NAME: Aneshkumar Maharaj STAFF NUMBER: 1641 Rationale for ...utlo.ukzn.ac.za/Files/Maharaj, A...

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TEACHING PORTFOLIO STATEMENT

NAME: Aneshkumar Maharaj STAFF NUMBER: 1641 Rationale for approach to education My teaching career which began in 1983; as mathematics teacher (1983-1991) at Greytown and then Woodlands Secondary Schools for grades 7 to 12 mathematics, then as a lecturer in the Department of Mathematics at Springfield College of Education (1992-2000) and South African College for Open Learning (2001-2002) which focused on the training of mathematics teachers; prepared me to serve as a senior mathematics tutor at the University of Natal (2003-2005) and then the University of KwaZulu-Natal (2006 onwards) where I was promoted to mathematics lecturer (2008) and then senior lecturer (2015). I strongly believe that: One can only teach the students one has, not the students that one would like to have! One of my areas of interest was and still is the teaching and learning of mathematics, with particular focus on how to improve these with an emphasis on understanding. I conducted research on advanced mathematical thinking, e-learning, diagnostics and remediation, and higher order thinking skills (see Annexure A1). These have provided me with a good platform from which to plan, implement, reflect and improve on my teaching. I strongly believe one should plan well and provide the students with opportunities to progress with their studies in mathematics. The theory that informs the rationale for my approach to under-graduate education is APOS (action-process-object-schema) Theory. See Annexure A2 for how I used this theory to guide my rationale. In particular the relevant write-ups for Figure 1 in both the first and second publications in Annexure A2 indicate the overview to my working situation. The figure below ties up APOS Theory and ACE Teaching Cycle in the context of mathematics e-learning which I am using at UKZN in the School of Mathematics, Statistics and Computer Science.

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My teaching focuses on: moving from the known to the unknown via the framing of appropriate mathematical questions; studying the underlying structures of mathematical objects (expressions, equations, functions) with the intention of unpacking the implied embedded information; verbalizing and visualizing in order to promote sense making; the developing and refining of schemata or mind maps; the presenting of solutions in order to promote communication and bring to the fore mathematical reasoning; setting a good pool of tutorial questions for the students to work through. The latter is informed by my belief that to learn mathematics students need to be exposed to and work through appropriate problems. See Appendices A3 to A6 for evidence. My rationale towards post graduate supervision was informed by my own experience as a student, attending relevant workshops and three NRF/SAARMSTE Winter Research Schools, reading on supervision and discussing with fellow supervisors. Based on that, I presented at a research supervision session (Annexure A7, invitation and snapshots of 1st two slides from 9 slide presentation). Methods of Teaching and supervision

Undergraduate teaching See Annexure B1, for undergraduate teaching from 2003 to 2015. Since most of the class sizes were very large (Annexure E6: Photograph 1) I generally used a teaching approach based on well planned transparencies [2003 to 1st semester of 2008] and a PC from the 2nd semester of 2008. Those lectures included carefully planned key questions to focus on to develop concepts/theory, and examples based on the application of theory. In Annexure B2 see Snapshot 1 for an example of a lecture outline and Snapshots 2 and 3 for examples from the delivered lecture using the PC tablet). Another example of delivered lecture is given in Snapshot 4 in Annexure B2. The use of a tablet gives me greater flexibility to deal with student queries during lectures. Where possible I encourage students to attempt certain problems, then I discuss these so that they could get instant feedback. Lecture outlines and other support materials are available to students on the module website; see Annexure B3. Tutorials are organised and implemented so that students could benefit from them, group interaction is encouraged (see Annexure A2, the first paper on tutorials). Informed by that research Annexure B4 gives an insight into how I organise, implement (see Snapshots 1 and 2) and monitor tutorials (see Snapshot 3). With regard to general information regarding requirements for tutorials these are found in the folder Information and Handouts indicated in Annexure B3. In the Notices section in Annexure B3 relevant notices indexed by dates are put up, for example to inform students of new material put into different folders on the website. The manner in which the delivery of the modules was organised and the methods of blended learning/teaching used were successful, as can be gauged from: the exam results (see SMS Final Marks sheets, Annexure B5); student feedback (see Annexures B6: Snapshot 1; student evaluations (see Annexures B6: Snapshots 2 to 7). Note that from 2012 student evaluations were done online and the responses were very low; for example for 2012 Math150W1 the student response was about 11% and for 2014 Math140W1 about 9%. The student evaluation indicated in Annexure B6: Snapshots 6 and 7 is discussed below. The focus is on this since it was the last module that I coordinated before my sabbatical. This group had students of mixed ability levels from different programmes. From the evaluation which had a response rate of 77% the following conclusions can be made:

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1. With regard to general questions on the module, the positive responses ranged from 72 to 84%, see responses to questions 1 to 5. Annexure B6: Snapshot 6

2. The responses to the questions on the tutorials and support indicated that in the main most of the students benefited from these. What stood out was that 81% of the students felt that tutorials helped them to understand the module material better. For this students had to attempt the tutorial questions.

3. For questions based on my lectures, the responses were very positive; see questions 27 to 39. Annexure B6: Snapshot 7

4. The report indicated that 84% of the students benefited from the module website. It was concluded that about 91% of the respondents downloaded lecture notes and about 94% downloaded test solutions. A similar finding for the module Math133W1 is indicated in Annexure B6: Snapshot 5

5. The comments indicated in italics are taken verbatim from the report. Positive comments. These are varied, some more positive than others, for example: Dr Maharaj was great and encouraging. Mathematics 145 was a well organized and well taught module with precision

and clearly always coming from the lectures. Mr Maharaj is a good lecturer even his tutorials well handled well, with his

tutors trained well. All of this helped out. Best work ever may the maths this term carry on working this hard.

Very organized. Dr Maharaj is a very nice lecturer, approachable. Keep up the good work. Your lecture class is awesome.

This module was very interesting and very helpful. The work was much better understood if tutorials was done. Dr Maharaj had his own interesting ways of explaining things to us.

The module was well organized, every support was available. It was too us as students to do our part. Student who did they part will pass with flying colours. Thank very much many other students experience the same thing.

[7] Negative comments. My remarks to these follow each comment, where necessary. Give harder examples in the lecture notes Should reduce tutorial work. Some of the work could be reduced as some of the times we are writing tests

and other projects. It’s not always possible to attempt these questions.

In one of the earlier reports for Math1S2 in 2004, I was motivated by the following comment made by a student: Smaller tut groups cause a proper environment for studying, there is less noise and more productivity. From the year 2005 I introduced a control sheets for each tutorial group, not for attendance at tutorials, but for completion of the relevant tutorials. Students were put into groups. A fixed tutor was in charge of each group. From each of these groups I randomly choose students after their tutors attended to them. The purpose of this was/is to make my inputs with regard to aspects/areas that require attention, and moderate the quality of the feedback given to the students by their tutors. I found that this significantly improved test and examination results. This is one of the reasons for the pass rates of 73.06% for Math134W1 in the first semester of 2006 and 82.91% in 2007, and 90.45% for Math145W2 in 2007 (these are from UKZN’s data base). With the exception of Math140W2 in 2008, the procedure for credits towards completion of tutorials; outlined above; was followed – even for Math130W1 and Math140W2 in 2009. In 2010 with the smaller class for Math145W2 I fine-tuned this to allocate a mark for each homework unit. These changes were made from 2009; for Math140 in 2008 we used tutorial tests but found that students detected loopholes. Their final results (2008 Math140) showed

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that their performance was not at the level of those students who were exposed to the system of credits towards completion of tutorials. The evidence is in Annexure A2, see the first paper on the design and implementation of university mathematics tutorials. One of the reasons for my success is that I have sought advice from the lecturers who previously taught the modules, and tried to plan for potential difficulties whether in terms of student behavior or the administration of the relevant module. When coordinating a module I always tried and succeeded to work with the other lecturers as part of a team. Further, at the beginning of a module I encourage students to give constructive feedback on how to improve my delivery of lectures or coordination of modules, instead of them complaining at the end of a module when it is too late. Many of the students I have lectured to have contacted me and expressed their appreciation for the manner in which I delivered the relevant module, and the usefulness of the material covered. Some students indicated they prefer tutorial tests. To cater for such students I spent a lot of my time during my sabbatical (July 2012 to June 2013) to study and work on the design of online quizzes for pre-calculus and undergraduate mathematics. For communication with students regarding the online quizzes see Annexures B7.

Post-graduate teaching

From 2004 onwards I was co-supervisor for the dissertations towards the degree of Master of Education (Mathematics Education) in the School of Mathematics, Science, Computer Science and Technology Education at UKZN. Student details and the status of their dissertations are as follows: Mkhize S.A (Student Number 961115063) – completed; Molebale.J.J.L (Student Number 964121004) – completed; Zingiswa M.M.J (Student Number 201506651) – completed. The quality of my advice to these students was informed by my own studies in Mathematics Education. Further I learned important aspects of supervision by attending three SAARMSTE Winter Research Schools (2004, 2006, 2007) that were funded by the NRF. Post graduate supervision [2007 onwards] at UKZN. Co-supervised Zingiswa M.M.J (Student Number 201506651) for her Phd which

was awarded in 2012: An exploration of the conceptual understanding of the chain rule in calculus by first year engineering students

Main supervisor for the phd student Molebale.J.J.L (Student Number 964121004): An APOS analysis of the development of cognitive constructions for local maximum/minimum in grade 12 Calculus. Submission target: November 2015

Main supervisor for phd student Chhagwiza C.J (Student Number 213574316): Exploring University Students' Mental Constructions of the Limit Concept in Relation to Sequences and Series. Status: ongoing should complete in 2017

Main supervisor for the phd student Krishnannair A (Student Number 206523383): Introduction of a semi-integrated curriculum for the mathematics module offered as part of a science foundation programme at a South African university. Submission target: November 2016

Supervisor for phd student Tarr H (Student Number 932402953): An investigation of students’ understanding of concepts in Integral Calculus: Implications for teaching. This study is informing the development of online diagnostics for integral calculus. Status: ongoing should complete in 2017 via the submission of papers route

Main supervisor for phd student Noor A (Student Number 951049841): Online diagnostics for undergraduate engineering mathematics. At time of writing his application was submitted for processing.

Supervision of two honors’ projects in 2014 based on the NRF funded project: Online diagnostics for undergraduate mathematics. The students Ashish Singh and

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Sugan Naidoo (with student numbers 209508477 & 206504922 respectively) passed their projects.

Supervision of Mohammed Mustafa (student number: 206505831) honors’ project in 2015 based on the NRF funded project: Online diagnostics for undergraduate mathematics.

Supervisor of UNISA students for Master of Education with specialization in mathematics, from 2015. Mhlanga T [email protected] Integration of mobile technology

(cellphones) in the teaching and learning of mathematics at the Further Education and Training Phase. Status: ongoing on track to submit in November 2016

Stewart HB [email protected] The performance of Grade 10 mathematics learners in a school in Tshwane West district, Gauteng with different learning styles along Bloom’s taxonomy levels. Status: ongoing on track to submit in November 2016

As a (co)-supervisor I am or was involved in [1] the refining of formulated research proposals, and meetings to clarify the requirements to be satisfied, [2] setting target dates for students to write up draft chapters for their dissertations, [3] reading through student submissions of chapters, correcting and making suggestions on these, and [4] meeting students to discuss their submissions and the way forward. See Annexures C1 two examples of records that give an insight into the type of advice given to students and Annexure C2 for a letter from student who completed her Phd. Methods of assessing students’ work and performance I regard the quality and standard of assessment of student work for tutorial/homework problems, tests and the examination as being an integral part of the planning, and then implementation of the learning and teaching process. There has to be a good match between the delivery of the module and the assessment; see Annexure B6: Snapshots 3 and 6 - student responses to Question 4. All questions have to be carefully phrased so as to avoid ambiguity. For example see Annexure D1 and Annexure A5, for illustrations of the grading of tutorial problems. One of the requirements from university mathematics students is that they present their solutions to problems in a logical manner, so that it makes sense to whoever is looking at their solutions. I believe that one has to lead by example; see Annexure B2: Snapshots 2 to 4. Also see for an example the expected answers and marking guide in Annexure D2. Here the allocation of marks takes into account the required knowledge and thinking processes to answer questions. [Note, when I am the coordinator of the module I work out the expected answers and marking guide on a draft typed copy of the test/exam paper. Then the typographical errors are corrected, and the paper is printed. This is done to eliminate or minimise typing errors. Annexure D2 refers to a test for a module that I coordinated.] Bearing in mind the large number of students for the service modules Math134W1, Math133W1 and Math150W1 to minimise the administrative problems with regard to marking I introduced MCQs for the tests and examinations. This approach reduced administrative work for our secretaries, reduced my work as the coordinator and also reduced our school’s marking budget. When advised by Prof S Maharaj in 2006 to explore the setting of completely MCQ tests and examinations for Math134, my initial response was negative. After experimenting I came to the conclusion that a high standard of assessment is still possible. See Annexure D3 for an example of part of an MCQ test. Note that solutions were made available to students to impress on them that

mailto:[email protected]

mailto:[email protected]

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they should do the necessary working and not guess. The majority of students followed the advice. I now focus on new online assessments put into place from 2013 to gauge students work performance. Here I am referring to the online quizzes which students are expected to take on a voluntary basis to gauge their strengths/weaknesses with regard to required knowledge and skills, and then take the necessary remedial measures (if required) before formal tests and examinations. The research and planning for online diagnostics began in 2010 and much of my energy was focused on that during my sabbatical; from July 2012 to June 2013. The online support is designed so that students could take responsibility for their own learning. New students generally lack the knowledge and skills required to study calculus. To address this, pre-calculus diagnostic quizzes were formulated. See Annexure D15: Snapshot 1 for such quizzes and Annexure D15: Snapshot 2 for diagnostic questions on the content for Math130. I found that many students took the quizzes on a voluntary basis; see Annexure D15: Snapshot 3 which gives the situation for in the first week of April 2015 for the 2015 website for those quizzes indicated in Annexure D15: Snapshot 1. It was observed that voluntary student attempts during 2015 increased by up to 400% when compared to attempts for 2014. Annexure D15: Snapshot 4 suggests that an interested student could within a short period of time achieve success. Note that the first student took about 45 to answer the questions on limits and after completion obtained a grade of 5 out of 10. After a break and possible studying the student retook the same quiz and completed in about 12 minutes to obtain a grade of 9.38. The questions were the same but the system scrambles the order of the MCQ alternatives. On 7 April 2014 the Math130W1 students wrote Test 2 at 17:30, which included the section on limits. Note that the system gives students immediate feedback (Annexure D15: Snapshot 5). Insight into the monitoring, impact of the online quizzes and also that some students perceive it as benefitting them is given in Annexure B7: Snapshots 1 to 4). When test scripts are returned to students, for transparency, the expected answers and the marking guide were/is made available to students, on the relevant module website. The general shortcomings, common errors and areas that require attention are normally indicated by the markers on the students’ scripts. A summary of this, according to feedback from the markers to me, is discussed with the whole class. For evidence of the systematic manner in which assessment is done so that it benefits the students see Annexure D4: Examples 1 to 4. Example 1 gives an insight into the planning that goes into the overseeing of the assessment process for tests; Examples 2 and 3 give an insight into the type of advice I provide to colleagues as an external examiner of examination papers; Example 4 gives an insight into the quality of advice I give as an external examiner for a dissertation/thesis. Peer and student evaluation of teaching For the modules that I lectured on from 2004 onwards student evaluations were done in consultation with the UKZN’s QPA Unit. The student evaluation for the last module that I fully coordinated in 2011, before going on sabbatical (July 2012-June2013), was discussed and cited as evidence (Annexure B6) under the section Methods of Teaching. Those evaluations were done at almost the end of the semester. As indicated earlier on my return from sabbatical online evaluations were in place and the response rates were very low. For each module I lectured in, from the 1st week of lectures I encouraged students to give me constructive feedback on what is good, and what can be done to improve things that were not good (via email). The reason for this was to improve

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things so that it could benefit the students, instead of them complaining at the end when it was too late. See Annexure B7. See Annexures C2 and B8 for letters from students. I have always sought advice from the lecturers who previously taught the modules, and tried to plan for potential difficulties whether in terms of student behavior or the administration of the relevant module. When coordinating a module I always tried and succeeded to work with the other lecturers as part of a team. Even in my capacity as external examiner for Engineering Maths 1(a) and 1(b) I tried to work as part of a team. For evidence, see feedback from peers in Annexure D5 [these were responses to an email that I sent requesting feedback]. Further confidential reports received in 2014 by my former line manager, Prof Simon Mukwembi, for which he obtained permission for me to use the reports in this application are given in Annexures D6 and D7. The scholarship and study of teaching I am fortunate in that my studies at the Masters and Phd levels focused on these in the context of mathematics teaching and learning. Further my university teaching is informed by research conducted on content related to university mathematics and the Mathematics e-learning projects that I oversee at UKZN. See Annexures A1 and A2, also the figure on page 1 of this document. Further evidence: Annexure D8 - a list of peer reviewed articles in conference proceedings. Annexure D9 – list of presentations on projects Annexure D10 - a list of research projects I am working on, and grants awarded. Annexure D11- Letter from John Bourne who headed the Multiversity

Consortium for the HP Global Catalyst; on my contributions Annexure D12 – Grant award letters from ESKOM (for UKZN-ESKOM

Mathematics Project) and NRF (for the project, Online diagnostics for undergraduate mathematics).

Annexure D13 - main supervisor for Phd studies on Mathematics Education for students registered through the School of Education at UKZN. Served as external examiner for post graduate studies (Annexure D13: Snapshot 3). Annexure D13: Snapshots 1 and 2 – evidence that my research using APOS Theory as a theoretical framework is having an international impact. The paper attached in my email reply (Annexure D13: Snapshot 2) is the 5th paper listed in Annexure A1. From the student’s email it can be concluded the 9th publication in Annexure A1 was referred to.

Annexure D14 – letters from: (1) research office granting ethical clearance for an HP project, Applying Virtual Worlds to Ethics Education in Science; (2) acting DVC and Head of College in response to my sabbatical report.

Further evidence is indicated by the Dean of the School of Mathematics, Statistics and Computer Science in Annexure D16. In the self-evaluation report prepared by him as part of our school review in 2014 the following extract occurs under the sub-section on Mathematics Education and Outreach:

Members of the Mathematics Education Research Group led by Dr Aneshkumar Maharaj are engaged with research projects to improve the teaching and learning of school and university levels of mathematics. Current work includes diagnostic testing based on the content of our main stream mathematics modules. A meeting was held with Trevor Anderson from Purdue University (USA) in June 2012 to discuss and plan for education based research related to the different disciplines in our school. During 2012 and 2013 discussions for collaborations were initiated with the TATA Homi Bhabha Centre for Science Education in Mumbai, Dr

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Ambedkar University in Delhi, AGASTYA International Foundation in Bangalore, research units at Amrita University in Kerala (India), Central India Research Institute (CIRI) and Centre for Scientific Thinking (both in Nagpur, India), and University of British Columbia in Vancouver (Canada).

Development of new courses In 2010 I oversaw the revision of curriculums for Math133W1 and Math145W2; see Annexure E1. During 2013 and 2014 I worked with the acting Leader for Teaching and Learning in our school (Dr Paddy Ewer) to develop new courses; see Annexure E1: Snapshot 2. I made suggestions as to how the curriculum for Math130 should be revised. Each of the modules I lectured were improved and developed by me. What I tried to do is increase the teaching and learning materials for students. For example some evidence of this can be found on the university’s MOODLE platform for the following modules that were taught or coordinated by me: Math150W1, Math145W2, Math140W2, Math130W1 and Math133W1. See Annexure E6: Photograph 2 for an insight into how students engage with the e-learning the materials. The sites contain general information on the relevant module, notices, past exam papers, solutions to test questions, lecturer feedback to module related queries raised by students in the discussion forum section, and summaries for the relevant topics covered in the module. For example see the Screenshot 1, which gives the homepage of the 2014 Math130W1 website. Topic 3 focuses on online diagnostic quizzes. The pre-calculus quizzes are a result of work for the HP project on Mathematics e-learning and Assessment: A South African Context and the UKZN-ESKOM Mathematics Project; both of which I coordinate(d) at UKZN. The development of online diagnostics for Math 130 content is a result of the work I am coordinating for the NRF funded project (duration 2014-2016), Online diagnostics for undergraduate mathematics. Screenshot 1: Homepage of 2014 Math130W1 website

Sharing teaching experience with others Evidence that I share my teaching experience with others:

Annexure D9 – list of presentation on projects from 2010 onwards

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Annexure D13: Snapshot 2 – responding to a student from Indonesia on how to use APOS theory to develop teaching material on the integral concept for undergraduate students

Annexure E1: Snapshots 2 and 3 – my willingness to share my experience with colleagues from different higher education institutions

Annexure E2 – part of a presentation on Mathematics e-learning which gives an insight to what I shared with others

Annexure E3: Snapshot 1 – Mathematics Development Initiative; by post graduate students in our school.

Annexure E3: Snapshot 2 – sharing maths stuff with others Annexure E3: Snapshot 3 – coordinating of school projects for outreach with

local government representative Annexure E3: Snapshot 4 – making mathematics support material available to

others Annexure E4: reference letter from the Central India Research Institute Annexure E5 – internship report of intern to NRF; who I supervised/mentored

for the period May 2013 to April 2014. Mr Nzuza is now a lecturer at the University of Zululand. He will assist in rolling out online diagnostics (developed during the piloting phases at UKZN) at UNIZUL during 2015/2016.

Annexure E6: photographs 3 to 8, evidence of sharing ideas locally and internationally

Additional information video (Video 1) on the HP funded project Maths e-learning and Assessment: A South African Context. Also available at http://mathselearning.ukzn.ac.za/ Additional video profiling more recent teaching & learning activities may be found at http://youtu.be/X-EjbTujqe0

http://mathselearning.ukzn.ac.za/

http://youtu.be/X-EjbTujqe0

1. Maharaj A 2015. An outline of possible in-course diagnostics for elementary logic, limits and continuity of a

function. International Journal of Educational Sciences, 8(2), 281-291.

2. Maharaj A, Brijlall D, Narain O 2015 Designing website-based tasks to improve proficiency in mathematics: a

case of basic algebra. International Journal of Educational Sciences, 8(2), 369-386.

3. Brijlall D & Maharaj A 2014. Exploring Support Strategies for High School Mathematics Teachers from

Underachieving Schools. International Journal of Educational Sciences, 7(1), 99-107.

4. Maharaj A & Wagh V 2014. An outline of possible pre-course diagnostics for differential calculus. The South

African Journal of Science, 110(7/8), 27-33.

5. Maharaj A 2014. An APOS Analysis of Natural Science Students’ Understanding of Integration. REDIMAT, 3(1),

54-73.

6. Brijlall D & Maharaj A. (2013). Pre-service teachers understanding of continuity of functions in the context of

assessment items. South African Journal of Higher Education, 27(4), 797-814.

7. Jojo, Z.M.M., Maharaj, A. & Brijlall D. (2013). Schema development for the chain rule: A South African Case

Study. South African Journal of Higher Education, 27(3), 645-661.

8. Jojo, Z.M.M., Maharaj, A. & Brijlall D. (2013). From Human Activity to Conceptual Understanding of the Chain

Rule. REDIMAT, 2(1), 77-99.

9. Maharaj, A. (2013). An APOS analysis of natural science students’ understanding of derivatives. South African

Journal of Education, 33(1), 146-164.

10. Maharaj, A. (2012). Some findings on the design and implementation of mathematics tutorials at a university.

South African Journal of Higher Education, 26(5), 1001–1015.

11. Brijlall, D., Maharaj, A.,. & Molebale, J. (2011). Understanding the teaching and learning of fractions: A South

African high school case study. US-China Education Review A, 4, p497-510.

12. Brijlall, D. & Maharaj, A. (2011). A Framework for the Development of Mathematical Thinking with Teacher

Trainees: The Case of Continuity of Functions. US-China Education Review B Education Theory, 1(5), 654-668.

13. Pillay, S. & Maharaj, A. (2011). Collaborative learning of mathematics by educationally disadvantaged

students at a university. Journal of Independent Teaching and Learning, Volume 6, pp.55-68.

14. Maharaj, A (2010). An APOS Analysis of Students’ Understanding of the Concept of a Limit of a Function.

Pythagoras, 71, July 2010, pp.41-52.

15. Brijlall,D.& Maharaj, A. (2009). Using an inductive approach for definition making: monotonicity and

boundedness of sequences. Pythagoras, 70. pp. 68 – 79.

16. Maharaj A. (2008). Some insights from research literature for teaching and learning mathematics. South

African Journal of Education. Volume 28, pp.401-414.

17. Maharaj A., Brijlall D. & Molebale J. (2007). Teachers’ views on practical work in the teaching of fractions: a

case study. South African Journal of Education. Volume 27(4), pp.597-612.

18. Maharaj A. (2007). Using a task analysis approach within a guided problem-solving model to design

mathematical learning activities. Pythagoras. Volume 66(Dec), pp.34-42.

19. Brijlall D., Maharaj A. & Jojo Z. M. M. (2006). The development of geometrical concepts through design

activities during a Technology education class. African Journal of Research in Mathematics, Science and

Technology Education. Volume 10(1), pp. 37-45.

20. Maharaj. A. (2003). Work in Progress: An Investigation into the Senior Certificate Mathematics Examination

Papers of South Africa and Some Teaching Implications. In D. Fisher & T. Marsh (Eds.), Proceedings of the

Third International Conference on Science, Mathematics and Technology Education (pp. 85-95). Perth: Curtin

University of Technology.

21. Maharaj A. (2001). Research and Some Teaching/Learning Implications on the Solving of Polynomial

Equations. Pythagoras; Number 56, Dec. 2001, pp.17-25.

Annexure A1 - List of Published Peer Reviewed Papers

1. Maharaj, A. (2012). Some findings on the design and implementation of mathematics tutorials at a

university. South African Journal of Higher Education, 26(5), 1001–1015.

http://reference.sabinet.co.za/webx/access/electronic_journals/high/high_v26_n5_a10.pdf

Abstract: This article reports on the design and effectiveness of four tutorial types in the context of first year

mathematics tutorials, at a South African university for the period 2003 to 2011. A model for the design of

mathematics tutorials was formulated. This model informed the design, implementation and refining of the

mathematics tutorials over the nine year period. It was found that mathematics students get greater benefit from

tutorials that are more organised and include a completion of homework unit requirement.

2. Maharaj A 2014. An APOS Analysis of Natural Science Students’ Understanding of Integration.

REDIMAT, 3(1), 54-73.

http://dx.doi.org/10.4471/redimat.2014.40

Abstract: This article reports on a study which used the APOS (action-process-object-schema) Theory framework and

a classification of errors to investigate university students’ understanding of the integration concept and its

applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The

relevant rules for finding antiderivatives, the link between derivatives and antiderivatives, interpreting a definite

integral as area under the relevant curve and their context-based applications were taught to undergraduate science

students. This paper reports on the analysis of two students’ responses to questions on integrals and their

applications. The findings of this study suggest that those students had difficulty in applying the rules for integrals

and their applications, and this was possibly the result of them not having appropriate mental structures at the

process, object and schema levels.

3. Maharaj A 2015. An outline of possible in-course diagnostics for elementary logic, limits and

continuity of a function. International Journal of Educational Sciences, 8(2), 281-291.

http://www.krepublishers.com/02-Journals/IJES/IJES-08-0-000-15-Web/IJES-08-2-000-15-Abst-PDF/IJES-

8-2-281-15-475-Maharaj-A/IJES-8-2-281-15-475-Maharaj-A-Tx%5B5%5D.pdf

Abstract: This paper focuses on in-course sample diagnostic questions relating to elementary logic, and the two

concepts of limits and continuity of a function. These are for students who choose to take a course on differential

calculus, in a South African context. However, the diagnostic questions could be useful worldwide. Learning

outcomes and in-course diagnostic questions for the technical knowledge and skills required for the indicated

sections were formulated. The questions were designed to check for the relevant learning outcomes that the

researcher detected for the indicated sections 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. Investigations into the validity of those assumptions, including their

attainment levels and student performance correlations to relevant examination questions will be the focus of

another paper.

Annexure A2 - Reflection of Practice Publications

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Annexure A4 - Lecture Schedule Math145 2011

MATH145W2: TUTS BASED ON PRESCRIBED TEXT FOR MATH145

All chapter references are to Calculus with Applications by Lial, Greenwell and Ritchey (9e).

[Leave out examples and exercises based on Business and Economics. Concentrate on examples

and exercises based on the Life and Physical Sciences]

HW unit 1: Due for tutorial, week beginning 1 Aug

7.1 Antiderivatives Problems (p438): odd numbers [1-43], 61, 63, 65, 67

7.2 Substitution Problems (p449): odd numbers [1-37], 44


7.3 Area and the Definite Integral Problems (p458): 1, 5, 11, odd numbers [15-21], 26

7.4 The Fundamental Theorem of Calculus Problems (p471): odd numbers [1-53], [57-65], 71


7.5 Area Between Two Curves Problems (p483): odd numbers [1-23], 39a, 42

7.6 Numerical Integration [only Simpson’s rule] Problems (p493): odd numbers [1-9]b&c, 11b

8.1 Integration by parts & Integration Tables Problems (p514): odd numbers [1-11]


8.1 Integration by parts & Integration Tables Problems (p514): odd numbers [13-31], 37, 41, 43

8.2 Volume and Average Value Problems (p517): odd numbers [1-29], 39, 43*


8.4 Improper integrals Problems (p536): odd numbers [1-33], 49, 51

9.1 Functions of several variables Problems (p554): odd numbers [1-15], 19, [21-25], 39, 41, 47

HW unit 6: Due for tutorial, week beginning 5 Sept

9.2 Partial Derivatives Problems (p566): odd numbers [3-41], 53, 55, 59, 65, 67

9.3 Maxima and Minima Problems (p577): odd numbers [1-29], 31, 39, 41


9.4 Lagrange Multipliers Problems (p588): odd numbers [1-9], 15, 35

10.1 Solutions of Elementary and Separable Differential Equations Problems (p629): odd

numbers [1-33], 43, 49, 51


10.2 Linear First-Order Differential Equations Problems (p639): odd numbers [1-21], 23*

10.4 Applications of Differential Equations Problems (p656): 7, 9, 17, 21*

HW unit 9: Due for tutorial, week beginning 3 Oct

12.3 Taylor Polynomials at 0 (p738): odd numbers [1-13], [21-27], 44

12.4 Infinite Series (p744): odd numbers [1-17], 27


12.5 Taylor Series (p754): odd numbers [1-13], 19, 25, 27

13.1 Definitions of the Trigonometric Functions (p787): odd numbers [1-19], [33-47], 7


13.2 Derivatives of Trigonometric Functions Problems (p799): odd numbers [1-21], 33, 35, 41

13.3 Integrals of Trigonometric Functions Problems (p809): odd numbers [1-35], 41, 43

HW unit 12: Due for tutorial, week beginning 24 Oct. See Revision questions Math145

Annexure A5 - Tutorials Math145

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Annexure A6 - Revision Questions Math145

Annexure A7 - Reflections on Supervision of Masters and PhD Students

Undergraduate teaching from 2003 to 2014

Year 1st semester 2nd semester

2003 MathsC - specialised first year

2 classes, about 300 students per class,

contact time per week 5.25 hours each.

Engineering Maths2(b) - specialised 2nd yr

About 326 students, contact time 6 hours per

week.

2004 MathsC - specialised first year

2 classes, about 300 students per class,

contact time per week 5.25 hours each.

Maths1S2 - specialised first year


week.

2005 Math134H1- specialised first year

About 320 students, contact time 6

hours per week.

Math145H2 - specialised first year


week.

2006 Math134W1-specialised first year

About 520 students (1 class), contact

time 6 hours per week.

Math145W2 - specialised first year


week.



time 6 hours per week.

Math145W2 - specialised first year

About 100 students (1 class), contact time 6

hours per week.



time 6 hours per week

Math140W2- specialised first year

About 360 students (2 classes), contact time 8

hours per week


About 530 students (2 classes),

contact time 8 hours per week


About 380 students (2 classes), contact time 8

hours per week





About 120 students (1 class),

contact time 8 hours per week.





About 150 students (1 class),

contact time 8 hours per week.




Sabbatical

2013 Sabbatical Math140W1 specialised first year


contact time 8.45 hours per week.



contact time 8.45 hours per week

Math140W1 specialised first year


contact time 8.45 hours per week.

2015 Math150W1 specialised first year


time 4.5 hours per week

*Academic Leader: Teaching and

Learning for School of Mathematics,

Statistics and Computer Science

N.B. Bold indicates modules I coordinated

Annexure B1 - Undergraduate Teaching

Maharaja32

Typewritten Text

/5

Annexure B2 - Lectures Using PC Tablet

Maharaja32

Typewritten Text

Snapshot 1: Lecture outline

Maharaja32

Typewritten Text

Snapshot 2: Part of a delivered lecture

Maharaja32

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Snapshot 3: Page 2 of the delivered lecture in Snapshot 2

Maharaja32

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Snapshot 4: Part of another delivered lecture

Example of a module website

Dr Maharaj’s stuff

Annexure B3 - Online Material

Annexure B4 - Tutorial Organisation and Monitoring

Maharaja32

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Organisation and monitoring of tutorials

Maharaja32

Typewritten Text

Snapshot 1: Available to tutors and students on module website

Maharaja32

Typewritten Text

Snapshot 2: Available to both students and tutors on module website

Maharaja32

Typewritten Text

Snapshot 3: Monitoring of tutorials, example of News Forum to students and tutors

Annexure B5 - Pass Rates for Modules

Maharaja32

Typewritten Text

Pass rates: some service and mainstream modules from 2010 to 2014

Annexure B6 - Student Feedback

Maharaja32

Typewritten Text

Student feedback: email communication and from UKZN's Quality Promotions and Assurance (QPA) Unit NB: online evaluations responses from 2012 to 2014 were too low according to QPA

Maharaja32

Typewritten Text

Snapshot 1: 2014 Math130W1 email feedback from a student in response to my email in Annexure B4: Snapshot 3

Maharaja32

Typewritten Text

Snapshot 2: Student comments for 2014 Math140W1 module received from UKZN's QPA Unit

Maharaja32

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Snapshot 3: UKZN's QPA Unit report on 2010 Math133W1 module for the students I lectured to

Maharaja32

Typewritten Text

Snapshot 4: From UKZN's QPA Unit report for 2010 Math133W1 module - student responses to lecturer questions on Dr A Maharaj

Annexure B6 - Student Feedback

Maharaja32

Typewritten Text

Snapshot 5: From UKZN's QPA Unit report for 2010 Math133W1 module - student responses on module website

Maharaja32

Typewritten Text

Snapshot 6: From UKZN's QPA Unit report for 2011 Math145W2 module - student responses to general questions

Maharaja32

Typewritten Text

Snapshot 7: From UKZN's QPA Unit report for 2011 Math145W2 module - lecturer evaluation questions

Annexure B7 - Email Commuication on Online Quizzes with Students

Maharaja32

Typewritten Text

Email communication on online quizzes with 2014 Math130W1 students

Maharaja32

Typewritten Text

Snapshot 1: email using News Forum to students encouraging them to take online quizzes

Maharaja32

Typewritten Text

Snapshot 2: student response to my email

Maharaja32

Typewritten Text

Snapshot 3: my response to the student's email

Maharaja32

Typewritten Text

Snapshot 4: email from a student after a written test indicating the online quizzes helped him

Maharaja32

Typewritten Text

Snapshot 5: my request to the student for further feedback.

To whom it may concern,

I was first introduced to Dr. A. Maharaj in my first year when he taught me pre-calculus

techniques and linear algebra. I remember his lectures with fondness as well as his mannerisms

and refined etiquette. In the first semester he taught pre-calculus, as in: limits and continuity, and

I also remember a few lectures on logarithms with a purpose, I believe, to prepare us, as much as

possible, for what was to come later on in the course and in our careers.

I have been lectured now by many individuals over the last few years and I would put Dr.

Maharaj up there with the very best I’ve had, for a few reasons. First, of course, is his style of

delivery. It was concise, bold. His notes (which I still have) were very well written (they were

scribed as he lectured) and made learning what was then, a very strange and new language, a lot

less stressful than it could have been. Second was his candor, not only in his lecturing, but in his

interactions with students. Whether disciplinary or motivational, this quality has never been

absent.

A fine example of this also happens to be one of my fondest memories of being in his class.

During breaks in-between ‘double lectures’ Dr. Maharaj would often come and sit by me to find

out how the course was going and how I was. He would also share some insights on life in

general and academia. Since academia was always my intention in life, I found this useful and

moving, and I am forever grateful for these interactions.

I have always been an individual with a passion and inkling for mathematics as a science but also

as an art form. I believe to my core that mathematics is a perfect art, as daring as the most secret

dreams of imagination, full of the clearest honesty, it fills me with a sense of eudemonia.

Mathematical genius and artistic genius must touch one another. To not mention that Dr.

Maharaj has played a role in, not just my mathematical education, but my enrichment in the

science, would be a sin. Over these last few years my passion for this art has turned into a

romance, and my hope is that it will be a lifelong romance.

I am forever thankful to Dr. Maharaj, for being one of the individuals whom has contributed to

my career and to my personal fulfillment.

Byron P. Brassel

Doctoral Student

School of Mathematics, Statistics and Computer Science

Astrophysics and Cosmology Research Unit

Annexure B8 - Letter from First-year Student

Maharaja32

Typewritten Text

Letter received from a former 1st year student, received via email

Justin record of meetings: Student number: 964121004

7 July 2011

Meeting at Edgewood campus. APOS paper on limits.

26 July 2011

Quotes for laptop. Ethical clearance documents. Application for grant.

30 September 2011

1. Signed supervision guideline of understanding.

2. Made available electronic copies of papers on Schemata, Framework.

3. Suggestions to write the beginning stages of proposal.

4. Advised on content of proposal: literature review and theoretical framework.

2 April 2012

1. Draft proposal. Discussion of write up.

2. Qualitative research methodology. See book by A de Vos (Ed), Research at Grass Roots.

3. Feedback on his theoretical framework and Literature review, which was given to us in January.

4. State sources where work is not your own.

5. Scaling up of section on methodology.

July 2012

1. Draft proposal

2. Read and feedback given

17 September 2012

1. Draft proposal

2. Work on literature review.

3. Consent forms

4. Questionnnaire

5. Work on initial genetic decomposition

6. Structure budget and timeframes.

25 September 2012 [2 hours]

1. Discussed proposal final draft. Good work has been done.

2. Suggestions given to improve title, and sub-questions for main research question.

3. Advice given on the write up of literature review.

29 April 2013 [90 minutes]

1. Discussion on draft chapter 1. Include sections for definition of terms, overview of chapters.

2. APA referencing style. Document emailed to Justin.

3. Generation of table of contents using Word.

4. Discussion of chapters to follow.

July to October 2013

Received details of pilot project, chapter 2 (Literature Review) and chapter 3 (Theoretical framework).

Application for funding. Feedback on some of these via email. Setup meeting to discuss draft chapters.

25 November 2013 (4hrs 30 minutes)

1. We need to meet to discuss each chapter on time, to avoid same type of shortcomings in subsequent

chapters.

2. Work on papers for publishing. Two possibilities: Genetic decomposition for extrema of functions, and pilot

study based on refinement of research instrument.

3. Formatting. Setup suitable margins for binding purposes – especially the left margin. See document

forwarded to you by me from Bongi – follow requirements.

4. For each chapter use word to generate titles and different heading levels. Then use word to generate the

table of contents.

5. Chapter 2: Needs serious editing. Use the term pupil and qualify it in the terminology section. Sentences too

long. KISS – keep it short and simple. Where possible give context with suitable illustrations. Writing could

be more focused.

6. Use equation editor function in word for typing involving mathematics. Eg. ℎ ≠ 0.

7. Chapter 3. Editing. Rearrange subsections – see draft. Separate subsection for a research framework for

APOS based studies. Provide illustrations for APOS mental constructions. Diagram for ACE teaching cycle –

how it ties up with social cultural perspective.

8. Next meeting to be decided by Justin.

14 February 2014 [1 hour]

1. Sort out your registration.

2. Funding application form, signed.

3. Chapter 2. You indicated that the chapter that was emailed was the incorrect one. Also the section on

curve sketching within this chapter still needs to be included. Supervisors should wait for finalized

chapter 2.

6 May 2014 [1 hour]

Laptop problems with software and discussion on funding

14 May 2014 [2.5 hours]

1. For each chapter use from MS word: title, heading 1, heading 2, …..

2. Chapter 3: too long – reduce length. Leave out section 3.7

3. See tracked comments.

20 June 2014 [received revised Chapter 3]

27 June to 2 July 2014 [reading of Chapter 3; 56 pages]

1. See my tracked comments.

2. Very good to excellent work Justin! I have gone through this chapter in detail and will not do so again.

The methodology section should not be more than 10 pages. Much of what should be there is included

in this chapter. In the next chapter you need to give the links. We could discuss this when we meet. The

whole thesis should be around 200 pages.

3. Go through my tracked comments and sort out things before we meet. This will save us time.

10 February 2015 [meeting to note progress and way forward; 45 minutes]

1. Chapter 4: after introduction indicate the IGD and its implications for the design of the research instruments.

2. Chapter 5: Methods and Methodology

3. Submit chapters 1 to 5 including table of contents and lists of references – target end of February.

4. Chapter 6: Analysis and discussion of data – mid March to April 2015.

5. Chapter 7: Recommendations and conclusions – writing target end of June 2015

6. Editing from end of June 2015

7. Target to submit by end of November 2015

8. July onwards writing of papers: possibilities 1 on chapter 4 (unpacking of Research paradigm - How to refine

a research instrument using APOS); 2 on chapter 6

9. Funding check NRF

24 April 2015

1. Received chapters 4 and 5 on 22 April. The work in both the chapters was of a very good quality.

2. Check the left hand margins. This should be broader for binding of hardcopies.

3. Stationary Point could be a turning point or point of inflection. I think you focused on TPs so use the term

turning point.

4. Tracked comments provided for both chapters.

5. Keep up the good work. We look forward to receiving the remaining two chapters.

Record of advice: MHLANGA T [email protected]

Topic: Integration of mobile technology (cellphones) in the teaching and learning of mathematics at the Further

Education and Training Phase

10 March 2015

1. Received email from student.

2. Student asked to frame main research question and the sub-questions that would help to answer the main

research question.

3. Email from Online Learning Consortium forwarded to student. Student advised that go to the website of that

Consortium – to find useful information/ideas.

8 April 2015

1. Received the main research questions and related sub-questions. [Please see my tracked feedback].

2. You should now use the sub-questions to identify suitable research instruments that would you gather

information to answer the each sub-question. A suitable research instrument could provide

information/data for more than one sub-question. My advice is to formulate a table with the following

headings:

Research sub-question Method of data collection Limitations

22 April 2015

1. Received table. Tracked feedback. This is should be considered as a draft, so you may need to improve on

things as the study unfolds.

2. For the limitations you indicated think of how these could be addressed or minimised.

3. Think of the chapter headings and the sub-sections for each chapter. These don’t have to be finalised now,

they will take shape as each chapter is written.

4. Possible chapters: Introduction and overview; Literature review; Conceptual/theoretical framework;

Methodology; Analysis of data and discussion of findings; Conclusions and recommendations.

5. Begin to write Chapter 1 – some sections could be written for example the background of the study and

motivation; main research question and sub-questions. Think of the sub-sections carefully. You will only be

able to complete this chapter once the other chapters are written.

6. Begin work on the Literature review. This could include what other studies found about the use of mobile

technology and smartphones in the teaching and learning situation – especially in the high school

mathematics context.

29 May 2015

1. Tracked feedback provided for chapter 1.

2. Please follow APA style of referencing and citing. This needs attention.

3. In Word, under Home there is provision for Title, Heading 1, Heading 2 and so on. Rather use this for

uniformity within each chapter. The use of the heading 1, heading 2 and so on does not allow numbering of

subsections. If you want to number the subsections then you need to think about the use of different font

sizes and styles for main headings and sub-headings.

4. In the body of the text ‘fully justify’ the text.

5. You need to proof read properly before submitting. Also note that once I point out what needs attention

then this advice needs to be followed for future submissions also.

Annexure C1 - Supervision

Maharaja32

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Student supervision records

Maharaja32

Typewritten Text

Example 1

Maharaja32

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Example 2

Annexure C2 - PhD Supervision Dr. Jojo

MATH140 HOMEWORK UNITS: LECTURER DR A MAHARAJ

HW1: Due for tutorial week beginning 28 July

Linear equations and matrices [from LINEAR ALGEBRA NOTES]

Tutorial 1 on page 10: Numbers 1(a), (b), (c), (d), (e), (f).

HW2: Due for tutorial week beginning 4 August

Linear equations and matrices, operations with matrices [from LINEAR ALGEBRA NOTES]

Tutorial 1 on page 10: Numbers 2; 3 (a), (b), (c), (d), (e), (f); 4(a), (b); 5(a), (b); 6.


Multiplication of matrices, inverse and determinant of a square matrix (from LINEAR ALGEBRA

NOTES)

Tutorial 2 on page 21: Numbers 1; 2; 3; 4; 5; 6(a), (b), (c); 7; 8.

Tutorial 3 on page 32: Numbers 1(a) and (b), 2


Tutorial 3 on page 32: Numbers 1(c) and (d), 3, 4, 5, 6, 7


Inverses from cofactors and determinants (from LINEAR ALGEBRA NOTES)

Tutorial 4 on page 40: Numbers 1, 2, 3, 4, 5, 6, 7, 8 (a), (b), (c), (d).

Polar coordinates [10.3 exercises, page 678]. 1, 3, 5

HW6: Due for tutorial week beginning 1 September

Polar coordinates [10.3 exercises, page 678]. 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33,

37, 41, 45, 47, 49


3D-Coordinates [12.1 exercises, page 814]. 1, 3, 5, 6, 7, 10, 11, 13, 15, 17, 21, 23, 25, 27, 29, 31, 33,

35, 37, 39, 41


Vectors [12.2 exercises, page 815]. 1, 2, 3, 4, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 29, 35, 37, 39, 41,

45,51

Dot product [12.3 exercises, page 824]. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35,

37, 41, 45, 51, 55, 56, 57, 58, 60.


The cross product [12.4 exercises, page 838]

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 45, 49

HW10: Due for tutorial week beginning 6 October Equations of lines and planes [12.5 exercises, page 848]

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 27, 29, 31 33, 35, 37, 39, 41, 45, 47, 49, 51, 61, 65, 67, 73

HW11: Due for tutorial week beginning 13 October

Complex numbers page A61. Numbers 1, 2, 3, 4, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25, 29, 31, 33, 35.

HW12: Due for tutorial week beginning 20 October

Complex numbers page A61. Numbers 37, 39, 41, 43, 45, 47.

Improper Integrals page 551. Odd numbers (1 to 23), 29, 31, 35, 49, 51, 53, 57, 61, 77.

Annexure D1 - 2014 Math140 Tutorials

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Annexure D2 - Test 2 2014 with Solutions

of 10 MATH133W1 TEST 2 [7 April 2011]

______________________________________________________________________________

SCHOOL OF MATHEMATICAL SCIENCES: WESTVILLE CAMPUS

MATH133W1 TEST 2 [7 April 2010] Duration: 1 hour Marks: �� × � = ��

Instructions:

[1] Answer all 14 questions. This paper consists of 10 pages.

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[5] Note the instruction on how to fill in the MCQ card. [6] Each question is worth 3 marks.

[7] The MCQ card must be handed to the invigilator before you leave the test venue.

QUESTIONS

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Page 2 of 10 MATH133W1 TEST 2 [7 April 2011]

______________________________________________________________________________

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Annexure D3 - MCQ Test with Solutions

2014 INVIGILATION FOR TESTS: MATH130W1

10 March 7 April 2014 2 May 2014

1. Diarize the above dates. Time from 17:00 to 19:20 for each test.

2. The following table gives the distribution of invigilators per test venues. A tutor will take care of his/her

tut group for the administering of the test

3. You must be inside the test venue promptly at 17:05. From 17:00 to 17:15 the test scripts should be

distributed [see 5. below for venues T block].

4. No students are allowed in the test venue before 17:15. Tests should commence promptly at 17:30 and

terminate at 19:00.

5. In the raked venues T1, T4, T6, L17 alternate seats and rows apply for seating under exam conditions.

Close the back doors. Only allow students to enter through one of the front entrances.

6. Under exam conditions students should have their pens and rulers. No borrowing is allowed. Bags are

also not allowed. [Read out this instruction to students.] STUDENT CELLPHONES MUST BE

SWITCHED OFF.

7. Address all queries to the staff member overseeing the conducting of the test for the different venues.

8. Check student registration cards, and that the student number appears correctly on the test script.

9. The number of scripts collected should tally with the number of students who wrote in the venue. Make

sure every student hands in their test script.

10. At the end of the test the test scripts from the venue(s) T1 [10 March, 7 April] or from T4, T6 and L17 [2

May] must be brought to the Main Hall. Markers should collect their scripts and marking guide from the

Main Hall. The meeting with markers to discuss the making guide will be in the Main Hall.

VENUE STAFF INVIGILATORS for Tut Groups

Main Hall

[M H

Joosab]

[350]

A. Maharaj

B1 to B13, C5

T1 [150]

[10 March,

7 April]

*T4 & T6

[2 May]

G. Govinder

C1, C2, C3, C4, C6

Note that extreme left back section in T1 should be

reserved for the Math195W1 students. On 2 May

Math195W1 students will write in L17. Their lecturer(s)

will invigilate and mark the scripts. [The lecturer(s)

should come to the Main Hall for the discussion of the

marking guide.]

*T4, T6 & L17 will be used only on 2 May.

Report on MATH141P2 main examination

question paper

The following are my suggestions/comments after going through the paper: 1. Overall the paper has a good spread of questions which have a satisfactory grading.

2. I increased the marks for a few questions (see paper).

3. Please indicate how the marks will be allocated. This will be important when marking the scripts.

4. Question 1(b): Include in the last part of the question what I0 is.

5. Question 2(c)(ii): In the last line remove the brackets.

6. Question 3(b): include the restriction on x. The assumption in the working is that x is not equal to -1.

7. Question 3(c): change the word number to amount, for consistency. [Or change amount to number]. Increase

marks to 6.

8. Question 4(a): use the word give instead of determine. My understanding is that determine requires reasons.

The solutions indicate no reasons are required, merely the type of curve.

9. Question 4(c): 2nd sentence 2nd line remove the word ‘If’ and the word ‘and’. 3rd line remove comma and replace

with the word ‘with’. Increase marks to 6.

10. Question 5(b): 3rd line include (where a > 0)

11. Question 6(b): check solution

12. Question 6(c): the working indicates that the roots are required in polar form not x + iy as indicated in the

question.

Anesh 15/10/2014

Please read the following in conjunction with the pdf on which my written

comments/suggestions/queries appear.

Chapter 1: overall very satisfactory to good.

There are some technical issues

Page 1: CAPS document, quote more than 40 words should be separated and double indented, et al for the

first – all authors or the first six should be given.

Page 3: When introducing a concept for the first time the concept should be in italics, for example

proportional reasoning.

Proportion and proportional reasoning. Is there a link? See page 40. My suggestion is to change the

description of proportional reasoning on page 3 to that given under 3.2.1 on page 48.

When reporting the writing should be in the past tense. Eg. Page 11 ‘was’ instead of ‘is’.

Participants: Where they from 3 classes or 1 class?

One instance found of a sentence that requires rephrasing. See page 14, last sentence of the first paragraph.

Chapter 2: overall very satisfactory to good

What is meant by the term algebra? How does is differ from arithmetic? Check if explained.

Pages 29 and 30. Check instrumental and relational understanding. Both can’t refer to ‘what and how’.

Within a chapter there are headings. Each heading is followed by sub-headings. It is advisable that under

each heading a brief write-up of what is focused on is given. Possibly as done for 2.5 on page 32.

: Indicate what is meant by Maths anxiety.

Page 35: second sentence. Check formulation.

Page 39: 2.5.10 Teachers’ mathematical knowledge

Page 43: Check strategic knowledge, in particular that it enables learners to memorise content. Page 45:

figure 3 should read Figure 2.4

Chapter 3: Writing at times is disjointed and lacks flow. There are parts that are well written. Overall,

average.

My suggestion is to change the description of proportional reasoning on page 3 to that given under 3.2.1 on

page 48. Otherwise the reader gets the impression that proportional reasoning as described on page 3 and the

concept proportion are not linked or related.

Page 49: last paragraph, first sentence. Give an example to illustrate what is meant by this. Same for last

sentence.

Page 55: Paragraph before 3.2.6, in the 5th/ 6th line should read ‘the larger the numerator …….

Page 56: 3.2.7, 6th line. Check ‘hundreds squares’

Be consistent with decimal notation, for example 0.3 or 0,3.

Page 58: under 3.3, explain what is meant by ‘composite unit’.

Page 59. Last paragraph. Where do those sequences come from?

Page 60. Under 3.4, 2nd line. Replace the word ‘alternative’ with the word ‘incorrect’. [one could have an

alternative conception and this need not be a misconception.]

Towards the end of 3.4 the writing lacks flow; disjointed.

A lot of repetition of ideas in different sections. It would be better to illustrate ideas with different examples

of the type that learners should be exposed to, to develop proportional reasoning.

Chapter 4: overall very satisfactory. For some sections if repetitions were left out the writing could be

more compact.

Page 79: last sentence. Rephrase as: Those 18 learners took part in the task-based interviews.

Addendum D

• In some cases a point is used to denote the decimal sign and in others a comma. Lacks consistency.

Was this deliberate? If so this needs to be indicated and a motivation given as to why this was done.

• 5.2 There is no box below.

• 7. The question mark should not be on its own on the next line.

• 7. Observation, options c and d are the same.

• 8. b not typed properly

• On page 164, last line. Check typing.

Page 80. Last paragraph, first sentence. Check formulation.

Chapter 5: ranging from satisfactory to at times poor. See my comments/suggestions/remarks below and

on the pdf.

Page 88: under introduction, check number of research questions. Rather say “The first four research

questions….”

Page 98. First paragraph after Figure 5.8, the evidence does not support scaling down. So remove reference

to this. Last sentence, check English, replace yielded by indicated.

Next line. Correct if to of. Check next sentence.

Page 99. Figure 5.9 does not support the preceding write-up. The only mistake in Learner B’s explanation is

that the scaling factor is given as 2,5cm instead of 2,5. Suggestion replace with a response that supports the

write-up. Or change accordingly.

Page 109: check written comments on pdf.

Page 111. Bottom of page typing.

Page 112. Last line. Opinion of the researcher. Where is the evidence to support this?

Page 114. Last sentence. What was the misconception? Was the response probed to determine the

misconception?

Annexure D4 - Assessment planning and advice

Maharaja32

Typewritten Text

Assessment planning and advice

Maharaja32

Typewritten Text

Example 1: Planning for tests

Maharaja32

Typewritten Text

Example 2: Advice given by me for an MCQ paper in 2011

Maharaja32

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Example 3: Advice given by me for a written paper in 2014

Maharaja32

Typewritten Text

Example 4: External examiner report by me for a dissertation

Annexure D5 - Peer Testimonials

Maharaja32

Typewritten Text

From peers received via email in 2011

Annexure D6 - Peer Evaluation Dr A Maharaj from Heather Tarr

“Our Mission is to be an outstanding teaching and research university, educating for life and addressing the challenges facing our society.”

Deputy Head

Department of Mathematics and Applied Mathematics David Erwin University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa Tel: +27 (0) 21 650 3208 Fax: +27 (0) 21 650 2334 E-mail: [email protected]

27 May 2015 Promotion to Senior Lecturer: Dr Anesh Maharaj Anesh and I worked closely together during 2008 and 2009 teaching the UKZN School of Mathematical Sciences’ standard first year calculus and linear algebra courses, MATH130 and MATH140. During that time, as the Course Coordinator for both those courses, I acquired a great deal of respect for Anesh 's teaching. He is a competent, highly committed, and very professional teacher. He spent a great deal of time preparing for lectures. He posted PDF versions of his lectures on the course website, something which was greatly appreciated by the students. At that time, MATH130/140 was taught in two timetable-blocks and consequently there were two 2.5 - 3 hour tutorials each week. School policy was that each lecturer attend one of these. When I approached Anesh and asked him whether, to maximize the value of the tutorials for the students, he would consider attending both, he was immediately enthusiastic about the idea and did it ever since. This kind of enthusiasm is extremely unusual and clearly demonstrates a commitment to his students far in excess of what the School expected of him. At tutorials, he was hard-working and dedicated to helping the students. Many lecturers at tutorials simply wait for students to ask questions of them , but Anesh was an exception. He moved through the tutorial venues, sitting down next to students and asking them about the problems they were working on. Anesh is very affable and easy to work with. He has high standards and expects a lot from his students. He is an extremely committed teacher who is always willing to put in extra effort to make the course better and increase the understanding of his students. I cannot comment on his research (I don’t work in his field), but certainly his teaching is beyond the level that we would expect from someone at the academic rank of Senior Lecturer. Sincerely,

David Erwin

Annexure D7 - Peer Evaluation Anesh Maharaj from David Erwin

List of peer reviewed conference proceedings (unrelated to the supervision of my Phd)

1) Maharaj A. (2002). A Model/method for Solving Polynomial Equations. In M. Moodley, S.

Moopanar & M. de Villiers (Eds), Proceedings of the 8th National Congress of the

Association for Mathematics Education of South Africa, Senior Secondary and FET Phases

(pp.120-134). Durban: Association for Mathematics Education of South Africa.

2) Maharaj A. (2003). Work in Progress: Investigating the mathematics senior certificate

examinations in South Africa: Implications for teaching. In S. Jaffer & L. Burgess (Eds.),

Proceedings of the Ninth National Congress of the Association for Mathematics Education

of South Africa (pp.205-215). Cape Town: Association for Mathematics Education of South

Africa.

3) Jojo Z. M. M, Brijlall D. & Maharaj A. (2005). Mathematical Concepts Embedded in

Technology Education. Proceedings of the 1st African Regional Congress of the

International Commission on Mathematics Instruction (ICME). On CD cut by University of

Witwatersrand.

4) Brijall, D & Maharaj, A. (2008). Applying APOS theory as a theoretical framework for

collaborative learning. This paper was presented in TSG 17 at ICME 11 in Monterrey,

Mexico, 6 to 13 July 2008. The article; 17 pages; appears on the website of ICME-11 under

the link for TSG 17.

5) Brijall, D & Maharaj, A. (2009). An APOS analysis of students’ constructions of the concept

of continuity of a single-valued function. In D. Wessels (Ed.), The Seventh Southern Right

Delta Conference on the Teaching and Learning of Undergraduate Mathematics and

Statistics, Proceedings of the Gordon’s Bay Delta ’09 (p.36-49). Stellenbosch, South Africa:

International Delta Steering Committee.

6) Brijall, D & Maharaj, A. (2010). An APOS analysis of students’ constructions of the

Concepts of monotonicity and boundedness of Sequences. In V. Mudaly (Ed.), Proceedings

of the Eight Annual Meeting the Southern Africa Association for Research in Mathematics,

Science and Technology Education (p.51-62). Durban, South Africa: SAARMSTE

7) Molebale.J., Brijlall.D.& Maharaj. A. (2010). Exploring the learning of fractions at grade

seven. Proceedings of the 18th annual meeting of the Southern African Association for Research

in Mathematics, Science and Technology Education (Vol 2, pp.215 – 220). University of

KwaZulu- Natal, South Africa.

8) Molebale.J., Brijlall.D. & Maharaj. A. (2010). Exploring the teaching of fractions at grade

seven. Proceedings of the 18th annual meeting of the Southern African Association for

Research in Mathematics, Science and Technology Education (Vol 2, pp.221 – 236).

University of KwaZulu- Natal, South Africa.

9) Jojo.N., Brijlall.D. & Maharaj. A. (2010). A genetic decomposition of the chain rule.

Proceedings of the 18th annual meeting of the Southern African Association for Research in

Mathematics, Science and Technology Education (Vol 3, pp.77 – 81). University of

KwaZulu- Natal, South Africa.

List of peer reviewed conference proceedings (related to my Phd)

1. Maharaj. A. (2003). Work in Progress: An Investigation into the Senior Certificate

Mathematics Examination Papers of South Africa and Some Teaching Implications. In D.

Fisher & T. Marsh (Eds.), Proceedings of the Third International Conference on Science,

Mathematics and Technology Education (pp. 85-95). Perth: Curtin University of

Technology.

2. Maharaj A. (2003). Work in Progress: Investigating the mathematics senior certificate

examinations in South Africa: Implications for teaching. In S. Jaffer & L. Burgess (Eds.),

Proceedings of the Ninth National Congress of the Association for Mathematics Education

of South Africa (pp.205-215). Cape Town: Association for Mathematics Education of South

Africa.

While the first paper was directed at researchers, the latter was directed at school mathematics

teachers.

Annexure D8 - List of Peer Reviewed Conference Proceedings

List of presentations related to projects from 2010 onwards

1) Maharaj.A. & Brijlall.D. (2010). Application of Dubinsky's theoretical framework. Presentation at the School of Mathematical

Sciences – University of KwaZulu-Natal.

2) Maths e-learning and assessment: A South African Context. Presentation to the HP Multiversity Consortium Meeting in Beijing,

China [13 April 2012]

3) Research and Opportunities: HP Multiversity projects. One of the webinar presenters to a worldwide audience of about 600

participants. [May 2012]

4) Some useful Mathematics websites. Presentation to teachers at the AMESA Regional Conference at Edgewood Campus of UKZN

[July 2012]

5) Maharaj, A. (2012). Maths e-learning and Assessment: A South African Context. Presentation to teachers, lecturers and

educational leaders in South Africa at a Maths, Science and Technology Education Conference in Randburg, South Africa.

Published on CD. [27 August 2012]

6) Maths e-learning: Basic Algebra. Presentation to teachers from West Bengal at the Homi Bhabha Centre for Science Education,

Mumbai, India. [4 October 2012]

7) Educational Challenges in South Africa. Presentation to teachers from West Bengal at the Homi Bhabha Centre for Science

Education, Mumbai, India. [5 October 2012]

8) Research framework for APOS Theory. Presentation to faculty and students at Homi Bhabha Centre for Science Education,

Mumbai, India. [18 October 2012]

9) Maths e-learning and Assessment. Presentation to students and staff at Dr Ambedkar University, Delhi, India. [21 November

2012].

10) Progress report on project at UKZN. Maths e-learning and assessment: A South African Context. Presentation to the HP

Multiversity Consortium Meeting in Sao Paulo, Brazil. [17 April 2013]

11) Pre-course diagnostics and remediation for mathematics: Content and possible strategies. Presentation to teachers and selected

staff at AGASTYA International Foundation Campus, Andra Pradesh, India. [February 2013]

12) Research framework for APOS Theory. Presentation to faculty at AGASTYA International Foundation Campus, Andra Pradesh,

India. [February 2013]

13) WORK HABITS AND EXPECTED LEARNING OUTCOMES: STUDENT PRESENTATION. At Amrita University Kollam, Kerala, India. [7

March 2013]

14) RESEARCH FRAMEWORK FOR APOS THEORY. Address to mathematics department lecturing staff at Amrita University Kollam,

Kerala, India. [8 March 2013]

15) Maths e-learning: Basic Algebra. Presentation to mathematics and science educators in Rautekela, Orissa, India. [May 2013]

16) Maths e-learning and Assessment. Presentation at South African Mathematical Society Conference at UKZN, Pmburg Campus.

[30 October 2013]

17) Maharaj, A. (2013). Some reflections on supervision of Masters and Phd studies in Mathematics Education. To students and

prospective supervisors at UKZN, Howard College Campus. [1 November 2013]

18) Maths e-learning, assessment and online diagnostics. Presentation to faculty at Durban University of Technology. Request from

Head of Department of Mathematics at DUT. [11 November 2013]

19) Mathematics E-learning. Presentation to faculty at UNIZUL one of our partners, to indicate what is possible with regard to

student support in the content of the NRF funded collaborative project that I am heading at UKZN. [17 April 2014]

20) UKZN-ESKOM Mathematics Project 2014 report back. At ESKOM Learning Academy, Midrand. [29 May 2014]

21) Maharaj A & Tarr H 2014. INVESTIGATING STUDENTS’ UNDERSTANDING OF MATHEMATICAL CONCEPTS IN CALCULUS USING

APOS THEORY AND e-LEARNING. 8th ANNUAL UKZN TEACHING & LEARNING HIGHER EDUCATION CONFERENCE

22) MATHEMATICS E-LEARNING AND DIAGNOSTICS. Presentation to faculty and post graduate students at Homi Bhabha Centre for

Science Education, Mumbai, India. [18 December 2014]

23) USING E-LEARNING FOR MATHEMATICS TEACHING. Presentation at conference (Re) Making the South African University:

Curriculum development and the problem of place, at Rhodes University. [18 April 2015]

Annexure D9 - List of Presentations

Research projects, details, grants and partnerships from 2007 onwards 1. Title of Project: Investigations into the teaching and learning of advanced mathematical

concepts/constructs/topics using APOS theory as a theoretical framework. This is a continuing general project in which (a) Prof D. Brijlall is a co-researcher, (b) we encourage prospective Phd students to work on particular mathematical topics at first year university level, (c) Ed Dubinsky; the founder of APOS theory, a USA based mathematician who also does research in mathematics education; is advising us on the university mathematics topics/concepts/constructs that need to be researched, and (d) we prepare for presentation at conferences, and publication in accredited journals at least one paper a year. One Phd student; Zingiswa M.M.J (Student Number 201506651) – was awarded her Phd (in 2012) on engineering students’ conceptual understanding of the chain rule when differentiating and integrating trigonometric functions. With regard to the general project, the following concepts/constructs were identified for further investigations: [a] limits and continuity, [b] infinite real sequences and series, [c] curve sketching and interpretation, [d] derivatives and applications, [e] the concept of infinity, and [f] the integration concept. Some lecturers have found that students experience difficulties with these concepts/constructs. For each investigation teaching and learning activities are/were designed based on the following four concepts that are used in APOS [action-process-object-schema] theory of conceptual understanding. I prepared two articles for publication on natural science students understanding of the topics in [a] and [d]. Together with Prof Brijlall, I am presently designing the investigation into students’ understanding of the concept of infinity. We have three Phd studies on the concepts indicated in [a], [c] and [f]. I am the principal supervisor for the Phd studies on concepts [a] and [c], and the only supervisor for the concept indicated in [f] above.

2. Title of Project: UKZN- ESKOM Mathematics Project. Eskom Tertiary Education Support Programme (TESP) has made available funding for this project from 2011 onwards; R600 000. I am the grant holder. The project focuses on first year students’ preparedness for university mathematics, and the pass and failure rates for some 1st level university mathematics modules at UKZN Durban and Howard College Campuses. The investigations look at reasons for this from the perspective of lecturers and students, and the effectiveness of the Maths Booster Programme that is used to prepare students for the demands of university mathematics. What could be done to improve the situation and through-put of students, is also reported on. This implies that the project also focuses on improving the quality of teaching and learning of mathematics at grades 11 and 12. I am working with Deonarain Brijlall, Ojen Narain, Andree Henning and Moses Mogambery on this project. Bursaries were provided from 2013 to 2015 to cover the costs for interested mathematics teachers to study part-time Math130 (Introduction to Calculus) and then Math140 (Linear Algebra and Calculus. Of the 15 students registered for Math130 in 2013, 12 of them passed the module. In 2015 bursaries were provided to 16 students who passed Math130 and wanted to enroll for Math140.

3. Title of Project: Maths for the Natural Sciences. As an associate member of the Multiversity Consortium of the 2010 HP Catalyst Initiative I looked at how the use of Moodle could be exploited to improve learning and instruction in STEM+ (Science, Technology, Engineering, Mathematics). I setup a website for Math133W1 at learning@ukzn. The theme of ‘shared purpose’ for the Multiversity Consortium is to investigate and demonstrate new and best practices in online education for STEM+ students and the professional development of instructional faculty. The long-term goal is to provide students with a broader selection of learning opportunities by creating a network of online courses and projects. Grant award opportunities were available for associate members. I motivated for a grant award during April 2011.

4. Title of Project: Mathematics e-learning and Assessment: A South African Content. In August 2011 I received a grant from the International Society for Technology Education for this project. This is one of the focus areas of the UKZN Maths Education Research Group, which I head. I coordinated the developed of online material for the pre-calculus phase which we called Basic Knowledge and Skills for Mathematics. Other team members who worked on the development of material were Dr S Moopanar, Andree Henning, Dr Narain and Dr P Winter. My plan was to use the ideas gained in the above project to develop other ideas to exploit the use of Moodle for other mathematics modules. In particular we focused on how to use e-learning to improve our school’s Maths Booster Programme, and the use of online assessment for modules that have large student numbers.

5. Science Ethics. During the second semester of 2011 coordinated the piloting of modules (to honors’ students in our school) on Science Ethics created and developed by West Chester University, in the USA. These were online modules based on virtual simulation.

6. Title of Project: Online diagnostics for undergraduate mathematics. The NRF made available for the period 2014 to 2016 funds amounting to R 600 000 for this project, which I head. The work involves researching and providing pre-calculus and undergraduate mathematics’ content diagnostics in online formats for the sections covered in our modules for Math130 and Math140. My plan is to pilot and improve in phases the online diagnostics at UKZN. In 2014 the focus was on the Pre-calculus diagnostics and diagnostics for Math130 content. 2015 will focus on the piloting of online diagnostics for Math140 content. Once the rollout for a phase is done at UKZN then with the collaborating partners from DUT, UNIZUL and UNISA the rollout to those institutions will be discussed. Research is planned for the different phases of the project and the overall impact of the project. I identified 6 possible mini-projects for honors students. At the time of writing 2 students passes their honors’ projects in 2014, 1 student is completing the paper work for an honors’ project in 2015, and it seems that a further 2 new Phd/masters studies will result from this project.

Annexure D10 - Research Projects Grants Collaborations

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Annexure D11 - John Bourne Anesh Maharaj HP Catalyst Plant

Reference: ERSA13101856509Grant No: 9039528 February 2014

Direct telephone

Direct fax

e-mail

: (012) 481-4230

: 086 562 9590

: [email protected]

NRF GRANT for 2014 : EDUCATION RESEARCH IN SOUTH AFRICA (ERGR)

I take pleasure in informing you that your research proposal for funding has been accepted for support.

Short title: Online diagnostics for undergraduate mathematics

Duration of funding: 3

The grant decision below is the outcome of the NRF review process.

Contact person : Mr Lebusa Monyooe

Dr A MaharajDepartment of Mathematics, Statistics and Computer ScienceUniversity of [email protected]

Dear Dr Maharaj

Category 2016 Award2015 Award2014 Award

Student Support

Masters/Doctoral Summary 60,000.0060,000.00 60,000.00

Research Operating Costs

Running Expenses 151,000.00111,000.00 118,500.00

Research Equipment 0.0050,000.00 0.00

Total 211,000.00178,500.00221,000.00

The following categories of funding were available in the application:

· Running Expenses (Materials and Supplies)

· Research/Technical/Ad Hoc Assistants

· Local Conferences Attendance (Travel and Subsistence)

· Local Travel (Travel and Subsistence)

· International Conferences (Travel and Subsistence)

· International Visits (Travel and Subsistence)

· Research Equipment

· Sabbatical

Please be aware that not all the items in the original application have been awarded due to budget constraints. The first 6

bullet items were totalled as running expenses.

Please refer to the above budget table and note that the budget items that were awarded under the main heading RESEARCH

RELATED OPERATING COSTS, are research funds and must be used for the approved NRF project mentioned above and in

accordance with the attached Acceptance of Conditions document.

All expenses incurred during the tenure of the above-mentioned project, may be claimed according to the allowable budget

guidelines as contained in the Guide for this Call and the auditable budget items according to your Institution�s financial

guidelines.

RELEASE OF FUNDS

· Funds for RESEARCH RELATED OPERATING COSTS will be released upon receipt of a signed hard copy of the

Acceptance of Grant Conditions.

· Funds which have been awarded within the student categories will be released upon receipt of the relevant nomination

forms, which is available on the NRF online system: https://nrfsubmission.nrf.ac.za - (Quick Links- Grantholder Tools

section). Please complete a nomination form for each student and submit online by 31 March with proof of

registration.

· Funding in consecutive years, provided that you have been awarded funding for multiple years (refer to table of the

approved award), will be released on receipt of your Annual Progress Report by 31 March each year available at

https://nrfsubmission.nrf.ac.za - (Quick Links- Grantholder Tools section), from December of the previous year.

GRANT STATEMENTS

Grant-holders will be able to access grant statements on the NRF Online system on a continuous basis. These statements

will provide a complete status of the grant in terms of amounts released, claimed (expensed) and paid. Statements can be

accessed at https://nrfsubmission.nrf.ac.za - (Quick Links- Grantholder Tools section). An updated statement will be

generated twice a month after payments has been made to institutions.

COPIES TO CO-INVESTIGATORS

Please ensure that all co-investigators listed in your research proposal receive a copy of this letter and of subsequent

correspondence relating to the grant.

In making this award, the NRF anticipates that you, as a grant holder, will actively participate in the peer and panel review

process to strengthen and expand quality research in South Africa.

We wish you well with your research.

Yours sincerely,

Electronic signature

Mr L Monyooe

Grant Director: Strategic Knowledge Fields

Copies to: University of KwaZulu-Natal

List of Enclosures

1) Grant conditions

2) Bursary Conditions

Annexure D12 - Grant Award Letters

Maharaja32

Typewritten Text

Grant award letters from ESKOM (for 2013) and NRF (for 2014 to 2016)

Phd supervision

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Snapshot 1: Impact of research

Snapshot 2: Evidence of international impact following from downloads - Research Gate

Snapshot 3: External examiner for dissertation which was accepted; related to Annexure D4: Example 4

Annexure D13 - PhD Supervision and Impact of Research

Annexure D14 - Letters Research Office and DVC

Snapshot 1: Diagnostics for Pre-calculus – large scale rollout 2014

Snapshot 2: Diagnostic quizzes on Math130 content – pilot phase 2014

Snapshot 3: 2015 student attempts for pre-calculus quizzes 1st week of April 2015

Snapshot 4: Student results on the quiz on limits – content for Math130

Snapshot 5: Immediate feedback to

student

Annexure D15 - Online Support

School of Mathematics, Statistics and Computer Science Postal Address: Private Bag X54001, Durban 4000, South Africa

Telephone: +27 (0) 31 260 3021 Facsimilie: +27 (0) 31 260 7806 Email: [email protected] Website: www.ukzn.ac.za

6 July 2015

To whom it may concern,

HELTASA National Excellence for Teaching Award: Dr A Maharaj

I write in support of the nomination of Dr A Maharaj for the HELTASA National Excellence for Teaching Award in the category “Excellent Teacher”. Dr Maharaj is an excellent candidate for this award given his expertise and practice as an accomplished Mathematics Educator.

I have worked with Dr Maharaj for over ten years and so am very familiar with his techniques and approach. He is a very caring individual who is greatly concerned with the ability of students to think and learn. He has devoted considerable time and energy in order to develop these abilities in students.

Dr Maharaj has constantly reflected on the impact of his teaching, even at the beginning of his career as a lecturer. While he was trained as a secondary school teacher, he applied his pedagogic skills to good effect in tertiary education. His understanding of the secondary school sector has ensured that his approach to first year students was nuanced to ensure that the required learning took place.

This background has been instrumental in him driving a program to improve the qualifications of secondary school teachers. We have successfully graduated in excess of twenty teachers from this program.

Dr Maharaj has a history of introducing innovative approaches and techniques to teaching at the University of KwaZulu-‐Natal. He introduced the concept of “e-‐learning” to first year teaching long before this became the trend across the sector. More recently he has pioneered the introduction of “diagnostic testing” to improve the learning (and hence throughput) of first year students. This has led to a remarkable increase in learning among these students. Our throughput rates have never been better.

In addition, Dr Maharaj has been successful in attracting funding from industry to support these endeavours. This reflects the appreciation for his projects from outside the academic sector.

In summary, Dr Maharaj is an eminently suitable candidate for this position. He is an innovative lecturer whose research has produced tangible positive results with long ranging impacts.

Yours sincerely

Professor K S Govinder: Dean and Head of School

Annexure D16 - Letter from Kesh Govinder

Developing the modules for Math150 and Math145: Math133 was replaced by Math150

Snapshot 1: Email from Paddy Ewer to work on a new module

Snapshot 3: sharing ideas with colleagues at DUT

Snapshot 3: sharing ideas with colleagues at UNIZUL

Annexure E1 - Development of Courses Sharing Ideas

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Annexure E2 - University of Zululand Presentation

Annexure E3 - Sharing Ideas Outreach

Maharaja32

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Snapshot 1: guiding post graduate involved in MDI

Maharaja32

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Snapshot 2: sharing maths stuff with others

Maharaja32

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Snapshot 3: outreach with local government representative

Maharaja32

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Snapshot 4: making mathematics support material available to others

Dr Sanjay M Wagh June 10, 2015

Professor and Director Our Reference: 2015/smw/am-sa/01

To whomsoever it may concern

It is my pleasure to appreciate Dr. Anesh Maharaj as a collaborator of long standing association of

our institute in the field of mathematics education. I had met Dr. Maharaj at the University of

KwaZulu-Natal about a decade ago.

I had invited Dr. Anesh Maharaj to visit us, with his visit materializing during 2012 for a period

of three weeks. During his visit in 2012, Dr. Maharaj delivered a talk in CIRI sharing his ideas on

APOS Theory and e-learning. While at Nagpur, he had meaningful interaction with colleagues at

the Center for Scientific Learning. When I introduced him to other colleagues, he also shared

these ideas at the Jawaharlal Nehru University, New Delhi and at the Homi Bhabha Center for

Science Education, Mumbai.

After his first sabbatical, Dr. Maharaj has been a regular visitor of our institute, visiting Nagpur at

least once a year to share ideas and work on diagnostics for undergraduate mathematics. He had

been energetic and enthusiastic to share ideas with other researchers in India and at the HP Global

Catalyst Summits held during 2011 to 2013. He also has the driving nature to network with and

meaningfully interact with researchers at other institutions in India, for example, at the Agasthya

International Foundation, Bangalore and at the Amrita University, Amritpuri (Kerala).

With our best wishes to him for continuing with his important studies,

(Sanjay M Wagh)

CENTRAL INDIA RESEARCH INSTITUTE (A Rashtrasant Tukadoji Maharaj Nagpur University Recognized

Center for Higher Learning & Research)

Address: 34, Farmland, Ramdaspeth, Nagpur 440 010, India

Phone: (O) (+91) (712) 246 1632 (M) (+91) 94036 16908

Fax: (+91) (712) 246 1632 (OPA/OR)

Annexure E4 - Reference Letter CIRI

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Annexure E5 - Internship Report

An insight into the lecture context for large

class sizes, 2014 Math 130

Students with e-learning materials during a

lecture on complex numbers for Math140 in 2014

At HBCSE in Mumbai in December 2014 with some of

the post graduate students who attended my talk.

At the ESKOM Academy of Learning in Midrand,

report back meeting May 2014

At a 2014 meeting at University of Zululand to

share ideas on mathematics e-learning

With 2nd intake of teachers for Math130 in July 2014

At Rhodes University 2015, sharing ideas with colleagues in the

mathematics department

At the 2013 HP Catalyst Summit in Sao Paulo (Brazil),

with members of the Multiversity consortium

Annexure E6 - Photos Sharing Ideas and Student Context

NAME: Aneshkumar Maharaj STAFF NUMBER: 1641 Rationale for ...utlo.ukzn.ac.za/Files/Maharaj, A...

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