scholarly journals Yngre elevers uppfattningar av det matematiska i algebraiska uttryck

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Sanna Wettergren ◽  
Inger Eriksson ◽  
Torbjörn Tambour
Keyword(s):  
Full Text ◽  
Ways Of Knowing ◽  
Algebraic Expression ◽  
Research Project ◽  
Algebraic Expressions ◽  
Preschool Class ◽  
Critical Aspects

Det övergripande syftet med denna artikel är att analysera och beskriva yngre elevers uppfattningar av det matematiska i ett algebraiskt uttryck och utifrån det diskutera vad som kan utgöra kritiska aspekter för utvecklandet av mera kvalificerade uppfattningar. Artikeln bygger på data från ett forskningsprojekt där elever i förskoleklass, årskurs 1 och årskurs 4 intervjuades med syfte att analysera de aktuella elevernas kvalitativt skilda sätt att uppfatta det matematiska i algebraiska uttryck. Intervjuerna analyserades fenomenografiskt. Studiens resultat visar tre kvalitativt skilda kategorier av yngre elevers uppfattningar av det matematiska i algebraiska uttryck. Det matematiska i ett algebraiskt uttryck erfars som ”något som kan och bör räknas ut”, ”något som beskriver en relation mellan komponenter” och ”något som representerar en situation”. Vidare identifierades tre kritiska aspekter i relation till kategorierna. De kritiska aspekter som ger eleverna möjlighet att kvalificera sina uppfattningar för att utveckla ett mer komplext kunnande av algebraiska uttryck är att kunna urskilja att 1) ett uttryck består av olika komponenter som har olika funktioner, 2) en och samma variabel i ett uttryck har samma värde och 3) värdet på en variabel i ett uttryck bestäms relationellt. Att urskilja sådana kritiska aspekter kan hjälpa eleverna att kvalificera sitt kunnande. Således måste de kritiska aspekterna beaktas vid utformningen av undervisningen. Abstract in English The overall purpose of this article is to analyze and describe younger students’ conceptions of or ways of experiencing the mathematics in an algebraic expression and to discuss what can be critical aspects for the development of more qualified conceptions. The article is based on data from a research project where students in preschool class, Grade 1 and Grade 4 were interviewed with the aim of analyzing the students' qualitatively different ways of experiencing the mathematics in algebraic expressions. The interviews were analyzed with phenomenography. The results show three qualitatively different categories of younger students’ conceptions of the mathematics in algebraic expressions. The mathematics in an algebraic expression is experienced as ”something that can and should be calculated", ”something that describes a relationship between components”, and ”something that represents a situation”. Furthermore, three so-called critical aspects the students need to discern were identified in relation to the categories 1) an expression consists of different components that have different functions, 2) one and the same variable in an expression has the same value and 3) the value of a variable in an expression is determined relationally. Discerning such critical aspects may help the students to qualify their ways of knowing. Thus, the critical aspects need to be considered in the design of teaching. FULL TEXT IN SWEDISH.

scholarly journals Examination of Semantic Structures Used by Teacher Candidates to Transform Algebraic Expressions into Verbal Problems

2021 ◽  
Vol 4 (3) ◽  
Author(s):  
Ayten Pinar Bal ◽  
Keyword(s):  
Teacher Candidates ◽  
Quantitative Research ◽  
Algebraic Expression ◽  
Study Group ◽  
State University ◽  
Algebraic Expressions ◽  
Purposeful Sampling ◽  
Division Problems ◽  
Addition And Subtraction ◽  
Research Types

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the primary school mathematics teaching department of a state university in the south of Turkey in the 2019-2020 academic years. 73.2% of the teacher candidates in the study group are female and 26.8% are male. Criterion sampling method, one of the purposeful sampling methods, was used in the selection of teacher candidates in the study group. While the Algebraic Expression Questionnaire Form was used as the data collection tool, the evaluation rubric of verbal problems was used in the analysis of the data. As a result of the research, it has been revealed that pre-service teachers are more successful in transforming algebraic expressions into verbal problems, but they have problems in creating problems with algebraic expressions that make up systems of equations. Again in the study, it was concluded that pre-service teachers used addition and subtraction problems more than multiplication and division problems. On the other hand, when the problems in the type of addition and subtraction are examined in the study, in the type of combining and separating; It has been concluded that the category of equal groups is mostly used in the problems of multiplication and division.

scholarly journals Organizational building versus teachers’ personal and relational needs for school improvement

2020 ◽  
pp. 136548022097287
Author(s):  
Mette Liljenberg ◽  
Ulf Blossing
Keyword(s):  
Public School ◽  
School Improvement ◽  
Collaborative Research ◽  
Research Team ◽  
School Leaders ◽  
School Organization ◽  
School Leader ◽  
Research Project ◽  
Critical Aspects

Organizational building is essential if school leaders are to promote school improvement, but it can be difficult to combine with school leaders’ requirements to satisfy teachers’ personal and relational needs. The the aim of this study is to explore critical aspects when combining organizational building with requirements to satisfy teachers’ personal and relational needs in efforts to strengthen improvement capacity. The paper draws on a 3-year collaborative research project between a research team at a Swedish university and a municipality. It is based on data acquired in 137 interviews with 535 respondents in 28 public school and preschool units. The results highlight the importance of combining organizational building with efforts to improve teachers’ understanding of, motivation to promote, and adaptation to, the goals of the school organization. The significance of the study lies in clearly distinguishing the need to link organizational building and requirements to meet teachers’ personal and relational needs. Continually telling the story of the school and thus enabling teachers to personally connect to the improvement history is suggested as an innovative school leader strategy.

scholarly journals Generative listening: Using arts-based inquiry to investigate young children’s perspectives of inclusion, exclusion and disability

2018 ◽  
Vol 17 (1) ◽  
pp. 54-69 ◽  
Author(s):  
Kathy Cologon ◽  
Timothy Cologon ◽  
Zinnia Mevawalla ◽  
Amanda Niland
Keyword(s):  
Young Children ◽  
Critical Pedagogy ◽  
Inclusive Education ◽  
Meaning Making ◽  
Ways Of Knowing ◽  
Theoretical Framework ◽  
Research Project ◽  
Arts Based Research ◽  
Children’S Perspectives ◽  
Critical Approaches

While the importance of inclusive approaches to research has been identified, much childhood research is still done ‘to’ not ‘with’ young children, with research focusing on the experiences of children who experience disability commonly involving data from parents/families/practitioners, rather than from children themselves. In this article, we explore the development of an arts-based research project involving young children who experience disability as active participants in an exploration of their perspectives on inclusive education. Accordingly, we ruminate on questions about how we can genuinely ‘listen’ to children who experience disability in an aesthetic and ethical manner, and how we can use artistic ways of knowing to engage in meaning-making with children. Using arts-based research as an aesthetic framework alongside insights from critical pedagogy as a theoretical framework, we explore ‘aesthetic’ approaches to being, teaching, researching and knowing. As a team of researchers who do and do not experience disability, we share reflections on arts-based methodologies informed by critical approaches to conceptualising disability and research. As artistic modes of expression are central to young children’s everyday lives and play and can create enjoyable and safe communicative spaces, we share dialogues, artwork and methodological reflections on opportunities for children to choose ways of interacting and communicating, allowing possibilities for agency, expression and creativity. Specifically, we conceptualise and concentrate on possibilities for using arts to foster ‘listening’, meaning-making and generative or transformative praxis, in order to explore how arts-based research can be a powerful, authentic, ethical and meaningful provocateur for listening ‘generatively’ to young children who experience disability in research.

Helping Students Make Sense of Algebraic Expressions: The Candy Shop

2002 ◽  
Vol 7 (9) ◽  
pp. 492-497
Author(s):  
Diana Underwood Gregg ◽  
Erna Yackel
Keyword(s):  
Algebraic Thinking ◽  
Instructional Sequence ◽  
Algebraic Expression ◽  
Instructional Approaches ◽  
Algebra For All ◽  
Algebraic Expressions ◽  
Experience Difficulty

Increasing emphasis on “Algebra for all” (NCTM 1997a, 1997b) compels educators to identify and address fundamental ideas that build the foundations for algebraic thinking and reasoning. Identifying these foundational concepts and developing appropriate instructional approaches are the focuses of our work. One area in which students often experience difficulty is adding and subtracting algebraic expressions. Although students may be able to memorize a procedure, such as “distribute the negative” when subtracting algebraic expressions, they are often unable to make sense of this procedure. Our work suggests that part of students' difficulty in this area is that they do not conceptualize an algebraic expression as a composite unit. In the paragraphs below, we explain what is meant by composite units and how this construct helped frame our development of an instructional sequence to help students make sense of, and find meaning in, algebraic expressions and operations on algebraic expressions.

Fusion in relational structures and the verification of monadic second-order properties

2002 ◽  
Vol 12 (2) ◽  
pp. 203-235 ◽  
Author(s):  
B. COURCELLE ◽  
J. A. MAKOWSKY
Keyword(s):  
Second Order ◽  
Algebraic Expression ◽  
Order Property ◽  
Unary Predicate ◽  
Free Graph ◽  
Relational Structures ◽  
Clear Cut ◽  
Algebraic Expressions ◽  
Common Framework ◽  
Fusion Operation

Relational structures offer a common framework for handling graphs and hypergraphs of various kinds. Operations like disjoint union, the creation of new relations by means of quantifier-free formulas, and relabellings of relations make it possible to denote them using algebraic expressions. It is known that every monadic second-order property of a structure is verifiable in time proportional to the size of such an algebraic expression defining it. We prove here that this result remains true if we also use in these algebraic expressions a fusion operation that fuses all elements of the domain satisfying some unary predicate. The value mapping from these algebraic expressions to the structures they denote is a monadic second-order definable transduction, which means that the structure is definable inside the tree representing the algebraic expression by monadic second-order formulas. It follows (by using results of other articles) that, with this fusion operation, we cannot generate more graph families, but we can generate them with less unary auxiliary predicates. We also obtain clear-cut characterizations of Vertex Replacement and Hyperedge Replacement context-free graph grammars in terms of four types of operations, amongst which is the fusion of vertices satisfying a specified predicate.

scholarly journals Teknik i de tidiga skolåren – om vad det innebär att kunna konstruera en länkmekanismTechnical knowing in the early school years – A learning study of the meaning of knowing how to construct a linkage mechanism

2015 ◽  
Vol 11 (1) ◽  
pp. 35-53 ◽  
Author(s):  
Eva Björkholm
Keyword(s):  
Lesson Study ◽  
Learning Study ◽  
Linkage Mechanism ◽  
Primary School Teachers ◽  
Early School ◽  
Post Test ◽  
Preschool Class ◽  
Grade One ◽  
Different Characteristics ◽  
Critical Aspects

This study within primary technology education aims at exploring the capability to construct a specific linkage mechanism. The study reported was integrated in a Learning study, a kind of design experiment inspired by the Japanese Lesson Study, and was carried out in collaboration with two primary school teachers and their two classes, a preschool class and a grade one class. The study reports on the analysis of the video-recorded pre- and post-test. The tests were analysed phenomenographically resulting in four categories describing qualitatively different ways of experiencing the object of learning. The categories were then analysed in terms of critical aspects, describing aspects necessary to discern for this group of students in order to learn how to construct a linkage mechanism. The result indicates the importance of discerning the two joints and their different characteristics in terms of a fixed and a moving joint as well as the placement of the moving joint in relation to the resulting movement.

What Contributions, if Any, Can Non-Indigenous Researchers Offer Toward Decolonizing Health Research?

2019 ◽  
Vol 30 (2) ◽  
pp. 205-216 ◽  
Author(s):  
Emily Krusz ◽  
Tamzyn Davey ◽  
Britta Wigginton ◽  
Nina Hall
Keyword(s):  
Health Research ◽  
Ways Of Knowing ◽  
Lessons Learned ◽  
Research Project ◽  
Indigenous Australian ◽  
Indigenous Ways Of Knowing ◽  
Indigenous Land ◽  
Health Research Project ◽  
Reflective Processes

Four non-Indigenous academics share lessons learned through our reflective processes while working with Indigenous Australian partners on a health research project. We foregrounded reflexivity in our work to raise consciousness regarding how colonizing mindsets—that do not privilege Indigenous ways of knowing or recognize Indigenous land and sovereignty—exist within ourselves and the institutions within which we operate. We share our self-analyses and invite non-Indigenous colleagues to also consider socialized, unquestioned, and possibly unconscious assumptions about the dominance of Western paradigms, asking what contributions, if any, non-Indigenous researchers can offer toward decolonizing health research. Our processes comprise of three iterative features—prioritizing attempts to decolonize ourselves, acknowledging the necessary role of discomfort in doing so, and moving through nonbinary and toward nondualistic thinking. With a nondual lens, working to decolonize ourselves may itself be seen as one contribution non-Indigenous researchers may offer to the collective project of decolonizing health research.

Little We Know of Each Other

2018 ◽  
Vol 19 (1) ◽  
pp. 39-42
Author(s):  
Marguerite Müller
Keyword(s):  
Higher Education ◽  
South Africa ◽  
Collaborative Research ◽  
Ways Of Knowing ◽  
Experiential Knowledge ◽  
Creative Expression ◽  
Free State ◽  
Research Project ◽  
Performative Text ◽  
The University

This performative text is rooted in arts-based inquiry and expressed as the textual portraits of five educators working at the University of the Free State (UFS), South Africa. These portraits were created as part of a collaborative research project in which participants shared their experiential knowledge of working toward antioppressive practice in higher education at the UFS between 2014 and 2016. The textual portraits highlight the contradictions, uncertainty, and messiness of educator identity in this complex and volatile space. Furthermore, the performative text serves as a creative expression of different ways of knowing and different ways of becoming.

scholarly journals Examination of Semantic Structures Used by Teacher Candidates to Transform Algebraic Expressions into Verbal Problems

2021 ◽  
Author(s):  
Ayten Pinar Bal
Keyword(s):  
Teacher Candidates ◽  
Quantitative Research ◽  
Algebraic Expression ◽  
Study Group ◽  
State University ◽  
Algebraic Expressions ◽  
Purposeful Sampling ◽  
Division Problems ◽  
Addition And Subtraction ◽  
Research Types

The aim of this study is to examine the semantic structures used by mathematics teacher candidates to transform algebraic expressions into verbal problems. The research is a descriptive study in the survey model, which is one of the quantitative research types. The study group of the research consists of 165 teacher candidates studying in the primary school mathematics teaching department of a state university in the south of Turkey in the 2019-2020 academic years. 73.2% of the teacher candidates in the study group are female and 26.8% are male. Criterion sampling method, one of the purposeful sampling methods, was used in the selection of teacher candidates in the study group. While the Algebraic Expression Questionnaire Form was used as the data collection tool, the evaluation rubric of verbal problems was used in the analysis of the data. As a result of the research, it has been revealed that pre-service teachers are more successful in transforming algebraic expressions into verbal problems, but they have problems in creating problems with algebraic expressions that make up systems of equations. Again in the study, it was concluded that pre-service teachers used addition and subtraction problems more than multiplication and division problems. On the other hand, when the problems in the type of addition and subtraction are examined in the study, in the type of combining and separating; It has been concluded that the category of equal groups is mostly used in the problems of multiplication and division.

scholarly journals “Community First” for Whom? Reflections on the Possibilities and Challenges of Community-Campus Engagement from the Community Food Sovereignty Hub

2019 ◽  
Vol 4 (2) ◽  
pp. 43-60
Author(s):  
Lauren Kepkiewicz ◽  
Charles Z. Levkoe ◽  
Abra Brynne
Keyword(s):  
Community Engagement ◽  
Food Sovereignty ◽  
Ways Of Knowing ◽  
Community Leadership ◽  
Postsecondary Institutions ◽  
Research Project ◽  
Campus Engagement ◽  
Difficult Conversations ◽  
Goals And Objectives ◽  
Do So

While community-campus engagement (CCE) has gained prominence in postsecondary institutions, critics have called for a more direct focus on community goals and objectives. In this paper, we explore the possibilities and limitations of community-centred research through our collective experiences with the Community First: Impacts of Community Engagement (CFICE) and the Community Food Sovereignty (CFS) Hub. Drawing on a four-year research project with twelve community-campus partnership projects across Canada, we outline three key areas for reflection. First, we examine the meanings of community-centred research—called “community first”—in our work. Second, we explore key tensions that resulted from putting “community first” research into practice. Third, we discuss possibilities that emerged from attempts to engage in “community first” CCE. We suggest that while putting “community first” presents an opportunity to challenge hierarchical relationships between academia, western ways of knowing, and community, it does not do so inherently. Rather, the CCE process is complex and contested, and in practice it often fails to meaningfully dismantle hierarchies and structures that limit grassroots community leadership and impact. Overall, we argue for the need to both champion and problematize “community first” approaches to CCE and through these critical, and sometimes difficult conversations, we aim to promote more respectful and reciprocal CCE that works towards putting “community first.”

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