge. We found that the FMKT provided detailed, specific information on teacher learning and
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Chua, Boon Liang. Justification in Mathematics (JiM). National Institute of Education, Nanyang Technological University, Singapore, 2020. https://doi.org/10.32658/10497/22628.

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This JiM project set out to research the current state of understanding of mathematical justification by both Singapore secondary school students and Mathematics teachers across the different content strands in the Singapore secondary Mathematics curriculum. This timely and relevant project was started to complement the current goal of the Ministry of Education (MOE) on fostering reasoning in the learning of Mathematics in schools. While MOE focuses on the reasoning process, our study examined the outcomes of this reasoning process. For many years, mathematical reasoning and communication have
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Orbán, Levente. Understanding Hypothesis Testing and the t-test. Orban Foundation, 2025. https://doi.org/10.69642/9543.

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This lecture note provides an accessible and pedagogically informed walkthrough of null hypothesis significance testing (NHST) and the t-test, based on a live undergraduate statistics lecture. I discuss both independent and related samples t-tests, common assumptions and their verification, and show how to manually implement these tests using R. Emphasis is placed on conceptual clarity, mathematical underpinnings, and hands-on implementation.
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Orbán, Levente. Understanding Intelligence and Psychometrics: A Quantitative and Historical Perspective. Orban Foundation, 2025. https://doi.org/10.69642/6423.

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This paper provides an overview of the concept of intelligence and the field of psychometrics from both a historical and quantitative perspective. Drawing on lecture material and expanded with mathematical formulations and R-based analytical scripts, we discuss the origins of intelligence testing, standardization, reliability and validity of psychometric instruments, and controversies surrounding the measurement and interpretation of intelligence. Real-world examples and illustrative data are used to clarify core concepts.
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Roschelle, Jeremy, Britte Haugan Cheng, Nicola Hodkowski, Lina Haldar, and Julie Neisler. Transfer for Future Learning of Fractions within Cignition’s Microtutoring Approach. Digital Promise, 2020. http://dx.doi.org/10.51388/20.500.12265/95.

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In this exploratory research project, our team’s goal was to design and begin validation of a measurement approach that could provide indication of a student’s ability to transfer their mathematics understanding to future, more advanced mathematical topics. Assessing transfer of learning in mathematics and other topics is an enduring challenge. We sought to invent and validate an approach to transfer that would be relevant to improving Cignition’s product, would leverage Cignition’s use of online 1:1 tutoring, and would pioneer an approach that would contribute more broadly to assessment resea
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Perdigão, Rui A. P. Earth System Dynamic Intelligence - ESDI. Meteoceanics, 2021. http://dx.doi.org/10.46337/esdi.210414.

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Earth System Dynamic Intelligence (ESDI) entails developing and making innovative use of emerging concepts and pathways in mathematical geophysics, Earth System Dynamics, and information technologies to sense, monitor, harness, analyze, model and fundamentally unveil dynamic understanding across the natural, social and technical geosciences, including the associated manifold multiscale multidomain processes, interactions and complexity, along with the associated predictability and uncertainty dynamics. The ESDI Flagship initiative ignites the development, discussion and cross-fertilization of
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Orbán, Levente. Lecture Notes: Null Hypothesis Testing and the t-test. Orban Foundation, 2025. https://doi.org/10.69642/5734.

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This document presents a structured overview of null hypothesis significance testing (NHST) and the t-test. Theoretical foundations, mathematical formulations, and base R implementations are provided to enhance understanding of statistical hypothesis testing in psychology.
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Wei, Xin, Amanda Wortman, Cristina Heffernan, et al. Language and Mathematics Learning: A Comparative Study of Digital Learning Platforms. SEERNet, Digital Promise, 2024. http://dx.doi.org/10.51388/20.500.12265/206.

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This paper presents a conceptual exploration of how Digital Learning Platforms (DLPs) can be utilized to investigate the impact of language clarity, precision, engagement, and contextual relevance on mathematics learning from word problems. Focusing on three distinct DLPs—ASSISTments/E-TRIALS, MATHia/UpGrade, and Canvas/Terracotta—we propose hypothetical studies aimed at uncovering how nuanced language modifications can enhance mathematical understanding and engagement. While these studies are illustrative in nature, they provide a blueprint for researchers interested in leveraging DLPs for em
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Gibbs, James. Applied Demography. American Museum of Natural History, 2006. http://dx.doi.org/10.5531/cbc.ncep.0173.

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Applied demography involves using the knowledge gained from analyzing and understanding populations in order to manage them effectively. The synthesis reviews basic concepts of demography and their application to management of wild populations. There are several major drivers of population change that operate in different ways, including birth rates, death rates, changes in sex ratios, and migration. These concepts can be formalized into mathematical population models that can be used to make predictions about populations under different management scenarios. Four case studies (including the G
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Agardy, Tundi, Daniel Brumbaugh, Nora Bynum, et al. Introduction to Marine Conservation Biology. American Museum of Natural History, 2005. http://dx.doi.org/10.5531/cbc.ncep.0088.

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Dynamic and interconnected marine systems cover about 70% of the earth’s surface. Marine and coastal systems are vital to many ecological processes necessary for general life and human well being, including food provisioning, climate regulation, and the freshwater cycle. This module serves as an introduction to the aspects of marine biology concerning conservation. An overview is provided of marine biodiversity and physical oceanography, as well as major marine ecosystems and marine ecology. Sections focus on topics specifically relevant to conservation, namely resource use, threats, and manag
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