Relevant bibliographies by topics / Numbers, Rational – Study and teaching

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Numbers, Rational – Study and teaching'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Numbers, Rational – Study and teaching.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Numbers, Rational – Study and teaching"

1

Sowder, Judith, and Carole B. Lacampagne. "Promising Research, Programs, and Projects: Teaching and Learning Quantities and Rational Numbers." Arithmetic Teacher 41, no. 7 (1994): 410. http://dx.doi.org/10.5951/at.41.7.0410.

Full text
Abstract:
The Teaching and Learning of Quantities and Rational Numbers Working Group has a complex purpose. The goal is to investigate the changes in classroom teaching and the effects on students' learning of teachers' opportunities for in-depth study of the mathematics in grades 3 to 7.
APA, Harvard, Vancouver, ISO, and other styles
2

Omoruan, Bertha Ese, and Patrick Uzo Osadebe. "Models Connecting Points on Pupils’ Achievement in Rational Numbers." Journal of Educational and Social Research 10, no. 4 (2020): 1. http://dx.doi.org/10.36941/jesr-2020-0059.

Full text
Abstract:

 The study investigated pupils’ achievement in rational numbers, using constructivist models and traditional approach of instruction as connecting points between pupils’ prior knowledge of whole numbers concept and the new concept. Pre-test post-test non-equivalent control group quasi-experimental research design was adopted. A research question guided the study and was answered using descriptive statistics; and a formulated corresponding null hypothesis was tested at 0.05 level of significance, using analysis of covariance (ANCOVA). A sample of 103 pupils was used for the study. A test
APA, Harvard, Vancouver, ISO, and other styles
3

Carpes, Patricia Pujol Goulart, and Eleni Bisognin. "Textbook: an Analysis in the Light of the Ontosemiotic Focus on Rational Numbers." Acta Scientiae 22, no. 5 (2020): 122–42. http://dx.doi.org/10.17648/acta.scientiae.5973.

Full text
Abstract:
Background: Many teachers consider the textbook the primary guide for the curriculum materialisation. This work analyses the content of the rational numbers in a textbook used in the 7th-grade of elementary school. For this analysis, the theoretical and methodological tools of the Ontosemiotic Approach to Knowledge and Mathematical Instruction (OSA) are used. Objective: Our goal was to understand the level of didactic suitability of the instruction process in the textbook. Design and setting: Thus, we analysed a section of the textbook about rational numbers using the categories described by O
APA, Harvard, Vancouver, ISO, and other styles
4

Kanbekova, Rimma Valeevna, Elvira Albertovna Izhbulatova, and Liliya Khazinurovna Salimova. "Methods of Increasing Motivation and Quality of Potential Primary School Teachers’ Mathematical Education." Development of education, no. 4 (6) (December 18, 2019): 19–22. http://dx.doi.org/10.31483/r-53754.

Full text
Abstract:
The article describes the implementation of project tasks in the study of rational and irrational numbers, presents the results of a questionnaire survey of students, potential primary school teachers, while studying the numerical line in a course on mathematics. The purpose of the article is to consider the effect of supplementing a material of a numerical line with original content on motivation when teaching mathematics to students of non-mathematical profiles. Methods. A questionnaire survey was conducted on the indifferent or negative attitude of students to the study of the rational and
APA, Harvard, Vancouver, ISO, and other styles
5

Naveen, Avula, and M. R. Sravani. "Study of drug utilization trends in respiratory tract infections in a tertiary care teaching hospital: a retrospective study." International Journal of Basic & Clinical Pharmacology 6, no. 11 (2017): 2583. http://dx.doi.org/10.18203/2319-2003.ijbcp20174635.

Full text
Abstract:
Background: Drug utilization studies play crucial role in the health sector and ultimately it provides insight into the efficiency of drug use and results of such research can be used to help to set priorities for the rational use of medicines and allocation of health care budgets. Respiratory tract infections (RTIs) contributing to significant mortality and morbidity of populations especially in developing countries like India. Polypharmacy and irrational prescription are significant negative fallouts in treatment of RTIs. Keeping in view of this, our study was undertaken to analyze the drug
APA, Harvard, Vancouver, ISO, and other styles
6

Hunting, Robert P., Gary Davis, and Catherine A. Pearn. "Engaging Whole-Number Knowledge for Rational-Number Learning Using a Computer-Based Tool." Journal for Research in Mathematics Education 27, no. 3 (1996): 354–79. http://dx.doi.org/10.5951/jresematheduc.27.3.0354.

Full text
Abstract:
We present data from a two-year teaching experiment involving 8- and 9-year-old children. The purpose of the teaching experiment was to investigate children's fraction learning and the role their whole-number knowledge might play in it. A major source for the children's experiences and experiments was an operator-like computer program called Copycat. In particular, we focus on the accomplishments of Elliot and Shannon as they solved fraction comparison problems. We identify and discuss three cognitive schemes that Elliot and Shannon used. These were an Equal Outputs scheme, limited in effectiv
APA, Harvard, Vancouver, ISO, and other styles
7

Das, Lakshman, Shubhaleena Debnath, and Prithul Bhattacharjee. "Evaluation of anti-diabetic prescriptions at Tripura medical college and Dr. BRAM teaching hospital: a cross- sectional study." International Journal of Research in Medical Sciences 6, no. 12 (2018): 3883. http://dx.doi.org/10.18203/2320-6012.ijrms20184683.

Full text
Abstract:
Background: Diabetes mellitus (DM) is a chronic disease which requires lifelong treatment. The management of type 1 DM depends mainly on insulin, whereas the oral anti-diabetic drugs (OADs) are the first line treatment for type 2 DM. Rational use of the drugs in populations can be effectively studied by analysing the prescription pattern. As there are limited numbers of studies carried out on drug utilization in diabetic patients in North Eastern region of India, authors planned to carry out this study in a tertiary care set up of this region.Methods: A cross-sectional study was carried out in
APA, Harvard, Vancouver, ISO, and other styles
8

Lemonidis, Charalambos, and Ioanna Kaiafa. "The Effect of Using Storytelling Strategy on Students’ Performance in Fractions." Journal of Education and Learning 8, no. 2 (2019): 165. http://dx.doi.org/10.5539/jel.v8n2p165.

Full text
Abstract:
Research findings in the field of Mathematics Education emphasize that storytelling is an effective instructional tool in the teaching of mathematics, as it provides a meaningful context that attracts students’ interest and makes learning a pleasant process. The use of stories and fairy tales in the teaching of mathematics motivates students to learn and provides students with an authentic context to understand mathematical concepts and procedures. It is a clear way to incorporate mathematics into other, broader cognitive domains and promotes mathematical discussion in the classroom.
APA, Harvard, Vancouver, ISO, and other styles
9

Dutta, Shakti B., Mirza A. Beg, Shalu Bawa, Amanjot Kaur, Subhash Vishal, and Nand Kishore Singh. "Study on drug usage pattern of anxiolytics in psychiatric department in a tertiary care teaching hospital at Dehradun, Uttarakhand, India." International Journal of Basic & Clinical Pharmacology 6, no. 7 (2017): 1661. http://dx.doi.org/10.18203/2319-2003.ijbcp20172726.

Full text
Abstract:
Background: Psychopharmacology is a rapidly growing field, in which the number of patients is continuously increasing. Newly introduced drugs are projected as the better alternative to the traditional psychiatric medicines. The utilization and consequences on real life effectiveness and safety of antianxiety drugs in actual clinical practice need continuous monitoring. Aim of the present study was to analyze the pattern of various anxiolytic drugs prescribed to the patients in psychiatric department of a tertiary care teaching hospital.Methods: The present study was conducted by the department
APA, Harvard, Vancouver, ISO, and other styles
10

Lo, Jane Jane, and Tad Watanabe. "Developing Ratio and Proportion Schemes: A Story of a Fifth Grader." Journal for Research in Mathematics Education 28, no. 2 (1997): 216–36. http://dx.doi.org/10.5951/jresematheduc.28.2.0216.

Full text
Abstract:
There is a growing theoretical consensus that the concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this developmental process. One fifth-grade student, Bruce, was encouraged to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Bruce made during the teaching experiment an
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Numbers, Rational – Study and teaching"

1

Brown, Bruce John Lindsay. "The initial grounding of rational numbers : an investigation." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1006351.

Full text
Abstract:
This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of
APA, Harvard, Vancouver, ISO, and other styles
2

Armstrong, Barbara Ellen. "The use of rational number reasoning in area comparison tasks by elementary and junior high school students." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184910.

Full text
Abstract:
The purpose of this study was to determine whether fourth-, sixth-, and eighth-grade students used rational number reasoning to solve comparison of area tasks, and whether the tendency to use such reasoning increased with grade level. The areas to be compared were not similar and therefore, could not directly be compared in a straightforward manner. The most viable solution involved comparing the part-whole relationships inherent in the tasks. Rational numbers in the form of fractional terms could be used to express the part-whole relationships. The use of fractional terms provided a means for
APA, Harvard, Vancouver, ISO, and other styles
3

Sehlmeyer, Peter August. "Use of learning-logs in high school pre-algebra classes to improve mastery of rational numbers and linear equations for high-risk minority students." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1497.

Full text
Abstract:
The purpose of this study was to determine whether there was a relationship in the use of learning-logs to traditional or current math instruction in secondary school pre-algebra classes to improve the mastery of single-variable equations by high-risk minority students.
APA, Harvard, Vancouver, ISO, and other styles
4

Santos, Alan Silva dos. "Um estudo sobre o conceito de densidade do conjunto dos números racionais e do conjunto dos números irracionais: uma abordagem com tecnologias." Pontifícia Universidade Católica de São Paulo, 2017. https://tede2.pucsp.br/handle/handle/20104.

Full text
Abstract:
Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-05-19T11:57:59Z No. of bitstreams: 1 Alan Silva dos Santos.pdf: 2565511 bytes, checksum: b1f037051a38c7fab75725edb0d9af53 (MD5)<br>Made available in DSpace on 2017-05-19T11:57:59Z (GMT). No. of bitstreams: 1 Alan Silva dos Santos.pdf: 2565511 bytes, checksum: b1f037051a38c7fab75725edb0d9af53 (MD5) Previous issue date: 2017-03-15<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This research aims to analyze, through a didactic sequence, the students' conceptions of an mathematics university course that invo
APA, Harvard, Vancouver, ISO, and other styles
5

Krug, Carbone Bruno Schmidt. "Ensino dos números racionais comparando medidas de unidade." Universidade Tecnológica Federal do Paraná, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/1697.

Full text
Abstract:
CAPES<br>A presente pesquisa teve como objetivo investigar a possibilidade de desenvolver o processo de ensino e aprendizagem da divisão de números racionais com tarefas pautadas na interpretação da medida. Adotamos como metodologia a Engenharia Didática e elaboramos uma sequência didática a fim de desenvolver o trabalho com estudantes do Ensino Médio. Participaram das sessões de ensino doze estudantes de uma escola estadual do município de Porto Barreiro - Pr. Os resultados da aplicação da sequência didática sugerem a importância da utilização de atividades pautadas na interpretação da medida
APA, Harvard, Vancouver, ISO, and other styles
6

Fuglestad, Anne Berit. "Computers and the understanding of mathematics : a study of teaching decimal numbers." Thesis, University of Nottingham, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339608.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Corr, Catherine Ann. "Developing understanding and fluency with numbers." CSUSB ScholarWorks, 1999. https://scholarworks.lib.csusb.edu/etd-project/1936.

Full text
Abstract:
This project will provide support for teachers who have solid understanding of math as the goal for the students in their classrooms. Using the district adopted course of study as the foundation, this project will provide a curriculum supplement for the first grade.
APA, Harvard, Vancouver, ISO, and other styles
8

Wolffenbüttel, Reni. "Investigando números racionais com o software GeoGebra." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/133653.

Full text
Abstract:
A presente pesquisa tem como foco o ensino dos números racionais no Ensino Fundamental. Seu objetivo é analisar as potencialidades e proposta de ensino que utiliza o computador, em particular do so fltiwmaitraeç dõee sg edoem uemtriaa dinâmica GeoGebra, e a metodologia de aulas de matemática investigativa. Essa proposta de ensino foi aplicada em turmas de 8º ano do Ensino Fundamental de uma escola pública, localizada na cidade de Sapucaia do Sul/RS. Esses estudantes já traziam conhecimentos sobre números racionais e, diante disso, esse campo numérico foi retomado com a intenção de verificar e
APA, Harvard, Vancouver, ISO, and other styles
9

Valio, Denise Teresa de Camargo. "Frações: estratégias lúdicas no ensino da matemática." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5964.

Full text
Abstract:
Made available in DSpace on 2016-06-02T20:29:27Z (GMT). No. of bitstreams: 1 6172.pdf: 12347251 bytes, checksum: 13431f4e524b082003ce456c4a9de23e (MD5) Previous issue date: 2014-08-21<br>Financiadora de Estudos e Projetos<br>The main aim of this master´s degree dissertation is the Mathematics teaching as well as the pedagogical and teaching practices related to the topic of rational numbers, particularly, fractions. The Fractions project, main title of this paper, aims at reaching not only basic education students but also educators with the objective of proposing understandable and attrac
APA, Harvard, Vancouver, ISO, and other styles
10

Schmidt, Martina, and University of Lethbridge Faculty of Education. "Putting rational constraints on divergent thought : the development of scientific reasoning." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Education, 1999, 1999. http://hdl.handle.net/10133/103.

Full text
Abstract:
The purpose of this study was to investigate how students in Grade Five and Six generate explanation for scientific phenomena and how they evaluate the quality of these explanations. In part, this was done by analyzing the in-class explanations that the students gave in response to questions stemming from two topics in the 1996 Alberta program of studies for Grade Five Science. In addition, the students shared their own perceptions of the sources of their questions and ideas and the methods by which they evaluated them. Analysis of in-class discussions and activities occurred on an ongoing bas
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Numbers, Rational – Study and teaching"

1

Mary, Stroh, and Sopris West Inc, eds. TransMath: Making sense of rational numbers. Cambium Learning/Sopris West, 2010.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

1948-, Silver Edward A., and Stein Mary Kay, eds. Improving instruction in rational numbers and proportionality. Teachers College Press, 2005.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

S, Bezuk Nadine, ed. Understanding rational numbers and proportions. National Council of Teachers of Mathematics, 1994.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Dale Seymour Publications, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Dale Seymour Publications, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

Numbers & Deuteronomy: A self-study guide. Moody Press, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Griffiths, Rose. Numbers to 20: Photocopiable activities. 2nd ed. Scholastic, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Football numbers: Graphing data. Norwood House Press, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Enright, Brian E. Division of whole numbers. Curriculum Associates, 1985.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

Franco, Betsy. Counting and numbers. Creative Publications, 1987.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Numbers, Rational – Study and teaching"

1

Olfos, Raimundo, Masami Isoda, and Soledad Estrella. "Multiplication of Whole Numbers in the Curriculum: Singapore, Japan, Portugal, the USA, Mexico, Brazil, and Chile." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_2.

Full text
Abstract:
AbstractThis chapter shows how the teaching of multiplication is structured in national curriculum standards (programs) around the world. (The documents are distributed by national governments via the web. Those documents are written in different formats and depths. For understanding the descriptions of the standards, we also refer to national authorized textbooks for confirmation of meanings.) The countries chosen for comparison in this case are two countries in Asia, one in Europe, two in North America, and two in South America: Singapore, Japan, Portugal, the USA (where the Common Core State Standards (2010) are not national but are agreed on by most of the states), Mexico, Brazil, and Chile, from the viewpoint of their influences on Ibero-American countries. (The National Council of Teachers of Mathematics (NCTM) standards (published in 2000) and the Japanese and Singapore textbooks have been influential in Latin America. Additionally, Portugal was selected to be compared with Brazil). To distinguish between each country’s standard and the general standards described here, the national curriculum standards are just called the “program.” The comparison shows the differences in the programs for multiplication in these countries in relation to the sequence of the description and the way of explanation. The role of this chapter in Part I of this book is to provide the introductory questions that will be discussed in Chaps. 3, 4, 5, 6, and 7 to explain the features of the Japanese approach. (As is discussed in Chap. 1, the Japanese approach includes the Japanese curriculum, textbooks, and methods of teaching which can be used for designing classes, as has been explored in Chile (see (Estrella, Mena, Olfos, Lesson Study in Chile: a very promising but still uncertain path. In Quaresma, Winsløw, Clivaz, da Ponte, Ní Shúilleabháin, Takahashi (eds), Mathematics lesson study around the world: Theoretical and methodological issues. Cham: Springer, pp. 105–122, 2018). The comparison focuses on multiplication of whole numbers. In multiplication, all of these countries seem to have similar goals—namely, for their students to grasp the meaning of multiplication and develop fluency in calculation. However, are they the same? By using the newest editions of each country’s curriculum standards, comparisons are done on the basis of the manner of writing, with assigned grades for the range of numbers, meanings, expression, tables, and multidigit multiplication. The relationship with other specific content such as division, the use of calculators, the treatment of multiples, and mixed arithmetic operations are beyond the scope of this comparison. Those are mentioned only if there is a need to show diversity.
APA, Harvard, Vancouver, ISO, and other styles
2

Reséndiz, Laura, and David Block Sevilla. "“Necklaces”: A Didactic Sequence for Missing-Value Proportionality Problems." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_9.

Full text
Abstract:
AbstractThis research presents a sequence of didactic situations involving a proportionality relationship in which every value in a set (a number of necklaces) is mapped to a pair, a triad, or a quartet of values (numbers of blue beads, red beads, green beads, etc., required to make that number of necklaces) from another set. The sequence includes relatively simple multiplication and division problems, as well as more complex “missing-value” problems. This paper also presents the results of applying the sequence with a group of 4th grade students in a Mexican primary school (9 and 10 years old).
APA, Harvard, Vancouver, ISO, and other styles
3

Mendes, Fátima, Joana Brocardo, and Hélia Oliveira. "Building Opportunities for Learning Multiplication." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_10.

Full text
Abstract:
AbstractThis chapter seeks to illustrate a comprehension-based learning approach focused on multiplication. We use episodes to show the potential of a teaching design of multiplication focused on the development of mental calculation based on tasks with appropriate contexts and calculations anchored in the use of benchmark numbers and operation properties, with examples to explain the ideas that are introduced. They are based on a collaborative work experience between a third-grade primary teacher and a researcher (the first author of this chapter). Using these specific examples, we discuss mathematical ideas and didactic options that can guide the actions of teachers when teaching multiplication. Finally, we discuss some points of convergence between the approach introduced here and the lesson study approach.
APA, Harvard, Vancouver, ISO, and other styles
4

Isoda, Masami, Raimundo Olfos, and Takeshi Noine. "The Teaching of Multidigit Multiplication in the Japanese Approach." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_7.

Full text
Abstract:
AbstractMultidigit multiplication in vertical form uses the idea of the distributive law such as 27 × 3 = (20 + 7) × 3 = 20 × 3 + 7 × 3 for using a multiplication table under the base ten place value system. Multiplication in vertical form is not simply repeated addition such as 27 + 27 + 27. In this meaning, through the extension of multiplication from single digit to multidigit by use of vertical form with a multiplication table, students have to integrate their knowledge on the base ten system with the definition of multiplication by measurement (a group of groups; see Chaps. 10.1007/978-3-030-28561-6_3, 10.1007/978-3-030-28561-6_4, 10.1007/978-3-030-28561-6_5, and 10.1007/978-3-030-28561-6_6 of this book) and so on. How does the Japanese approach enable students to develop multiplication in vertical form by and for themselves based on their learned knowledge?This chapter illustrates this process as follows. Firstly, the diversity of multiplication in vertical form is explained in relation to the multiplier and multiplicand, and the Japanese approach in comparison with other countries such as Chile and the Netherlands is clearly illustrated. Secondly, how a Japanese teacher enables students to develop multiplication in vertical form beyond repeated addition is explained with an exemplar of lesson study. Thirdly, the exemplar illustrates a full-speck lesson plan under school-based lesson study which demonstrates how Japanese teachers try to develop students who learn mathematics by and for themselves including learning how to learn (see Chap. 1). Fourthly, it explains the process to extend multiplication in vertical form to multidigit numbers by referring to Gakko Tosho textbooks.
APA, Harvard, Vancouver, ISO, and other styles
5

Chavez, Julia McCord, and Robert C. Hauhart. "Teaching Dickens by the Numbers: A Case Study of The Mystery of Edwin Drood." In Teaching Victorian Literature in the Twenty-First Century. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58886-5_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Olfos, Raimundo, and Masami Isoda. "Japanese Lesson Study for Introduction of Multiplication." In Teaching Multiplication with Lesson Study. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-28561-6_5.

Full text
Abstract:
AbstractIn Chap. 10.1007/978-3-030-28561-6_2, we posed questions about the differences in several national curricula, and some of them were related to the definition of multiplication. In Chap. 10.1007/978-3-030-28561-6_3, several problematics for defining multiplication were discussed, particularly the unique Japanese definition of multiplication, which is called definition of multiplication by measurement. It can be seen as a kind of definition by a group of groups, if we limit it to whole numbers. In Chap. 10.1007/978-3-030-28561-6_4, introduction of multiplication and its extensions in the Japanese curriculum terminology were illustrated to explain how this unique definition is related to further learning. Multiplicand and multiplier are necessary not only for understanding the meaning of multiplication but also for making sense the future learning. The curriculum sequence is established through the extension and integration process in relation to multiplication. In this chapter, two examples of lesson study illustrate how to introduce the definition of multiplication by measurement in a Japanese class. Additionally, how students develop and change their idea of units—that any number can be a unit in multiplication beyond just counting by one—is illustrated by a survey before and after the introduction of multiplication. After the illustration of the Japanese approach, its significance is discussed in comparison with the Chilean curriculum guidebook. Then, the conclusion illustrates the feature of the Japanese approach as being relatively sense making for students who learn mathematics by and for themselves by setting the unit for measurement (McCallum, W. (2018). Making sense of mathematics and making mathematics make sense. Proceedings of ICMI Study 24 School Mathematics Curriculum Reforms: challenges, changes and Opportunities (pp. 1–8). Tsukuba, Japan: University of Tsukuba.). A comparison with Chile is given in order to demonstrate the sense of it from the teacher’s side. In relation to lesson study, this is a good exemplar of how Japanese teachers develop mathematical thinking. It also illustrates the case for being able to see the situation based on the idea of multiplication (Isoda, M. and Katagiri, S. (2012). Mathematical thinking: How to develop it in the classroom. Singapore: World Scientific; Rasmussen and Isoda Research in Mathematics Education 21:43–59, 2019), as seen in Figs. 10.1007/978-3-030-28561-6_4#Fig2 and 10.1007/978-3-030-28561-6_4#Fig3 in Chap. 10.1007/978-3-030-28561-6_4 of this book.
APA, Harvard, Vancouver, ISO, and other styles
7

"Rational numbers." In Teaching School Mathematics: Pre-Algebra. American Mathematical Society, 2016. http://dx.doi.org/10.1090//mbk/098/02.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

"A Critical Analysis of Teaching Rational Number: Catherine A. Brown." In Rational Numbers. Routledge, 2012. http://dx.doi.org/10.4324/9780203052624-16.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

"Benefits and Costs of Research That Links Teaching and Learning Mathematics: James A. Hiebert." In Rational Numbers. Routledge, 2012. http://dx.doi.org/10.4324/9780203052624-17.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

"Halves, Pieces, and Twoths: Constructing and Using Representational Contexts in Teaching Fractions: Deborah Loewenberg Ball." In Rational Numbers. Routledge, 2012. http://dx.doi.org/10.4324/9780203052624-15.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Numbers, Rational – Study and teaching"

1

Thayer, Tomás, Alicia Venegas, and Jesus Tejada. "USING MUSIC AS METAPHOR TO TEACHING RATIONAL NUMBERS THROUGH NEW DESIGNED SOFTWARE. THE CASE OF PICALAB-AUDIOFRACTIONS." In 12th International Technology, Education and Development Conference. IATED, 2018. http://dx.doi.org/10.21125/inted.2018.0471.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Lehrer, Richard. "Keynote: Accountable assessment." In Research Conference 2021: Excellent progress for every student. Australian Council for Educational Research, 2021. http://dx.doi.org/10.37517/978-1-74286-638-3_9.

Full text
Abstract:
There is widespread agreement about the importance of accounting for the extent to which educational systems advance student learning. Yet, the forms and formats of accountable assessments often ill serve students and teachers; the summative judgements of student performance that are typically employed to indicate proficiencies on benchmarks of student learning commonly fail to capture student performance in ways that are specific and actionable for teachers. Timing is another key barrier to the utility of summative assessment. In the US, summative evaluations occur at the end of the school ye
APA, Harvard, Vancouver, ISO, and other styles
3

Marambio Carrasco, Cecilia Alejandra, and Carla Lobos Stevens. "Situational map: A strategy to develop critical thinking in the teaching of scientific research." In 6th International e-Conference on Studies in Humanities and Social Sciences. Center for Open Access in Science, Belgrade, 2020. http://dx.doi.org/10.32591/coas.e-conf.06.04041m.

Full text
Abstract:
The objective of the study is to support students in the rational, logical, and analytical process that they perform when faced with a scientific problem. This study uses qualitative methodology as its purpose is to present the strategy as learning stemming from the process of analysis, which is rooted on how to detect scientifically the research problem in the field of social sciences. A statistical analysis is made on the use and application of the diagram in a sample of 27 undergraduate students who have used the situational map in the elaboration of their theses. The trend shows that 92.6%
APA, Harvard, Vancouver, ISO, and other styles
4

Marambio Carrasco, Cecilia Alejandra, and Carla Lobos Stevens. "Situational map: A strategy to develop critical thinking in the teaching of scientific research." In 6th International e-Conference on Studies in Humanities and Social Sciences. Center for Open Access in Science, Belgrade, 2020. http://dx.doi.org/10.32591/coas.e-conf.06.04041m.

Full text
Abstract:
The objective of the study is to support students in the rational, logical, and analytical process that they perform when faced with a scientific problem. This study uses qualitative methodology as its purpose is to present the strategy as learning stemming from the process of analysis, which is rooted on how to detect scientifically the research problem in the field of social sciences. A statistical analysis is made on the use and application of the diagram in a sample of 27 undergraduate students who have used the situational map in the elaboration of their theses. The trend shows that 92.6%
APA, Harvard, Vancouver, ISO, and other styles
5

Wall, J. Gerard, and Katrina Lacey. "Lights, camera, action: Microbiology laboratory teaching in the spotlight." In Fifth International Conference on Higher Education Advances. Universitat Politècnica València, 2019. http://dx.doi.org/10.4995/head19.2019.9429.

Full text
Abstract:
Broadening of access to higher education, leading to increasing class sizes, presents particular challenges in teaching specialised, laboratory-based subjects such as Microbiology. The Republic of Ireland has seen a 20% increase in undergraduate student numbers in the past ten years, with this trend set to continue in the near future. To complement traditional learning approaches, we have designed, produced and trialled a comprehensive suite of teaching videos that demonstrate common techniques taught in our Microbiology degree programme. The 42 videos, each of 4-9 minutes duration, were filme
APA, Harvard, Vancouver, ISO, and other styles
6

Wałęga, Przemysław A., Bernardo Cuenca Grau, Mark Kaminski, and Egor V. Kostylev. "Tractable Fragments of Datalog with Metric Temporal Operators." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/266.

Full text
Abstract:
We study the data complexity of reasoning for several fragments of MTL - an extension of Datalog with metric temporal operators over the rational numbers. Reasoning in the full MTL language is PSPACE-complete, which handicaps its application in practice. To achieve tractability we first study the core fragment, which disallows conjunction in rule bodies, and show that reasoning remains PSPACE-hard. Intractability prompts us to also limit the kinds of temporal operators allowed in rules, and we propose a practical core fragment for which reasoning becomes TC0-complete. Finally, we show that thi
APA, Harvard, Vancouver, ISO, and other styles
7

Oraison, Humberto Manuel, Loretta Konjarski, Janet Young, Samuel Howe, and Andrew Smallridge. "Staff Experiences of Victoria University’s First Year College During the Implementation of Block Mode Teaching." In Sixth International Conference on Higher Education Advances. Universitat Politècnica de València, 2020. http://dx.doi.org/10.4995/head20.2020.10975.

Full text
Abstract:
This report reviews the findings of staff satisfaction surveys conducted in 2018 and 2019 following the creation of a transformative and revolutionary approach to tertiary education in Australia, namely the creation of a new First Year College at Victoria University. Lectures were abolished from all units; class sizes were reduced; class timetabling was dramatically changed to allow for greater student study flexibility and accessibility; learning and teaching professional staff numbers were increased and facilities were built and repurposed. This report discusses the staff satisfaction and ch
APA, Harvard, Vancouver, ISO, and other styles
8

Guo, Mingyu. "An Asymptotically Optimal VCG Redistribution Mechanism for the Public Project Problem." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/45.

Full text
Abstract:
We study the classic public project problem, where a group of agents need to decide whether or not to build a non-excludable public project. We focus on efficient, strategy-proof, and weakly budget-balanced mechanisms (VCG redistribution mechanisms). Our aim is to maximize the worst-case efficiency ratio --- the worst-case ratio between the achieved total utility and the first-best maximum total utility. Previous studies have identified the optimal mechanism for 3 agents. It was also conjectured that the worst-case efficiency ratio approaches 1 asymptotically as the number of agents approaches
APA, Harvard, Vancouver, ISO, and other styles
9

Tsakatikas, D., and M. Sfantsikopoulos. "Development of a Decision Support System for Unscheduled Maintenance MRO Component Safety Stock." In ASME 2007 International Manufacturing Science and Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/msec2007-31115.

Full text
Abstract:
The paper presents a methodology for the establishment of the MRO (Maintenance, Repair and Operation) material criticality that is focused on the Industrial Unplanned Maintenance needs. The thus obtained criticality is used to rationalize the efficiency of the Plant MRO-material Inventory. Through an appropriately adapted Top-Down FMECA (Failure Modes Effects and Criticality Analysis) the concept of the Component Dynamic Criticality is introduced and calculated for all the functional components of an industrial production facility. The components are assigned with characteristic code numbers.
APA, Harvard, Vancouver, ISO, and other styles
10

Kapaeva, A. E., and M. V. Glazyrin. "Determining the algorithm for overcoming grammar interference in Chinese bachelor’s language." In XXV REGIONAL SCIENTIFIC CONFERENCE STUDENTS, APPLICANTS AND YOUNG RESEARCHERS. Знание-М, 2020. http://dx.doi.org/10.38006/907345-63-8.2020.14.21.

Full text
Abstract:
This article presents the results of the study on algorithms of overcoming grammar interference in teaching Chinese language bachelor. The purpose of the study was to define algorithms for preventing grammatical interference, to compare them and to identify advantages and disadvantages. The relevance of the study is determined by the need to develop special manuals for foreign language education. The methodology of the study was to study and analyze scientific sources. The study presents two algorithms for overcoming interference — a rational method and a structural method. Both methods are de
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Numbers, Rational – Study and teaching' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography