Principles for designing mathematical tasks that enhance imitative and creative reasoning

Lithner, Johan

doi:10.1007/s11858-017-0867-3

Cited by 86 publications

(102 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The contributors promote students' development of forms of sophisticated mathematical reasoning, which are more than procedural expertise. Some contributors fostered students' domain-specific reasoning (Best & Bikner-Ahsbahs, 2017;Frieman, Polotskaia, & Savard, 2017;Johnson, McClintock, & Hornbein, 2017;Savard & Poloskaia, 2017;Strømskag, 2017), while other contributors fostered students' domain-transcendent reasoning (Chan & Clarke, 2017;Graven & Coles, 2017;Kuntze, Aizikovitsh-Udi, & Clarke, 2017;Lithner, 2017;Lozano, 2017). By domain specific reasoning, we mean reasoning related to mathematical content (e.g., number, algebra, geometry).…”

Section: Theoretical Perspectivementioning

confidence: 99%

Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Johnson

Coles

Clarke

2017

ZDM Mathematics Education

View full text Add to dashboard Cite

Section: Theoretical Perspectivementioning

confidence: 99%

Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Johnson

Coles

Clarke

2017

ZDM Mathematics Education

View full text Add to dashboard Cite

“…It is due to the answer and the process of mathematical argumentation done by him in giving the data and guarantee which are not directly related to supporting evidence in creating a claim. The student has actually understood the concept, but the process of completion done is still in the context of an imitative reasoning, which is the process of thinking that leads to the solution but based on learning by rote or the preceding algorithmic (Bergqvist & Lithner, 2012;Hershkowitz et al, 2017;Hidayat, 2017;Lithner, 2017). Figure 7 shows the students' work with AQ Quitter still has difficulty in understanding the concept of the maximum, minimum by using the second derivative.…”

Section: Resultsmentioning

confidence: 99%

The Mathematical Argumentation Ability and Adversity Quotient (Aq) of Pre-Service Mathematics Teacher

Hidayat¹,

Wahyudin

Prabawanto

2018

J. Math. Educ.

View full text Add to dashboard Cite

The Mathematical argumentation has been studied before, but no research has a focus on mathematical argumentation and adversity quotient of the pre-service mathematics teacher. This study is experimental research that aims to know and examine in depth about the influence of AQ of pre-service mathematics teacher toward the achievement of mathematical argument ability. The population of this study is the pre-service mathematics teacher in Cimahi City, West Java, Indonesia; while the sample is 60 pre-service mathematics teachers selected purposively. The instruments of this study are tests and non-tests. They are based on the assessment of good characteristics towards students' mathematical argumentation abilities, while the non-test instrument is based on the assessment of good characteristics towards AQ. The results of this research show that: (1) AQ gives positive influence to the development of mathematical argumentation ability of pre-service mathematics teacher with the influence of 60.2%, while the rest of it (39.8%) is influenced by other factors outside AQ; (2) The ability of mathematical argumentation of pre-service mathematics teacher is more developed on AQ of Climber type; (3) Students with the Quitter AQ type still tend to have less ability of mathematical argumentation.

show abstract

“…One framework used within mathematics education research about reasoning is the framework of imitative and creative reasoning. Three articles in our review use this framework to conceptualize students' reasoning [33][34][35]. Reasoning is regarded as a line of thought that results in assertions and conclusions [33].…”

Section: Creative and Imitative Reasoningmentioning

confidence: 99%

Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review

Hjelte

Nilsson

2020

Education Sciences

View full text Add to dashboard Cite

Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under investigation is diverse—which goes along with a diversity of understandings of the term reasoning. The aim of this article is to provide an overview on kinds of mathematical reasoning that are addressed in mathematics education research. We conducted a systematic review focusing on the question: What kinds of reasoning are addressed in empirical research in mathematics education? We pursued this question by searching for articles in the database Web of Science with the term reason* in the title. Based on this search, we used a systematic approach to inductively find kinds of reasoning addressed in empirical research in mathematics education. We found three domain-general kinds of reasoning (e.g., creative reasoning) as well as six domain-specific kinds of reasoning (e.g., algebraic reasoning). The article gives an overview on these different kinds of reasoning both in a domain-general and domain-specific perspective, which may be of value for both research and practice (e.g., school teaching).

show abstract

Principles for designing mathematical tasks that enhance imitative and creative reasoning

Cited by 86 publications

References 36 publications

Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

The Mathematical Argumentation Ability and Adversity Quotient (Aq) of Pre-Service Mathematics Teacher

Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review

Contact Info

Product

Resources

About