outline of possible pre-course diagnostics for differential calculus

Maharaj, Aneshkumar; Wagh, Vivek

doi:10.1590/sajs.2014/20130244

Cited by 7 publications

(9 citation statements)

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“…The literature review [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] as well as our experience in teaching calculus to students and assessing their abilities in the context of calculus, guided the formulation of principles which give an overview of the conceptual framework for this study. In particular, the formulation of the following four principles were informed by the work of Brookhart 1 , Maharaj and Wagh 7 , the Council of Regional Accrediting Commissions 8 , Godino 9 and Skemp 12 .…”

Section: Conceptual Frameworkmentioning

confidence: 99%

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Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

Maharaj¹,

Wagh²

2016

S. Afr. J. Sci.

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We describe an approach to develop higher-order thinking skills (HOTS) among first-year calculus students. The ideas formulated by Brookhart to develop HOTS were used to identify from the literature three core abilities that should be targeted. Then eight expected learning outcomes for the development of HOTS were documented, in the context of the study of first-year university calculus. Those expected outcomes were used to formulate sample tasks that were designed to target the development of the eight abilities. A pilot study was done to determine whether the tasks had the high mathematical demand envisaged. It was found that about 37% of the participants did not give any response to the tasks. Further it was found that about 31% of the participants were able to critically evaluate a given possible solution to a problem and make a value judgement. It is recommended that to promote HOTS among students, the formulation of tasks should focus on developing the following abilities: interpreting a general definition or statement in the context of a given model; translating a worded or graphically represented situation to relevant mathematical formalisms; identifying possible applications of mathematics in their surroundings; identifying linkages between groups of concepts and interpreting these linkages in the context of a model; working systematically through cases in an exhaustive way; critically evaluating one’s and others’ presented solutions to a problem; interpreting and extending solutions of problems; and using with reasonable skill available tools for mathematical exploration.

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Section: Conceptual Frameworkmentioning

confidence: 99%

“…8 (2) The identified learning outcomes should inform the development of tasks 7 that help in the development of abilities related to HOTS 1 . (3) The key abilities relate to the transfer of knowledge and skills, critical thinking and problem solving 1 across sections in mathematics relevant to the context of studying calculus.…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

Maharaj¹,

Wagh²

2016

S. Afr. J. Sci.

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“…The provision of suitable online diagnostic questions on basic arithmetic and algebra could improve the level of student competencies with regard to these. 11,12 4. There was a need to research the impact of the provision of online diagnostics for pre-calculus as offered at UKZN before a decision could be arrived at as to whether the quizzes should be made compulsory for all incoming students who want to study firstyear calculus.…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Revelations from an online diagnostic arithmetic and algebra quiz for incoming students

Maharaj¹,

Dlomo²

2018

S. Afr. J. Sci.

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A review of relevant literature revealed that research indicates an alarming number of secondary school students who enter tertiary institutions display a serious lack of mathematical basics required for the study of university mathematics. This so-called change from the secondary school to tertiary study of mathematics has become an important field of mathematical learning research. In this context, at the University of KwaZulu-Natal, online diagnostics for pre-calculus knowledge and skills were made available to first-year mathematics students. We report here on some findings from an analysis of the provision of diagnostic questions for basic arithmetic and algebra. The results show that the diagnostic questions which were in the form of an online quiz assisted students to cope with their mathematics module in the sense that it positively impacted on the final results of students who attempted the quiz. Significance: • Students who completed an online quiz on basic arithmetic and algebra to identify their strengths and weaknesses indicated that the quiz prepared them for the material they had to study for their mathematics module.

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“…The implication is that before the concept of the derivative of a function is introduced students should have adequately established algebraic manipulation skills and understanding of the concept of a function (Maharaj 2013). Maharaj and Wagh (2014) focused on algebraic manipulations in the context of precourse diagnostics for differential calculus. This paper focuses on functions, including their symbolic and graphical representations in the context of in-course diagnostics for differential calculus.…”

Section: Functionsmentioning

confidence: 99%

“…At the University of KwaZulu-Natal (UKZN) relatively low pass rates for the first year differential calculus (Math130) module was of concern. A previous paper (Maharaj and Wagh 2014) looked at the pre-course diagnostics for differential calculus. In the present paper the focus is to outline an in-course diagnostics for functions, as required for differential calculus.…”

Section: Introductionmentioning

confidence: 99%

An Outline of Possible In-course Diagnostics for Functions

Maharaj

Wagh

2015

IJES

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The present paper focuses on in-course sample diagnostic questions relating to functions for students who choose to take a course on differential calculus, in a South African context. However, the diagnostic questions should be useful at many places worldwide. The researchers formulated learning outcomes and in-course diagnostic questions for the technical knowledge and skills required for the section on functions, in the context of differential calculus. The questions were designed to check the relevant learning outcomes that they detected for the section on functions as informed by the literature review and conceptual framework. The learning outcomes and formulation of diagnostic outcomes, although based on a number of assumptions, should improve the performance of students. © Kamla-Raj 2015 Int J Edu Sci, 8(3): 629-643 (2015)

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outline of possible pre-course diagnostics for differential calculus

Cited by 7 publications

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Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

Revelations from an online diagnostic arithmetic and algebra quiz for incoming students

An Outline of Possible In-course Diagnostics for Functions

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