Experimental verification of the use of the mathematical balance in secondary teaching

Orlov, K.V.

doi:10.1007/bf00305448

Cited by 2 publications

(8 citation statements)

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“…Through the addition of these features, the reach of the balance model is extended to represent a wider range of problems. For example, the additional scales in the physical model of Orlov (1971; Fig. 2c), the arrow going down from the scales of the drawn balance model in the article of Marschall and Andrews (2015; Fig.…”

Section: Discussion Of the Findings Regarding The Types Of Used Balanmentioning

confidence: 99%

“…However, at the same time, these authors pointed out that caution with using such manipulatives for teaching formal equation solving is necessary, because not all students automatically connect their actions on manipulatives with their manipulations on abstract symbols. Also Orlov (1971) commented that the balance model as a physical instrument can help in forming • Assigning values to unknowns can hinder students when using the BM The real-time feedback some models provide about being in balance, which allows students to verify the results of their manipulations and their reasoning processes and as such to construct knowledge, was also deemed important (Austin & Vollrath, 1989). When combined with social experiences, physical experiences were also said to contribute to the construction of knowledge (Figueira-Sampaio et al, 2009), for example, because it creates shared meaning between teacher and students (Perry et al, 1995).…”

Section: Rationales Related To the Physical Experiencesmentioning

confidence: 99%

“…2b), the equation 3x + 5 = 11 is portrayed by, on the left side, three containers with unknown content and five washers and 11 washers on the right side (for similar models, see also, e.g., Andrews, 2003). A more complex example of a balance scale was utilized by Orlov (1971;Fig. 2c).…”

Section: Physical Balance Modelsmentioning

confidence: 99%

“…The duration of the interventions in which the balance model was used was also very diverse. The shortest interventions comprised one activity or one lesson (e.g., Figueira-Sampaio et al, 2009;Rystedt et al, 2016), while in other studies the balance model was integrated in a multiple-year teaching trajectory (e.g., Orlov, 1971;Warren & Cooper, 2009).…”

Section: Grade Levels and Intervention Durationmentioning

confidence: 99%

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The balance model for teaching linear equations: a systematic literature review

2019

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This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report why such a model is used, what types of models are used, and when they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

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Section: Discussion Of the Findings Regarding The Types Of Used Balanmentioning

confidence: 99%

Section: Rationales Related To the Physical Experiencesmentioning

confidence: 99%

Section: Physical Balance Modelsmentioning

confidence: 99%

Section: Grade Levels and Intervention Durationmentioning

confidence: 99%

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The balance model for teaching linear equations: a systematic literature review

2019

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“…Other researchers have used other contexts that also support using Counterbalance, like voting and good/bad deeds (Shore, 2005). 2015Weights Orlov (1971) Although the possibilities for contexts that support Counterbalance are infinite, Table 7 highlights some of the contexts that promote the counterbalance conceptual model in the literature. Most of the literature highlighted in Table 7 discusses the instructional experiences and focuses on descriptions of the activities, rather than on the student thinking that was utilized when making use of these contexts.…”

Section: Research On Student Thinking Emerging From Contextsmentioning

confidence: 99%

Developing & Describing the Use & Learning of Conceptual Models for Integer Addition and Subtraction of Grade 5 Students

Wessman-Enzinger¹

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This dissertation reports the results of a teaching experiment, which explored student thinking about integer addition and subtraction. Through the lens of commognitive theory (Sfard, 2008), interpreting negative integers as secondary intuitions (Fischbein, 1987), and employing teaching experiment methodology (Steffe & Thompson, 2000), this study was a first step in developing more robust descriptions of students' conceptual models for integer addition and subtraction. I investigated: (a) the conceptual models that students exhibited, (b) the various ways that students utilized conceptual models while learning about the addition and subtraction of integers, and (c), the ways that students' conceptions evolved over the course of a teaching experiment. This study of students' conceptual models led to the modification and refinement of the CMIAS descriptions (Wessman-Enzinger & Mooney, 2014, 2015). Three Grade 5 students were selected based on results of a pilot study and students' responses to a written assessment. Data for this study was used from the Open Number Sentence and Context Individual Sessions of the 12-week teaching experiment. All of the Individual Sessions were videotaped and transcribed. The transcripts paired with all of the drawings produced by the students for stories for open number sentences generated and open number sentences solved during all Individual Sessions constituted the unit of analysis. A constant comparative method (Merriam, 1998) was used to modify the previous descriptions and develop new descriptions of the CMIAS (Wessman-Enzinger & Mooney, 2014). A description of the changes in mathematical discourse (i.e., word use, visual mediators, narratives, routines) was used to highlight the learning of integer addition and subtraction across the Individual Sessions.

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Experimental verification of the use of the mathematical balance in secondary teaching

Cited by 2 publications

References 0 publications

The balance model for teaching linear equations: a systematic literature review

The balance model for teaching linear equations: a systematic literature review

Developing & Describing the Use & Learning of Conceptual Models for Integer Addition and Subtraction of Grade 5 Students

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