Exploring intermediate phase learners' use of mathematical language when learnin
The Hadebe Brief
Postgraduate milestones, dates, contacts
Where the milestones sit
- RDM compliance
- Due date 1 May 2026. Not yet completed. UP Library RDM training appears workshop-based, no automatic certificate module is published. Action: email rdm@up.ac.za with student number to confirm what completing this milestone requires.
- Memorandum of Agreement
- Due date 1 May 2026. Draft prepared (see fields below). Needs signatures from supervisor and co-supervisor.
- Title registration / Research Protocol
- Future milestone. Revised Chapter 1 PDF is ready to submit when the MoA is signed.
- Faculty / Health ethical clearance
- Future milestones, follow Title registration.
- Mandela Rhodes Scholarship
- 2026 cycle closed 14 April 2026. 2027 cycle expected to open around March 2027. Not currently active.
Schedule
- Sun 4 MayEmail rdm@up.ac.za with student number, ask what is required to complete the RDM compliance milestone. Save reply.
- Mon 5 MaySend Email A to Dr Mwambakana. Attach the revised Chapter 1 PDF and the MoA draft. CC Prof Ogbonnaya.
- Tue 5 MayPack for Pretoria. Bring laptop and a printed MoA draft in case an in-person signature becomes possible during the trip.
- Wed 6 MayTravel to Pretoria. Graduation regalia ready.
- Thu 7 MayGraduation ceremony.
- Fri 8 MayReturn travel.
- Mon 12 MayIf no reply by this point, send Email B to Prof Ogbonnaya, CC Dr Yolandi Woest (MEd Package Coordinator).
- Wed 14 MayIf still no movement, phone Ms Buhle Oliphant (SMTE Departmental Administrator) on 012 420 5659 to ask about the MoA process.
Forms
Research Data Management
Per the UP Library RDM page, training is workshop-based, not a self-paced module with an automatic certificate. Contact the RDM office to confirm what evidence the milestone requires before doing anything else.
Email: rdm@up.ac.za · Phone: 012 420 2267 · Office: Merensky 2 Library, Level 6
Student and supervisor MoA
Standard UP template. Student fills in most fields, supervisor and co-supervisor sign, signed PDF is uploaded to the milestones portal.
Estimated time, student-side: 20 min
MoA fields, pre-filled values
Verify the working title against the 2026 registration letter before submitting.
- Student
- Mthandeni Innocent Hadebe · u18034421 · u18034421@tuks.co.za · 072 675 0001
- Faculty / Dept
- Faculty of Education · Dept of Science, Mathematics and Technology Education
- Programme
- MEd, two-year. Confirm exact title from registration letter.
- Supervisor
- Dr Jeanine N. Mwambakana-Mutombo · jeanine.mwambakana@up.ac.za · 012 420 4515 · cell 072 780 7638
- Co-supervisor
- Prof Ugorji I. Ogbonnaya · ugorji.ogbonnaya@up.ac.za · 012 420 5871
- Working title
- Exploring intermediate phase learners' use of mathematical language during the teaching and learning of fractions in rural primary schools in Mpumalanga province.
- Start date
- 2026 registration date (typically February 2026)
- Target completion
- End of 2027 academic year
- Meeting frequency
- Monthly, in person or Google Meet (Dr Mwambakana offered Meet on 6 April)
- Communication
- Email primary · cell 072 780 7638 for time-sensitive issues (offered)
- Data ownership
- Standard UP clause, retained per UP RDM policy
- Authorship
- Student first author on publications arising from the dissertation
- Dispute path
- HoD → Faculty Postgraduate Coordinator → Faculty Dean
Emails
Contacts
- Supervisor
- Dr Jeanine N. Mwambakana-Mutombo · Head of Foundation Programmes, Nat & Agric Sciences · jeanine.mwambakana@up.ac.za · 012 420 4515 · cell 072 780 7638
- Co-supervisor + HoD SMTE
- Prof Ugorji I. Ogbonnaya · ugorji.ogbonnaya@up.ac.za · 012 420 5871 · office Nat Science 2-17, Groenkloof
- MEd Package Coordinator
- Dr Yolandi Woest · yolandi.woest@up.ac.za · 012 420 5532
- SMTE Dept Admin
- Ms Buhle Oliphant · buhle.oliphant@up.ac.za · 012 420 5659 · office Nat Science 2-16, Groenkloof · Ms Sophia le Roux · sophia.leroux@up.ac.za · 012 420 5693
- Faculty PG Admin
- Ms Pulane Tau · pulane.tau@up.ac.za · 012 420 2725 · Ms Baatseba Mphahlele · baatseba.mphahlele@up.ac.za · 012 420 5582
- RDM office
- rdm@up.ac.za · 012 420 2267 · Merensky 2 Library, Level 6
- Student Service Centre
- ssc@up.ac.za · 012 420 3111
- UP Counselling Careline
- 0800 747 747
- Milestones portal
- www1.up.ac.za/psp/psicsmpra/
Documents in Downloads
20260502211846.MP3
Recording of the planning call between Pierre and Hadebe. Notes are in Section 06.
Research title MI Hadebe 1.pdf
Revised Chapter 1 of the mini-proposal. Section by section comparison against the original draft is in the "What Changed" tab.
WhatsApp Image 21.19.40.jpeg
The PSP "View My Milestones" page. Lists all 21 MEd milestones for the programme. RDM compliance and Memorandum of Agreement are dated 1 May 2026.
WhatsApp Image 21.25.31.jpeg
Two outgoing WhatsApp messages from Hadebe to Dr Mwambakana, dated 24 April and 26 April.
Gmail Fwd: Milestone "RDM compliance" Due 2026-05-01
UP PeopleSoft notification (PSCSMPRA@up.ac.za, do not reply). Friendly reminder that the milestone is due 1 May.
Gmail Fwd: Milestone "Memorandum of Agreement" Due 2026-05-01
Same automated source. Friendly reminder for the MoA milestone.
Gmail Fwd: UPDATE ON MINI PROPOSAL
Email thread between Hadebe (Prof Ogbonnaya CC'd) and Dr Mwambakana. On 6 April Dr Mwambakana sent her comments, the central direction being to include teaching and learning of fractions in scope, and shared her cell number for follow-up.
Gmail Fwd: RECOMMENDATION LETTER
Initial coordination on a recommendation letter for the Mandela Rhodes Scholarship. The 2026 cycle has since closed; this thread is parked until the 2027 cycle opens.
Notes from the call
- ·Plan agreed: send revised proposal to Dr Mwambakana on Mon 5 May with the MoA draft attached, CC Prof Ogbonnaya. Wait for reply before any further action.
- ·Hadebe travels to Pretoria for graduation Wed 6 to Fri 8 May. Hotel booked. Regalia bought. No funding gap.
- ·Mandela Rhodes is parked: 2026 cycle closed, no current activity needed from either side.
- ·AI tooling: Hadebe to switch from ChatGPT free tier to Gemini 3.1 Pro, DeepSeek V4-Pro, Claude Sonnet 4.6, and NotebookLM. See AI Toolkit tab.
- ·Turn-it-in: Hadebe to keep his own draft files alongside any AI-assisted edits, so the writing trail is his.
Bursary funding
UP and NRF postgraduate funding typically reviews milestone progress at semester or year-end boundaries, not on the exact day a milestone is due. Documenting steps taken (emails sent, drafts prepared, RDM office contacted) is the standard evidence funders look for if a milestone is delayed.
What Changed
Original draft (13 Mar) → revised Chapter 1 (2 May), section by section
Most of Dr Mwambakana's flagged issues are genuinely fixed, not just papered over.
The biggest single change is on scope: Hadebe accepted Dr M's repeated nudge to include teaching and learning of fractions, and the Aim, Objectives and Research Questions all reflect that now. Grammar and prose flow are dramatically cleaner. Citations are properly grouped where multiple authors share an idea instead of being stacked one after another. Each paragraph carries a single theme, which was Dr M's most recurring criticism.
Comments → what the revision did
| Dr M's comment (on original) | What the new submission did |
|---|---|
| Title: "during the teaching and learning of fraction in… For example?" | Addressed. Title now reads "…during the teaching and learning of fractions in rural primary schools in Mpumalanga province." |
| "Do you think we will have enough data? What about including the teachers?" (asked three times) | Addressed. Teachers are now in scope. Aim explicitly: "and how teachers support the development of mathematical language during fraction lessons." Objective 4 + Secondary RQ 4 keep teachers in. |
| "You often miss conjunctions and prepositions. Please revise the grammar." | Addressed. Prose flows; the dropped "of / the / that / in" pattern is gone. |
| "Repetition. Please regroup these ideas together" (1.2) | Addressed. 1.2 restructured: CAPS → international research → SA context → linguistic registers → rural-school constraints. One theme per paragraph. |
| "Be careful putting different authors in one paragraph… what is the main idea? Who wrote about it?" (1.3) | Addressed. Citations now grouped properly. Cramer (2020) & Venkat (2020) reported together; Siegler et al. cited where appropriate. |
| "Who is 'they'?" (ambiguous pronouns flagged twice) | Addressed. Pronouns either replaced with explicit nouns or rewritten. |
| "Kindly review the referencing style and be consistent." | Addressed. In-text citations consistent: (Author, Year) throughout. |
| "There are many themes in five lines… Please rephrase this paragraph." (1.3) | Addressed. Misconception, evidence gap, and rural-context themes now sit in separate paragraphs. |
| Primary + secondary research questions ("yes" / "yes" from Dr M) | Kept. Secondary Q3 and Q4 are phrased more cleanly. |
| "Did Essien (2024) cite Robertson et al. (2021)? What is common in the two studies?" | Sidestepped, not answered. The new version drops the awkward Essien (2024) citation entirely and uses Robertson et al. (2021) once. Works on the page, but Hadebe should be ready to defend it verbally. |
| "Kindly help me understand: At what stage do learners explain fractions? To whom?" | Not directly addressed. The objectives are still abstract on this. Likely answer for the meeting: during classroom tasks, and in researcher-led interviews. |
Three small things to mention before sending
- aSecondary RQ 1 was broadened. The original asked "How accurately do learners use fractions vocabulary such as numerator, denominator and ordinal numbers?" Concrete and easy to operationalise. The new version asks "How do learners use different forms of mathematical language when explaining fraction concepts?" More open-ended, loses the vocabulary anchor. Dr Mwambakana did not comment on this. Worth checking it was a deliberate broadening.
- bRationale lost the teacher-training framework angle. The old 1.4 ended with "designing professional teacher training frameworks." The new version condenses it. Defensible: it just trims a forward-looking hook.
- cWhole-number bias example was added (1/3 vs 1/2). Dr M didn't ask for it. It strengthens the chapter pedagogically. Keep it.
Pierre's earlier instinct vs Dr M's preference
The "Decisions" tab on this page recommended keeping teachers out of scope to keep the project doable. Hadebe took the opposite call and kept teachers in, in line with Dr M's repeated nudge. That is the supervisor's call to make, and the revision now matches her steer. It does mean the workload is bigger: observation data on teacher practice will be needed, not just learner talk. Worth verbalising this in the next supervision meeting.
AI Toolkit
Six free AIs worth using for a Master's in social science
The reading library Pierre set up for you
Hadebe research notebook
Open this notebook, drop the four key papers in, and ask it questions. It only answers from the sources you've added. Every claim is cited back to a page in your readings, which is what you want for a literature review. Use it before you write any paragraph in Chapter 2.
General AI: writing, analysis, theory
Google AI Studio · Gemini 3.1 Pro
Free, no card needed, just sign in with the Google account you already use for tuks email. The huge context window means you can paste an entire chapter draft plus all four readings and ask it to check coherence in one shot.
aistudio.google.com ↗DeepSeek · V4-Pro
Strong at structured academic reasoning. Good for getting a second opinion on whether a problem statement holds together, or for breaking down a dense methodology paper.
chat.deepseek.com ↗Claude · Sonnet 4.6
Strong for nuanced academic writing and qualitative analysis: paraphrasing, tightening prose, working through coding categories for interview transcripts. Free tier needs a phone number. Daily message limit, but generous.
claude.ai ↗Research-specific tools
NotebookLM
Upload PDFs, then chat with them. The killer feature: it only answers from your sources, with citations back to the page. No hallucinated references. Pierre has already started a notebook for you (see top of this tab).
notebooklm.google.com ↗Elicit
Specifically built for academic research synthesis. Ask a research question and it returns a table of relevant papers with extracted findings. Useful for finding the next four papers once you've outgrown the starter set.
elicit.com ↗Perplexity
AI-powered search that cites sources. Faster than Google Scholar for quick "what does the literature say about X" queries. Treat its citations as starting points to verify, not as references in their own right.
perplexity.ai ↗What I'd actually run as a stack
DeepSeek or Google AI Studio for the writing itself, NotebookLM as your dedicated reading library (your four papers live here), and Elicit when you want to discover the next paper. Three tabs open, each with a clear job. Don't mix them. When you're drafting, draft. When you're reading, read. When you're hunting, hunt.
A note on academic integrity
UP's policy is that AI can be used to support writing (paraphrasing, tightening, checking grammar), but the ideas, arguments and analysis must be yours. Turn-it-in is a future milestone on your portal. Keep your own draft files alongside whatever AI you use, so the writing trail shows your thinking.
What Are We Deciding?
These are the open questions. Nail these down and the proposal writes itself.
DECISION 1: Are teachers in or out?
Dr M asked this 3 times. This changes everything.
Our thinking: Teachers are OUT
- We are looking at learners' language, not teaching methods
- The study is about: what happens when a Grade 4-6 kid tries to explain fractions in their 2nd/3rd language?
- Teachers are part of the context (they set the tasks, they use certain language) but they are not the object of analysis
- Keeping scope tight = doable masters, not a PhD
But Objective 4 says "how do educators aid..." so either rewrite that objective or accept teachers are partially in scope.
DECISION 2: What exactly are we analysing?
What is the data? What do we collect? What do we look at?
- DATA Learner talk when they explain fractions (recorded, transcribed)
- DATA Written work where learners use maths vocabulary
- DATA The tasks themselves (what language do the questions use?)
- SCOPE Q Do we also look at what language the teacher uses when setting up the task? (context, not analysis)
DECISION 3: What are we looking FOR in the data?
When Innocent reads a transcript, what does he code/tag?
- LOOK FOR Vocabulary accuracy - do they say "numerator" correctly? Do they confuse terms?
- LOOK FOR Language switching - when do they drop into home language? What triggers it?
- LOOK FOR Misconceptions revealed by language - "the bigger number goes on top" shows a whole-number mindset
- LOOK FOR The gap between what the task asks (in English) and what the learner understood
DECISION 4: Why does this matter beyond school?
The "so what?" chain:
- Fractions are the gateway to algebra, ratios, percentages
- Fail fractions in Gr 4-6 = struggle in higher maths
- Struggle in maths = fewer career options
- If the barrier is language, not ability, that is fixable
- This study shows where language breaks down so teachers can intervene at the right point
Your proposal structure (simplified)
1.1 Intro = Language matters in maths. Here is why. 1.2 Background = SA context: CAPS, English as LoLT, rural Mpumalanga 1.3 Problem = Fractions are hard + language barrier + no research here 1.4 Rationale = Fractions affect life outcomes + language is fixable 1.5 Aims = Explore how learners USE maths language for fractions 1.6 Questions = 1 primary + 4 secondary (may need to drop Obj 4)
Exploring intermediate phase learners' use of mathematical language when learning
fractions in rural primary school in Mpumalanga province
By M.I Hadebe
Supervisors
Dr Jeanine Mwambakana and Prof Ogbonnaya
© University of Pretoria
Chapter 1: Introduction and background
1.1. Introduction
The language used in the mathematic class has a significant influence on learners’ communication of mathematical ideas and conceptual understanding of mathematics. Barwell (2016) added that mathematics is not only a subject of numbers and symbols, but a unique language utilized to convey mathematical reasoning and ideas (Prediger et al., 2016). Clarkson and Planas (2018) further noted that the evolution of mathematical language allows learners to explain and describe relationships and procedures, substantiate findings in the mathematical context (Plana, 2016). Barwell (2016) highlights that research in mathematics education the capability of a learner to engage with the mathematics language and discussions is fundamental to problem solving and conceptual understanding (Prediger et al., 2016).
Lamon (2012) noted that in the Intermediate phase (Grade 4-6) learners shift from basic whole numbers to more complicated mathematical concepts such as fractions (Siegler et al., 2016). Siegler et al. (2016) added that worldwide fractions are seen as one of the most demanding fields of mathematics for learners in primary schools because they need learners to comprehend relationships between quantities than whole numbers (Lamon 2012). Clarke et al. (2018) further added that to master fractions learners are required to understand and utilize mathematics language and terminology correctly, these terms involve ordinal numbers, mixed numbers, improper fractions, numerator and denominator (Charalambous, 2019).
of classrooms in South Africa, including those in Mpumalanga Province, mathematics is taught using English which is mostly the language of teaching and learning and often not the home language of the learners (Essien, 2021). Setati and Adler (2016) added that the language of teaching and learning can have a significant influence on learners’ discussions in the classroom and understanding of mathematical concepts (Essien, 2018).
Adler (2019) notes that research done in South Africa reveals that the diversity in language often create challenges for learners when explaining their thoughts, reasoning and when interpreting mathematical problems (Venkat & Adler, 2017).
Setati-Phakeng (2020) added that in a language diverse classroom, learners may have challenges understanding mathematics terminology and explain their reasoning using the language of learning and teaching (Essien, 2019).
Furthermore, research conducted by Clarke et al. 2018 suggests that learners often rely memorizing formulas instead of understanding mathematical concepts such as fractions (Siegler & Thompson, 2019). Hence, comprehending how learners use mathematical language when learning fractions is significant for enhancing learning and teaching methods.
This study aims to explore how learners in the intermediate phase (grade 4-6) in rural areas of Mpumalanga use mathematical language when learning fractions.
1.2. Background
The Curriculum and Assessment Policy Statement (CAPS) which was designed by the Department of Basic Education (DBE) guides mathematics education in South Africa. Hence, according to the (DBE, 2011) the CAPS curriculum in mathematics encourages conceptual understanding and procedural fluency and fosters learners to explain their reasoning using the correct mathematical language (DBE, 2011).
However, Planas (2016) noted that in the multilingual classrooms of South Africa, learners from Grade 4 going forward are mandated to learn mathematics in English even though English is not their home language (Prediger et al., 2016). Research conducted by Setati and Adler (2016) emphasizes that the language of learning and teaching have a significant influence on learners’ discussions in the classroom and understanding of mathematical concepts (Essien, 2018).
Research concentrating on linguistically diverse mathematics classrooms in South Africa have shown that language of teaching and learning can either challenge or support learners understanding of mathematics (Setati-Phakeng, 2020). For example, study conducted by Venkat and Adler (2017) shows that language used in South African plays a huge role in shaping learners mathematical thinking (Venkat & Adler, 2017). Similarly, research conducted by Setati and Adler (2016) highlights that language practices in classrooms have a significant effect on how learners participate in mathematical discussions and in translating mathematical activities (Setati & Adler, 2016).
Furthermore, studies conducted by Essien (2018) further highlight the significance of recognizing language as a resource for learning mathematics in linguistically diverse classrooms as opposed to it being a barrier (Essien, 2019). Such research shows that when a learner’s home language is integrated strategically by an educator in a mathematics classroom it can support conceptual understanding (Essien, 2021).
Alternative studies conducted in South African mathematics education by Robertson et al. (2021) demonstrates that learners in rural-underprivileged schools often encounters obstacles such lack of resources, poverty, and language diversity (Essien, 2024). Sepeng (2018) agrees that such background factors can have a significant effect on how learners conceptualize and engage with the mathematics language (Venkat, 2023).
As an educator who had the privilege to teach in the intermediate phase (grade 4-6), I have noticed that learners are experiencing challenges when dealing with fractions because they include abstract relationships between quantities and learners to translate symbolic and linguistic notations at the same time (Cramer, 2020). Ni and Zhou (2017) added that learners must understand mathematical vocabulary such as numerator, denominator and ordinal numbers to be able to explain mathematical problems (Ni & Zhou, 2017).
Regardless of the trend in international study on language in mathematics education, there is still lack of evidence-based study concentrating particularly on learners in the intermediate phase in rural Mpumalanga use the mathematics language when engaging fractions. Hence, exploring this challenge may present a significant outlook into how language impacts learners’ mathematical discourse and conceptualiation.
1.3. Problem statement
As Siegler et al. (2016) highlights that fractions create an essential element of the intermediate phase curriculum and as a bedrock for mathematical topics such as algebra and ratios in higher grades (Siegler et al., 2016). Nonetheless, Cramer (2020) emphasizes that studies demonstrate that majority of learners are still experiencing challenges when it comes to conceptualiing mathematics (Venkat, 2020).
Prediger et al. (2020) noted that a conceivable cause that influences these challenges is learners lack of use and understanding of mathematical language (Essien, 2019).
There are specialized mathematics terminology and symbolic notations which are used to communicate mathematical ideas (Essien, 2022) and learners must be able to translate and use this language to understand fractions (Prediger et al., 2020).
Adler (2019) supports this that in rural Mpumalanga classrooms, where learners are learning mathematics using a different language from their home language (Essien, 2019), issues such pertaining mathematical language may have a great impact on how learners understand fractions (Essien, 2021). A study conducted by Venkat (2023) in South African mathematics education adds to this that language used in the mathematics classroom when teaching fractions have a significant influence on how learners explain mathematical tasks and how they reason mathematically (Adler, 2019).
Furthermore, Robertson et al. (2021) also noted that learners may have challenges explaining their reasoning mathematically, misrepresent mathematical vocabulary and depend on fixed methods without conceptually understanding the operations of fractions (Cramer, 2020). Nqabeni et al. (2023) added that these obstacles can be seen in rural schools where learners who are speaking different languages and coming from different socio-economic backgrounds are found (Nqabeni et al., 2023).
Nevertheless, studies have investigated mathematical misconceptions about fractions, however there is still lack of empirical research on how learners’ use of mathematical language impacts how they comprehend fraction ideas in rural Mpumalanga classrooms. Lacking comprehension of this relationship may make intervention aimed at improving learner’s performance on fraction ineffective.
1.4. Rationale
This research is significant for numerous factors:
Firstly, as Siegler et al. (2016) notes that fractions are an important foundation for learning mathematics such as ratios and algebra in the higher grades. Studies have demonstrated that having challenges with fractions in the lower grades may hinder success in the higher grades (Siegler et al, 2016).
Secondly, as Barwell (2016) notes that mathematical language has a significant influence on learners’ conceptual understanding of fractions, and their ability to explain mathematical concepts (Prediger et al., 2020). Learners with a good grasp of mathematical terminologies are most likely to conceptually understand the operations of fractions (Charalambous, 2019).
Thirdly, as Essien (2022) notes that linguistically diverse mathematical classrooms offer different chances and obstacles for teaching and learning. This agrees with Setati-Phakeng (2020) who added that it is important to understand learners’ language needs and aid the development of mathematical classroom discussions (SetatiPhakeng, 2020).
Fourthly, as Robertson et al. (2021) states that most schools in the rural areas are under privileged with issues such as lack of resources and socio-economic factors. Challenges as such may have an impact on how learners participate during mathematics teaching and learning.
Lastly, the outcome of this research may have a significant contribution in enhancing mathematics teaching by giving an outlook into how educators can aid the advancement of mathematical language when teaching fractions in rural Mpumalanga. This research may also help in designing professional teacher training frameworks that can enhance mathematics learning and teaching in rural Mpumalanga.
1.5. Aims and objectives
The purpose of this study is to explore how intermediate phase learners in rural primary schools in Mpumalanga use mathematical language when learning fractions.
1.5.1. Objectives
To explore how accurately do learners use fractions vocabulary such numerator, denominator and ordinal number.
To investigate what language misconceptions, occur when learners explain fractions
To explore how does the instructional language impact learners’ explanation of fractions ideas.
To explore how do educators aid the advancement of mathematical language during lessons of fractions.
1.6. Research questions
1.6.1. Primary research questions
How do intermediate phase learners in rural primary schools in Mpumalanga use mathematical language when learning fractions?
1.6.2. Secondary research questions
How accurately do learners use fractions vocabulary such numerator, denominator and ordinal numbers?
What language misconceptions occur when learners explain fractions?
How does the instructional language impact learners’ explanation of fractions ideas?
How do educators aid the advancement of mathematical language during lessons of fractions?
Grammar: Top 20 fixes, ranked by impact
Each fix is rated 2-5 stars for how much it impacts your mark. Star rating = how likely an examiner is to flag this AND how much that flag costs you. Start at 5★ and work down. The 5 Hot Tips at the bottom are the moves that make you read like a rockstar researcher, not just a polished writer.
1. Tense discipline
2. Define every abbreviation on first use
3. Pronoun antecedents
4. No first person unless supervisor approves
5. Subject-verb agreement in long phrases
6. Cut intensifier crutches
7. Active voice for your contribution
8. Comma splices are a capital offence
9. Parallel structure in lists
10. Hedge calibration
11. Data show, not data shows
12. No 'thing' or 'stuff'
13. Quantify instead of 'many'
14. Strong verbs beat be-plus-noun
15. De-nominalise
16. Vary your connectives
17. Oxford comma — pick one, be consistent
18. Numbers: words under ten, digits above
19. No contractions
20. Pick UK or US English, set the spellcheck
TIP 1 Forecasting topic sentences
Every paragraph's FIRST sentence should preview the argument that paragraph will make. Not summarise it, preview it. Examiners skim first sentences. Make them work harder than any other sentence in the paragraph.
TIP 2 Read every page aloud, once
If you pause mid-sentence to breathe, the sentence is too long. If you stumble, the grammar is broken. If you lose the thread, a reader will too. Fifteen minutes of reading aloud catches more than two hours of silent editing. This is the single biggest jump between a mid-60s mark and an 80s mark.
TIP 3 Cite to pre-empt your examiner
When you make a claim you suspect an examiner will push back on, cite two studies that already survived the same pushback. The message: 'I know this is controversial. I am standing on established shoulders.' Works especially well for decolonial / language-as-resource framings in SA.
TIP 4 Echo your supervisor's published vocabulary
Read three of Dr Mwambakana's own papers. Note the verbs and framing she prefers. Use her phrasing subtly where it fits yours. Not plagiarism — alignment. She'll recognise her own words and trust your reading before she's consciously aware why.
TIP 5 End every chapter with 'So what?'
One paragraph that links your findings to a bigger claim. Without this, you have described. With it, you have argued. This single move — explicit implications — is what separates a distinction thesis from a pass. Don't bury it in the conclusion; put one at the end of every chapter.
Tool: Grammarly (free tier) catches a lot of the 2-3 star stuff. It misses the 4-5 star semantic / hedging / framing issues — those need a human (or an LLM) read.
4 Papers. Read Only These.
Each paper answers a specific question you need for the proposal. Read with those questions in your head.
1. Essien (2022) DEFINES YOUR LENS
Language and multilingualism in mathematics education
Read this to answer: What IS mathematical language? Is it just vocab words, or something bigger?
- Does Essien treat language as a BARRIER (problem to fix) or RESOURCE (tool to use)? Your proposal must pick one.
- What does "mathematical language" actually include? List the categories. This becomes your coding framework.
- When learners switch to home language during maths, is that a failure or a strategy? What does Essien say?
After reading, you should be able to say: "In my study, mathematical language means X, Y, and Z. I am treating it as [barrier/resource/both]."
2. Prediger, Clarkson & Bose (2016) TELLS YOU WHAT TO LOOK FOR
Purposefully relating multilingual registers
Read this to answer: What are the different "registers" and how do you spot them in data?
- 3 registers: everyday ("sharing pizza"), school ("equal parts"), technical ("numerator"). Can you hear the difference?
- When a learner says fractions wrong, is it a MATHS misconception or a LANGUAGE problem? How do you tell?
- What data collection method would let you capture register-switching? (This shapes your methodology.)
After reading, you should be able to say: "I will analyse learner language across [X] registers. I will collect data by [method]."
3. Siegler, Thompson & Schneider (2016) PROVES WHY IT MATTERS
Integrated theory of whole number and fractions development
Read this to answer: Why are fractions the make-or-break moment? What goes wrong in kids' heads?
- The "whole number bias": kids think 1/3 > 1/2 because 3 > 2. How would this show up in what they SAY?
- At what stage (age/grade) do fraction misconceptions solidify? Does Grade 4-6 catch them in time?
- Fail fractions = fail algebra = fewer life options. Can you trace this chain with their evidence?
After reading, you should be able to say: "Fractions matter because [X]. The common misconceptions are [Y]. My study catches learners at the critical window."
4. Robertson, Lovemore & Graven (2021) YOUR CONTEXT
Mathematics learning in contexts of poverty
Read this to answer: What is different about rural SA classrooms? Why does your study need to happen HERE?
- What obstacles do rural Mpumalanga schools face that make the language problem WORSE than in cities?
- Did they study language specifically, or just general maths performance? (If general, that is your gap.)
- What was their sample? How did they collect data? Can you adapt their method?
After reading, you should be able to say: "My study fills the gap because Robertson et al. looked at [X] but not [Y]. I am looking at [Y]."
Audio Deep Dives
Three episodes covering all 4 papers. Start simple, build to expert-level insights. Listen while commuting, walking, or just thinking.
Episode 1: Why Fractions Matter
Siegler + Essien foundations
From "what is a fraction" through whole number bias, to why fractions predict life outcomes and how language shapes conceptual understanding.
Episode 2: Language as the Hidden Variable
Prediger's registers + Essien on language-as-thinking
Everyday vs school vs technical registers. Code-switching in multilingual classrooms. What to listen for when you observe teachers and learners.
Episode 3: Designing Your Study
Robertson + Graven context, then methodology synthesis
Rural SA reality. Case study design. What data to collect, how to code it, how to write the proposal as a coherent story. Walk away ready to write.
Study Notes
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Grade 4-6 learner language when explaining fractions in 2nd/3rd language, SA multilingual context. Star rating = how directly applicable. Category = where each paper fits in the argument.
Assessed from titles and author expertise, not from reading each paper. Prioritisation view, not a review — verify key bullets against the paper itself before citing.
- Foundational SA code-switching work. Documents how learners translanguage while explaining mathematics
- Establishes multilingualism as resource, not deficit. This is the framing Hadebe's whole study depends on
- Caveat: teaching-oriented. But the classroom episodes show learner language in action, that's the usable data
- Most recent Setati-Phakeng synthesis. Updates the 2006 deficit-to-resource argument with current SA data
- IsiZulu / English switching during maths tasks is exactly Hadebe's context
- Essential for positioning the study within the SA research lineage
- Demolishes the 'learn English first, then maths' fallacy. Learners build maths and language together through practice
- Directly addresses the '2nd or 3rd language learner explains fractions' scenario
- US ELL context but theoretically transferable to SA learners
- Specifies what 'doing maths in a 2nd language' actually looks like for young learners, with concrete examples
- Defines 'mathematical discourse' in a way Hadebe can adopt directly
- Pairs with the 2017 paper, cite together
- Planas is the learner-discourse specialist. Her work focuses on what learners actually say, not what teachers teach
- Her analytic framework for learner talk in multilingual settings is probably adoptable verbatim
- Directly aligned with Hadebe's Decision 1 (learners in, teachers out)
- Most recent Planas synthesis. Brings her framework up to date
- Critical for theoretical positioning. Cite in the theoretical framework chapter
- If you cite only one Planas paper, make it this one
- Essien is the African (not just SA) multilingual maths ed voice, broader than Setati
- Situates SA within continental patterns. Useful for the 'why does this matter beyond Gauteng' question
- Recent enough to be current, established enough to be uncontested
- SA-specific, post-2016. Fills the recency gap between Setati-Adler and today
- Likely a methodological template for classroom observation in SA multilingual rooms
- Less-cited than the big names, which is why it's a stronger contribution marker
- SA primary phase, exactly Hadebe's age bracket and population
- Graven's SANC project work. Poverty is a variable you can't ignore even if not central to Hadebe's question
- Cite once in the context chapter, then again if any findings cluster by SES
- Primary phase SA, Hadebe's exact grade range
- Pairs with Graven as the 'SA primary maths landscape' paired cite
- Wits numeracy work, rigorous, recent, locally grounded
- Europe-SA collaboration. Positions SA work in international conversation
- Research agenda paper: what's been done, what's missing. Hadebe can use this to justify his contribution
- Good for the 'gap in literature' paragraph
- German design-based research tradition, strongest version of the 'language is content' argument
- Provides an analytic framework for learner language that could inform Hadebe's methodology
- Worth a close read for the methods section
- Classroom-observation based. Shows actual multilingual practice in African primary settings
- Useful methodological template for Hadebe's observation scheme
- Pairs with Sepeng 2018 for the 'how to observe' framing
- Systemic Functional Linguistics lens. Schleppegrell is the SFL voice in maths education
- Essential if Hadebe's methodology leans on discourse analysis
- Introduces 'language of mathematics as a register', a conceptual tool Hadebe can deploy
- Edited volume, cite the introduction chapter for comparative framing
- Demonstrates that SA multilingual maths patterns aren't unique, they generalise internationally
- Good for the 'why this matters beyond SA' paragraph
- Most recent Essien. Current status of the field
- Recency signal for the literature review (examiners notice when newest citations are 5+ years old)
- Continental perspective, complements SA-specific Setati-Phakeng
- Two-sided framing: language is both resource AND challenge. Prevents Hadebe from being naively optimistic
- Early Planas, foundational but superseded by her later syntheses
- Cite for conceptual origin, then use Planas 2022 or 2024 for current argument
- Edited volume with Setati and others. Foundational reference
- Useful to cite alongside Setati-Adler 2016 as the pair of seminal 2016 works
- One good intro chapter, then let Prediger and Wessel 2020 do the heavy lifting
- Most recent Moschkovich, current state of her argument
- Cite alongside 2017 and 2019 works as the Moschkovich trilogy
- Useful for recency, but conceptually the 2017 paper does most of the work
- Broad SA maths ed overview. Useful for intro chapter context
- Gives the big-picture backdrop before zooming into Hadebe's specific question
- One paragraph, not central
- LoLT policy, why SA learners code-switch in the first place. Structural context
- Background for why the study matters politically, not central to the learner-language question
- Decision 1 puts teachers out of scope, and this is policy. Keep it as context only
- Cognitive angle. How language shapes mathematical thinking, not just talk
- Useful if Hadebe wants to connect his discourse findings to cognitive outcomes
- Adds depth but not central
- Observational work, what learners actually do in bilingual Australian settings
- Transferable insights, but SA context-specific literature is stronger
- Use if a non-African comparator is wanted
- Teaching-oriented (partly out of scope per Decision 1)
- Cite if the literature review needs a general multilingual-teaching reference
- Planas has better learner-focused work. Prefer that
- Edited collection. Probably one chapter is relevant, the rest not
- Cite for recency, don't let it shape the argument
- Review paper. Useful for a recency footnote in the lit review
- Doesn't advance the argument, just surveys the field
- Equity framing. Useful if a Critical paragraph is wanted
- Decision 2 is about what's being analysed, not equity framing, so probably tangential
- Restatement of the resource argument. Already covered by stronger sources
- Cite only if the Essien 2022 and 2024 line needs extending backward
- Edited overview. Recency signal only
- Contains the important voices but you'll cite them individually anyway
- Review of the research field. Cite once for landscape
- If Essien 2021 'Language Practices' is already in your 4-star list, this one duplicates too much
- Teaching-focused, partly out of scope
- Pair with Venkat 2020 if needed, otherwise drop
- Teacher-oriented framework. Backdrop, not foreground
- Decision 1 puts teachers out of scope. Use Prediger 2020 for methods instead