An Arts-Based Approach to Teaching Fractions

2007 ◽  
Vol 14 (2) ◽  
pp. 74-80
Author(s):  
Mary Barr Goral ◽  
Lynda R. Wiest

“Fractions have always represented a considerable challenge for students, even into the middle grades,” noted Van de Walle (2004, p. 242), and the instructional experiences of most teachers validate this statement. Despite the fact that proportional reasoning is an important curriculum topic and a valuable life skill, students struggle to meaningfully grasp fraction concepts. To aid development of the concept of fractions, the National Council of Teachers of Mathematics (2000) recommends that students represent fractions by using physical materials and number lines. The visual and tactile input these materials afford, coupled with carefully designed reflection on the use of these tools, can bolster learning about fractions.

2018 ◽  
Vol 13 (2) ◽  
pp. 238-253
Author(s):  
Sean Colbert-Lewis ◽  
Drinda E. Benge

Purpose The increase of Islamophobia-inspired hate crimes toward Sikh Americans led the Sikh Coalition of America and the National Council for the Social Studies to request social studies educators to conduct a content analysis on the presentation of Sikhism in social studies textbooks. The Sikh Coalition hopes to use the findings of such research to encourage more appropriate inclusion about the religion in textbooks by the leading publishing companies and as a legitimate social studies subject of instruction in the state standards for all 50 states. The paper aims to discuss this issue. Design/methodology/approach The incorporation of critical pedagogy, as a tool of critical multiculturalism, serves as the theoretical design of this study. Content analysis serves as the method of research for this study. The authors also employed an online survey to determine the scope of religious literacy of the pre-service teachers with regard to Sikhism before the conducting of content analysis of social studies textbooks for the presentation of Sikhism. Findings The current presentation of Sikhism in social studies textbooks has the potential to help fuel the Islamophobia that Sikh Americans now face. The authors found that the pre-service teachers possess little religious literacy regarding Sikhism. Furthermore, from the content analyses, the authors found that a total of 21 out of the sample of 32 textbooks (5 elementary, 11 middle grades and 16 high school) mention Sikhism. Eight textbooks include a mention of the origins of Sikhism. Nine textbooks misidentify the religion as a blending of Hinduism and Islam. Nine textbooks mention the religion in relation to the assassination of Indira Gandhi. Research limitations/implications The originality of this research led the authors to find that the very limited and inaccurate information we found present in the most-used textbooks for elementary, middle grades and high school social studies made the employing of inferential statistics like correlation difficult. Also, the authors found from the literature that research addressing Islamophobia in the classroom has centered on the role of licensed teachers only. The research gives a model to how pre-service teachers may address Islamophobia in the classroom and also gain religious literacy regarding Sikhism. Practical implications The rise of Islamophobia-inspired violence toward students of South Asian descent has led to the call to address this matter. The research introduces a method to how social studies education professors may help engage their pre-service teachers in proactively addressing Islamophobia. Social studies professors have a responsibility to help promote social justice through critical pedagogy that explores the religious literacy of their pre-service teachers beyond Buddhism, Christianity, Hinduism, Islam and Judaism. Social implications The Sikh Coalition, by telephone, has formally acknowledged to the authors that the textbook research has been the most extensive they have received since making their joint request with the National Council for the Social Studies. They have used the research to successfully convince the state education boards of Texas and recently Tennessee to adopt the inclusion of Sikhism in social studies content. More Americans, at a young age, need to learn about Sikh culture, so they are less likely to develop prejudicial ideas about Sikh Americans and commit violent acts of religious-based discrimination. Originality/value The research is extremely rare. To date, no one else in the country has conducted research on the presentation of Sikhism in textbooks to the extent that the authors have. The authors hope that the research will encourage more dialogue and further research. The authors hope that the research will help prevent further acts of religious-based violence toward followers of the world’s sixth largest religion.


2002 ◽  
Vol 8 (6) ◽  
pp. 356-361
Author(s):  
John Olive

Teaching fractions has been a complex and largely unsuccessful aspect of mathematics instruction in the elementary grades for many years. Students' understanding of fraction concepts is a big stumbling block in their mathematical development. Some researchers have pointed to children's whole-number knowledge as interfering with, or creating a barrier to, their understanding of fractions (Behr et al. 1984; Streefland 1993; Lamon 1999). This article illustrates an approach to constructing fraction concepts that builds on children's whole-number knowledge using specially designed computer tools. This approach can help children make connections between whole-number multiplication and their notion of a fraction as a part of a whole, thus bridging the gap between whole-number and fraction knowledge.


2012 ◽  
Vol 43 (4) ◽  
pp. 391-427 ◽  
Author(s):  
Andrew Izsák ◽  
Erik Jacobson ◽  
Zandra de Araujo ◽  
Chandra Hawley Orrill

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the mixture Rasch model that allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. Some teachers, however, were easier to classify than others.


2003 ◽  
Vol 18 (3) ◽  
pp. 193-198 ◽  
Author(s):  
Emilie A. Naiser ◽  
Wendy E. Wright ◽  
Robert M. Capraro

2019 ◽  
Vol 50 (2) ◽  
pp. 210-213
Author(s):  
Cynthia W. Langrall

In today's world, data and statistical information permeate our lives, making it imperative that we educate students to be statistically literate. Statistical literacy is the ability to read and interpret statistical information to make informed decisions about events under conditions of uncertainty. Recently, the National Council of Teachers of Mathematics (NCTM) published a document, Catalyzing Change in High School Mathematics: Initiating Critical Conversations (2018), in which it proposed statistics as one of four essential content domains in secondary school mathematics and acknowledged quantitative literacy—the ability to reason both statistically and numerically—as a crucial life skill for all students. For a number of years, statistics has been an important content strand across grade levels in the school mathematics curricula of many countries. Thus, it is understandable that students and even teachers might perceive statistics simply as another topic in mathematics.


2006 ◽  
Vol 11 (6) ◽  
pp. 262-268
Author(s):  
Arthur Hyde ◽  
Katie George ◽  
Suzanne Mynard ◽  
Christina Hull ◽  
Sharon Watson ◽  
...  

As teachers of mathematics in the middle grades, we were excited to find an approach to teaching algebra concepts that could be readily modified to be successful with all our students.


1996 ◽  
Vol 2 (1) ◽  
pp. 3
Author(s):  
Kay McClain

As the national council of teachers of Mathematics begins the third year of publishing Mathematics Teaching in the Middle School, the Editorial Panel thought it appropriate to highlight some of the changes that have occurred in the journal's short history. Although the intent of the journal is to target teaching in the middle grades, the variety of interests expressed by middlegrades teachers has prompted the inclusion of articles on a wide range of such issues as professional development and middle school mathematics education in other parts of the world. The journal was originally established with numerous departments to reflect readers' interests and to prompt the solicitation of manuscripts. However, the large number of unsolicited manuscripts being submitted and accepted for publication has allowed the balance of content to change so that the departments do not dictate the content of the journal but merely serve as overarching guides for themes that the Panel believes need to be addressed. These themes include assessment, technology, and professional development. Other features of the journal have remained because of their popularity with readers, such as the “Menu of Problems,” “Now & Then,” “Mathematics Detective,” “Cartoon Comer,” and “Window on Resources.”


2004 ◽  
Vol 10 (3) ◽  
pp. 132-135
Author(s):  
Shannon O. S. Driskell

Children often begin to construct an informal understanding of fractions before entering school as they learn to share their crayons or snacks fairly with friends. NCTM (2000) recommends that teachers recognize and build on each child's informal knowledge of fractions during grades K–2. In grades 3–5, children should be actively engaged in constructing conceptual knowledge about fraction concepts, with an emphasis on computational fluency as they progress into grades 6–8. The NCTM (2000) further suggests that “The study of rational numbers in the middle grades should build on students' prior knowledge of whole-number concepts and skills and their encounter with fractions, decimals, and percents in lower grades and in everyday life” (p. 215).


2016 ◽  
Vol 50 (6) ◽  
pp. 655-657 ◽  
Author(s):  
Russell Gersten ◽  
Robin F. Schumacher ◽  
Nancy C. Jordan

Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part–whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.


Author(s):  
Teresa Cristina Etcheverria ◽  
Marta Élid Amorim

Este texto tem como propósito oportunizar uma discussão sobre conhecimentos relacionados ao conteúdo frações e ao seu ensino. A discussão sobre o ensino das frações está apoiada nas ideias de Magina e Campos e de Morales, dentre outros; e de Shulman no que se refere aos conhecimentos necessários para o ensino. Os dados foram coletados por meio da aplicação de dois questionários com cinco situações problema envolvendo os diferentes conceitos de fração, um para estudantes do Ensino Fundamental e outro para estagiários do Curso de Matemática – Licenciatura. Os resultados sinalizam que apesar dos licenciandos evidenciarem saber responder corretamente situações envolvendo os diferentes significados de fração, as estratégias de ensino propostas por eles deixam claro que no momento de pensar em uma forma de explicar esse conteúdo costumam recorrer ao significado de fração como parte-todo, demonstrando, assim, conhecimento pedagógico do conteúdo insuficiente para lecionar frações. E que acreditam que o uso de recursos materiais auxiliares pode contribuir no aprendizado desse conhecimento.   Palavras-chave: Estratégias de Ensino. Frações. Formação de Professores.   Abstract The goal of this paper is to present a discussion on knowledge related to fractions and how to teach them. The discussion on teaching fractions is based on the ideas of Magina and Campos and on Morales, among others; and on Shulman regarding the knowledge necessary for teaching. The data were collected from two questionnaires with five situations involving the different fraction concepts, one applied to students in Basic Education and the other applied to interns in the Mathematics Teaching Degree Program. The results indicate that while the student-teachers know how to correctly respond to situations involving the different meanings of fractions, the teaching strategies they proposed make it clear that when they have to think about how to explain the subject, they usually appeal to the part-whole meaning of fractions, thus demonstrating insufficient pedagogical knowledge for teaching fractions. Moreover, they believe that using auxiliary material resources can contribute to learning this knowledge.   Keywords: Teaching Strategies. Fractions. Teacher Training.  


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