The interaction between intuitive and formal mathematical thinking: a case study

Farmaki, Vassiliki; Paschos, Theodorus

doi:10.1080/00207390601035302

Cited by 10 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For example utilization of pictorial presentations might help to deduce simply and directly [41]. In a more general saying all kinds of relationships of a mathematical object can be apprehended easier and more rapidly due to visualization [22].…”

Section: Introductionmentioning

confidence: 99%

The Effects of Visualization on Mathematics Achievement in Reference to Thesis Studies Conducted in Turkey: A Meta-Analysis

TURGUT¹,

Turgut²

2018

ujer

View full text Add to dashboard Cite

In this study, it is aimed to determine the effect of visualization on mathematics achievement in the thesis studies conducted in Turkey. In this context, the findings obtained from individual studies are combined via meta-analysis. For this purpose, Council of Higher Education (CoHE) National Thesis Center database was thoroughly scanned by using keywords. A total of 35 thesis studies, 26 of which are master's thesis and 9 of which are doctoral dissertations were reached as a result of the scanning performed. 34 theses are included in the meta-analysis in line with their inclusion criteria and 42 effect sizes were calculated pertaining to these thesis. To examine the normal distribution of effect sizes and to perform other analyses, statistical programs of MetaWin and Comprehensive Meta-Analysis (CMA) were used respectively in the study. In the calculation of effect sizes, quantities of studies included in meta-analysis Hedges's g was used and confidence level in calculations of effect sizes was taken as 95%. The average effect size value calculated in accordance with random effect model was found as 0.811 with the standard error of 0.076. Positivity of effect size shows that the implication effect is in favour of the experimental group. Basing on this, it can be said that visualization has a moderate effect on mathematics achievement.

show abstract

Section: Introductionmentioning

confidence: 99%

The Effects of Visualization on Mathematics Achievement in Reference to Thesis Studies Conducted in Turkey: A Meta-Analysis

TURGUT¹,

Turgut²

2018

ujer

View full text Add to dashboard Cite

show abstract

“…From the above explanations, it could be drawn any conclusion within inquiry learning, student reasoning ability always be trained and thus, student math reasoning could upgrade through inquiry learning. According to Farmaki & Paschos (2007), through empirical materials of progressive mathematical, student could improve graphic representation models to manipulate images concept that could led them to fulfil their needs on formal math argumentation. This statement also signalled when someone conducted reasoning activity, then representation systems would work to produce any argument or conclusion.…”

Section: Relation Between the Guided Inquiry Learning With Reasoning mentioning

confidence: 99%

Abilities of Reasoning and Mathematics Representation on Guided Inquiry Learning

Yumiati

Noviyanti

2017

EduLearn

View full text Add to dashboard Cite

This research initiated by some research result regarding the lower Reasoning and Mathematics Representation of student on the math learning. In order to upgrade the abilities is passing through the guided inquiry learning. The aim of the reasearch is to analyze comprehensively on accomplishment reasoning and math representation of student who gain the guided inquiry learning and conventional learning. The research is applying experiment method by design of one group pretest-posttest. The result of research indicates the guided inquiry learning is more effective in accomplishment and improvement of student representation capabilities and student comprehend compared with the conventional learning. Reasoning and Mathematics Representation of group student or guided inquiry learning is higher from the group student of conventional learning. The improvement of Mathematics Reasoning of Group Student of guided inquiry learning values 0.33 on the medium category, while the improvement of Mathematics Representation of group student of conventional learning values 0.19 on the low category. The amount of improvement on Mathematics Representation of group student of the guided inquiry learning is 0.41 on the medium category, and the improvement on Mathematics Representation of group student of conventional learning is 0.26 is on the low category.

show abstract

“…There are several approaches to evaluate the mathematical reasoning process (Farmaki & Paschos, 2007;Fischbein, 1999;Lithner, 2008;Skemp, 1976;Wyndhamn & Saljö, 1997). In this paper, Lithner's framework was adopted.…”

Section: Introductionmentioning

confidence: 99%

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

Engin¹

2021

TURCOMAT

View full text Add to dashboard Cite

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.

show abstract

The interaction between intuitive and formal mathematical thinking: a case study

Cited by 10 publications

References 8 publications

The Effects of Visualization on Mathematics Achievement in Reference to Thesis Studies Conducted in Turkey: A Meta-Analysis

The Effects of Visualization on Mathematics Achievement in Reference to Thesis Studies Conducted in Turkey: A Meta-Analysis

Abilities of Reasoning and Mathematics Representation on Guided Inquiry Learning

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

Contact Info

Product

Resources

About