Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking

Kieran, Carolyn

doi:10.1007/978-3-319-68351-5_4

Cited by 30 publications

(18 citation statements)

References 24 publications

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“…In her discussion of multiple meanings of structure, Kieran (2018) emphasizes that structure does not necessarily require pattern generalization, but is also useful for capturing students' ways of connecting representations, among other things. The articulation of our epistemological background builds upon Kieran's (1989) conceptualizations of structure.…”

Section: Three Characterizations For Equivalence Of Expressionsmentioning

confidence: 99%

“…We denote systemic structures as deeper (systemic) structures when their involved properties are (explicitly or implicitly) also connected to structures in other representations, for instance, in these structured figures. Thus, our third conceptualization of structure reflects the need to also connect the systemic properties to other representations (Cooper & Warren, 2011;Mason et al, 1985) and Kieran's (2018) call to focus on seeking, using, and expressing (deeper) structures.…”

Section: Three Characterizations For Equivalence Of Expressionsmentioning

confidence: 99%

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Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations

Tondorf

Prediger

2022

Educ Stud Math

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One typical challenge in algebra education is that many students justify the equivalence of expressions only by referring to transformation rules that they perceive as arbitrary without being able to justify these rules. A good algebraic understanding involves connecting the transformation rules to other characterizations of equivalence of expressions (e.g., description equivalence that both expressions describe the same situation or figure). In order to overcome this disconnection even before variables are introduced, a design research study was conducted in Grade 5 to design and investigate an early algebra learning environment to establish stronger connections between different mental models and representations of equivalence of expressions. The qualitative analysis of design experiments with 14 fifth graders revealed deep insights into complexities of connecting representations. It confirmed that many students first relate the representations in ways that are too superficial without establishing deep connections. Analyzing successful students’ processes helped to identify an additional characterization that can support students in bridging the connection between other characterizations, which we call restructuring equivalence. By including learning opportunities for restructuring equivalence, students can be supported to compare expressions in graphical and symbolic representation simultaneously and dynamically. The design research study disentangles the complex requirements for realizing the design principle of connecting multiple representations, which should be of relevance beyond the specific concept of equivalence and applicable to other mathematical topics.

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Section: Three Characterizations For Equivalence Of Expressionsmentioning

confidence: 99%

Section: Three Characterizations For Equivalence Of Expressionsmentioning

confidence: 99%

Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations

Tondorf

Prediger

2022

Educ Stud Math

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“…Los resultados obtenidos después de la intervención son congruentes con lo que se ha reportado sobre lo complejo y tardado que resulta desarrollar el sentido estructural, ya que requiere abstraer las relaciones dentro de una expresión y entre varias expresiones, como concluyeron Banerjee y Subramaniam (2005). Kieran (2018) coincide en que desarrollar la capacidad de ver la estructura es un proceso largo que necesita reinventarse con cada nuevo objeto matemático que se observa.…”

Section: Conclusionesunclassified

Desarrollo del sentido estructural en alumnos universitarios mediante el uso de la Teoría de la Variación en el manejo de expresiones algebraicas racionales

Gonzalez¹,

Eccius-Wellmann²

2019

EduMate

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Resumen: Desarrollar un sentido estructural permite al alumno realizar tareas algebraicas de formas más eficientes y menos propensas a errores, por lo que es relevante fortalecerlo. Se presentan en este artículo los resultados de una investigación cuyo objetivo fue desarrollar el sentido estructural en estudiantes universitarios, mediante la elaboración, implementación y prueba de actividades de enseñanza-aprendizaje que, a la par, promuevan el desarrollo de habilidades para simplificar y operar expresiones algebraicas racionales. El diseño de las actividades se basó en la Teoría de la Variación. Se definieron y ponderaron descriptores del sentido estructural, para fines de comparación. Se aplicaron evaluaciones antes y después de la implementación de las actividades, a cuatro grupos experimentales y tres de control. Se observó un incremento del nivel de sentido estructural estadísticamente superior en los grupos experimentales con respecto a los grupos de control. Se comprobó que es posible desarrollar, en mayor medida, el sentido estructural en los alumnos, al incluir, en las actividades que realizan, contrastes y variaciones elegidos con esa intención.

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“…Unfortunately, algebra is a difficult material for students, specifically for middle school students [4,5,6,7,8,9,10,11]. Kriegler and Lee [12] said that the mastery of algebra in equivalence topics by students of eighth-graders in California was twenty-two percent.…”

Section: Introductionmentioning

confidence: 99%

Realistic Mathematics Education: A Learning Innovation in Enhancing Students' Algebraic Thinking Ability

Suhaedi¹

2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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Algebra thinking is one of the abilities students must have in learning school algebra. The weak algebraic thinking ability of junior high school students is one part of the problems in mathematics education. One effort to solve these problems is to innovate learning with a realistic mathematics education (RME) approach. This study is a quasiexperiment about improving students' algebraic thinking abilities, with the experimental class using the RME approach and the control class using expository learning. The research sample consisted of 134 eighth grade students of junior high schools in Bandung. The results of the study show that increasing the algebraic thinking ability of students who get learning with an RME approach is better than students who get expository learning at every level of students' initial mathematical knowledge.

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Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking

Cited by 30 publications

References 24 publications

Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations

Connecting characterizations of equivalence of expressions: design research in Grade 5 by bridging graphical and symbolic representations

Desarrollo del sentido estructural en alumnos universitarios mediante el uso de la Teoría de la Variación en el manejo de expresiones algebraicas racionales

Realistic Mathematics Education: A Learning Innovation in Enhancing Students' Algebraic Thinking Ability

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