7.6 Lines and Planes in 3D Space: Exploring Mathematics Through Text
In the previous section, you practised reading and performing dialogues (spoken communication) about mathematics, and explored written communication through email correspondence. In this section, you will focus on longer written mathematical communication. This book uses several different types of text across the chapters. This gives you exposure to a variety of mathematical writing.
The text below is a fictional agenda for a meeting of the Students and Staff Liaison Group (S&SLG) for Year 1 at a fictional UK university. It opens with standard procedural items – welcome, apologies, and a Chair’s statement – followed by the main section, in which student representatives report feedback on their modules. Imagine that the feedback items below represent a selection from a longer meeting in which several modules are discussed. This structure is typical of genuine S&SLG agendas used in UK universities, where student representatives play an active role in quality assurance and module feedback.
Your task is to read the text and work through the activities. The activities have a logical structure: they begin with more global or whole-text activities, that examine the purpose and audience of the text, and they gradually narrow to a focus on individual language items. In mathematical writing, there is an inherent connection between ‘macro’ text-external elements (such as audience and purpose) and ‘micro’ text-internal aspects (such as individual words and phrases).
By working through the various activities below, you will be able to:
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Work with extended mathematical prose texts to enhance your understanding of both mathematical concepts and the structure of mathematical writing.
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Identify and develop your command of useful academic phrases and sentence structures within text.
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Apply this language in your own writing and mathematical discussions.
Activity 1: The overall audience and purpose of the text
The purpose of this activity is to help you think about three features of a text: its audience (who reads it), its purpose (why it was written), and its structure (how it is organised). Academic writing takes many different forms. Each form has its own conventions, purposes, and ways of organising information. Noticing these differences will help you become a stronger academic reader and writer.
Question 1: Overall purpose of the text
Read the whole text and select which of the following four prompts best summarises its overall purpose. Next, select the ‘Answer’ button below.
- The primary purpose of this agenda is as a ‘look-back’ document with the aim of providing only a record of previous discussions. The document does not look ahead to any future actions or activities.
- The primary purpose of this agenda is to give certain students power to influence other students’ decision in the School of Mathematics.
- The primary purpose of this agenda is to provide a schedule of the planned discussions so that attendees know what will be talked through.
- The primary purpose of this agenda is to record the decisions that mathematics faculty have taken and to inform students of them.
Answer
The correct answer is Statement 3. Meetings such as this, between staff and students, are discussions and the agenda sets the scene or provides a schedule for the discussions.
- The structure and headings of Section 5 of the text (which is the longest section) indicate that comments and questions will be raised. Each sub-section of this consists of a student reporting back on some activity within the School. Sometimes this is simply a report, on other occasions, one or more questions are raised.
- The discussion element of the text is implicit in the fact that questions are being raised.
The remaining statements are incorrect for the following reasons:
Statement 1 is incorrect because the agenda does look forward; both in terms of potential actions arising from the meeting, and in terms of a proposed next meeting date.
Statement 2 is incorrect because the students present are representing the wider student body, not exercising power over other students. We might note that the S&SLG is designed to give voice, which is a form of power, to the student body as a whole.
Statement 4 is incorrect because information flows primarily from students to staff, not the other way around. It is the student representatives who are reporting back and raising questions; staff are not presenting decisions for students to receive.
Question 2: The overall tone of the text
The discussions, decisions, and actions recorded in meeting agendas can vary in tone. Some parts may be positive (things are going well), some may be negative (there are problems or concerns), and some may be neutral (information is simply reported without strong feeling). In this context, tone refers to the general feeling or attitude expressed in a text; for example, whether the writer seems worried, satisfied, or simply informative.
Your task: Read the three summaries below. Each one describes the overall tone of S&SLG. Choose the summary that is most accurate. Next, select the ‘Answer’ button below.
Summary 1: Some sections of S&SLG are very positive about the teaching and learning in this department. However, there are also several places where students raise serious concerns that require urgent action.
Summary 2: The overall tone of S&SLG is mostly positive. There are a few areas where teaching staff could make improvements, but none of these is serious. The issues are minor and the changes requested are straightforward.
Summary 3: The overall message of S&SLG is that everything is ‘broadly fine’. Most students are getting on OK but there’s nothing that stands out as particularly positive or noteworthy, nor is there anything that needs addressing.
Answer
Summary 2 is the best summary. Section 5, Feedback from reps, indicates that many of the teaching and extracurricula activities in the School are very well received. We see language such as a resounding success, they particularly enjoy and warmly appreciate. That said, there are a few things to be thinking about, specifically in items (iv) to (vii).
Summary 1 is incorrect in that nothing in the agenda indicates serious concerns that require urgent action.
Summary 3 is incorrect in that there are a number of positive comments made.
Students and Staff Partnership Forum
A meeting of the Students and Staff Liaison Group (S&SLG) for Year 1 will be held in Room 3.05 (Mathematics Building) and on Teams on Thursday 24th February 2028, 10.00–11.00 (UK time).
A G E N D A
- Welcome and introductions
- Apologies
- Dr James Okafor, Module Leader, MA1020 Linear Algebra and Geometry – attending an external examiners’ meeting.
- Ahmed Hassan, BSc Mathematics – unable to attend due to illness.
- Chair’s Statement by María López, BSc Financial Mathematics
- The Chair will note that this is the second Students and Staff Liaison Group of the academic year and will thank student representatives and staff for their strong engagement with the new Year 1 cohort so far.
- The Chair will highlight the positive start to teaching in Semester 2, including very good attendance in the core mathematics modules.
- Minutes and actions from previous S&SLG by María López, BSc Financial Mathematics
- Module leaders to confirm timetable for office hours and post this information, by Week 3 on the School intranet and on their staff email signature. Owner: Teaching Team. Status: Complete.
- Student representatives to circulate a brief survey to Year 1 students on their initial experience of lectures and tutorials. Owner: Student Representatives. Status: Complete.
- Department to investigate options for attendance monitoring and to report back at the next S&SLG. Owner: Undergraduate Programme Director. Status: In progress; see below.
The Undergraduate Director will provide a brief update on current attendance monitoring procedures across MA1010, MA1020, and MA1030. The Forum is invited to consider whether the existing mechanisms are sufficient, and whether any additional steps, such as early-alert notifications for students with unexplained absences, would be beneficial to introduce during next semester.
- Feedback from Reps
- Appreciation for the Mathematics Games and Puzzles Club (all Year 1 programmes) by Aisha Khan, MMath
Students report that the weekly Mathematics Games and Puzzles Club has been a resounding success. They particularly enjoy how the games encourage informal discussion of topics such as vectors, coordinates and geometric reasoning, and they feel that this relaxed environment helps them gain confidence in using mathematical language. Students would be very happy if the Club could continue every week and, if possible, be expanded with occasional themed sessions linked to current lecture topics. - Appreciation for the visiting PhD speaker on robotics by Daniel Li, BSc Mathematics and Statistics
Students warmly appreciated the recent visit from a PhD researcher from the School of Computing, whose talk introduced how the mathematics of lines and planes in three-dimensional space underpins collision detection in robotics. Students who attended found it genuinely motivating to see how concepts introduced in MA1010 (such as normal vectors, the equation of a plane, and the intersection of lines) appear directly in problems that active researchers work on. Students would like to thank the School for organising this event and would very much welcome further talks of this kind during the semester. It was, however, felt that attendance, while buoyant, could have been higher. Is there a mechanism for wider and earlier advertising of these events? - Appreciation for clear lecture structure for MA1010 Calculus and Vectors by María López, BSc Financial Mathematics
Students state that the structure of the lectures on vectors, lines and planes has been very clear, with definitions, key examples and short summary slides at the end of each session. They feel that this approach, together with the use of colour-coded diagrams, has supported their understanding of how to distinguish between different forms of the equation of a line or a plane. Students would like to express their thanks to the teaching team for this careful planning and organisation. - More step-by-step worked examples on 3D lines and planes are expected in MA1010 Calculus and Vectors by Ahmed Hassan, BSc Mathematics
Some students point out that, although they understand the main ideas in lectures, they sometimes find it difficult to solve new problems involving the intersection of lines and planes or the distance from a point to a plane without additional guidance. It would be highly appreciated if more step-by-step worked examples could be demonstrated in class, especially where the algebra is long, so that students can see clearly how to set up the problem, which method to choose, and how to check whether the final answer makes sense geometrically. - Slower pace and more ‘thinking time’ in tutorial classes are expected in MA1010 Calculus and Vectors by Jing Zhao, BSc Mathematics with Philosophy
Students report that the tutorial classes are very helpful but that the pace sometimes feels too fast when moving between questions on vector equations, normal vectors and angles between lines and planes. They would be grateful for a slightly slower pace, with a little more quiet time to think individually before the solution is discussed, so that they can try to use the mathematical terminology and notation themselves before seeing a full model answer. - More visual resources for three-dimensional geometry are expected in MA1020 Linear Algebra and Geometry by Luca Rossi, BSc Mathematics
Students comment that they sometimes find it hard to imagine three-dimensional objects when only two-dimensional board drawings are available. To support their learning, they would appreciate access to additional visual resources, such as interactive 3D graphing tools, short video clips showing how a line moves within a plane, or dynamic diagrams illustrating families of parallel planes. These resources could be particularly helpful for students who are studying mathematics in English for the first time, as graphs can support both conceptual understanding and the acquisition of new terminology. - More guidance on independent practice and resources is expected in MA1010 and MA1020 by Olivia Smith, BSc Mathematics and Computer Science
Students report that they value the existing problem sheets and online quizzes but are sometimes unsure which questions are essential for consolidation and which are extension. They suggest that a short weekly note on the School intranet could highlight a small core set of ‘must-do’ questions on lines and planes for revision, together with optional challenge problems. Clear signposting of which resources are most helpful for practising specific skills (for example, converting between different forms of the equation of a plane) would help students manage their study time more effectively. - Appreciation for supportive workshop tutors in the Mathematics Skills and Communication module (MA1030) by Ravi Patel, BSc Mathematics
Students say that the workshop tutors in MA1030 have created a friendly atmosphere where they feel comfortable asking questions about both the mathematical content and the language used to explain it. They particularly value opportunities to practise writing short explanations of geometric ideas, such as describing the relative positions of two lines in space, and to receive constructive feedback on their phrasing. Students would like to thank the tutors for their patience and encouragement.
- Appreciation for the Mathematics Games and Puzzles Club (all Year 1 programmes) by Aisha Khan, MMath
- AOB
- Additional items from staff or student representatives.
- Date of next meeting
- To be confirmed. Proposed for late June, after the summer assessment period.
Activity 2: Comparing the purpose of two texts
If you are working through this book sequentially, you may recall that the text in Section 6.6 was the announcement of a fictional inaugural lecture of a fictional professor, Sandra Hernandez. We will refer to this text as ‘SH’ for Sandra Hernandez. We will compare this with the text in this section as (referred to as S&SLG, for Student-and-Staff Liaison Group).
Your task: Re-read SH in Section 6.6, and S&SLG above. For each of the three statements below, decide whether it is True or False. Next, select the ‘Answer’ button below the statements.
- Two terms are defined below. Use them to answer this statement.
- Public audience: The text is intended for readers beyond the people mentioned in it.
- Non-public audience: The text is intended primarily for the specific people mentioned in it. The text is essentially private.
Statement 1: Both S&SLG and SH are intended for a public audience.
- SH has two main purposes: (1) to inform readers about Sandra Hernandez’s talk and the launch of her book, and (2) to persuade people to attend, that is, it is also a marketing or advertising text.
Statement 2: S&SLG has exactly these same two purposes and no others.
- S&SLG differs from SH in two ways: it is longer (more words and more sections), and it has a more explicit structure, with numbered sections and subsections.
Statement 3: S&SLG uses numbered sections and subsections only because it is longer than SH.
Answer
Statement 1 is False: SH is a public document. It was distributed widely (for example, by email and on mailing lists) and was intended for a broad audience, possibly worldwide. S&SLG, by contrast, appears to be an internal document intended primarily for meeting participants and relevant staff/student representatives. It is therefore non-public in purpose, even if the text does not specify exactly where it is stored. It could reasonably be characterised as confidential.
Statement 2 is False: Like SH, S&SLG aims to inform. However, it is not a marketing text; it does not try to persuade anyone to do anything. S&SLG has an additional purpose that SH does not: record-keeping. It tracks decisions and actions from a formal meeting and sets out new actions to be completed. This purpose is absent from SH.
Statement 3 is False: Although S&SLG is longer, its use of numbered sections is not simply a consequence of its length. The numbered structure is a standard convention for the agenda of a formal meeting. Even if the meeting were short and covered only a few items, the same kind of numbered structure would typically be used. Structure in this type of text reflects convention and purpose, not just length.
Activity 3: Given and new information
In this activity we will analyse a sequence of paragraphs on the basis of given and new information.
The paragraph below is from Section 5(i) of the text, with square brackets indicating the end of sentences:
Students report that the weekly Mathematics Games and Puzzles Club has been a resounding success. [1] They particularly enjoy how the games encourage informal discussion of topics such as vectors, coordinates and geometric reasoning, [2a] and they feel that this relaxed environment helps them gain confidence in using mathematical language. [2b] Students would be very happy if the Club could continue every week and, if possible, be expanded with occasional themed sessions linked to current lecture topics. [3]
The table below breaks the paragraph into sentences and clauses (smaller units of meaning within a sentence). For each sentence and clause, the table notes two kinds of information: Given and New. These are defined below:
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- Given information: something the reader already knows either, from general context or from an earlier sentence in the same text.
- New information: something that has not been mentioned before.
This approach can help us become more confident readers by training us to follow the logical thread of a text more readily. It can also support clearer writing: if we are aware of the given-then-new principle in our own work, we are more likely to produce text that is easy to follow.
| No. | Given and New |
|---|---|
| 1 | Given: As this is the first sentence in the paragraph, there is no preceding sentence to draw on. However, the opening phrase Students report that … is given information from the context. This is exactly what we would expect to find at the head of a paragraph reporting information from a student representative.
New: (a) the weekly Mathematics Games and Puzzles Club is identified as a topic; (b) has been a resounding success. |
| 2a | Given: Both elements that were new in Sentence 1 are echoed in the given information in this clause. Specifically, the string They particularly enjoy how the games… echoes success from Sentence 1, and the games picks up the specific topic mentioned there. The pronoun They refers back to The students.
New: The string …informal discussion of topics such as … is new information, which is a detail about what is enjoyed. |
| 2b | Given: … this relaxed environment … Although a relaxed environment has not been mentioned explicitly, it is implied by the context of a games club, which is likely more relaxed than a lecture or seminar. The word this points back to the games club described in Sentences 1 and 2a.
New: … helps them gain confidence in using mathematical language. A detail of how the relaxed environment of the games club helps students. |
| 3 | Given: Students, every week, and the adjective happy all echo earlier content and attitudes.
New: New information is everything after and which constitutes a suggestion for future directions for the club. Note: Sentence 3 is worth examining carefully. Although it contains several words that echo earlier sentences (students, games, every week) its overall direction is new: it shifts from reporting what has already happened to suggesting what could happen next. This shows that given and new are not simply about individual words, but about the overall purpose of a sentence within the paragraph. Note also that happy, whilst it echoes the positive tone of earlier sentences, is also part of this forward-looking shift; so whether it counts as given or new is a matter of interpretation. In linguistic analysis, such ambiguities are normal and worth discussing. |
Your task: Create a sentence-by-sentence analysis of Section 5(ii) of the text. Next, select the ‘Answer’ button below.
Answer
Students warmly appreciated the recent visit from a PhD researcher from the School of Computing, [1a] whose talk introduced how the mathematics of lines and planes in three-dimensional space underpins collision detection in robotics [1b]. Students who attended found it genuinely motivating to see how concepts introduced in MA1010 (such as normal vectors, the equation of a plane, and the intersection of lines) appear directly in problems that active researchers work on [2]. Students would like to thank the School for organising this event and would very much welcome further talks of this kind during the semester. [3] It was, however, felt that attendance, while buoyant, could have been higher. [4] Is there a mechanism for wider and earlier advertising of these events? [5]
| No. | Given and new |
|---|---|
| 1a | Given: Students warmly appreciated can be considered given for the same reasons that the opening words of 5(i) are considered given: they are predictable from context.
New: the recent visit from a PhD researcher… |
| 1b | Given: whose talk… Here, whose refers to the PhD researcher; talk is strongly implied by visit in Sentence 1a and may be considered a synonym in effect.
New: the topic of the talk |
| 2 | Given: Students who attended found it… Here, Students refers back as standard, but note that it does not refer to the talk. This use of it is the same as that found in sentences such as I find it interesting to apply equation X to this example. We may consider the string concepts introduced in MA1010 (such as….) as given, since readers of this document are expected to know the module and its contents.
New: appear directly in… |
| 3 | Given: Like Sentence 3 in Section 5(i), this sentence has many lexical links but overall represents a shift in the text from summarising the positives to making suggestions for the future. Lexical links include Students, this event and talk.
New: As noted above, the New information here is the overall content of the sentence that further talks are welcome. |
| 4 | Given: The however at the head of this sentence indicates another shift in topic. That said, the noun attendance refers to attendance at the event, that is, we are still talking about the event itself.
New: New information here is the introduction of the perceived problem of attendance specifically that it could have been higher. |
| 5 | Given: There are few lexical links to the previous sentence here although events is clearly given. Nevertheless, this sentence builds on the previous one as it raises the question of how to address the perceived problem in Sentence 4.
New: The topic of this sentence is noted above: raising a possible response to the perceived problem of Sentence 4. |
In Activity 1 you noted that at least some of the document is positive or very positive in tone. In this Language Focus, we focus on the positive language itself. Other sections that look at positive language include Language Focus 1 in Section 1.6 and Activity 2 in Section 3.6.
When writing mathematics for problem sheets, a report, a project, or a dissertation, we aim to keep our language neutral and objective. However, this is not necessarily the case for all kinds of writing in the academy. For example, an email from a student expressing thanks to a tutor may contain positive language. Indeed, the text in Section 6.6 advertising an inaugural lecture also contained a lot of positive language.
In Section 5(i) of the text, reproduced below, there are a number of examples of positive language. We group them into three types:
- [N] – nominal (noun-type)
- [V] – verbal (verb-type)
- [A] – adjectival (adjective-type)
The relevant strings are underlined and annotated accordingly. We also provide related words from the same word family, as well as additional examples of use in an academic context.
Note on classification: When labelling an example as [N], [V], or [A], it is the positive word in the phrase that receives the label. For example, relaxed environment contains both an adjective and a noun, but it is the adjective that contributes the positive sense to the phrase, so it is labelled [A]. Remember that the grammatical specifics are not critical; the classification approach is simply a tool for thinking.
Appreciation for [N] the Mathematics Games and Puzzles Club (all Year 1 programmes) by Aisha Khan, MMath
Students report that the weekly Mathematics Games and Puzzles Club has been a resounding success [N]. They particularly enjoy [V] how the games encourage informal discussion [V] of topics such as vectors, coordinates and geometric reasoning, and they feel that this relaxed environment [A] helps them [V] gain confidence in using [V] mathematical language. Students would be very happy [A] if the Club could continue every week and, if possible, be expanded with occasional themed sessions linked to current lecture topics.
Notes on the language of the above highlights:
- Appreciation is a noun. The related verb is appreciate and the related adjective is appreciative. The noun appreciation is typically followed by the preposition for. The adjective appreciative is typically followed by the preposition of. We might use this in an academic context, for example in an email to a tutor: I have been extremely appreciative of your assistance.
- Enjoy is a verb. Here it is pre-modified by the adverb particularly, which is a common collocate. The related adjective is enjoyable and the related noun is enjoyment.
- encourage is a verb. Its object here is informal discussion. The typical pattern is ‘encourage + object + to + infinitive’, for example: we encourage students to verify each step. The related adjective is encouraging and the related noun is encouragement.
- relaxed is an adjective related to the verb relax and the noun relaxation. Note that relax can be used in a more formal academic context with the meaning of loosen, for example: The department decided to relax the rules around assessment.
- help is a verb. The related adjective is helpful and its opposite is unhelpful. Both appear frequently in academic mathematical writing, for example: This is a helpful example of the theorem. / An unhelpful choice of notation can obscure the argument.
- gain is a verb and confidence is a noun. The related adjective is confident. The phrase gain confidence is a useful collocation to memorise, and it appears frequently in the learning outcomes of mathematics courses, for example: …to assist students in gaining confidence in communicating mathematics to a specific audience.
- happy is an adjective. The related noun is happiness and the opposite is unhappy. In academic writing, happy is often used in formal expressions of willingness, for example:
Your task: Do a similar word-class analysis of Section 5(ii) of the text. Identify the positive words and phrases, label them [N], [V], or [A], and note related words from the same word family. Remember that the grammatical specifics are not critical; the classification approach is simply a tool for thinking. Next, select the ‘Answer’ button below the statements.
Answer
Some of the positive language of Section 5(ii) of the text, reproduced below for convenience.
Appreciation for [N] the visiting PhD speaker on robotics by Daniel Li, BSc Mathematics and Statistics
Students warmly appreciated [adverb and V] the recent visit from a PhD researcher from the School of Computing, whose talk introduced how the mathematics of lines and planes in three-dimensional space underpins collision detection in robotics. Students who attended found it genuinely motivating [A] to see how concepts introduced in MA1010 (such as normal vectors, the equation of a plane, and the intersection of lines) appear directly in problems that active researchers work on. Students would like to thank [V] the School for organising this event and would very much welcome [V] further talks of this kind during the semester. It was, however, felt that attendance, while buoyant, could have been higher. Is there a mechanism for wider and earlier advertising of these events?
- The heading follows the same pattern as Section 5(i) of the text: Appreciation is a noun typically followed by the preposition for. See the note in Section 5(i) above.
- appreciated is a verb here, modified by the adverb warmly. The expression warmly appreciated is a common fixed phrase in academic English and often appears in the passive voice, for example in a thank-you email to a guest lecturer: Your stimulating lecture was warmly appreciated.
- motivating is an adjective in this context, as in the talk was very motivating. The related verb is motivate, the noun is motivation, and the opposite adjective is demotivating.
- thank in would like to thank is a verb. The whole phrase is a standard expression of thanks in formal academic English. It is more polite and less direct than simply saying we thank, and it is a useful fixed expression to memorise for use in academic correspondence.
- welcome in the string [would] very much welcome is also a verb, and it is used in conjunction with would like to thank in (iv) above. The two verbs together form a coordinated pair: students are simultaneously thanking the School and expressing a wish for more events. Note that very much intensifies the verb welcome here, which is a formal and emphatic pattern.
Activity 4: The language of making suggestions for improvements
While much of the agenda is positive about the students’ experiences of the mathematics programmes at this fictional university, most sections nevertheless make some suggestions for improvement. Here we look at the formal language used to make these suggestions.
Question 1: Consider sections 5(i) and 5(ii), reproduced below. Read the extracts and identify the suggestions being made. Note down the specific language used to make these suggestions, and decide whether each suggestion aims to develop an already positive experience or correct a problem. Next, select the ‘Answer’ button below the extracts.
5(i): Students report that the weekly Mathematics Games and Puzzles Club has been a resounding success. They particularly enjoy how the games encourage informal discussion of topics such as vectors, coordinates and geometric reasoning, and they feel that this relaxed environment helps them gain confidence in using mathematical language. Students would be very happy if the Club could continue every week and, if possible, be expanded with occasional themed sessions linked to current lecture topics.
5(ii): Students warmly appreciated the recent visit from a PhD researcher from the School of Computing, whose talk introduced how the mathematics of lines and planes in three-dimensional space underpins collision detection in robotics. Students who attended found it genuinely motivating to see how concepts introduced in MA1010 (such as normal vectors, the equation of a plane, and the intersection of lines) appear directly in problems that active researchers work on. Students would like to thank the School for organising this event and would very much welcome further talks of this kind during the semester. It was, however, felt that attendance, while buoyant, could have been higher. Is there a mechanism for wider and earlier advertising of these events?
Answer
| Section | Nature of suggestion | Language used | Develop or correct? |
|---|---|---|---|
| 5(i) | For the games club to continue and expand if possible. | … would be very happy if the club could continue … and, if possible, be expanded … | Develop: This suggestion builds on an already positive part of the students’ experience. |
| 5(ii) | Suggestion A: For further talks of this kind to occur.
Suggestion B: To explore how to increase attendance. |
Suggestion A: … would very much welcome further talks of this kind …
Suggestion B: It was, however, felt that … Is there a mechanism …? |
Suggestion A is development: Keep doing this well!
Suggestion B is corrective: It highlights a problem and invites discussion of a possible solution. |
Question 2: Sections 5(iii) and 5(viii) of the agenda contain no suggestions; they are simply positive feedback. However, sections 5(iv) to 5(vii) inclusive do contain suggestions. Re-read each of these four sections. Identify the problem being addressed, the specific suggestion being made, and the formal language used to make it. Next, select the ‘Answer’ button below.
Answer
| Section | Problem | Suggestion | Language used |
|---|---|---|---|
| 5(iv) | Solving new problems. | More step-by-step examples. | It would be highly appreciated if more step-by-step worked examples could be demonstrated in class |
| 5(v) | The pace in tutorials feels too fast. | A slower pace and more quiet time to think. | Students would be grateful for a slightly slower pace, with … more quiet time to think individually before the solution is discussed |
| 5(vi) | Visualising 3D objects with 2D learning resources | Additional learning technology to support learning. | To support their learning, [students] would appreciate … These resources could be particularly helpful for students who …. |
| 5(vii) | Distinguishing between core and additional questions. | Clear signposting or a note to make the distinction clear. | They suggest that …Clear signposting of … would help students manage their study time more effectively. |
Language Focus 2: Softening suggestions
In formal academic feedback, we rarely use direct commands (e.g., Do this, We want this). Instead, we use specific grammatical structures to be polite and constructive:
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Modal verbs: could and would soften the request (e.g., Students would very much welcome…).
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Conditional forms: if frames the suggestion as a possibility rather than a demand (e.g., … if the Club could continue…).
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Indirect questions: Instead of saying Advertise this better, the writer asks gently, Is there a mechanism for wider and earlier advertising…?
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Passive voice/Impersonal phrasing: Distancing the writer makes the critique sound objective (e.g., It was, however, felt that…).
- Softening phrases: phrases that create space or soften the strength of a request (e.g. when a moment allows; whenever possible).
Your task: Consider section 5(i) of the text, reproduced below for convenience. Identify which of the above language forms are used. Next, select the ‘Answer’ button below.
Students would be very happy if the Club could continue every week and, if possible, be expanded with occasional themed sessions linked to current lecture topics.
Answer
Modal verb: would
Conditional: if
Modal verb: could
Softening phrase: if possible
You may wish to look over other relevant sections of the text and identify the softening strategies used.
Activity 5: Identifying the conventional language of meeting agendas
Different types of academic texts use specific vocabulary and structures. For example, mathematics problem sheets heavily rely on instructional verbs like calculate, solve, and show your working.
Meeting agendas also have their own highly specific language. Because agendas are functional, semi-technical texts with a clear purpose and audience, they use words, phrases, and formatting that you are unlikely to see in other contexts (such as textbooks or lecture notes). This activity invites you to identify some of these text-specific features.
Before completing the task, consider these three examples of features specific to meeting agendas:
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Formatting and phrasing: The document opens with A meeting … will be held in [Room] and on Teams on [date]. Most academic texts do not begin with logistical details centred on the page, but in an agenda, this is standard practice. This sentence, therefore, is a good example of meeting agenda-specific language.
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Specific vocabulary: The word Apologies usually means expressing regret for a mistake. However, in a meeting agenda, it refers to the list of people who have formally informed the committee that they cannot attend. They have ‘given their apologies’. There are other examples in the text of individual meeting-specific language.
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Consistent paragraph structure: As seen in Section 5, student reports follow a highly predictable and repetitive paragraph structure to efficiently deliver feedback.
Your task: Look over the agenda text again. Note down any words, phrases, or structural features that are typical of meeting agendas but would be unusual in other types of text (such as exam instructions, lecture notes, or student-to-tutor emails). Next, select the ‘Answer’ button below
Answer
Here are the key agenda-specific features you may have noticed, divided into structural aspects and specific vocabulary.
Structural aspects
- The text consists of numbered main sections (1–7) with sub-sections using Roman numerals (i, ii, iii, …). While final-year projects or lengthy exams also use numbered sections, the brief, list-like format here is highly characteristic of agendas. Other texts that may have this numbered structure include lengthy exam instructions, updates from a Director of Studies and final year projects and theses, which almost have numbered chapter and sub-sections.
- The agenda follows a formal sequence, beginning with a broad overview of the year (Section 3) and a review of actions from the previous meeting (Section 4).
- The sub-sections in Section 5 frequently begin with a standard reporting phrase (e.g., Students report… or Students say…), followed by comments and suggestions.
Specific Words and Grammar
- The preposition by is used at the heading of each section (e.g., by Dr Smith) to indicate who will be presenting that specific item.
- In Section 3, the future tense is used to describe what the committee will do during the meeting (e.g., will note, will highlight). We also see this in Section 4.
- In the action points of Section 4, the infinitive verb form is used to assign future tasks efficiently (e.g., to confirm, to circulate, to investigate).
- In Section 4 we see the terms Owner and Status. Owner refers to the individual responsible for an action. Status refers to the current progress of the action, usually labelled as either complete (finished) or ongoing (still being worked on).
Activity 6: Specific words and phrases of academic writing
In this activity, you will locate specific words and phrases in the text that have particular meanings in a university context. Read the instructions below, find the word or phrase in the text, and then select the ‘Answer’ button to check your response and reflect on how you use this language.
- Read Section 3 of the text and identify a single-word noun that means a defined group of students with shared characteristics.
Answer
The word is cohort. This is a very common term in higher education to describe a group of students studying together (e.g., the Year 1 cohort, the taught master’s cohort, the research student cohort).
Reflection task: Think about your own learning context. What are the different cohorts in your programmes? How do these cohorts differ from each other in terms of the modules they take and the mathematics they study?
- Read Section 5(ii) and identify a single-word verb that means to support, justify, or form the basis of something.
Answer
The word is underpins. In academic writing, we often say that one theory or concept underpins another (e.g., Calculus underpins much of modern physics).
Reflection Task: Reflect on your own approach to and understanding of mathematics. What underpins your interest in the subject? Is it a desire to solve real-world problems, a love for logical puzzles, or something else?
- Read Section 5(v) and identify a two-word phrase that means taking a period of time to reflect or sit quietly.
Answer
The phrase is quiet time. In educational settings, this refers to a deliberate pause in an activity to allow students to process information or think individually before discussing it.
Reflection Task: Reflect on your own approach to studying and learning. Do you give yourself regular opportunities for quiet time to process new mathematical concepts?
In this section, you have focused on longer written mathematical communication. To conclude the chapter, the final section provides a glossary of important mathematical terms from the chapter.
