The transition to formal thinking in mathematics

Tall, David

doi:10.1007/bf03217474

Cited by 199 publications

(166 citation statements)

References 10 publications

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“…It is possible that students simply guessed their answers in the conceptually-oriented test since the given test is a multiple choice type. Procedural and conceptual knowledge are complementary (Bossé & Bahr, 2008) since procedural knowledge is part of conceptual knowledge (Tall, 2008).…”

Section: Pretest and Post-test Performance Of Participants In The Expmentioning

confidence: 99%

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Mendezabal

Tindowen

2018

J. Technol. Sci. Educ.

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This study examined the effects of using Microsoft Mathematics on students' attitude, conceptual understanding, and procedural skills in Differential Calculus. A quasi-experimental research design was used in which two different learning environments were compared. The participants of the study were two classes of Electrical Engineering students enrolled in Differential Calculus course, assigned randomly as control and experimental groups with 30 students in each group. The control group was taught using the traditional approach of teaching Differential Calculus while the experimental group was taught the same lessons using the Microsoft Mathematics embedded activity sheets. The experimental group learned through exploration and discovery of various concepts. The findings indicated that the participants had little understanding of the concepts and processes of Calculus prior to the conduct of the study. A significant improvement in their performances was noted after the experimentation. This suggests that the use of Microsoft Mathematics in teaching and learning Differential Calculus improves students' conceptual understanding and procedural skills. It is also found that the use of Microsoft Mathematics in teaching and learning calculus is equally effective as the traditional approach. In terms of attitude, the experimental group demonstrated a "favorable" to "very highly favorable" attitude along the five (5) domains of the MTAS. A significant difference exists between the pretest and posttest attitude of the participants on the domain "learning Mathematics with technology".

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Section: Pretest and Post-test Performance Of Participants In The Expmentioning

confidence: 99%

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Mendezabal

Tindowen

2018

J. Technol. Sci. Educ.

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“…There may also be disparities in approaches to thinking about mathematics at secondary and tertiary levels. Tall (2008) suggests that as students' progress from secondary to tertiary mathematics, their thinking must move from a symbolic world to a more formal world. However if tertiary courses are trying to build thinking in the formal world with students who are primarily symbolic thinkers, then difficulties will arise (Hong et al, 2009).…”

Section: Insert Table 1: Project Maths Implementation Timelinementioning

confidence: 99%

Mind the gap: an initial analysis of the transition of a second level curriculum reform to higher education

Prendergast

Faulkner²,

Breen³

et al. 2017

Teaching Mathematics Applications

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This paper details an initial analysis of the transition of a second level curriculum reform to higher education in Ireland. The reform entitled 'Project Maths' involved changes to what second level students learn in mathematics, how they learn it and how they are assessed. Changes were rolled out nationally on a phased basis in September 2010. Students who were taught and assessed through the new curriculum first entered third level education in September 2012. It is important that third level mathematics lecturers are aware of the changes to the curriculum since certain topics such as vectors and matrices are no longer taught at second level. Hence third level courses may need to be adapted accordingly. This study investigates mathematics lecturers' awareness of Project Maths and whether they have made any adaptions to their course content, teaching and assessment approaches as a result of the new curriculum being introduced. The findings, from a return rate of 23% of eligible respondents, show that although many lecturers are mindful of the concept of Project Maths, they are not aware of the changes in full and how it affects their own course content, teaching and assessment strategies. Accordingly, the gap between second and third level education remains. This study highlights that more needs to be done to ensure there is coherent and uniform approaches to the teaching, learning and assessment of mathematics in the transition from second to third level education.

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“…The facility for building sophisticated knowledge structure is based on a phenomenal array of neuronal facilities for perception and action that are present in the new-born child and develop rapidly through experience in the early years. Tall (2008) refers to these abilities as 'set-befores' (because they are set before birth as part of our genetic inheritance and develop through usage) as opposed to 'met-befores' that arise as a result of previous experience and may be supportive or problematic when that experience is used in new contexts. He hypothesizes that three major set-befores give rise to three distinct developments of mathematical thinking and proof through:…”

Section: Theories Of Cognitive Growthmentioning

confidence: 99%

“…The full cognitive development of formal proof from initial perceptions of objects and actions to axiomatic mathematics can be formulated in terms of three distinct forms of development (Tall, 2004(Tall, , 2008:…”

Section: A Global Framework For the Development Of Mathematical Thinkingmentioning

confidence: 99%

Cognitive Development of Proof

Tall

Yevdokimov

Koichu

et al. 2012

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The transition to formal thinking in mathematics

Cited by 199 publications

References 10 publications

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Improving students' attitude, conceptual understanding and procedural skills in differential calculus through Microsoft mathematics

Mind the gap: an initial analysis of the transition of a second level curriculum reform to higher education

Cognitive Development of Proof

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