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Research on Powerful Ideas for Enriching School Mathematical Learning
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Research on Powerful Ideas for Enriching School Mathematical Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 49946

Special Issue Editor

Dr. Marta Molina

E-Mail Website
Guest Editor
Mathematics education Area, Department of Mathematics Education and Science Education, Education and Tourism School of Avila, University of Salamanca, Madrigal de las Altas Torres, 3, 05003 Ávila, Spain
Interests: mathematics education; early algebra; school algebra; numerical thinking; algebraic thinking; problem posing; problem solving; primary teachers’ education; design research; teaching experiments

Special Issue Information

Dear colleagues,

The MDPI journal Mathematics will have a Special Issue on Mathematics Education. It will focus on powerful ideas with the potential to enrich mathematics learning at any level from kindergarten to secondary school (i.e., age range of students: 3-17 years old).

The chosen topic encompasses a wide variety of research on mathematics education aiming to explore, inform about or assess ways in which school mathematics learning can be enriched and promoted so that students experience meaningful ways of doing and learning mathematics. For the purposes of this call for papers, "powerful ideas" include those that facilitate in-depth learning and understanding of key mathematical concepts or practices that have implications for students’ continuing development in mathematics. Powerful ideas can include, for example, a theoretical construct, principles of task design or a resource.

You are welcome to disseminate this Call to others whose research you think would be relevant to the Special Issue.

Dr. Marta Molina
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Mathematics education
  • Powerful ideas
  • Understanding
  • Mathematics
  • Learning
  • Pre-school education
  • Elementary education
  • Secondary education

Published Papers (16 papers)

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Research

18 pages, 1776 KiB  
Article
Interacting with Indeterminate Quantities through Arithmetic Word Problems: Tasks to Promote Algebraic Thinking at Elementary School
by Cristina Ayala-Altamirano, Eder Pinto, Marta Molina and María C. Cañadas
Mathematics 2022, 10(13), 2229; https://doi.org/10.3390/math10132229 - 25 Jun 2022
Cited by 1 | Viewed by 1806
Abstract
In this study, we analyze how 9–10-year-old pupils work with equations, a central aspect of algebraic thinking in early grades and a cornerstone for more formal learning of algebra. Specifically, we seek: (a) to describe the main characteristics of the tasks that support [...] Read more.
In this study, we analyze how 9–10-year-old pupils work with equations, a central aspect of algebraic thinking in early grades and a cornerstone for more formal learning of algebra. Specifically, we seek: (a) to describe the main characteristics of the tasks that support algebraic thinking through a translation process from arithmetic word problems to algebraic language and vice versa, and (b) to identify how pupils refer to indeterminate quantities in these contexts and what meaning they give to them. The analysis focuses on the semantic congruence of the expressions proposed by them and on the dialogue they held during the translation process. We analyzed the oral discussion in the pools and the written responses to the problem that pupils posed. The results show that arithmetic word problems allow the indeterminate to become an object of thought for pupils, who represent it in multiple ways and refer to it when proposing equations that represent the structure of each problem. Another finding highlights that reflection on the interpretation of the equations supports the identification of two meanings associated with indeterminate quantities, namely, unknown and variable. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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22 pages, 6251 KiB  
Article
Arousing Early Strategic Thinking about SDGs with Real Mathematics Problems
by Rodrigo Domínguez-González and Laura Delgado-Martín
Mathematics 2022, 10(9), 1446; https://doi.org/10.3390/math10091446 - 25 Apr 2022
Cited by 3 | Viewed by 3794
Abstract
In this article, we ask whether it is possible to reinforce problem design skills in secondary school mathematics teachers around the UN Sustainable Development Goals (SDGs), so that young students can try out a first numerical approach to sustainable development. If this is [...] Read more.
In this article, we ask whether it is possible to reinforce problem design skills in secondary school mathematics teachers around the UN Sustainable Development Goals (SDGs), so that young students can try out a first numerical approach to sustainable development. If this is possible, we ask whether it would significantly improve their relationship with sustainability and their perception of the usefulness of mathematics. The present paper aims to proactively contribute to the field of civic education through the design of original math problems combining math secondary education curriculum with the predicament of the 2030 Agenda and the 17 interlinked SDGs. Conceived as a qualitative research tool for teacher training, generating adequate resources for their professional practice, five of these chosen workshop activities have been presented to a group of forty-seven students who were asked to complete a questionary afterwards about their attitude towards the proposal. The article’s main findings are that SDGs are a powerful source of inspiration for problem design grounded in real-world contexts and that students of this age are mostly ready to feel curiosity and motivation about the mathematical approach to sustainability and their capacity to analyze real data, regardless of the inevitable oversimplification of the problem. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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21 pages, 1004 KiB  
Article
Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students
by Rafael Ramírez-Uclés and Juan F. Ruiz-Hidalgo
Mathematics 2022, 10(5), 789; https://doi.org/10.3390/math10050789 - 1 Mar 2022
Cited by 1 | Viewed by 3373
Abstract
Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and comparing different points of view. [...] Read more.
Proof, a key topic in advanced mathematics, also forms an essential part of the formal learning experience at all levels of education. The reason is that the argumentation involved calls for pondering ideas in depth, organizing knowledge, and comparing different points of view. Geometry, characterized by the interaction between the visual appearance of geometric elements and the conceptual understanding of their meaning required to generate precise explanations, is one of the foremost areas for research on proof and argumentation. In this qualitative analysis of the arguments formulated by participants in an extracurricular mathematics stimulus program, we categorized students’ replies on the grounds of reasoning styles, representations used, and levels of generality. The problems were proposed in a lesson on a quotient set based on the similarity among triangles created with Geogebra and the responses were gathered through a Google form. By means a content analysis, the results inform about the reasoning style, the scope of the argumentation, and the representation used. The findings show that neither reasoning styles nor the representations used conditioned the level of generality, although higher levels of argumentation were favored by harmonic and analytical reasoning and the use of algebraic representations. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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24 pages, 861 KiB  
Article
Preservice Teachers’ Eliciting and Responding to Student Thinking in Lesson Plays
by Ji-Eun Lee and Woong Lim
Mathematics 2021, 9(22), 2842; https://doi.org/10.3390/math9222842 - 9 Nov 2021
Viewed by 1893
Abstract
This study presents an analysis of 95 lesson play scripts—hypothetical dialogues between the teacher and a student—written by 32 preservice teachers (PSTs). Writing lesson scripts was part of the assessment design activities to elicit and respond to students’ thinking. The findings present the [...] Read more.
This study presents an analysis of 95 lesson play scripts—hypothetical dialogues between the teacher and a student—written by 32 preservice teachers (PSTs). Writing lesson scripts was part of the assessment design activities to elicit and respond to students’ thinking. The findings present the types and frequencies of teacher talks/moves in fraction-related tasks during a stage of lesson plays, such as launch, active elicitation, and closure. Our analysis indicates a wide range in the number of turns taken by the PSTs, while there is little correlation between the number of turns and effectiveness at eliciting and responding to student thinking. The study also confirmed that some unproductive talk moves were still present in the lesson play context, although the PSTs had plenty of time to craft a script. This study drew implications of PSTs’ prior perceptions, experiences, knowledge, and needs in mathematics teacher education regarding the ways to create learning opportunities for them to elicit and respond to student thinking. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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22 pages, 7498 KiB  
Article
The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry
by José L. Rodríguez, Isabel Romero and Antonio Codina
Mathematics 2021, 9(19), 2411; https://doi.org/10.3390/math9192411 - 28 Sep 2021
Cited by 22 | Viewed by 3764
Abstract
The use of dynamic, three-dimensional software with virtual reality offers new possibilities for the teaching and learning of geometry. We explore the effects of introducing the immersive virtual reality software NeoTrie VR in real classes. Within a Design Research framework, we present qualitative [...] Read more.
The use of dynamic, three-dimensional software with virtual reality offers new possibilities for the teaching and learning of geometry. We explore the effects of introducing the immersive virtual reality software NeoTrie VR in real classes. Within a Design Research framework, we present qualitative observational data to report how the collaboration among a software development company, university researchers, and schools produces improvements in the design and updating of the software; the geometrical content, representations, and mathematical activity that students have access to as well as the way teachers conceive and manage the teaching of geometry. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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21 pages, 3899 KiB  
Article
Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them
by Oscar Molina, Vicenç Font and Luis Pino-Fan
Mathematics 2021, 9(18), 2296; https://doi.org/10.3390/math9182296 - 17 Sep 2021
Cited by 1 | Viewed by 2125
Abstract
This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class [...] Read more.
This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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20 pages, 4815 KiB  
Article
Levels of Sophistication in Elementary Students’ Understanding of Polygon Concept and Polygons Classes
by Melania Bernabeu, Salvador Llinares and Mar Moreno
Mathematics 2021, 9(16), 1966; https://doi.org/10.3390/math9161966 - 17 Aug 2021
Cited by 2 | Viewed by 3856
Abstract
This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking [...] Read more.
This paper reports sophistication levels in third grade children’s understanding of polygon concept and polygon classes. We consider how children endow mathematical meaning to parts of figures and reason to identify relationships between polygons. We describe four levels of sophistication in children’s thinking as they consider a figure as an example of a polygon class through spatial structuring (the mental operation of building an organization for a set of figures). These levels are: (i) partial structuring of polygon concept; (ii) global structuring of polygon concept; (iii) partial structuring of polygon classes; and (iv) global structuring of polygon classes. These levels detail how cognitive apprehensions, dimensional deconstruction, and the use of mathematical language intervene in the mental process of spatial structuring in the understanding of the classes of polygons. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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13 pages, 6726 KiB  
Article
Teaching Combinatorial Principles Using Relations through the Placemat Method
by Viliam Ďuriš, Gabriela Pavlovičová, Dalibor Gonda and Anna Tirpáková
Mathematics 2021, 9(15), 1825; https://doi.org/10.3390/math9151825 - 2 Aug 2021
Cited by 2 | Viewed by 2904
Abstract
The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. [...] Read more.
The presented paper is devoted to an innovative way of teaching mathematics, specifically the subject combinatorics in high schools. This is because combinatorics is closely connected with the beginnings of informatics and several other scientific disciplines such as graph theory and complexity theory. It is important in solving many practical tasks that require the compilation of an object with certain properties, proves the existence or non-existence of some properties, or specifies the number of objects of certain properties. This paper examines the basic combinatorial structures and presents their use and learning using relations through the Placemat method in teaching process. The effectiveness of the presented innovative way of teaching combinatorics was also verified experimentally at a selected high school in the Slovak Republic. Our experiment has confirmed that teaching combinatorics through relationships among talented children in mathematics is more effective than teaching by a standard algorithmic approach. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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17 pages, 2839 KiB  
Article
Strategies for Solving Addition Problems Using Modified Schema-Based Instruction in Students with Intellectual Disabilities
by Alicia Bruno, Irene Polo-Blanco, María José González-López and Jon González-Sánchez
Mathematics 2021, 9(15), 1814; https://doi.org/10.3390/math9151814 - 30 Jul 2021
Cited by 4 | Viewed by 4053
Abstract
A study is presented on the strategies employed to solve additive change problems by three students with intellectual disabilities (two of them with autism spectrum disorder). The students followed a program involving modified schema-based instruction. The results show an improvement in the problem-solving [...] Read more.
A study is presented on the strategies employed to solve additive change problems by three students with intellectual disabilities (two of them with autism spectrum disorder). The students followed a program involving modified schema-based instruction. The results show an improvement in the problem-solving skills of the three students, who achieved successful formal strategies associated with identifying the operation. We analyze the importance of adapting and/or emphasizing certain steps in the instruction process in order to tailor them to the difficulties of each student. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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16 pages, 2102 KiB  
Article
Cognitive Conflict in Technological Environment: Cognitive Process and Emotions through Intuitive Errors in Area, Perimeter and Volume
by Juhaina Awawdeh Shahbari
Mathematics 2021, 9(14), 1672; https://doi.org/10.3390/math9141672 - 16 Jul 2021
Viewed by 1733
Abstract
This study was conducted among 28 seventh-grade students. They worked in groups in an activity with modeling features; the activity consisted of three tasks dealing with an intuitive error, namely, same A–same B. The data source was nine video recordings of three groups [...] Read more.
This study was conducted among 28 seventh-grade students. They worked in groups in an activity with modeling features; the activity consisted of three tasks dealing with an intuitive error, namely, same A–same B. The data source was nine video recordings of three groups across the three activities. The results obtained from analyses of students’ discussions and interactions indicate that they moved through three central stages: the intuitive error stage, the revealing of the intuitive error connected with cognitive conflict and the stage of overcoming the intuitive errors. In each of the three stages in the three tasks, we identified similar emotion features among the three groups across the three tasks. In the intuitive error stage, the participants were characterized by confidence, comfort and enjoyment. In revealing the intuitive errors, we identified several indicators and signs of non-comfortable situations by revealing the errors in the three tasks, such as a high sound or sad tone of voice, physical movements such as moving closer to the computer screen and other physical indicators such as opening the mouth and putting a hand on the head or the face. After overcoming and understanding the sources of the errors, the participants showed confidence that was clear in their facial signs, joy and smiles, loud tone and eye contact between students and the teacher, or between students. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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15 pages, 10412 KiB  
Article
Graph Theory for Primary School Students with High Skills in Mathematics
by Rocío Blanco and Melody García-Moya
Mathematics 2021, 9(13), 1567; https://doi.org/10.3390/math9131567 - 3 Jul 2021
Cited by 3 | Viewed by 3080
Abstract
Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The [...] Read more.
Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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17 pages, 7144 KiB  
Article
How the Theme of ‘Doing and Undoing’ Applied to the Action of Exchange Reveals Overlooked Core Ideas in School Mathematics
by John Mason
Mathematics 2021, 9(13), 1530; https://doi.org/10.3390/math9131530 - 29 Jun 2021
Viewed by 1670
Abstract
The theme of ‘undoing a doing’ is applied to the ubiquitous action of exchange, showing how exchange pervades a school’s mathematics curriculum. It is possible that many obstacles encountered in school mathematics arise from an impoverished sense of exchange, for learners and possibly [...] Read more.
The theme of ‘undoing a doing’ is applied to the ubiquitous action of exchange, showing how exchange pervades a school’s mathematics curriculum. It is possible that many obstacles encountered in school mathematics arise from an impoverished sense of exchange, for learners and possibly for teachers. The approach is phenomenological, in that the reader is urged to undertake the tasks themselves, so that the pedagogical and mathematical comments, and elaborations, may connect directly to immediate experience. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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19 pages, 2177 KiB  
Article
Generalization Process by Second Grade Students
by María D. Torres, Antonio Moreno and María C. Cañadas
Mathematics 2021, 9(10), 1109; https://doi.org/10.3390/math9101109 - 14 May 2021
Cited by 7 | Viewed by 4514
Abstract
This study is part of a broader study on algebraic reasoning in elementary education. The research objective of the present survey, namely to describe generalization among second grade (7- to 8-year-old) students, was pursued through semi-structured interviews with six children in connection with [...] Read more.
This study is part of a broader study on algebraic reasoning in elementary education. The research objective of the present survey, namely to describe generalization among second grade (7- to 8-year-old) students, was pursued through semi-structured interviews with six children in connection with a contextualized generalization task involving the function y = x + 3. Particular attention was paid to the structures recognized and the type of generalization expressed by these students as they reasoned. In all six, we observed three phases of inductive reasoning: (a) abductive, (b) inductive and (c) generalization. The students correctly recognized the structure at least once during the interview and expressed generalization in three ways. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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21 pages, 6969 KiB  
Article
Teachers’ Use of Technology Affordances to Contextualize and Dynamically Enrich and Extend Mathematical Problem-Solving Strategies
by Manuel Santos-Trigo, Fernando Barrera-Mora and Matías Camacho-Machín
Mathematics 2021, 9(8), 793; https://doi.org/10.3390/math9080793 - 7 Apr 2021
Cited by 6 | Viewed by 3620
Abstract
This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments such as Wikipedia to contextualize problem statements or to [...] Read more.
This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments such as Wikipedia to contextualize problem statements or to review involved concepts. Likewise, they activated GeoGebra’s affordances to construct and explore dynamic models of tasks. The Apollonius problem is used to illustrate and discuss how the participants contextualized the task and relied on technology affordances to construct and explore problems’ dynamic models. As a result, they exhibited and extended the domain of several problem-solving strategies including the use of simpler cases, dragging orderly objects, measuring objects attributes, and finding loci of some objects that shaped their approached to reasoning and solve problems. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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14 pages, 2041 KiB  
Article
Comparison between a Modern-Day Multiplication Method and Two Historical Ones by Trainee Teachers
by María José Madrid, Alexander Maz-Machado, Fernando Almaraz-Menéndez and Carmen León-Mantero
Mathematics 2021, 9(4), 349; https://doi.org/10.3390/math9040349 - 10 Feb 2021
Viewed by 2745
Abstract
Different studies consider the possibility of including history of mathematics in the classroom. However, its inclusion in the teaching and learning of mathematics depends on the conceptions of it that teachers have, among other factors. This study displays a comparative analysis between the [...] Read more.
Different studies consider the possibility of including history of mathematics in the classroom. However, its inclusion in the teaching and learning of mathematics depends on the conceptions of it that teachers have, among other factors. This study displays a comparative analysis between the opinions of primary education teachers-to-be and the opinions of mathematics teachers-to-be at secondary school and A-levels after the realization of an activity related to two historical or unusual multiplication methods. These trainee teachers were asked to identify the differences between these methods and the multiplication algorithm usually used in Spain. We collected these data and conducted an exploratory, descriptive and qualitative study. In order to analyse the information obtained, we used the technique content analysis. The answers given by these trainee teachers show their lack of knowledge about other multiplication methods and the various differences which they observed. These differences are mainly related to the structure of each method, the procedure and application of these methods and the mathematical processes carried out for each method. The comparison between the opinions of the teachers-to-be at different levels shows similarities but also some differences, probably due to the different mathematical knowledge they have. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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15 pages, 788 KiB  
Article
Third Grade Students’ Use of Relational Thinking
by Marta Molina and Encarnación Castro
Mathematics 2021, 9(2), 187; https://doi.org/10.3390/math9020187 - 18 Jan 2021
Cited by 7 | Viewed by 2746
Abstract
Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of [...] Read more.
Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense. Full article
(This article belongs to the Special Issue Research on Powerful Ideas for Enriching School Mathematical Learning)
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