Algebraic Reasoning through Patterns

2009 ◽  
Vol 15 (4) ◽  
pp. 212-221
Author(s):  
F. D. Rivera ◽  
Joanne Rossi Becker
Keyword(s):  
Algebraic Reasoning ◽  
And Algebra

Findings, insights, and issues drawn from a three-year study on patterns are intended to help teach prealgebra and algebra.

scholarly journals PROSPECTIVE TEACHERS’ INTERPRETATIVE KNOWLEDGE ON EARLY ALGEBRA

2018 ◽  
Vol 24 (esp.) ◽  
pp. 208
Author(s):  
Rosa Di Bernardo ◽  
Gemma Carotenuto ◽  
Maria Mellone ◽  
Miguel Ribeiro
Keyword(s):  
Prospective Teachers ◽  
Mathematical Knowledge ◽  
Primary Teachers ◽  
Algebraic Thinking ◽  
Early Years ◽  
Algebraic Reasoning ◽  
Early Algebra ◽  
Very Young Children ◽  
And Algebra ◽  
Prospective Primary Teachers

 Abstract: Starting from the assumption that very young children exhibit some naive forms of algebraic skills, in this paper we discuss some of our work aimed at inquiry, and in the same time develop, prospective primary teachers’ knowledge involved and required in recognize and interpret pupils’ early forms of algebraic thinking. The research dimension is perceived intertwined with teacher education and practice and thus, the tasks we develop for such work focus on early years’ prospective teachers’ mathematical knowledge specifically related with the work of teaching Early Algebra. Thus, our focus of attention concerns their knowledge that would sustain the work on supporting the development of pupils’ knowledge and reasoning toward more refined algebraic skills. We present promising preliminary results from an experiment conducted on 60 prospective Italian teachers’, which paves the way for further research about the expected early years teachers’ knowledge on Early Algebra and Algebra and even more refined didactic methods aimed at developing it.Keywords: Teachers’ knowledge. Algebraic Reasoning. Interpretative knowledge. Early years.CONHECIMENTO INTERPRETATIVO DE FUTUROS PROFESSORES DA EDUCAÇÃO INFANTIL E ANOS INICIAIS NO ÂMBITO DO PENSAMENTO ALGÉBRICO Resumo: Considerando que as crianças desde cedo possuem algumas capacidades, competências e conhecimentos algébricos, ainda que intuitivos, neste artigo discutimos uma parte de nosso trabalho que tem por objetivo acessar e desenvolver o conhecimento de futuros professores envolvido e requerido em reconhecer e interpretar produções de alunos no âmbito do Pensamento Algébrico. Pesquisa, formação e prática são consideradas de forma indissociada e, assim, as tarefas que conceitualizamos para desenvolver esse trabalho focam-se no conhecimento matemático de futuros professores especificamente relacionado com as tarefas de ensinar Pensamento Algébrico. Assim, o nosso foco de atenção refere-se, especificamente, ao conhecimento de futuros professores que contribua para o desenvolvimento do conhecimento e raciocínio dos alunos no sentido de refinar as suas competências algébricas. Apresentamos alguns resultados preliminares a partir da análise de uma tarefa para a formação de professores implementada em Itália a 60 futuros professores e que revelam alguns aspetos centrais do conhecimento do professor relativamente ao Pensamento Algébrico e à Álgebra e indicam necessidades de pesquisa que contribua para um desenvolvimento de tal conhecimento.Palavras-chave: Conhecimento do professor. Pensamento Algébrico. Conhecimento Interpretativo. Anos Iniciais. CONOCIMIENTO INTERPRETATIVO DE FUTUROS PROFESSORES DE INFANTIL E PRIMÁRIA EN EL CONTEXTO DEL PENSAMIENTO ALGEBRAICOResumen: Considerando que los niños desde edad temprana poseen algunas capacidades, competencias y conocimientos algebraicos, aunque intuitivos, en este artículo discutimos una parte de nuestro trabajo que tiene por objetivo acceder y desarrollar el conocimiento de futuros profesores involucrado y requerido en reconocer e interpretar producciones de alumnos en el ámbito del Pensamiento Algebraico. Investigación, formación y práctica se consideran de forma indisociada y así, las tareas que conceptualizamos para desarrollar ese trabajo se enfocan en el conocimiento matemático de futuros profesores específicamente relacionado con las tareas de enseñar Pensamiento Algebraico. Nuestro foco de atención se refiere específicamente al conocimiento de futuros profesores que contribuya al desarrollo del conocimiento y raciocinio de los alumnos en y para refinar sus competencias algebraicas. Presentamos algunos resultados preliminares a partir del análisis de una tarea para la formación de profesores implementada en Italia a 60 futuros profesores y que revelan algunos aspectos centrales del conocimiento del profesor respecto al Pensamiento Algebraico y al Álgebra e indican algunas necesidades de investigación que contribuya a un desarrollo de dicho conocimiento.Palabras claves: Conocimiento del profesor. Pensamiento Algebraico. Conocimiento Interpretativo. Educación Infantil e primaria 

Take Time for Action: From Kinesthetic Movement to Algebraic Functions

2009 ◽  
Vol 14 (7) ◽  
pp. 388-391
Author(s):  
Mary G. Goral
Keyword(s):  
Algebraic Function ◽  
Physical Models ◽  
Algebraic Reasoning ◽  
Mathematical Functions ◽  
Spatial Intelligence ◽  
Algebra Students ◽  
Beginning Algebra ◽  
Geometric Thinking ◽  
And Algebra ◽  
Pictorial Representations

Are students able to work through a series of geometric spatial activities, discover a pattern, and find an algebraic function? Can they move from using spatial intelligence to number sense to algebraic reasoning? Are they able to connect geometric thinking and algebra, physical models, and numeric relationships? Friel, Rachlin, and Doyle (2001) state, “Explorations that develop from problems that can be solved by using tables, graphs, verbal descriptions, concrete or pictorial representations or algebraic symbols offer opportunities for students to build their understandings of mathematical functions” (p. v). Further, combining physical spatial activities with algebraic reasoning can better engage beginning algebra students in the task at hand. According to Jensen (2001), the kinesthetic arts can provide a significant vehicle that can enhance content-area learning.

Developing Algebraic Reasoning Through Generalization

2003 ◽  
Vol 8 (7) ◽  
pp. 342-348
Author(s):  
John K. Lannin
Keyword(s):  
Mathematical Models ◽  
Middle Grades ◽  
Algebraic Reasoning ◽  
Mathematical Content ◽  
General Rules ◽  
Formal Algebra ◽  
And Algebra

NCTM's (2000) recommendations for algebra in the middle grades strive to assist students' transition to formal algebra by developing meaning for the algebraic symbols that students use. Further, students are expected to have opportunities to develop understanding of patterns and functions, represent and analyze mathematical situations, develop mathematical models, and analyze change. By helping students move from specific numeric situations to develop general rules that model all situations of that type, teachers in fact begin to address the NCTM's recommendations for algebra. Generalizing numeric situations can create strong connections between the mathematical content strands of number and operation and algebra (as well as with other content strands). In addition, these generalizing activities build on what students already know about number and operation and can help students develop a deeper understanding of formal algebraic symbols.

scholarly journals Geometry and Algebra of the Deltoid Map

2021 ◽  
Vol 128 (1) ◽  
pp. 25-39
Author(s):  
Joshua P. Bowman
Keyword(s):  
And Algebra

scholarly journals Algebraic reasoning for object-oriented programming

2004 ◽  
Vol 52 (1-3) ◽  
pp. 53-100 ◽  
Author(s):  
Paulo Borba ◽  
Augusto Sampaio ◽  
Ana Cavalcanti ◽  
Márcio Cornélio
Keyword(s):  
Object Oriented ◽  
Object Oriented Programming ◽  
Algebraic Reasoning

Aunt Bertha's Ice Cream Shoppe

2015 ◽  
Vol 108 (9) ◽  
pp. 720
Author(s):  
Katie A. Hendrickson ◽  
Gabrielle Kisner
Keyword(s):  
Problem Based Learning ◽  
Ice Cream ◽  
And Algebra

Problem-based learning motivates students to use their knowledge of geometry and algebra.

Geometric reasoning with logic and algebra

1988 ◽  
Vol 37 (1-3) ◽  
pp. 37-60 ◽  
Author(s):  
Dennis S. Arnon
Keyword(s):  
Geometric Reasoning ◽  
And Algebra
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