Academic literature on the topic 'The equal sign'

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Journal articles on the topic "The equal sign"

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Growney, Joanne. "Crossing the equal sign." Mathematical Intelligencer 30, no. 1 (March 2008): 78–79. http://dx.doi.org/10.1007/bf02985767.

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Kusuma, N. F., S. Subanti, and B. Usodo. "Students’ misconception on equal sign." Journal of Physics: Conference Series 1008 (April 2018): 012058. http://dx.doi.org/10.1088/1742-6596/1008/1/012058.

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De Clerck, Goedele A. M. "Introduction: Sign Language, Sustainable Development, and Equal Opportunities." American Annals of the Deaf 162, no. 1 (2017): 34–38. http://dx.doi.org/10.1353/aad.2017.0013.

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Cox, Nicholas J. "Stata Tip 70: Beware the Evaluating Equal Sign." Stata Journal: Promoting communications on statistics and Stata 8, no. 4 (December 2008): 586–87. http://dx.doi.org/10.1177/1536867x0800800413.

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Vermeulen, Cornelis, and Bronwin Meyer. "The Equal Sign: Teachers’ Knowledge and Students’ Misconceptions." African Journal of Research in Mathematics, Science and Technology Education 21, no. 2 (May 4, 2017): 136–47. http://dx.doi.org/10.1080/18117295.2017.1321343.

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Luo, Li Bo. "The Theory of Finite Models without Equal Sign." Acta Mathematica Sinica, English Series 22, no. 3 (December 22, 2005): 865–72. http://dx.doi.org/10.1007/s10114-005-0537-1.

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Sartati, Setiawan Budi, Subanji Subanji, and Sisworo Sisworo. "Pemahaman Siswa Tentang Equal Sign dalam Menyelesaikan Tugas Matematika." Jurnal Penelitian dan Pengkajian Ilmu Pendidikan: e-Saintika 2, no. 1 (December 31, 2018): 19. http://dx.doi.org/10.36312/e-saintika.v2i1.80.

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[Title: The Students' Understanding of Equal Sign in Completing Mathematics Tasks]. This study aims to describe the student's understanding of the equal sign to solve mathematical tasks. This study was included in the qualitative descriptive study. In this study, the data collected is the data of students work and verbal data (the interview). The subjects were six students of 7th class of MTs Attariqie Malang 2014/2015 (Junior High School), with details of two high-ability students, two students capable of being, and two low-ability students. Students' understanding of the equal sign examined further by providing tests and interviews in six research subjects. Interviews were conducted individually after the students work on the problems individually. The mathematical task load arithmetic and algebra problems. Based on the results of the study, all subjects were able to understand the equal sign as operational and the equal sign as a substitution. For equal sign as the basic relational, only high-ability students were able to understand it. Understanding of medium and low student capable entrenched in the operational pattern that is an equal sign as operational cause confusion to understanding equal sign as the basic relational, eg, 14+11=25+8 where students only pay attention to the results of operations that 14 plus 11 is 25 without notice relation of the addition of 8.
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Powell, Sarah R. "Equations and the Equal Sign in Elementary Mathematics Textbooks." Elementary School Journal 112, no. 4 (June 2012): 627–48. http://dx.doi.org/10.1086/665009.

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Blanton, Maria, Yenny Otálora, Bárbara M. Brizuela, Angela Murphy Gardiner, Katharine B. Sawrey, Aliska Gibbins, and Yangsook Kim. "Exploring Kindergarten Students’ Early Understandings of the Equal Sign." Mathematical Thinking and Learning 20, no. 3 (July 3, 2018): 167–201. http://dx.doi.org/10.1080/10986065.2018.1474534.

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Fyfe, Emily R., Percival G. Matthews, and Eric Amsel. "College developmental math students’ knowledge of the equal sign." Educational Studies in Mathematics 104, no. 1 (May 2020): 65–85. http://dx.doi.org/10.1007/s10649-020-09947-2.

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Dissertations / Theses on the topic "The equal sign"

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Meyer, Bronwin Colleen. "The equal sign: Teachers’ specialised content knowledge and Learners’ misconceptions." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2369.

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Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.
Numerical and algebraic equations require understanding of the equal sign as an equivalence relation. Teachers and learners, however, often have an operational, rather than a relational, understanding of the equal sign. This conception is viewed as a misconception. This study investigates the extent to which Grade 6 learners at a particular school have this and other misconceptions regarding equality, with the equal sign as focus. It also investigates this school’s Grade 1 to 6 teachers’ specialised content knowledge (SCK) regarding equality, again focusing on the equal sign. Ultimately the study wishes to establish whether there might be a possible relationship between the level of these teachers’ SCK of the equal sign and learners’ misconceptions of the equal sign. In particular, it tries to answer the question whether teachers’ SCK of the equal sign could possibly promote or prevent the forming of such misconceptions in learners, as well as whether teachers’ SCK of the equal sign could possibly help them identify learners’ misconceptions and help learners form the correct conceptions. This research project is framed within an interpretive paradigm. It focuses on one school taking the form of a theory-led case study in which a mixed method approach is used. Data collection methods include teacher questionnaires followed by two focus group interviews with teachers, based on data collected from questionnaires. In addition, data is collected through a series of lesson observations on number concepts and assessment. Grade 6 learners answered a set of questions structured in the form of a test to investigate their understanding of equality and the equal sign. Six learners were purposefully selected, based on their answers to the questions, and interviewed. Although this school is a high-performing academic school, results indicate that few learners have a flexible operational or basic relational view of the equal sign. The same group of learners that struggle with closure seems to struggle with the misconception of using all the numbers in an equation to solve a particular equation. The majority of Grade 6 learners cannot define the equal sign correctly. According to results, the nature of Grade 1- 6 teachers’ SCK of the equal sign shows that teachers lack skills to prevent, reduce or correct misconceptions about the equal sign.
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Dickson, Chelsea Lynn. "Making Sense of the Equal Sign in Middle School Mathematics." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7605.

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One of the main reasons that students struggle as they transition from arithmetic to algebra in the middle grades is that they fail to develop the appropriate understanding of the equal sign. Previous research has suggested that students need to move past an operational understanding and develop a relational understanding of the equal sign in order to work with algebraic equations successfully. Other research has suggested that the way that we interpret and utilize the equal sign is based on three main factors: multiple meanings of the equal sign, equation types, and structural conventions. This study extends both areas of research by analyzing two middle grade curricula and looking for what meanings, equation types, and structural conventions appear in both teacher and student materials. The study confirms that students are exposed to three main meanings of the equal sign in the middle grades. The study also describes which meanings of the equal sign are associated with particular equation types and the frequency with which these equation types appear throughout the 7th and 8th grade curricula. Study findings can be used to inform instruction, as they delineate the factors that are attended to while making sense of the equal sign in the middle grades.
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Abramsson, Matilda. "Elevers förståelse av likhetstecknet : En studie i årskurs 3." Thesis, Högskolan för lärande och kommunikation, Högskolan i Jönköping, Matematikdidaktik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-30647.

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Studiens syfte är att bilda kunskap om elevers förståelse av likhetstecknet och hur undervisning om likhetstecknet i årskurs 3 kan varieras för att bli så effektiv som möjligt. Syftet ska besvaras genom frågeställningarna: vilka variationsmönster som de studerade eleverna kan möta och vilka kritiska aspekter som elever kan identifiera. Kritiska aspekter är det som elever behöver identifiera för att förstå det som ska läras. Variationsmönster innebär att det som är kritiskt i undervisningen ska varieras för att synliggöras. Studien har sin ansats i variationsteorin, där variationsmönster och kritiska aspekter är centrala begrepp. En lektion observerades i årskurs 3 och sex elever valdes ut och intervjuades om likhetstecknet. Resultatet av studien visar att eleverna mötte sex kritiska aspekter i undervisningen. I varje kritisk aspekt mötte eleverna ett eller flera variationsmönster. Studien visar också att alla de intervjuade eleverna har en relationell och instrumentell förståelse av likhetstecknet. Eleverna har förståelse av en kritisk aspekt, som den observerade lektionen inte hade berört, nämligen att alla tal måste ingå i en uppgift för att lösningen ska vara korrekt. Fyra av sex elever har förståelse av den kritiska aspekten att det ska vara ekvivalens i en kedja av likheter. Resultatet visar också att elevernas förståelse av likhetstecknet inte är beroende av att de möter variationsmönster i undervisningen, men att de möter de kritiska aspekterna på något sätt.
The aim of the study is to explore the understanding of the equal sign and how the teaching about the equal sign among third grade students can be varied to be as effective as possible.  The aim will be answered trough the questions: what patterns of variation can the studied students meet and what critical aspects have the students identified. Patterns of variation means that what is critical in the teaching should be varied to become visible. Critical aspects is what students need to identify to understand what should be learned. The foundation of the study is the Variation Theory, where patterns of variation and critical aspects are central concepts. The observations were accomplished during a third grade lesson and six students were selected for interviews about the equal sign. The result of the study shows that the students met six critical aspects during the lesson. For every critical aspect there were one or several patterns of variation that was exposed to the students. The result also states that the students who were interviewed have a relational and instrumental understanding of the equal sign. The students also have understanding of a critical aspect that they did not meet in the observed lesson, namely that all numbers have to enter in a task. Four out of six students have understanding of the critical aspect that there should be equivalence in a chain of similarities. The result also show that the students understanding of the equal sign is not dependent of that they meet patterns of variation in the teaching, but that they meet the critical aspects somehow.
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Sköldin, Madeleine, and Natalie Engström. "Möjligheter och hinder i arbetet med likhetstecknet : En kvalitativ studie om lärares beskrivning av att introducera och arbeta med likhetstecknet." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55233.

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Syftet med studien är att studera hur lärare introducerar och arbetar med likhetstecknet för att inkludera alla elever och ge dem förutsättningar i sin undervisning. Studiens urval är fyra verksamma lärare som genom semistrukturerade kvalitativa intervjuer belyser sina tankar, erfarenheter och åsikter om hur de arbetar och introducerar likhetstecknet, samt vilka svårigheter som kan uppstå. Resultatet visar att lärarna i studien har ett entydigt arbetssätt men att det finns faktorer som skiljer sig åt. Att det finns faktorer som skiljer sig åt tydliggörs genom att lärarna introducerar likhetstecknet med bland annat konkret material medan introduktionen av likhetstecknet kan se olika ut, lärarna använder olika arbetsmetoder där en lärare väljer att introducera addition och talkamrater innan likhetstecknet, medan en annan lärare uttrycker att likhetstecknet bör introduceras först. Studiens problem är att forskning och myndigheter visar på att elever missuppfattar likhetstecknets betydelse. Den slutsats vi kan dra utifrån syfte, problem och resultat är att lärare behöver anpassa undervisningen för att ge eleverna goda kunskaper för att kunna bemästra matematiken.
The purpose of the study is to observe how teachers introduce and work with an equal sign in order to include all students. This is to give them the prerequisites in their teaching. The study sample involves four active teachers who, through semi-structured qualitative interviews, shed light on their thoughts, experiences, and opinions on how teachers work and introduce the sign of equality as well as what difficulties may arise. The results show that the teachers involved in the study have an unambiguous way of working, however, there are factors that differ. This is shown by the teachers introducing the equals sign with, among other things, concrete material while the introduction of the equals sign can look different. The teachers use different working methods where one teacher chooses to introduce additions and speech mates before the equal sign, while another teacher expresses that the equal sign should be introduced first. The problem with the study is that the research and authorities show that students misunderstand the meaning of the equal sign. The conclusion we can draw based on purpose, problems, and results is that teachers need to adapt the teaching to give students sufficient knowledge to be able to master mathematics.
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Kvist, Johanna, and Demirbag Kasirga Zelal. "Förståelser av likhetstecknet och hur de framställs i digitala spel för låg- och mellanstadiet : En systematisk litteraturstudie och en innehållsanalys om förståelser av likhetstecknet." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-84954.

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Syftet med den här studien är att belysa faktorer som möjliggör eller hindrar förståelsen av likhetstecknet hos elever och dess övergång mellan aritmetik och algebra. Med en systematisk litteraturstudie som metod söktes vetenskapliga artiklar som sammanställdes i fem olika kategorier. Svårigheter i tidig algebra, matematikens språk, relationell/instrumentell förståelse samt relationella tolkningar och till sist lärarperspektivet. Resultatet från den systematiska litteraturstudien bekräftade att elever inte har en relationell förståelse av likhetstecknet. Artiklarna visade framför allt att traditionell aritmetikundervisning hindrar elevers utveckling i algebraiskt tänkande. Uppgifter med operationer skrivna i vänsterled visade sig stärka elevers instrumentella förståelse av likhetstecknet. Ett instrumentellt och relationellt språk (både skriftligt och verbalt) framträdde också som en avgörande faktor för elevers förståelse. Utifrån artiklarnas resultat undersöktes vilka faktorer av likhetstecknet som elever får möjlighet att öva i digitala spel med hjälp av en innehållsanalys. Det visade sig att de digitala spelen i den här studien inte är utformade för att stödja elevers relationella förståelse av likhetstecknets betydelse utan fortsätter att stärka den instrumentella förståelsen hos elever.
The purpose of this study is to illustrate factors concerning the concept of the equal sign and its impact on the transition from arithmetic to algebra. Using a systematic literature study as a method, scientific articles were compiled into five different categories. Difficulties linked to early algebra, The language of Mathematics, Relational/instrumental understanding as well as relational interpretations and finally the Teacher perspective. Our systematic literature review confirmed that students do not have a relational understanding of the equal sign. Indeed, it highlighted that traditional arithmetic teaching methods tended to hinder student development in algebraic thinking through tasks, such as operations being on the left side of the equal sign and the answer as an outcome on the right side of the equal sign. This has been shown to strengthen students' instrumental understanding of the sign rather than dismantling it. Further, instrumental, and relational language (both written and verbal) proved to be decisive factors in students’ learning. Based on the results of our scientific articles, we undertook a content analysis of digital resources and examined whether the equal sign strengthens students instrumental or relational understanding of the equal sign. It turned out that the digital games analysed in this study are not designed to support students’ relational understanding of the equal sign but continues to strengthen their instrumental understanding.
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Kvist, Johanna, and Kasirga Zelal Demirbag. "Förståelser av likhetstecknet och hur de framställs i digitala spel för låg- och mellanstadiet : En systematisk litteraturstudie och en innehållsanalys om förståelser av likhetstecknet." Thesis, Karlstads universitet, Institutionen för matematik och datavetenskap (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-84954.

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Syftet med den här studien är att belysa faktorer som möjliggör eller hindrar förståelsen av likhetstecknet hos elever och dess övergång mellan aritmetik och algebra. Med en systematisk litteraturstudie som metod söktes vetenskapliga artiklar som sammanställdes i fem olika kategorier. Svårigheter i tidig algebra, matematikens språk, relationell/instrumentell förståelse samt relationella tolkningar och till sist lärarperspektivet. Resultatet från den systematiska litteraturstudien bekräftade att elever inte har en relationell förståelse av likhetstecknet. Artiklarna visade framför allt att traditionell aritmetikundervisning hindrar elevers utveckling i algebraiskt tänkande. Uppgifter med operationer skrivna i vänsterled visade sig stärka elevers instrumentella förståelse av likhetstecknet. Ett instrumentellt och relationellt språk (både skriftligt och verbalt) framträdde också som en avgörande faktor för elevers förståelse. Utifrån artiklarnas resultat undersöktes vilka faktorer av likhetstecknet som elever får möjlighet att öva i digitala spel med hjälp av en innehållsanalys. Det visade sig att de digitala spelen i den här studien inte är utformade för att stödja elevers relationella förståelse av likhetstecknets betydelse utan fortsätter att stärka den instrumentella förståelsen hos elever.
The purpose of this study is to illustrate factors concerning the concept of the equal sign and its impact on the transition from arithmetic to algebra. Using a systematic literature study as a method, scientific articles were compiled into five different categories. Difficulties linked to early algebra, The language of Mathematics, Relational/instrumental understanding as well as relational interpretations and finally the Teacher perspective. Our systematic literature review confirmed that students do not have a relational understanding of the equal sign. Indeed, it highlighted that traditional arithmetic teaching methods tended to hinder student development in algebraic thinking through tasks, such as operations being on the left side of the equal sign and the answer as an outcome on the right side of the equal sign. This has been shown to strengthen students' instrumental understanding of the sign rather than dismantling it. Further, instrumental, and relational language (both written and verbal) proved to be decisive factors in students’ learning. Based on the results of our scientific articles, we undertook a content analysis of digital resources and examined whether the equal sign strengthens students instrumental or relational understanding of the equal sign. It turned out that the digital games analysed in this study are not designed to support students’ relational understanding of the equal sign but continues to strengthen their instrumental understanding.
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Berg, Birgitta, and Marie-Therése Eriksson. "Likhetstecknet - Att öka förståelsen i förskoleklass med hjälp av Learning study metoden : Ett laborativt arbetssätt där till och med namn kan väga jämnt!" Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-9080.

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Syftet med denna empiriska studie är att undersöka hur lärare kan erbjuda möjligheter för 6-åringar att vidga sin förståelse av likhetstecknets innebörd. Undersökningen är inspirerad av Learning Study metoden vilket är en metod som har sin utgångspunkt i variationsteorin. Barnens initiala förmågor analyseras före planeringen av undervisningen och det ger en uppfattning om barnens kunskaper. Utifrån det planeras lektionerna och de aspekter som är de mest kritiska för barnen lyfts och på så sätt utvecklas deras kunskap. Vår slutsats är att det är viktigt att arbeta utifrån ett variationsinriktat lärandeperspektiv. Barnen lyckas bra i de uppgifter där de får laborera med konkret material.
The purpose of this empirical study is to examine how teachers can provide opportunities for children aged 6 to extend their understanding of the equal sign. This study is inspired by the Learning Study method which is a method that has its origins in variation theory.  By analyzing the children's initial abilities before planning our lessons, it gives us an idea of the children's knowledge. From there the lessons are planned and the aspects that are the most critical for the children are lifted and thereby develop their knowledge. Our conclusion is that it is important to work with variety oriented learning. The children are successful in tasks in which they are allowed to experiment with concrete materials.
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Wheeler, Gregory D. "Assessment of College Students' Understanding of the Equals Relation: Development and Validation of an Instrument." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/815.

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Research indicates that many elementary students do not comprehend that the equal sign is an indication that an equality relation exists between two structures. Instead, they perceive the equal sign as an indication that a particular procedure is to be performed. As students mature, and as their exposure to the equal sign and equality relations in multiple contexts increases, most obtain the ability to interpret the equal sign as an indicator of an equivalence relation. Incorrect usages of the equal sign, however, by post-algebra students indicate a tendency for students to regress back to a comprehension of the equal sign as an operator symbol or to ignore the equal sign altogether. The purpose of this project was to develop an instrument that is relevant to objectives associated with the interpretation of the equals relation, and to perform a test reliability analysis to assess measurement reliability and construct validity for the instrument. The model that was utilized to develop items for the instrument followed a general item development and validity assessment model proposed by Cangelosi. This model requires an iterative process that includes a peer review of objectives and instrument items by a panel of experts and a revision of the items based upon recommendations from the panel. A pilot test was synthesized from the revised items and administered to a group of subjects, and an instrument reliability analysis and an item efficiency analysis were performed. The quantitative and qualitative data obtained from this process were used to create the 18-item instrument entitled, Wheeler Test for Comprehension of Equals. The researcher recommends further validity assessments for the instrument across multiple settings and subject groups.
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Landqvist, Rebecca. "“Likhetstecknet betyder ju att det ska vara lika mycket det är punkt slut.” : -En studie om hur elever ges möjlighet att urskilja kritiska aspekter av likhetstecknets inne- börd under en lektion." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-84396.

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Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer.
The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif- ferent patterns of variation that was created by the use of different forms of representation.
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Rebecca, Landqvist. "“Likhetstecknet betyder ju att det ska vara lika mycket det är punkt slut.”-En studie om hur elever ges möjlighet att urskilja kritiska aspekter av likhetstecknets inne-börd under en lektion." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-86275.

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Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer.
The equality sign means that it should be the same, end of discus-sion. -A study about how students are given possibilities to discern critical aspects of the meaning of theequality sign The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif-ferent patterns of variation that was created by the use of different forms of representation.
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Books on the topic "The equal sign"

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Féin, Sinn. Peace in Ireland: For a future as equals : justice issues, rights and safeguards : a Sinn Féin submission to Strands One and Two of the peace talks. Belfast: Sinn Féin, 1997.

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Crossing the Equal Sign. Plain View Press, 2007.

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Cohen, Marion Deutsche. Crossing the Equal Sign. Plain View Press, 2007.

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Sign Language, Sustainable Development, and Equal Opportunities: Envisioning the Future for Deaf Students. Gallaudet University Press, 2016.

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Leung, Patrick Sze-lok, and Bijun Xu. The Sino-Japanese War and the Collapse of the Qing and Confucian World Order in the Face of Japanese Imperialism and European Acquiescence. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199670055.003.0019.

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The First Sino-Japanese War (1894–95) has been perceived as a sign of a new East Asian power order, but the legitimacy of the war has yet to be clarified. The Japanese foreign minister Mutsu’s Kenkenroku shows that the reasons claimed by Japan were only pretexts for its ambition to put Korea under its control. The 1885 Convention of Tianjin, which was used to justify the Japanese behaviour, needs to be reinterpreted. The Chinese reaction can be understood by exploration into Confucianism, which opposed wars between equal peers. Meanwhile, the Western powers which invented and developed international law were self-interested and did little to prevent the war. The incident shows that international law, empowered by the strong states, failed to maintain peace efficiently in the late nineteenth century.
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DuBois, Ellen Carol. Women’s Rights, Suffrage, and Citizenship, 1789–1920. Edited by Ellen Hartigan-O'Connor and Lisa G. Materson. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780190222628.013.22.

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The United States was a pioneer in the development of women’s rights ideas and activism. Far-seeing women, determined to find an active and equal place in the nation’s political affairs, pushed long and hard to realize America’s democratic promise. Over three-quarters of a century, women’s rights and suffrage leaders steadily agitated their cause through a shifting American political landscape, from the careful innovations of the early national period, through the expansive involvements of antebellum politics, into the dramatic shifts of revolution and reaction in the post–Civil War years, up to the modernization of the Progressive Era. The meaning and content of “womanhood,” the sign under which these campaigns were conducted, also shifted. Labor, class, and especially race inclusions and exclusions were contentious dimensions of the American women’s rights movement, as they were of American liberal democracy in general.
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Peabody, Sue. Freedom Papers Hidden in His Shoe. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190233884.003.0010.

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The 1830 July Revolution brought a series of laws facilitating manumission and equal rights for free men of color. In Isle Bourbon, Joseph Lory expanded his sugar production with two large plantations in the parish of Saint-Benoît. Constance died of unknown causes in 1838. As a free man, Furcy continued to live in Port Louis, Mauritius, as a candy maker. He saved his money, bought a store in Port Louis and a farm in Moka, learned to sign his name, and eventually contacted allies in Paris, who arranged for him to travel to Paris to appeal his wrongful enslavement in French courts. In 1835, the Court of Cassation’s Petition Chamber allowed Furcy’s appeal to advance to the Civil Chamber of the Court of Cassation, which decided in 1840 that Furcy had been born free due to his mother’s early sojourn on the free soil of France.
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Lee, Dorothy A. Symbolism and ‘Signs’ in the Fourth Gospel. Edited by Judith M. Lieu and Martinus C. de Boer. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198739982.013.15.

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This chapter explores the symbolism of the Fourth Gospel. It demonstrates that religious symbol is substantial rather than decorative, containing cognitive meaning as well as affective impact. The metaphors of the gospel are linguistic forms of symbolism, apparent in the seven ‘I am’ sayings of the Gospel and in the use of the five senses as metaphors of faith. Johannine symbolism is inextricably linked to the narrative out of which it emerges. John’s symbols are not of equal value, some playing a core role in the narrative. The ‘signs’ or miracles of the Gospel are also important, functioning as Johannine symbols in revealing the divine glory in Jesus and summoning the reader to faith. The cross is the greatest of the Johannine ‘signs’. Theologically, the incarnation lies at the basis of John’s symbolism: the conviction that divine glory is apprehended in and through the flesh.
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Luzzi, Joseph. The Task of Italian Romanticism. Edited by Paul Hamilton. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199696383.013.20.

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This chapter revisits the heated controversies over Italian Romanticism to show that they actually represent a vital literarymode. In short, the debates led to the creation of literary masterpieces that carry within themselves the signs of the age’s literary polemics. The public debate about the relation between literary and national identity made authors aware of their political responsibilities toward the yet-to-be-born Italian nation. Foscolo, Leopardi, and Manzoni avoided direct alignment with mainstream Romantic thought, but enjoyed a greater literary and artistic freedom than their more doctrinaire (and less talented) contemporaries. Italy’s isolation from much of European intellectual life gave the nation’s controversies over Romanticism a dramatic, almost desperate air, as the subtext over whether Italy would become ‘Romantic’ was equal to asking whether it could become ‘modern’.
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Cowen, Philip, Paul Harrison, and Tom Burns. Shorter Oxford Textbook of Psychiatry. Oxford University Press, 2012. http://dx.doi.org/10.1093/med/9780199605613.001.0001.

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Widely recognised as the standard text for trainee psychiatrists, the Shorter Oxford Textbook of Psychiatry stands head and shoulders above the competition. Honed over five editions it displays a rare fluency, authority and insight, and it makes the process of assimilating information as smooth and enjoyable as possible. The resource provides an introduction to all the clinical topics required by the trainee psychiatrist, including all the sub-specialties and major psychiatric conditions. Throughout, the authors emphasize the basic clinical skills required for the full assessment and understanding of the patient. Discussion of treatment includes not only scientific evidence, but also practical problems in the management of patients their family and social context. It emphasizes an evidence-based approach to practice and gives full attention to ethical and legal issues. Introductory chapters focus on recognition of signs and symptoms, classification and diagnosis, psychiatric assessment, and aetiology. Further chapters deal with all the major psychiatric syndromes as well as providing detailed coverage of pharmacological and psychological treatments. It also gives equal prominence to ICD and DSM classification - often with direct comparisons.
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Book chapters on the topic "The equal sign"

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Pepin, Birgit, Ole Kristian Bergem, and Kirsti Klette. "Rethinking Algebra Teaching in the Light of ‘Orchestration of Signs’ – Exploring the “Equal Sign” in a Norwegian Mathematics Classroom." In Algebra Teaching around the World, 39–57. Rotterdam: SensePublishers, 2014. http://dx.doi.org/10.1007/978-94-6209-707-0_3.

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van den Kieboom, Leigh A., Marta T. Magiera, and John C. Moyer. "Learning to Notice Student Thinking About the Equal Sign: K-8 Preservice Teachers’ Experiences in a Teacher Preparation Program." In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks, 141–59. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-46753-5_9.

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Galinski, Christian. "A Sign Equals Thousand Words." In Infrastructure and Safety in a Collaborative World, 263–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18372-0_14.

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Cates, Dennis M. "ON THE DETERMINATION AND THE REDUCTION OF INDEFINITE INTEGRALS IN WHICH THE FUNCTION UNDER THE $$\int $$ SIGN IS THE PRODUCT OF TWO FACTORS EQUAL TO CERTAIN POWERS OF SINES AND OF COSINES OF THE VARIABLE." In Cauchy's Calcul Infinitésimal, 167–72. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11036-9_31.

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Kizach, Johannes. "Not all processing difficulties are created equal." In The Sign of the V: Papers in Honour of Sten Vikner, 373. Aahus University Library, 2019. http://dx.doi.org/10.7146/aul.348.104.

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Hettiarachchi, Shyamani, M. Dumini K. de Silva, Thilanka Wijesinghe, Brayan Susantha, Geshani Amila, Pubhodha Sarani, and Mohamed Rasak. "“Free But Not Fair”: A Critical Review of Access to Equal Education for Deaf Children in Sri Lanka." In Deaf Education Beyond the Western World, 211–38. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190880514.003.0012.

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The first special school for children with disabilities in Sri Lanka opened over 100 years ago, in 1912. Over the years, a number of students with disabilities have gone on to tertiary education. However, deaf sign language users appear to have been left behind: To date, no deaf learner accessing education exclusively through Sri Lankan Sign Language has entered a local university. This chapter begins with a critical review of the trajectory of educational provision for deaf children followed by an appraisal of the contributions made by the Sri Lankan deaf associations toward increasing education access for deaf children. This leads to an analysis of the audiological and speech-language therapy services available within the school context and an evaluation of the limited but growing local “insider” research on deaf education. The chapter ends with reflections and recommendations for ensuring full and equal access to education for deaf children by 2030.
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O'Brien, James. "Sherlock Holmes: Other Sciences." In The Scientific Sherlock Holmes. Oxford University Press, 2013. http://dx.doi.org/10.1093/oso/9780199794966.003.0012.

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Sherlock Holmes knew more chemistry than any other science. But in this chapter, we shall find that he was well informed in a number of other sciences as well. Since mathematics contributes to all sciences, we first examine the Canon for instances of mathematical knowledge. We find a number of references to and uses of math in nearly all the early stories. After Holmes and Moriarty supposedly went over the Reichenbach Falls in The Final Problem (FINA) and Holmes returned, he rarely used math again. In A Study in Scarlet (STUD), Watson scoff s at a magazine article that claims that the conclusions of a trained observer are as “infallible as so many propositions of Euclid.” He soon learns that his new roommate Holmes is the author of the article. So here, very early on, we have Holmes drawing a mathematical analogy to his deductive work. He invokes Euclid again in the second story, Sign of Four (SIGN). This time he chides Watson about his writing style. Holmes accuses Watson of allowing romanticism to creep into his narration of the previous case, STUD. According to Holmes, this awkward technique produces “much the same effect as if you worked a love-story or an elopement into the fifth proposition of Euclid.” The fifth proposition states that if two sides in a triangle are equal, then the angles opposite those two sides will also be equal. Note that Holmes makes no calculation using Euclid’s proposition, but he depends on Watson’s knowledge of math to make a point about the way the narrative of STUD was written. This is the first time, but not the last, that he criticizes Watson the chronicler. In SIGN, Holmes’s conversation again assumes that his listener is acquainted with mathematical terms. When he sees that Tonga has left a footprint in creosote, he claims that tracking him will be as easy as using the “rule of three,” which states that if three of the four terms in a proportion are known, then the fourth may be calculated.
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Magruder, Robin, and Margaret Mohr-Schroeder. "Solving Equations is All about Balance." In Common Core Mathematics Standards and Implementing Digital Technologies, 201–14. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-4086-3.ch013.

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Virtual manipulatives provide benefits to students as they encounter the Common Core State Standards for Mathematics content and practice standards. The National Library of Virtual Manipulatives provides an abundant supply of virtual manipulatives for all K-12 grades and mathematics content areas. Specifically, in this chapter, the authors explore the use of Algebra Balance Scale manipulatives in a middle school mathematics classroom. Using virtual manipulatives increases understanding of the equal sign, algebraic symbols, and increases procedural and conceptual knowledge. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. Additionally, practice standards, such as making sense of problems and persevering to solve them, modeling with mathematics, and using tools strategically through the use of virtual manipulatives are addressed. They conclude by considering practical issues related to incorporating virtual manipulatives in mathematics classrooms.
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Kirchner, Carl J. "TRIPOD: Answer to the Seeds of Discontent." In Co-Enrollment in Deaf Education, 25–40. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780190912994.003.0002.

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The 1980s and the following decades brought confusion regarding appropriate education programs for deaf and hard-of-hearing (DHH) students, especially related to inclusion. The movement for equal education using a visual approach came into existence, and research exploring the pros and cons of mainstreaming began. Sign language interpreting in the education setting emerged, along with individuals who did or did not believe it was needed. Many school districts/county offices were unprepared to adequately or appropriately serve the needs of DHH students. Even the parents of these students were lost in a maze of uncertainty. The seeds of discontent were being sown, and educational change was in the wind. It seemed that every aspect of the field, from educational choices, hiring practices, and financial concerns to administrative decisions, were up for review. TRIPOD, a program with a philosophy of co-enrollment, has provided a fruitful harvest from these seeds of discontent.
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Zhang, H. "Electrokinetic Properties." In Chemistry of Variable Charge Soils. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195097450.003.0010.

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Cations and anions adsorbed by soil particles carrying surface charges are not present totally on the surface of the particles. Actually, in a soil-water system, a portion of adsorbed ions is distributed near the surface, forming an electric double layer at the interface between the solid particle and the liquid phase. When the two phases have a relative movement in an electrical field or are affected by other forces, the system can exhibit certain electrical properties, called electrokinetic properties. Electrokinetic properties of soils are the overall reflection of the distribution of various kinds of ions in the electric double layer of a soil-water system. They are related to both the characteristics of the soil and the nature of ions. For variable charge soils, because they adsorb anions as well as cations and during the adsorption both electrostatic force and specific force are involved, their electrokinetic properties frequently manifest themselves in a complex manner. As shall be seen in the present chapter, the electrokinetic properties of variable charge soils exhibit certain characteristics different from those of constant charge soils, and these characteristics are of significance for further distinguishing soil types among these soils. All the electrokinetic phenomena occurring in any colloid system result from the existence of the electric double layer. The same holds true for soils. Therefore, in this section the theory of the electric double layer along with its relation to various electrokinetic properties will be introduced first, and then the complexities in soil systems in this respect will be examined. When two phases are in contact, owing to the difference in properties, a redistribution of electric charge will occur at the interface between the two phases, leading to the formation of two layers with charges equal in quantity but opposite in sign between the two sides of the interface. This pair of charged layers is called electric double layer. It is a microscopically charged system present in the interfacial region between the two phases. The electric potential may vary at different positions within the system, but the system as a whole is electrically neutral.
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Conference papers on the topic "The equal sign"

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Jacobs, David P., Robert E. Jamison, and Alice A. McRae. "On the complexity of sign-nonsingularity and equal unions of sets." In the 38th annual. New York, New York, USA: ACM Press, 2000. http://dx.doi.org/10.1145/1127716.1127767.

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Wahyuni, Reni, and Tatang Herman. "Students’ Understanding of the Equal Sign: A Case in Suburban School." In The Second International Conference on Social, Economy, Education, and Humanity. SCITEPRESS - Science and Technology Publications, 2019. http://dx.doi.org/10.5220/0009057100240028.

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Ying, Yufeng. "A conceptual analysis of the equal sign and equation –the transformative component." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-25.

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Kalender, Z. Yasemin, Emily Marshman, Christian D. Schunn, Timothy J. Nokes-Malach, and Chandralekha Singh. "Large gender differences in physics self-efficacy at equal performance levels: A warning sign?" In 2018 Physics Education Research Conference. American Association of Physics Teachers, 2019. http://dx.doi.org/10.1119/perc.2018.pr.kalender.

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Ertas, Bugra H., and John M. Vance. "The Influence of Same-Sign Cross-Coupled Stiffness on Rotordynamics." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84873.

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One of the main contributors to rotordynamic instability in modern day turbomachinery is cross-coupled stiffness. The terminology comes from the phenomenon in which the reactive stiffness force is normal to the rotor displacement. Cross-coupled stiffness (CCS) can be generated from fluid pressure forces in internal machine components such as gas/liquid seals, hydrodynamic bearings, axial flow turbomachinery stages, and centrifugal impellers. Some of these machine components exhibit a type of CCS that materializes as a follower-force, which is normal to the whirl orbit radius and therefore tangent to a circular whirl orbit. With the follower force collinear with the whirl velocity, energy is fed into the motion and makes it grow larger with time. This destabilizing force can be represented in a Newtonian coordinate system by opposite-sign CCS, Kxy = −Kyx. However, there are cases of CCS where the forces produced are not always in the direction of rotor whirl, and the net work of the force per cycle is zero. These CCS forces are purely distortive to the orbit and are not de-stabilizing. They are represented by same-sign CCS, Kxy, Kyx, not necessarily equal. This paper investigates the effects of same-sign CCS on rotordynamics. Experiments are presented that show the measurement of same-sign CCS on a pocket damper seal and the required testing scheme to determine the effect on rotordynamic stability.
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Gillard, Joel, and Terry Smith. "A Model for Sustainable Orthopedic Care in Low and Middle Income Countries." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23332.

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Abstract This paper describes a scalable and sustainable patient care model for low and middle-income countries (LMICs) that can improve the standard of care for hospitals with scarce resources and an ever growing backlog of patients. SIGN Fracture Care International (SIGN), a non-profit, humanitarian medical device organization, has developed technical solutions over the last 20 years, to address the yearly increasing number of patients affected by upper and lower extremity trauma, using a three-pronged approach. The model includes effective training of in-country local surgeons on current orthopaedic techniques; providing an on-going supply of appropriately designed surgical implants and instruments manufactured to ISO 13485 and FDA standards; and evaluating patient outcomes until healing occurs to validate the model is truly benefiting patients and the hospital throughput. By providing equal access to technology, knowledge, and timely feedback, LMIC surgeons can provide vital orthopedic care to their local communities and sustainably respond to the daily trauma cases they encounter and enable patients to return to work, school, keep families on the path out of poverty, and improve the lives of future generations. The model is describe in detail in the hopes that other entities can utilize the principles for additional healthcare specialties around the world.
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Parker, Anthony P. "Compound and Monobloc Cylinders Incorporating Reverse-Autofrettage to Reduce External Hoop Stresses." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78298.

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Reverse autofrettage involves the application of pressure to the OD of a tube which in turn produces bore yielding and a residual stress profile equal in magnitude but opposite in sign to conventional autofrettage. The analyses within this paper identify two potential new manufacturing procedures involving reverse autofrettage. The procedures are predicted to reduce external tensile hoop stress in an autofrettaged gun tube. This reduction should increase lifetime of tubes that are prone to OD fatigue or corrosion-related failure from manufacturing defects or notches. The first procedure involves traditional autofrettage of an inner tube and reverse autofrettage of a larger outer tube. The outer tube is then compounded with the inner tube by thermal shrink-fitting or some equivalent process. The second procedure employs a monobloc tube which is subjected to reverse autofrettage followed by conventional internal autofrettage. Both procedures significantly reduce OD residual hoop stress but in the case of the monobloc tube there is an associated loss of compressive residual bore hoop stress.
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Hill, Paul, Troy Swankie, Robert Bood, and Dina Mihsein. "Repair and Reinforcement of Blunt Defects on Pipeline Bends Using Composite Materials." In 2020 13th International Pipeline Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/ipc2020-9290.

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Abstract Previous research on the use of composite repair systems has focused on the repair of damage to straight sections. This paper reports verification testing completed on composite repairs for pipeline bends to support development of a safe and consistent approach that ensures an equal level of performance is maintained over the entire system. A series of finite element analyses were completed that considered the effects of bend size (diameter and wall thickness), material grade, bend radius and angle. From this work 90° , 1.5D, 12” NB, X52 bends were selected for test. The objective was to demonstrate restoration of the fatigue life of the pipe to acceptable levels rather than just considering burst pressure. Defects equal to 0.5 times the diameter axially and 0.25 times the diameter radially were machined into the intrados of the bend (the location of highest hoop stress). Wall losses of 20% and 80% were replicated. Bounding repair thicknesses were tested to confirm performance was predictable. Aggressive cyclic pressure ranges of 125Nmm−2 and 90mm−2 were applied to the repaired defects, with the lower stress range loaded for a larger number of cycles. A successful test was defined as one which exceeded the target number of cycles by a factor of 10 AND for which there was no visual sign of repair degradation. The number of load cycles was selected to ensure the repaired lines satisfied the slope of the S-N curve for pristine pipe, confirming the approach maintained the required margin of safety applicable to the rest of the system. A design method is proposed that addresses weaknesses in the methods given in ISO 24817 and ASME PCC-2 Article 401. It is proposed that this be adopted by the standards for repairs to high pressure gas transmission pipelines to ensure equality of performance with undamaged sections.
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Coleman, Jeffrey T., and David Sinton. "Three-Dimensional Microfluidic Focusing With Surface Charge Patterning." In ASME 3rd International Conference on Microchannels and Minichannels. ASMEDC, 2005. http://dx.doi.org/10.1115/icmm2005-75235.

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Electrokinetically-driven flow circulations resulting from heterogeneous surface patches have previously been employed to improve mixing in microchannels. Here, numerical simulations demonstrate local in-channel hydrodynamic focusing through the use of strategically-patterned surface charge. Presented first is the case of a single straight channel with an axially-localized cross-sectional surface patch (ring). The surface patch exhibits a zeta potential equal in magnitude to the native microchannel surface but opposite in sign. The unsteady species transport in the presence of the electrokinetically-induced circulations is modelled, and a mean residence time is quantified. In general, residence times indicate the potential application of these circulations to microfluidic-based memory storage. Next, an improved focusing process for pinched-injection is demonstrated that exploits non-uniform surface patches. Lastly, surface patches are applied to enhance stream focusing in the microfluidic cross geometry. It is demonstrated that with this technique three-dimensional hydrodynamic focusing can be achieved in a single planar microfluidic structure. In one case, the microfluidic fluid stream was constrained to the centre of the channel and focused to 12% of its original cross-sectional area. Extensions of this work are discussed, as are the microfabrication and surface modification processes required for lab-on-chip implementation of these numerically simulated processes.
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Omri, M., S. Moreau, and L. G. Fréchette. "3D Numerical Analysis of Heat Transfer in a Low Reynolds Number Microturbine Cascade." In ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/icnmm2012-73054.

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This paper presents the conjugate heat transfer in a submillimeter scale microturbine characterized by laminar yet highly three-dimensional flows. Such a miniature turbine is part of a MEMS (microelectromechanical system) power plant-on-a-chip currently under development for distributed power generation from waste heat. Adiabatic subsonic flows in the turbine have previously been studied numerically and are characterized by low Reynolds number laminar flow (Re < 2500) but with complex vortical structures. The present work addresses the influence of these flow structures on heat transfer, including the effect of the horseshoe and tip vortices. Calculations were done for tip clearance gaps equal to 0%, 5% and 10% blade height. Three different scenarios were considered: adiabatic walls, the hub and casing temperature of 573K or the hub at 573K and the casing at 450K, for incoming flow at 600K. The heat transfer is more variable in the suction side since dominant vortices are adjacent to this blade side. The heat flux even changes its sign where the vortices begin to separate from the suction side, indicating that gas cooled in the hub and casing boundary layers is transported on the blades by the horseshoe vortices. The tip vortex prevents the top passage vortex from interacting with the suction side, which eliminates the negative heat transfer in this region. Due to the dominant vortices, the Nusselt number is found to be a function of the thermal boundary conditions and cannot be predicted with traditional boundary layer correlations.
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Reports on the topic "The equal sign"

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Corlin Christensen, Rasmus, Martin Hearson, and Tovony Randriamanalina. At the Table, Off the Menu? Assessing the Participation of Lower-Income Countries in Global Tax Negotiations. Institute of Development Studies (IDS), December 2020. http://dx.doi.org/10.19088/ictd.2020.004.

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Since 2013, the formal structure of global corporate tax policymaking at the OECD has changed. Decisions are no longer made by 37 OECD members, but by 137 countries from all regions and levels of development through the ‘Inclusive Framework’ (IF). Official documentation emphasises that all countries participate on an ‘equal footing’, but some participants and observers have emphasised that developing countries in particular face practical obstacles that lead to unequal participation in practice. In this paper, we assess these claims, drawing primarily on 48 interviews with negotiators, policymakers and stakeholders involved in global tax discussions. We find that the explosion in formal membership has not in itself led to the step-change in developing country influence that the raw numbers imply. This is because of a combination of structural obstacles that are not unique to the IF, and some challenging aspects of the OECD’s way of working. Yet, lower-income countries have made some modest achievements to date, and there are signs of incremental progress towards a more effective presence. We develop a typology of mechanisms through which successes have been achieved: association with the efforts of more powerful states, anticipation of lower-income countries’ needs by the OECD secretariat and others, collaboration to form more powerful coalitions, and the emergence of expert negotiators with individual authority.
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