Learner Participation in the Functions Discourse: A Focus on Asymptotes of the Hyperbola

Mpofu, Sihlobosenkosi; Pournara, Craig

doi:10.1080/18117295.2017.1409170

Cited by 9 publications

(19 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As such, the definition with limits was not suitable for them. At the same time, the proposition that the curve should not cross the asymptote is not mathematically correct and should therefore be avoided in the teaching and learning situation (Mpofu & Pournara, 2018). As stated in the paragraphs above, the horizontal asymptote may, or may not cross the curve of a graph.…”

Section: The Asymptotementioning

confidence: 99%

“…The hyperbola and the exponential functions have asymptotes at the zero points of the denominator, and there is no intersection between the horizontal asymptote and the graphs. The reviewed literature showed that learners tended to struggle with the concept of the asymptote (Flesher, 2003;Kidron, 2011;Mpofu & Pournara, 2018).…”

Section: Challenges Concerning Learning Asymptotesmentioning

confidence: 99%

See 1 more Smart Citation

Learners’ Views on Asymptotes of a Hyperbola and Exponential Function: A Commognitive Approach

Mudaly¹,

Mpofu²

2019

PEC

Self Cite

View full text Add to dashboard Cite

Learners in South African schools often respond poorly in questions related to the asymptote. Despite the fact that there are only a few functions in the South African curriculum that actually explore the asymptote, learners still show some deficiency in their understanding of the concept. This research examined Grade 11 learners’ mathematical discourses about the asymptotes of the hyperbola and exponential functions. Data were analysed using the Realisation Tree of a Function, an adaptation of the Realisation Tree Assessment tool from Weingarden, Heyd-Metzuyanim and Nachlieli. While the Realisation Tree Assessment tool focused on teacher talk, the Realisation Tree of a Function focused on learner expression and responses. A qualitative research design was essentially adopted, with exploratory, descriptive and interpretive elements complementing both its data collection and analysis. A purposive sampling strategy was implemented. Data were collected by means of a test administered to a total of 112 Grade 11 participants from four selected secondary schools. Focus group interviews were conducted with 24 of the best-performing participants by using their responses from the written mathematical tests. The results revealed that the learners’ mathematical discourse is not coherent. While learners’ work on each representation was often mathematical there seemed to be a struggle when the task had an unusual orientation. Different expressions of the same mathematical object elicited different responses. The challenge is that learners exhibited a fragmented relationship between the mathematical objects of the function. Keywords: commognition, realization tree, ritualised learning, visual mediators.

show abstract

Section: The Asymptotementioning

confidence: 99%

Section: Challenges Concerning Learning Asymptotesmentioning

confidence: 99%

Learners’ Views on Asymptotes of a Hyperbola and Exponential Function: A Commognitive Approach

Mudaly¹,

Mpofu²

2019

PEC

Self Cite

View full text Add to dashboard Cite

show abstract

“…That is, rural areas have not been focused upon in general, especially within the South African context, to understand teachers and learners' discourses when engaging with the topic. It is also notable that previous studies on algebraic functions has predominately focused on learners' difficulties related to learning the topic (Malahlela, 2017;Mpofu & Pournara, 2018), overlooking researching with teachers who are the primary source of mathematical knowledge.…”

Section: Research On Algebraic Functionsmentioning

confidence: 99%

Rural Teachers’ Teaching of Algebraic Functions Through a Commognitive Lens

Mbhiza

2021

IJRCS

View full text Add to dashboard Cite

Rural contexts and their schools have continuously been overlooked by researchers of mathematics education in South Africa. This is despite the assumption that the educational landscape may vary markedly in rural areas compared to urban and township areas which have been solely researched in the post-apartheid dispensation. To address the dearth of mathematics education research located within South Africa's rural contexts, the study explored five Grade 10 rural mathematics teachers' discourses and approaches of teaching algebraic functions with five teachers from five different school sites. This qualitative multiple case study, using Sfard's commognitive theory, draws attention to rural mathematics teachers' classroom practices and views about the teaching of algebraic functions which is unexamined in the South African context. Three data generation tools were used to gain insight into teachers' discourses and approaches while teaching the topic. These are individual semi-structured interviews, classroom observations and Video-Stimulated Recall Interviews (VSRI). Research findings focus primarily on the data generated through classroom observations. To analyse the data, I use Sfard's commognitive theory to give meaning to teachers' classroom practices. Focusing on the distinction between two tenets of commognitive theory, ritual and explorative routines, the findings demonstrate that four participating teachers acted in an extremely ritualised way. The other teacher was more explorative in her classroom observable actions. The findings illuminate that teachers need to move more towards the participationist approach during teaching to enable them to think, observe, and communicate about mathematical objects that commognitively link more with explorative routines.

show abstract

“…It is based on the concept of thinking as a cognitive activity while answers are a form of communication conveyed by students. Commognition is a blend of communication and cognition [12], [13]. It can be defined as the conveyance of ideas that can be expressed in written or spoken form [14], [15].…”

Section: Introductionmentioning

confidence: 99%

“…Visual mediator is a tangible form of student work. Visual mediators are distinguished into three categories: concrete mediators, symbolic mediators, and iconic mediators [12], [17], [26]. Concrete mediators can be in the forms of real or familiar objects such as rulers, fingers and other objects to count.…”

Section: Introductionmentioning

confidence: 99%

Exploring the Argumentation Skills of Prospective Teachers based on Commognitive Approach using Moodle LMS

Lestari¹,

Nusantara²,

Susiswo³

et al. 2021

TEM Journal

View full text Add to dashboard Cite

While a pandemic is currently sweeping the world, technology becomes a necessity in almost the entire aspects of life, particularly in learning activities. One of conventional learning-based platforms that adopt online system is Moodle Learning Management System. This study explored the argumentation skills of prospective teachers based on commognitive approach using the LMS. This qualitative research used online-based semi-structured questionnaire and interview during a discussion group via LMS platform. The subjects of this study were 38 prospective teachers. The research instrument was a questionnaire with eight items. It was initially assessed with Cronbach’s alpha test in which the value indicated the questionnaire was reliable (0.852). The findings of this study indicate the argumentation skills of prospective teachers correlate with the commognitive framework, including claim with endorsed narratives; data with visual mediators; warrant with routine, word use, and endorsed narratives; and backing with endorsed narratives.

show abstract

Learner Participation in the Functions Discourse: A Focus on Asymptotes of the Hyperbola

Cited by 9 publications

References 5 publications

Learners’ Views on Asymptotes of a Hyperbola and Exponential Function: A Commognitive Approach

Learners’ Views on Asymptotes of a Hyperbola and Exponential Function: A Commognitive Approach

Rural Teachers’ Teaching of Algebraic Functions Through a Commognitive Lens

Exploring the Argumentation Skills of Prospective Teachers based on Commognitive Approach using Moodle LMS

Contact Info

Product

Resources

About