Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms

Staples, Megan; Bartlo, Joanna; Thanheiser, Eva

doi:10.1016/j.jmathb.2012.07.001

Cited by 70 publications

(34 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Staples, Bartlo, and Thanheiser (2012) argued that because the needs of a classroom community differ from those of a mathematical community, one would expect the role of justification and proof to differ within those communities as well. We agree that it might be appropriate for teachers and students to treat justification and proof differently than mathematicians if there are good pedagogical reasons for doing so.…”

Section: How Expert Practice Informs Instructionmentioning

confidence: 99%

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Weber

Inglis

Mejía-Ramos

2014

Educational Psychologist

View full text Add to dashboard Cite

Abstract. The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this paper, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for for mathematics instruction and theories of epistemic cognition

show abstract

Section: How Expert Practice Informs Instructionmentioning

confidence: 99%

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Weber

Inglis

Mejía-Ramos

2014

Educational Psychologist

View full text Add to dashboard Cite

show abstract

“…Argumentation in general is understood as a process in which one's opinions are justified, or a discourse in which one convinces others of his/her opinion (Krummheuer 2007;Wood 1999). Since justification or persuasion in argumentation is recognized as being similar to mathematical proof or theoretical demonstration in mathematics, argumentation is considered to be an important part of mathematical learning (Krummheuer 2007;Staples et al 2012). …”

Section: Argumentationmentioning

confidence: 99%

Design research on inquiry-based multivariable calculus: focusing on students’ argumentation and instructional design

Kwon

Bae

Oh³

2015

ZDM Mathematics Education

View full text Add to dashboard Cite

from traditional teacher-centered and textbook-dominated approaches to new instructional approaches that are student-centered and inquiry-based (Holton 2001). As part of this effort, inquiry-based undergraduate mathematics courses have been examined by some researchers (Kwon et al. 2005;Smith 2005;Rasmussen et al. 2006;Dhaler 2008).Multivariable calculus is a mandatory mathematics subject in most Korean universities, since it prepares students to study at an advanced level in diverse majors such as natural sciences, engineering, and economics. As Rasmussen et al. (2014) point out in the previous issue of ZDM, however, there is a shortage of studies that go beyond basic topics of calculus into areas such as multivariable calculus and differential equations. Also, there is a lack of instructional tasks developed for inquiry based learning (IBL) and a lack of research dealing with classroom interactions and the instructor's role in multivariable calculus teaching/learning. Accordingly, if an instructor wants to apply an inquirybased approach to a multivariable calculus course, he or she might face the difficulty of preparing suitable tasks to cultivate students' knowledge and find that students need to spend a long time at inquiry.In order to overcome this difficulty and to develop iteratively an inquiry-based multivariable calculus course, this study attempts to transform the curriculum and instruction by introducing an innovative instructional model to cover the entire curriculum with inquiry-based mathematical activities. In the fall semester of 2013, a multivariable calculus course for first year students majoring in mathematics education was organized as a flipped classroom at a university in Seoul, Korea. The flipped classroom enabled instructors' explanatory lectures of great amounts of content to be replaced by online video clips in order to assign more time to student inquiry during the face-to-face offline Abstract In this study, researchers design and implement an inquiry based multivariable calculus course in a university which aims at enhancing students' argumentation in rich mathematical discussions. This research aims to understand the characteristics of students' argumentation in activities involving proof constructions through mathematical discussions, and to derive instructional design principles in relation to three sites of intervention: instructional design, classroom interaction, and the instructor's role. Over the course of 14 weeks, 18 freshmen mathematics education majors participated in this study. Multiple sources of data were collected, students' reasoning in the classroom discussions were analyzed within the Toulmin's argumentation structure, and the instructional interventions were gradually revised according to the iterative cyclic process of the design research. The students' argumentation structures presented in the classroom gradually developed into more complicated forms as the study progressed, and the researchers conclude that the interventions were effective at improving student...

show abstract

“…Then, Harel and Sowder pointed out that they used 'proving' with the wider meaning of justification [1,2]. In a broad sense, proving can even be regarded as justification [3,4,5,6]. In addition, according to Staples et al [7] "Justifying is the act of developing arguments to demonstrate the truth (or falsehood) of a claim using mathematical forms of reasoning".…”

Section: Introductionmentioning

confidence: 99%

Mathematical Justification Ability: Studentsr Divergent and Convergent Process in Justifying Quadrilateral

Pamungkas¹,

Juniati²,

Masriyah³

2018

Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)

View full text Add to dashboard Cite

Justification is an important component in learning mathematicsto optimize reasoning skill, understanding concepts and mathematical communication. This research is qualitative descriptive research because it aims to obtain a natural picture of the student's mathematical justification on the quadrilateral material. The subjects of this study consists of two students who have different learning style that are divergent and convergent. Data collection was done by giving related statements about quadrilateral material and used semi-structured questionnaire to justify their statement. Data was analysed based on mathematical justification indicator that were recognition, building-with, awareness. Based on the research result, the subject of divergent and convergent showed differences, those were not so far in the process of mathematical justification. The divergent subject analysed the mathematical situation through the form of a rule based on the apparent (concrete) information, but the convergent subject considered how the previous rule was formulated to search for new rules. It showed that in the learning process, justification could provide a picture of the students' thinking flow and explanation of the truth of a statement

show abstract

Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms

Cited by 70 publications

References 34 publications

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

Design research on inquiry-based multivariable calculus: focusing on students’ argumentation and instructional design

Mathematical Justification Ability: Studentsr Divergent and Convergent Process in Justifying Quadrilateral

Contact Info

Product

Resources

About