509 research outputs found

    Evaluating the Integration of a Mathematics Enhancement Programme into Jamaican Primary Mathematics Classes

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    This embedded quasi-experimental research design examined the impact of an enrichment initiative entitled the Mathematics Enhancement Programme (MEP) on Jamaican students’ performance and attitude towards mathematics. It identified teaching strategies for integrating the MEP into Jamaican primary mathematics classes. It investigated the impact of the MEP on teachers’ pedagogical practices, and it identified the barriers to integrating the MEP. A sample of 331 students and 12 teachers were conveniently selected from three schools from three parishes in Jamaica for the intervention group. The comparison group consisted of 180 students and seven teachers conveniently selected from two schools in central Jamaica. The participating teachers were trained and certified in a mathematics Subject Knowledge Enhancement (SKE) programme prior the implementation of the MEP. The treatment involved teaching the Jamaican grades one and two mathematics standards using the MEP resources for nine months. Quantitative data collection over the school year included pre-tests, post-tests, and pre- and post- children’s mathematics attitudinal surveys. The qualitative data was obtained through classroom observations and interviews. The quantitative data was analysed by means of descriptive statistics which involved the use of the 25th version of the statistical software (SPSS). Descriptive and in vivo coding were used to analyse the qualitative data which involved the use of QRS international’s NVivo 12 qualitative software programme. A statistically significant impact and large effect size of the intervention was found, indicating that the MEP had a substantial impact on students’ achievement and attitudes towards mathematics. Additionally, numerous teaching strategies were found to be effective for integrating the MEP. The findings also indicated there are aspects of the MEP that participating teachers thought were worth adapting and implementing in their practices. It was also found that there are barriers to integrating the MEP into Jamaican primary mathematics classrooms. Implications for designing enrichment programmes geared at addressing mathematics underperformance in Jamaica and other countries are discussed

    Creating a Culturally Responsive Mathematics Education: The Case of Gebeta Game in Ethiopia

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    This chapter presents an example of creating a culturally responsive mathematics education in Ethiopia using a locally available game called Gebeta. The study is framed using two theoretical frameworks: funds of knowledge and cultural commognition. To this end, an ethnographic study has been employed, which helps to describe, analyze, and investigate a particular group, culture, or community. The findings show that the game is well situated as a developed body of knowledge and skills in the culture. It has remarkable potential to foster mathematical thinking and communication at different levels of the school context. Specifically, in terms of mathematical thinking, the game has affordances to foster early numerical and algorithmic thinking. Educators and stakeholders involved in designing tasks and activities for the curriculum and syllabus should consider incorporating the Gebeta game and other culturally available activities to embed them as part of formal school mathematics in a meaningful way

    The Expressive Power of CSP-Quantifiers

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    A generalized quantifier QK is called a CSP-quantifier if its defining class K consists of all structures that can be homomorphically mapped to a fixed finite template structure. For all positive integers n ≥ 2 and k, we define a pebble game that characterizes equivalence of structures with respect to the logic Lk∞ω(CSP+n ), where CSP+n is the union of the class Q1 of all unary quantifiers and the class CSPn of all CSP-quantifiers with template structures that have at most n elements. Using these games we prove that for every n ≥ 2 there exists a CSP-quantifier with template of size n + 1 which is not definable in Lω∞ω(CSP+n ). The proof of this result is based on a new variation of the well-known Cai-Fürer-Immerman construction.publishedVersionPeer reviewe

    Calculus I Companion

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    A course pack for supplementing Calculus 1 with algebra, geometry, trigonometry, and precalculus topics, including reading material, activities, and practice problems assembled from various OER texts.https://cupola.gettysburg.edu/oer/1015/thumbnail.jp

    Historical Burdens on Physics

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    When learning physics, one follows a track very similar to the historical path of the evolution of this science: one takes detours, overcomes superfluous obstacles and repeats mistakes, one learns inappropriate concepts and uses outdated methods. In the book, more than 200 articles present and analyze such obsolete concepts methods. All articles have the same structure: 1. subject, 2. deficiencies, 3. origin, 4. disposal. The articles had originally appeared as columns in various magazines. Accordingly, we had tried to write them in an easily understandable way

    (b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)

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    (b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!

    Cutting Planes Width and the Complexity of Graph Isomorphism Refutations

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    The width complexity measure plays a central role in Resolution and other propositional proof systems like Polynomial Calculus (under the name of degree). The study of width lower bounds is the most extended method for proving size lower bounds, and it is known that for these systems, proofs with small width also imply the existence of proofs with small size. Not much has been studied, however, about the width parameter in the Cutting Planes (CP) proof system, a measure that was introduced by Dantchev and Martin in 2011 under the name of CP cutwidth. In this paper, we study the width complexity of CP refutations of graph isomorphism formulas. For a pair of non-isomorphic graphs G and H, we show a direct connection between the Weisfeiler-Leman differentiation number WL(G, H) of the graphs and the width of a CP refutation for the corresponding isomorphism formula Iso(G, H). In particular, we show that if WL(G, H) ? k, then there is a CP refutation of Iso(G, H) with width k, and if WL(G, H) > k, then there are no CP refutations of Iso(G, H) with width k-2. Similar results are known for other proof systems, like Resolution, Sherali-Adams, or Polynomial Calculus. We also obtain polynomial-size CP refutations from our width bound for isomorphism formulas for graphs with constant WL-dimension

    Logical Equivalences, Homomorphism Indistinguishability, and Forbidden Minors

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    Two graphs GG and HH are homomorphism indistinguishable over a class of graphs F\mathcal{F} if for all graphs F∈FF \in \mathcal{F} the number of homomorphisms from FF to GG is equal to the number of homomorphisms from FF to HH. Many natural equivalence relations comparing graphs such as (quantum) isomorphism, spectral, and logical equivalences can be characterised as homomorphism indistinguishability relations over certain graph classes. Abstracting from the wealth of such instances, we show in this paper that equivalences w.r.t. any self-complementarity logic admitting a characterisation as homomorphism indistinguishability relation can be characterised by homomorphism indistinguishability over a minor-closed graph class. Self-complementarity is a mild property satisfied by most well-studied logics. This result follows from a correspondence between closure properties of a graph class and preservation properties of its homomorphism indistinguishability relation. Furthermore, we classify all graph classes which are in a sense finite (essentially profinite) and satisfy the maximality condition of being homomorphism distinguishing closed, i.e. adding any graph to the class strictly refines its homomorphism indistinguishability relation. Thereby, we answer various question raised by Roberson (2022) on general properties of the homomorphism distinguishing closure.Comment: 26 pages, 1 figure, 1 tabl

    ENTREPRENEUR–INVESTOR INFORMATION DESIGN

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    I consider an environment in which an entrepreneur generates information about the quality of his project prior to contracting with an investor. The investor faces a moral-hazard problem since the entrepreneur may divert the funding for private consumption. I find that the efficient amount of information is generated if and only if the bargaining power of the entrepreneur is high enough. I interpret this result in terms of investors' tightness, competitiveness, and generosity measures. I also show that the investor prefers not to have all the bargaining power when the project costs are high enough

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum
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