Word problems and equations: an historical activity for the algebra classroom

Ofir, Ron; Arcavi, Abraham

doi:10.2307/3620379

Cited by 4 publications

(2 citation statements)

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“…How did our modern algorithms for the basic operations evolve? Students might appreciate the crucial role representations play and the contrast of our own numeration system with other systems can be effective for a better understanding of its particular features (e.g., Heiede 2000; Ofir and Arcavi 1992;Smith 1923Smith /1958Swetz 1984Swetz , 1995.…”

Section: Discussionmentioning

confidence: 98%

Using History to Teach Mathematics: The Case of Logarithms

Panagiotou¹

2010

Sci & Educ

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Many authors have discussed the question why we should use the history of mathematics to mathematics education. For example, Fauvel (For Learn Math, 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing how to introduce history into mathematics lessons is a more difficult step. We found, however, that only a limited number of articles contain instructions on how to use the material, as opposed to numerous general articles suggesting the use of the history of mathematics as a didactical tool. The present article focuses on converting the history of logarithms into material appropriate for teaching students of 11th grade, without any knowledge of calculus. History uncovers that logarithms were invented prior of the exponential function and shows that the logarithms are not an arbitrary product, as is the case when we leap straight in the definition given in all modern textbooks, but they are a response to a problem. We describe step by step the historical evolution of the concept, in a way appropriate for use in class, until the definition of the logarithm as area under the hyperbola. Next, we present the formal development of the theory and define the exponential function. The teaching sequence has been successfully undertaken in two high school classrooms.

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Section: Discussionmentioning

confidence: 98%

Using History to Teach Mathematics: The Case of Logarithms

Panagiotou¹

2010

Sci & Educ

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“…The first accentuates the motivational aspect of the historical background of the studied issue. This can be exemplified by the work (Ofir and Arcavi, 1992), where historical resources are used to motivate pupils to think about mathematics and its potential for today. However, based on an experience Ofir and Arcavi recommend the use of the presented 'Egyptian method' only with above average pupils.…”

Section: The Ufa Strategy In School Mathematicsmentioning

confidence: 99%

The Strategy the Use of False Assumption and Word Problem Solving

Eisenmann

Přibyl

Novotná³

2019

ERIES Journal

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The paper describes one problem solving strategy -the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual difficulties when solving word problems using linear equations, namely construction of the equations. The paper presents the outcomes of a study conducted on three lower secondary schools in the Czech Republic with 147 14-15-year-old pupils. Pupils from the experimental group were, unlike pupils from the control group, taught the strategy the Use of false assumption before being taught the topic Solving word problems. The tool for the study was a test of four problems that was sat by all the involved pupils three weeks after finishing the topic "Solving word problems" and whose results were evaluated statistically. The experiment confirmed the research hypothesis that the introduction of the strategy the Use of false assumption into 8 th grade mathematics lessons (14-15-year-old pupils) helps pupils construct equations more successfully when solving word problems.

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