scholarly journals PRE-SERVICE MATHEMATICS TEACHERS’ KNOWLEDGE OF MATHEMATICS FOR TEACHING: QUADRATIC FUNCTIONS

2018 ◽  
Vol 76 (6) ◽  
pp. 847-863 ◽  
Author(s):  
Ifunanya Julie Adaobi Ubah ◽  
Sarah Bansilal
Keyword(s):  
Mathematics Teachers ◽  
Graphical Representation ◽  
Quadratic Function ◽  
Training Programme ◽  
Quadratic Functions ◽  
School Level ◽  
Graphical Form ◽  
Advanced Mathematics ◽  
Structured Interviews ◽  
Symbolic Equation

Many researchers and education stakeholders in South Africa point to the need to develop teachers' personal knowledge of the mathematics concepts that they teach to their learners. In this research study we explore the understanding of 42 pre-service mathematics teachers of one aspect of school level mathematics, that of quadratic functions. Data were generated from the written responses to an assessment as well as semi-structured interviews. The purpose was to explore the methods used by pre-service mathematics teachers to derive a symbolic equation for a quadratic function expressed in graphical form. Furthermore, we looked at whether the pre-service teachers were able to use different methods to generate the symbolic equation. The results showed that 25 participants were able to determine the equation of a parabola using one method, while 11 of them were able to use two different methods. The most common method used was based on the intercept form of the equation. Some students identified different forms that the equation of a quadratic function could be expressed as but were unable to apply this to derive the equation. These results indicate that these students are not yet ready to teach these school level concepts even though they have studied advanced mathematics topics as part of their pre-service training. The study recommends that pre-service teachers should also be provided with more structured opportunities to help develop pedagogic content knowledge of the school level content as part of their teacher training programme. Keywords: graphical representation, parabola, pre-service mathematics teachers, quadratic functions, symbolic representation.

scholarly journals Pre-service mathematics teachers’ nature of understanding of the tangent function

2020 ◽  
Vol 5 (2) ◽  
pp. 105-118
Author(s):  
Priestly Malambo
Keyword(s):  
Mathematics Teachers ◽  
Graphical Representation ◽  
School Mathematics ◽  
Advanced Mathematics ◽  
Structured Interviews ◽  
Trainee Teachers ◽  
Initial Task ◽  
Tangent Function

Mathematics teachers’ ability to translate and make connections between representations of functions requires investigation. Consequently, this qualitative case study article focuses on pre-service mathematics teachers’ nature of understanding of the tangent function; a function bearing unique characteristics compared with the sine and cosine functions. Twenty-two finalist pre-service teachers were conveniently selected and assessed concerning the ability to translate a tangent function to the graphical representation. Likewise, participants’ abilities to correctly explain this function and provide appropriate justifications for espoused perspectives were investigated. Although the teachers learned higher mathematics, their assessment was school mathematics-based. Descriptive analyses showed that only one teacher (5%) accurately completed the task. Eleven teachers (50%) did not provide graphs; suggesting a lack of knowledge required to change representation. Ten (45%) drew flawed graphs depicting a lack of understanding of discontinuity of the tangent function at certain angles and the role of a domain. Essentially, these demonstrated mere memorization of the appearance of the tangent graph. A purposive sub-sample of size six then participated in exploratory semi-structured interviews. The interviews allowed participants to elucidate their answers to the initial task. Content analysis of the transcripts corroborated the earlier finding as the interviewees could not coherently explain the tangent function, and failed to justify their reasoning. The teachers demonstrated a superficial understanding despite having studied advanced mathematics. This reinforces the view that studying advanced mathematics does not assure a relational understanding of school mathematics. Therefore, it is necessary for trainee teachers to explore school mathematics.

scholarly journals Subject Matter Knowledge of Prospective Mathematics Teachers on Quadratic Functions Using Problem-Based Learning

2021 ◽  
Vol 54 (1) ◽  
pp. 141
Author(s):  
Tina Sri Sumartini
Keyword(s):  
Mathematics Teachers ◽  
Subject Matter ◽  
Mathematics Teacher ◽  
Problem Based Learning ◽  
Quadratic Function ◽  
Subject Matter Knowledge ◽  
Quadratic Functions ◽  
Moderate Increase ◽  
Study Program ◽  
Prospective Mathematics Teachers

Subject matter knowledge is important knowledge possessed by prospective mathematics teachers. In general, this study aims to examine the achievement of Subject Matter Knowledge (SMK) of mathematics teacher candidate students who study with the Problem Based Learning (PBL) model. This study used a mixed-method. The research design used was explanatory sequential design. The population consisted of undergraduate students of the Mathematics Education Study Program.  The sample used was 80 students of prospective mathematics teachers consisting of 40 students in the PBL class and 40 students in the CL-class. The results obtained were: the achievement of the vocational students of mathematics teacher candidates who studied with PBL was better than those of prospective mathematics teacher students who studied with conventional learning. In addition, from the five indicators, four indicators experienced a high increase and one indicator experienced a moderate increase, namely the indicator of the ability to connect the concept of a quadratic function in everyday life.

Investigating the Effects of Parameters on Quadratic Functions

2012 ◽  
Vol 106 (1) ◽  
pp. 64-69 ◽  
Author(s):  
Jon D. Davis
Keyword(s):  
Graphical Representation ◽  
Quadratic Function ◽  
Quadratic Functions ◽  
Teaching With Technology ◽  
Constant State

Technology is in a constant state of flux. As a result, if we seek to use the latest forms of technology in our teaching, our teaching with technology must be ever changing. Edwards and Özgün-Koca (2009) describe an investigation involving the TI-Nspire CAS to understand the effect of b on the graphical representation of a quadratic function of the form f (x) = ax2 + bx + c. Adapting this idea, I show how updates to technology can enhance this investigation to create an even more motivating and compelling experience for students. The investigation will make use of sliders and the spreadsheet capability of the TI-Nspire (the directions provided here apply to the TI-Nspire CX CAS).

Pengembangan Media Pembelajaran Interaktif Berdasarkan Teori Apos pada Materi Fungsi Kuadrat

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10
Author(s):  
Arie Gusman ◽  
Kamid Kamid ◽  
Syamsurizal Syamsurizal
Keyword(s):  
Learning Theory ◽  
Teaching And Learning ◽  
Quadratic Function ◽  
Test Group ◽  
Quadratic Functions ◽  
High School Mathematics ◽  
Constructivist Learning Theory ◽  
Average Value ◽  
Long Time ◽  
Action Process

Learning quadratic functions that had been performed by the majority of vocational school and high school mathematics teacher in Kuala Tungkal is still using conventional learning media. The use of conventional learning media is experiencing a lot of obstacles, such as: a fairly long time in describing the graph function, especially when analyzing some quadratic function graphs with various characteristics. APOS is one of the constructivist learning theory which states that students learn through several stages, namely: action – process – object – schema. And to integrate into media APOS writer adapting ADDIE development model. The effectiveness of the use of media-based learning theory APOS seen from the student activity sheet can be concluded more increased activity of students in the learning process. Study of the test results, students were able to meet the completeness criteria stipulated minimum is 75. With an average value of learning outcomes, namely 87.14. It can be seen from the students' responses on a test group of small and large groups where it is concluded that researchers develop learning media can be categorized as good / interesting in the teaching and learning of mathematics.

Patient perceptions of experience with cardiac rehabilitation after isolated heart valve surgery

2017 ◽  
Vol 17 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Tina B Hansen ◽  
Selina K Berg ◽  
Kirstine L Sibilitz ◽  
Ann D Zwisler ◽  
Tone M Norekvål ◽  
...  
Keyword(s):  
Cardiac Rehabilitation ◽  
Heart Valve ◽  
Isolated Heart ◽  
Personal Responsibility ◽  
Training Programme ◽  
Valve Surgery ◽  
Rehabilitation Programme ◽  
Heart Valve Surgery ◽  
Structured Interviews ◽  
Cardiac Rehabilitation Programme

Background: Little evidence exists on whether cardiac rehabilitation is effective for patients after heart valve surgery. Yet, accepted recommendations for patients with ischaemic heart disease continue to support it. To date, no studies have determined what heart valve surgery patients prefer in a cardiac rehabilitation programme, and none have analysed their experiences with it. Aims: The purpose of this qualitative analysis was to gain insight into patients’ experiences in cardiac rehabilitation, the CopenHeartVR trial. This trial specifically assesses patients undergoing isolated heart valve surgery. Methods: Semi-structured interviews were conducted with nine patients recruited from the intervention arm of the trial. The intervention consisted of a physical training programme and a psycho-educational intervention. Participants were interviewed three times: 2–3 weeks, 3–4 months and 8–9 months after surgery between April 2013 and October 2014. Data were analysed using qualitative thematic analysis. Results: Participants had diverse needs and preferences. Two overall themes emerged: cardiac rehabilitation played an important role in (i) reducing insecurity and (ii) helping participants to take active personal responsibility for their health. Despite these benefits, participants experienced existential and psychological challenges and musculoskeletal problems. Participants also sought additional advice from healthcare professionals both inside and outside the healthcare system. Conclusions: Even though the cardiac rehabilitation programme reduced insecurity and helped participants take active personal responsibility for their health, they experienced existential, psychological and physical challenges during recovery. The cardiac rehabilitation programme had several limitations, having implications for designing future programmes.

scholarly journals Social injustice in learning of the second language among immigrant children in Finland: conventional narratives and perceptions

2021 ◽  
pp. 82-100
Author(s):  
Frank Ojwang
Keyword(s):  
Second Language ◽  
Education Policy ◽  
Primary School ◽  
International Schools ◽  
National Language ◽  
School Level ◽  
Theory Approach ◽  
Official Language ◽  
Structured Interviews ◽  
Host Countries

This is a comparative ethnographic research, comparing the primary school level migrant learners’ performance in the learning of the national language of the host countries in Finland and Tanzania. A response from nine teachers, drawn from Tanzanian International Schools, attended by expats’ children, was collected through structured interviews. Additionally, two In-Depth Interviews, targeting Tanzanian Swahili teachers at the international schools, was conducted using the narration approach. The study uses MAXQDA to comparatively analyze the findings of fourteen research articles on immigrant pupils’ learning challenges of the Finnish language as a second language in Finland, and gathered information from this study’s survey is used to analyze the use of Kiswahili as a second language in Tanzania. The research focuses on a comparative analysis of the learning and use of official languages of the host countries as second languages, used in facilitating learning among primary school learners. In Finland, the official language analyzed is Finnish, whereas in Tanzania, the official language analyzed is Kiswahili. The International schools in Tanzania offer Kiswahili lessons to all learners in primary school as guided by national education policy, whereas all public and international schools in Finland offer Finnish lessons for all learners under the education policy. The responses in both Finland and Tanzania are deconstructed qualitatively to illuminate the similarities and differences between European migrant learners and African migrant learners using a second language for learning, and to further deconstruct the nuanced epistemological injustice against minorities. The theories in this research are derived using the grounded theory approach.

scholarly journals Exploring Teachers' Views on Code-Switching as a Communicative Technique to Enhance the Teaching of Mathematics in Grade 4

2021 ◽  
Vol 7 (4) ◽  
pp. 637-6478
Author(s):  
Ailwei Solomon ◽  
Sizwe Blessing
Keyword(s):  
South Africa ◽  
Mathematics Teachers ◽  
Social Constructivism ◽  
Primary Schools ◽  
Single Case ◽  
Sampling Technique ◽  
Further Education ◽  
Code Switching ◽  
Structured Interviews ◽  
Learning And Teaching

<p style="text-align: justify;">The teaching and learning of mathematics in South Africa are conducted through the authorised Language of Learning and Teaching (LoLT). South Africa has eleven official languages, and English is a Language of Learning and Teaching (LoLT) from the Intermediate and Further Education and Training (FET) Phase. This study explores teachers' views on code-switching as a communicative technique to enhance teaching mathematics in Grade 4 in selected primary schools in South Africa. This qualitative single case study employed the interpretivist paradigm and social constructivism theory. A convenient purposive sampling technique was used to sample six grade 4 mathematics teachers from three primary schools in the Alexandra township in South Africa. Researchers collected data through the use of semi-structured interviews, which were later analysed and discussed using themes. Findings indicate that teachers often code-switch from LoLT (English First Additional Language) into Home Language (H.L.) to enhance learners' understanding of the mathematics concepts. Researchers suggested the integration of code-switching into the curriculum policy and followed by in-service training for Grade 4 mathematics teachers in code-switching.</p>

scholarly journals Exploring Grade 6 mathematics teachers' use of the language of learning and teaching in assessment for learning

2021 ◽  
Author(s):  
Sizwe B Mahlambi ◽  
Ailwei S Mawela
Keyword(s):  
South Africa ◽  
Language Proficiency ◽  
Mathematics Teachers ◽  
Primary Schools ◽  
Teaching And Learning ◽  
Assessment For Learning ◽  
Code Switching ◽  
Home Language ◽  
Structured Interviews ◽  
Learning And Teaching

In this study, we aimed to explore Grade 6 mathematics teachers' use of English, the language of learning and teaching in assessment for learning in selected primary schools in Alexandra Township, South Africa. From Grade 4, English is the language of teaching and learning for most learners, despite English being the home language of a minority of learners. Results of studies have shown that in South Africa, in Grades 1 to 3, in which learners are taught using their home-language performance appears to be better than in Grades 4 to 6 where English as a First Additional Language (EFAL) is used for teaching and learning. Guided by qualitative case study design, we used semi-structured interviews and non-participatory observation to collect data from nine purposefully sampled Grade 6 mathematics teachers. In conjunction with the literature reviewed and the theory underpinning the study, we used themes to analyse, interpret, and discuss the data we collected. This research revealed that learners in Grade 6 struggle to understand English as the language of learning and teaching, so, to augment concept development and understanding, teachers and learners use code-switching. In the classrooms observed, this practice has become the norm to improve the performance of learners with limited language proficiency. However, because of the differences between the home language of learners and that of teachers in mathematics classrooms, code-switching is often not enough to ensure understanding.

scholarly journals HISTÓRIA DA MATEMÁTICA DO ENSINO FUNDAMENTAL NOS LIVROS DE MINICURSOS DA SBHMat (2001-2017)

2020 ◽  
Vol 5 (1) ◽  
pp. 28-44
Author(s):  
Lucas Silva Pires ◽  
Iran Abreu Mendes
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Basic Education ◽  
School Level ◽  
Teaching Mathematics ◽  
Brazilian Society ◽  
School Grades ◽  
Mathematics History ◽  
Short Course

Resumo: Neste artigo apresentamos os resultados de uma pesquisa sobre os livros de minicursos de história da matemática publicados pela Sociedade Brasileira de História da Matemática no período de 2001 e 2017, cujos conteúdos matemáticos foram destinados aos anos finais do Ensino Fundamental. Nosso objetivo foi identificar e caracterizar as sugestões propostas nesses livros para as ações didáticas do professor de Matemática desse nível escolar. Para operacionalização da pesquisa, inicialmente realizamos um levantamento dos livros de minicursos classificando-os em três tendências de pesquisa em História da Matemática, para selecionar somente aqueles voltados à história para o ensino da matemática. Em seguida identificamos e caracterizamos os livros com conteúdos dos anos finais do Ensino Fundamental. Os resultados apontaram que, dos 101 livros de minicursos, 21,78% propõem abordagens centradas em conteúdos relativos ao Ensino Fundamental dos anos finais que podem ser utilizadas com vistas a facilitar as organizações e ações didáticas do professor nas suas aulas de matemática.Palavras-chave: Livros de minicursos; História para o ensino da matemática; Anos Finais; Ensino Fundamental. Abstract: In this article we present the results of a research on the Mathematics History short-course books published by the Brazilian Society of Mathematics History from 2001 to 2017 whose contents were aimed at Middle School grades. Our objective was to identify and characterize the suggestions proposed in these books for the didactic actions of Mathematics teachers at this school level. To operate the research, we carried out, at first, a survey of the short-course books, sorting them into three research tendencies in Mathematics History, in order to select only those that dealt with History for teaching Mathematics. Then we identified and characterized the books which included contents for Middle School. The results indicated that, from the 101 short-course books, 21,78% propose approaches centered around contents pertaining to Middle School which can be used to facilitate the teacher's organization and didactic actions in their Mathematics classes.Keywords: Short-course books; History for teaching Mathematics; Middle School; Basic education.

scholarly journals Migración de estudiantes internacionales a Chile: Desafíos de la nueva educación públic

2021 ◽  
Vol 29 ◽  
pp. 68
Author(s):  
Jorge Alarcón-Leiva ◽  
Catalina Gotelli-Alvial
Keyword(s):  
International Students ◽  
Empirical Evidence ◽  
Educational System ◽  
Immigrant Students ◽  
Educational Institution ◽  
School Level ◽  
Classroom Teachers ◽  
Structured Interviews ◽  
Educational Management ◽  
New Public

The article addresses the problem of immigration of international students in the Chilean educational system, collecting empirical evidence regarding the challenges of directive management and pedagogical management that the process of installing the new public educational institution in Chile faces. In this framework, the objective of the work is to elaborate a typology of the forms of implementation of the migratory policy at the school level, of the procedures adopted by the educational management and, finally, of the teaching practices related to the inclusion of immigrants. For this purpose, the analysis is carried out, from the Grounded Theory perspective, of semi-structured interviews applied to directive teachers and classroom teachers of school establishments, regarding situations in the context of which they have had to attend to emerging needs from the presence of international immigrant students. Finally, it ends by underlining the need to move from the stage of respect for rights to that of full recognition of the dignity of international immigrants.

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