Monomials and polynomials: the long march towards a definition

Bolondi, Giorgio; Ferretti, Federica; Maffia, Andrea

doi:10.1093/teamat/hry015

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…This could have been caused by lacking interpretive and symbolic skills (Blanton et al, 2019). Moreover, the learner lacks both graphical and equational connectors which assist in working with different representations of quadratic functions such as tables, graphs, equations, and words given in different contexts (Bolondi et al, 2020).…”

Section: Theme 1 Unexpressed Algebraic Thinkingmentioning

confidence: 99%

“…This is a result of failure to make links between connectors of graphs and equations which are coordinates, turning points, y-intercepts, an axis of symmetry, vertices, and the effect of all symbols on a standard form equation (Kotsopoulos, 2007;Mutambara et al, 2019). These connectors assist in working with different representations of quadratic functions such as tables, graphs, equations, and words given in different contexts (Bolondi et al, 2020). As explained by Shinariko et al in the proceeding entitled Mathematical representation ability on quadratic function through proof-based learning in 2021 conducted a study to explore learners' algebraic abilities while working with two representations.…”

Section: Introductionmentioning

confidence: 99%

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Exploring Grade 11 Learners’ Algebraic Thinking in the Formulation of Quadratic Equations From Graphs

Selowa,

Dhlamini

2023

IJE

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Algebraic thinking enables learners to devise algebra generalization when configuring quadratic equations from their graphical representations. Noticeable, learners grapple with this topic and there are some silent issues in the literature that should be explored in this discourse. Consequently, this prompted the current study, aimed to explore Grade 11 learners’ algebraic thinking when formulating quadratic equations from drawn graphs. The study adopted three tenets of the Lesh’s Translational model, pictorial and symbolic representations. An exploratory case study was used with 22 purposively sampled learners to explore algebraic thinking exhibited in learners’ responses to the graphical questions and transcripts from unstructured interviews. The algebraic thinking came from the exploration documents and interviews analysed through thematic analysis. The findings revealed that 17 learners lacked basic knowledge of algebra concepts which prevented the formulation of equations from graphs. This resulted from learners exploiting improper properties of algebra which were the requirement for the formulation of equations. The implication is that teaching, and learning should focus on the establishment of skills that permit exploiting appropriate prior knowledge relevant to this topic. Last, we suggest that empirical studies be conducted to focus on improving the instruction for the crafting of equations from graphs.

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Section: Theme 1 Unexpressed Algebraic Thinkingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploring Grade 11 Learners’ Algebraic Thinking in the Formulation of Quadratic Equations From Graphs

Selowa,

Dhlamini

2023

IJE

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“…Polynomials have been widely applied in physics and other natural and technical sciences [16][17][18][19][20]. Although polynomials are studied in high school [21,22] and in spite of their popularity in college courses, there are hardly any known features of polynomial functions. For example, many specific and complicated relations between the roots of a polynomial and its derivative can be found in conjecture theorems by Gauss-Lukas, Bôcher, Sendov, Marden, and others [23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Specific Features of Polynomials in Several Examples

Lipovetsky

2024

Axioms

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This paper considers polynomial characteristics useful for a better understanding of the behaviour of these functions. Taylor series for the polynomials are described by the items with even and odd derivatives and powered changes in the argument, which leads to more specific studying of their properties. Connections between the derivative and antiderivative of the polynomial functions are defined. The structure of polynomial functions reveals their specific characteristic that the mean value of their roots equals the mean value of the locations of the critical points such as the extrema and inflection points. Derivatives of the quadratic exponent in relation to an interesting connection of two transcendental numbers are also described. The discussed properties of the polynomials can be helpful for practical implementations and educational purposes.

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“…Next, Chaika² (2020) analyses the structure of bi-term monomials in English for Audit and Accounting and in Chaika³ (2020) the researcher 4 2021 refers to them as set term clusters in terminologies [10][11][12]. The idea traces back to mathematics and the paper by Bolondi, Ferretti and Maffia (2018) [13], which may help draw distinct similarities between monomials in algebra and those in linguistics. Apart from that, set speech expressions have remained in recent years under thorough study by many scholars [15; 20].…”

Section: Introductionmentioning

confidence: 99%

Verbal Monomials in English for Audit and Accounting

Чайка¹

2021

ijsshr

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The paper research is work in progress and makes part of a publication set devoted the study of the English monomials and polynomials in the professional domain of audit and accounting, on the one hand. On the other, the research can be treated as a standalone piece for the study into the nature of verbal monomials as set term clusters in English for Audit and Accounting. The scope of research arrives at the following objectives. One objective is to give an overview of the term ‘monomial’ in English for Audit and Accounting, or English for A&A, which leads to understanding of the verbal monomial in English for A&A, correspondingly. The other objective refers to the classification introduced earlier as attributable to the analysis of the structure of the mentioned monomials and polynomials in English for A&A from a morphological perspective of the head term in a monomial, i.e. nounal, verbal, adjectival and adverbial. The said classification in this work associates with verbal monomials in English for A&A only, and provides a relevant sub-classification of the relevant verbal monomials through the lens of their functional properties and roles in a sentence, under the professional language framework. The results and discussion section presents five distinct groups of verbal monomials in English for Audit and Accounting, each corresponding to a specific syntactical role and functional property in a sentence. A variety of the examples helps see and identify the type of the English verbal monomial in the area of audit and accounting.

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Monomials and polynomials: the long march towards a definition

Cited by 8 publications

References 12 publications

Exploring Grade 11 Learners’ Algebraic Thinking in the Formulation of Quadratic Equations From Graphs

Exploring Grade 11 Learners’ Algebraic Thinking in the Formulation of Quadratic Equations From Graphs

Specific Features of Polynomials in Several Examples

Verbal Monomials in English for Audit and Accounting

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