Sorting Symbol Strings

2005 ◽  
Vol 10 (7) ◽  
pp. 334-338
Author(s):  
Jodie D. Novak ◽  
Judith E. Jacobs
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Skilled Performance ◽  
Principles And Standards

Atheme Throughout All Grade Bands of the Algebra Standard of the NCTM's Principles and Standards for School Mathematics is the ability of students to “represent and analyze mathematical situations and structures using algebraic symbols” (p. 222). In the band for grades 6–8, this theme is further articulated as asking students to “develop an initial conceptual understanding of different uses of variables” (p. 222). Although variables sometimes occur alone, more often they occur in expressions, equations, and inequalities. We will refer to letters and numbers combined in equations, inequalities, and expressions as “symbol strings” as do Chazan and Yerushalmy (2003). The role of the variable is often determined by the symbol string in which it occurs; therefore, if students understand the different kinds of symbol strings, they will understand the roles that variables play. We have developed activities that ask students to identify, describe, compare, and classify symbol strings—in other words, to develop a feel for symbol strings. Chazan and Yerushalmy (2003) discuss it in this way: “Skilled performance [in school algebra] involves developing a feel for symbol strings … that indicates what sorts of creatures they are and what should be done with them.”

Spotlight on the Principles: Creating an Environment for Learning with Understanding: The Learning Principle

2005 ◽  
Vol 11 (1) ◽  
pp. 35-39
Author(s):  
Emily Fagan
Keyword(s):  
Prior Knowledge ◽  
Conceptual Understanding ◽  
School Mathematics ◽  
Factual Knowledge ◽  
Procedural Fluency ◽  
New Knowledge ◽  
Principles And Standards ◽  
Knowledge Learning

The learning principle in NCTM'S Principles and Standards for School Mathematics (2000) states: “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” Learning with understanding is defined as “being able to apply procedures, concepts, and processes” (NCTM 2000, p. 20). This view of learning represents a departure from a view that emphasizes a student's factual knowledge and ability to apply procedures. Although facts and procedures are important, they will not, in and of themselves, result in learning with understanding. Instead, factual understanding, procedural fluency, and conceptual understanding must coexist so that students reach learning with understanding. The extent to which a student can apply his or her learning to a new problem or situation is often an indicator of this understanding.

Abi, A. M. (2016). Integrasi Etnomatematika Dalam Kurikulum Matematika Sekolah. Jurnal Pendidikan Matematika Indonesia, 1-6. François, K. (2009). The Role of Ethnomathematics within Mathematics Education. Proceedings of CERME 6 (pp. 1517-1526). Lyon France: INRP 2010. Mansur HR. (2015, February). Menciptakan Pembelajaran Efektif melalui Apersepsi. Retrieved from LPMP Sulsel: http://www.lpmpsulsel.net/v2/index.php?option=com_content&view=article&id=327:pembelajaran‐efektif‐ M.Balamurugan. (2015). ETHNOMATHEMATICS; AN APPROACH FOR LEARNING MATHEMATICS FROM MULTICULTURAL PERSPECTIVES. INTERNATIONAL JOURNAL OF MODERN RESEARCH AND REVIEWS, 716-720. NCTM. (1989). Curriculum and Evaluation Standards for School Mathematics. Snipes, V., & Moses, P. (2001). Linking Mathematics and Culture to Teach Geometry Concepts. Retrieved from Semantic Scholar: https://www.semanticscholar.org/paper/Linking-Mathematics-and-Culture-to-Teach-Geometry-Snipes/de16ae98aa72c9eef916e40f2e91dd17deb5a179 Stylianides, A. J., & Stylianides, G. J. (2007). Learning Mathematics with Understanding: A Critical Consideration of the Learning Principle in the Principles and Standards for School Mathematics. The Mathematics Enthusiast, 103-114. Sukayati, & Suharjana, A. (2009). PEMANFAATAN ALAT PERAGA MATEMATIKA DALAM PEMBELAJARAN DI SD. Yogyakarta: PPPPTK Matematika Yogyakarta. Wijaya, A., Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students’ errors. The Mathematics Enthusiast, 555-584. Yusuf, M. W., Ibrahim Saidu, I., & Halliru, A. (2010). ETHNOMATHEMATICS (A Mathematical Game in Hausa Culture). International Journal of Mathematical Science Education, 36-42. Yvette d’Entremont, Y. (2015). Linking mathematics, culture and community. Procedia - Social and Behavioral Sciences, 2818 – 2824.

2017 ◽  
Vol 3 (2) ◽  
pp. 1928-1941
Author(s):  
Ernawati . ◽  
◽  
Kurniawati . ◽  
Keyword(s):  
School Mathematics ◽  
Mathematical Science ◽  
Evaluation Standards ◽  
Mathematics Tasks ◽  
Learning Mathematics ◽  
Mathematical Game ◽  
Principles And Standards ◽  
Multicultural Perspectives ◽  
Critical Consideration

Spotlight on the Principles: The Role of Textbooks in Implementing the Curriculum Principle and the Learning Principle

2003 ◽  
Vol 9 (2) ◽  
pp. 120-124
Author(s):  
Barbara J. Reys ◽  
Jennifer M. Bay-Williams
Keyword(s):  
School Mathematics ◽  
Principles And Standards

Welcome to the new “Spotlight on the Principles.” September's “Spotlight on the Standards” brought to a close the set of articles examining the ten Standards envisioned in NCTM's Principles and Standards for School Mathematics (2000). With this article, the MTMS Editorial Panel is directing the focus of the department on the six Principles, beginning with an overview of the Curriculum Principle and Learning Principle.

A Case of Units

2003 ◽  
Vol 9 (7) ◽  
pp. 397-399
Author(s):  
Christopher M. Kribs-Zaleta ◽  
D'Lynn Bradshaw
Keyword(s):  
Young Children ◽  
Learning Opportunities ◽  
School Mathematics ◽  
Learning Potential ◽  
Mathematical Development ◽  
Great Learning ◽  
The World ◽  
Principles And Standards ◽  
Children’S Work

Young children learn by playing, and they first learn mathematics through exploration that develops naturally from their curiosity and experiences. They count, build, draw, model, and measure the world around them. The informal origins of their first mathematical insights remain an important link to the role of context in learning at any age. It is especially important for teachers to know this, in order to be alert to learning opportunities that arise. By paying attention to the details in students' conversations, we can develop the habit of listening to their mathematical discoveries. Encouraging and focusing these discoveries often releases the great learning potential inside students. Principles and Standards for School Mathematics (NCTM 2000) elaborates on the idea of play being children's work by observing, “Adults support young children's diligence and mathematical development when they direct attention to the mathematics children use in their play, challenge them to solve problems, and encourage their persistence” (p. 74).

Build Your Own Fraction Computer!

2002 ◽  
Vol 8 (4) ◽  
pp. 204-208
Author(s):  
Peter L. Glidden
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Addition And Subtraction ◽  
Principles And Standards ◽  
Fraction Addition

The NCTM's Curriculum and Evaluation Standards (1989) called for increased emphasis on promoting students' conceptual understanding of fractions and fraction operations; this call was reaffirmed in Principles and Standards for School Mathematics (NCTM 2000). Currently, many manipulatives, including pattern blocks, fraction circles, fraction squares, geodot paper, and fraction strips, are available to help teachers promote this understanding. This article describes another manipulative, the fraction computer, that I have found helpful for teaching fraction addition and subtraction.

Making the Most of Mathematical Discussions

2007 ◽  
Vol 101 (4) ◽  
pp. 257-261
Author(s):  
Megan Staples ◽  
Melissa M. Colonis
Keyword(s):  
Conceptual Understanding ◽  
Classroom Discourse ◽  
Good Practice ◽  
Mathematical Discourse ◽  
Experienced Teachers ◽  
Mathematical Discussions ◽  
Principles And Standards ◽  
Key Aspects ◽  
Insight Into

The importance of mathematical discourse and its connection to developing conceptual understanding, communication, and reasoning is well documented throughout NCTM's Principles and Standards for School Mathematics (2000). For example, NCTM's Learning Principle emphasizes the role of discourse in supporting student learning, noting that “classroom discourse and social interaction can be used to promote the recognition of connections among ideas and the reorganization of knowledge (Lampert 1986)” (NCTM 2000, p. 21). The skillful facilitation of discussions is something both novice and experienced teachers find challenging. Most teachers can recall a well-planned lesson that did not unfold as expected. From this article, we hope readers gain insight into planning mathematically focused, collaborative discussions. We illuminate three key aspects of the pedagogy of teachers who were successful in consistently organizing whole-class discussions. These teachers created learning environments aligned with NCTM's vision of good practice, where students were given conceptually demanding tasks, worked together to develop ideas, and consistently were asked to make sense of mathematics.

Are We Overemphasizing Manipulatives in the Primary Grades to the Detriment of Girls?

2002 ◽  
Vol 9 (1) ◽  
pp. 16-21
Author(s):  
Rebecca C. Ambrose
Keyword(s):  
Problem Solving ◽  
Instructional Practice ◽  
Primary Grades ◽  
School Mathematics ◽  
High Expectations ◽  
Equity Principle ◽  
Promising Practice ◽  
Research Findings ◽  
Principles And Standards

In keeping with the Equity Principle of the Principles and Standards for School Mathematics (NCTM 2000), educators must maintain high expectations for all children and continually examine their practices to ensure that all children learn mathematics with understanding. The instructional practice of using manipulatives for problem solving merits closer examination because it may send the wrong message to some children. Recent research indicates that some girls' understanding seems to be limited by their overreliance on manipulatives. Before presenting the research findings, I will outline the role of manipulatives in supporting the development of children's understanding, then examine how this promising practice can be detrimental when used too often.

Social Development and Police Reform: Some Reflections on the Concept and Purpose of Policing and the Implications for Reform in the UK and USA

2020 ◽  
Author(s):  
Andrew Williams ◽  
Craig Paterson
Keyword(s):  
Social Development ◽  
Conceptual Understanding ◽  
Critical Question ◽  
Police Reform ◽  
Liberal Democratic ◽  
The Usa ◽  
Anglo American ◽  
The Uk ◽  
Common Understanding

Abstract The increase in calls for police reform following the death of George Floyd has led to renewed debate about social inequality and the role of policing in society. Modern bureaucratic police systems emerged from locally administered structures and Anglo-American policing models continue to be aligned, to varying degrees, with the political, socio-cultural, legal, and ideological aspects of contemporary liberal democratic society with its emphasis on democratic localism and decentralised accountability. However, at a time when society is reimagining itself and technology, government, and nations are radically re-shaping themselves, a critical question is whether there is a sufficiently common philosophical and conceptual understanding of policing to support its development rather than just a common understanding of police functions. This is profoundly important when considering the current calls for reform of policing in the USA and other western democratic states. The article argues that there is an urgent need to reconsider how we conceptualize policing and its relationship with social development.

Descriptive Analysis of Coach Augmented Feedback Given to High School Varsity Female Volleyball Players

1988 ◽  
Vol 7 (4) ◽  
pp. 289-301 ◽  
Author(s):  
Regina Markland ◽  
Thomas J. Martinek
Keyword(s):  
High School ◽  
Multivariate Analysis ◽  
Descriptive Analysis ◽  
Augmented Feedback ◽  
Skilled Performance ◽  
Dependent Variables ◽  
Volleyball Players ◽  
Analysis System ◽  
To Receive

This study examined the nature and amount of feedback that more successful and less successful high school varsity volleyball coaches gave to their starting and nonstarting volleyball players. Two of the four coaches studied were considered more successful and two were considered less successful, based on previous regular season win-loss percentages. Players of all the coaches (N=41) were also used as subjects and identified as having either a starting or nonstarting role on the team. All subjects were observed on three occasions for 30 minutes per observation during regular season practice. The Cole Descriptive Analysis System (Cole-DAS) was used to observe coach augmented feedback as it was given to individual players in response to skilled performance. A 2 × 2 multivariate analysis of variance was used to describe the effects of (a) success of the coach, (b) role of the player, and (c) both success of the coach and role of the player on the dependent variables of coach augmented feedback. Results indicated that successful coaches varied considerably from less successful coaches in the types of feedback given to their players. Starting players were also found to receive significantly more audio, audiovisual, and immediate terminal feedback than nonstarting players.

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