From the options below, decide which summary you think most accurately describes the overall structure of the dialogue. Next, select the ‘Answer’ button below the options.

Option 1: William works with Callum to successfully solve the homework problem by working through four terms of a problem.

Option 2: William and Callum don’t agree as to how to apply the relevant formulae to the homework problem.

Option 3: William works with Callum to successfully solve the homework problem although both of them forget something at different points in the discussion.

Option 4: Time runs out before William and Callum solve the problem.

Question 1: In (6), William says Before we go and apply the power rule to our problem, can you see for which values of r it works? By saying this, William describes a two-step process. There are many ways of expressing a two-step process in English. Using grammatical and meaning cues, match each sentence beginning on the left with its corresponding ending on the right, so that both parts express the same two-step process that William is describing. Reflect on how these different expressions order the two parts of the information. Next, select the ‘Answer’ button below the table.

Question 2: In (15) Callum says, Integration is quite straightforward, if you know which rules to apply. Which three of the five sentences below have a similar meaning to (15)? Next, select the ‘Answer’ button below.

1. It’s easy when you know how.
2. Let’s just get on with it; there’s no point in waiting!
3. If you’re clear on the principles, the application falls out relatively naturally, I find.
4. If you need to triple check it, you’re in deep trouble.
5. The actual calculation isn’t too onerous when you’ve fully grasped the mathematical principles.

Goal

Practise having conversations about integration problems in English. Focus on communication, not necessarily on solving new math problems.

Set-up

In pairs, take the following roles:

Speaker A is the student that has a question about a problem in integration. Speaker A can either choose something that is an actual problem, or something that they already understand and pretend they don’t.

Speaker B is the student that has the answer to the question and needs to explain it to Speaker A.

Procedure

Step 1: Assign the roles – one student takes Speaker A and the other student takes Speaker B.

Step 2: Decide a problem from the topic integration to discuss.

Step 3: Take 3 to 5 minutes to look over the dialogue above and note down any useful phrases.

Step 4: Run the dialogue. Speaker A should start, either with a variation on Mary’s opening above, or with something else, for example, Hi [Speaker B]. Do you have a quick moment to help me out with [Problem P]. It shouldn’t take more than a couple of minutes. 

Step 5: Switch roles and practise again to experience both asking and answering.

Step 6: Together reflect on what went well. You might reflect on how accurately and fluently the dialogue was produced, how confident you felt, and if there are alternative ways of going through the dialogue.

From the options below, decide which summary you think most accurately describes the email correspondence. Next, select the ‘Answer’ button below the options.

Option 1: John has no idea at all how to begin solving the problem.

Option 2: After getting some helpful insights from Professor Badawi, John is able to solve the problem.

Option 3: Professor Badawi’s first response is to suggest that John works through some of the problems in the course notes.

Option 4: Professor Badawi’s first response suggests that John should not be contacting her about this matter.

John Johnson’s opening email (1) is both clear and appropriate. It is clear because John explicitly explains what the problem is. It is appropriate because as well as explaining the problem, sections of the email are addressed directly to Professor Badawi. The first two examples of this in John’s email are below.

Example 1: Formal greeting

Dear Professor Badawi: John uses the term Dear and addresses Catriona Badawi using her title. John might also have written Good morning, Professor Badawi. John might also have written Dear Catriona. While this is an acceptable address form in some cultures, it may not be in all. The best things to do is to ask your lecturer how they prefer to be addressed. John does not write Hello Catriona nor does he leave the addressee section blank.

Example 2: Professional opening statement

I hope you are well. This opening section is standard in much academic correspondence in English. It is not necessary but can help to maintain a positive professional relationship between the addressee and the addressor.

Find three more examples of appropriate language use in John Johnson’s opening email in (1). Next, select the ‘Answer’ button below.

Professor Badawi’s first reply in (2) is also both clear and appropriate. In paragraph 3, reproduced below for convenience, she provides a clear step-by-step explanation that helps John understand the solution method. Notice that each sentence (except the first) begins with a linking word, which has been underlined, to guide John through her reasoning. Linking words help connect ideas and show how they relate to one another, making mathematical explanations easier to follow.

From our course notes, you may recall that integration by parts tells us that the integral of u dv is equal to uv minus the integral of v du. Now we need to decide which function we will denote by u and which function we will denote by dv. That is, we need to decide which function to integrate and which function to differentiate. Since x cubed is a polynomial, when we differentiate it the power goes down by one, so it makes sense to pick u to be x cubed. On the other hand, both the integral and the derivative of e to the x, is still e to the x. So, if we let dv to be e to the x, our integral does not get any more complicated.

Your task: Re-read the paragraph, and then decide which of the underlined linkers in the email best matches each of the linkers in the list below. Next, select the ‘Answer’ button below.

• Because
• Therefore
• In other words
• On the basis of this preceding information, we can now proceed directly to …
• However / Alternatively

Beyond the clarity of paragraph 3 (and the whole email), Professor Badawi writes in an appropriate academic tone. Specifically, she writes in a supportive and encouraging manner, showing in her language choices that she values John Johnson’s question and is pleased to help him.

The first example of this in her first email is the first complete line: Thank you for your email. More than happy to help you with this integration problem. Both sentences here help to maintain a positive relationship between the addressee and addressor. She might also have written Happy to address this question. This is clearly shorter and slightly more informal, but still appropriate.

Find three more examples of encouraging, supportive or polite language in Professor Badawi’s first email. Next, select the ‘Answer’ button below.

You have read and studied the email correspondence between John Johnson and Professor Badawi. Now write a similar but imaginary email of your own. Imagine that you have understood a problem set in class and have answered it correctly. However, you now wish to ask the (imaginary) lecturer, Dr Jin Yitang, for a similar, but more advanced problem.

Write this email in which you do the following:

1. Introduce yourself appropriately and begin the email in a standard way.
2. State clearly what you have already done, i.e. you have understood and completed a problem set in the module.
3. Politely and clearly ask Dr Jin for a second more challenging problem.
4. End the email appropriately.

You may also wish to write a reply from Dr Jin, providing the requested additional problem.