A framework for primary teachers’ perceptions of mathematical reasoning

Herbert, Sandra; Vale, Colleen; Bragg, Leicha A.; Loong, Esther; Widjaja, Wanty

doi:10.1016/j.ijer.2015.09.005

Cited by 41 publications

(20 citation statements)

References 26 publications

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“…This result shows similarity with the findings of Loong, Vale, Bragg and Herbert (2013) that although some teachers are able to tell the meaning of reasoning, some use unclear expressions. Furthermore, it shows similarity with some of the responses (problem-solving, predicting, thinking, thinking relevantly…) given by the elementary school teachers regarding what they understand from mathematical reasoning in the study of Herbert, Vale, Bragg, Loong (2015). It has been concluded that the expressions which are included in the definition of the mathematical reasoning skill such as the ability to make a logical deduction, inference, and the ability to predict are few.…”

Section: Discussion-conclusionmentioning

confidence: 64%

İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Akıl Yürütme Becerisi Üzerine Görüşleri*

Öz

Işık

2017

Erzincan Üniversitesi Eğitim Fakültesi Dergisi

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The purpose of this study is to determine the opinions of preservice elementary school mathematics teachers on the "Mathematical reasoning skill". 117 preservice elementary school mathematics teachers receiving education in the undergraduate program of elementary school mathematics teaching at the faculty of education at a university in the spring term of the 2014-2015 academic year constituted the study group of the research.The case study method among qualitative research approaches was used in the study, and the written opinion form consisting of 6 questions was used as a data collection tool. The content analysis was used when analyzing the data obtained from the study. According to the results of the study, it was determined that there are various opinions on what the mathematical reasoning skill means. While pre-service teachers generally say that they do take any lesson or seminar on mathematical reasoning skill, they think that mathematical reasoning skill should be included in the secondary school mathematics course curriculum and it is beneficial for students.

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Section: Discussion-conclusionmentioning

confidence: 64%

İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Akıl Yürütme Becerisi Üzerine Görüşleri*

Öz

Işık

2017

Erzincan Üniversitesi Eğitim Fakültesi Dergisi

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“…Furthermore, it facilitates recognition of similitudes in the structure of mathematical problems and generalization of methods of resolution when students work with situations that have different contexts but the same underlying structure (Sriraman & Adrian, 2004). Nevertheless, as in the study of Herbert et al (2015), the teachers seem to be less aware of the relationship between mathematical reasoning-inductive, in our case-and problem resolution than they were in the previous categories. In particular, we find that these teachers omitted the description of the inductive strategy for solving a mathematical problem; neither pointed out the potential of this reasoning for recognising methods of solving problems that have the same structure.…”

Section: Category D: Strategy For Solving Problemsmentioning

confidence: 83%

“…Some studies suggest that promoting and interpreting inductive reasoning in the classroom is a complex task for teachers. Herbert, Vale, Bragg, Loong, and Widjaja (2015) reported that elementary school teachers have little understanding of the distinctive aspects of the mathematical reasoning types and how to encourage mathematical reasoning in the classroom. Furthermore, noticing and interpreting the actions of students' reasoning in generalization tasks is complicated for both pre-service and in-service teachers (Callejo & Zapatera, 2017;El Mouhayar, 2018;Melhuish, Thanheiser, & Guyot, 2018).…”

mentioning

confidence: 99%

Secondary School Mathematics Teachers’ Perceptions About Inductive Reasoning and Their Interpretation in Teaching

Moguel

Landa

2021

J. Math. Educ.

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Inductive reasoning is an essential tool for teaching mathematics to generate knowledge, solve problems, and make generalizations. However, little research has been done on inductive reasoning as it applies to teaching mathematical concepts in secondary school. Therefore, the study explores secondary school teachers’ perceptions of inductive reasoning and interprets this mathematical reasoning type in teaching the quadratic equation. The data were collected from a questionnaire administered to 22 teachers and an interview conducted to expand their answers. Through the thematic analysis method, it was found that more than half the teachers perceived inductive reasoning as a process for moving from the particular to the general and as a way to acquire mathematical knowledge through questioning. Because teachers have little clarity about inductive phases and processes, they expressed confusion about teaching the quadratic equation inductively. Results indicate that secondary school teachers need professional learning experiences geared towards using inductive reasoning processes and tasks to form concepts and generalizations in mathematics.

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“…In addition to its significance in all disciplines, reasoning has special and essential place in mathematics (NCTM, 2009, p.4). In many countries, mathematical reasoning is valued and activities that improve mathematical reasoning are included in the mathematics curriculum (Fujita & Jones, 2014;Herbert, Vale, Bragg, Loong & Widjaja, 2015;Thompson, Hatfield, Yoon, Joshua & Byerley,2017). Mathematical reasoning provides a strong foundation for students to understand a wide range of mathematical ideas such as rate of change and linearity, exponential growth, rate (Adu-Gyamfi & Bossé, 2014;Ellis, Ozgur, Kulow, Dogan & Amidon, 2016;Lobato & Siebert, 2002).…”

Section: Introductionmentioning

confidence: 99%

An Analysis of High School Student's Understanding and Reasoning of Average Concept

Engin¹

2021

TURCOMAT

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The aim of this study is to identify high school student's understanding of average concept and the reasoning types they appeal to solve average problems. The case study approach was used in this study and the participants were selected by purposeful sampling. The participants consisted of five 9th grade and four 10th grade students, studying at a high school in Istanbul. In order to identify student's understanding of average, a test consisting of 5 open-ended problems were used and semi-structured interviews were held with each of the students. The data were analyzed by thematic analysis approach. For data analysis, framework proposed by Mokros and Russel (1995) was used to determine student's understanding of average and Lithner's (2008) framework was used to reveal their reasoning types. Results showed that students mostly understood average as mathematical point of balance. Creative mathematically founded reasoning and algorithmic reasoning was used the most. Creative reasoning is effective in reaching the right answer. In solutions where creative reasoning is used, students generally also have the idea of representativeness. The type of problem influences the reasoning process. Inadequacy of student's prior mathematics knowledge hinders both their understanding of the average and their reasoning skills.

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A framework for primary teachers’ perceptions of mathematical reasoning

Cited by 41 publications

References 26 publications

İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Akıl Yürütme Becerisi Üzerine Görüşleri*

İlköğretim Matematik Öğretmeni Adaylarının Matematiksel Akıl Yürütme Becerisi Üzerine Görüşleri*

Secondary School Mathematics Teachers’ Perceptions About Inductive Reasoning and Their Interpretation in Teaching

An Analysis of High School Student's Understanding and Reasoning of Average Concept

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