qǐng kàn kèchéngbiǎo shàng de sījiàokè.

请 makes the sentence polite. Here it works like please in English.

So 请看…… means please look at... or please check...

A few notes:

• 请 often appears in polite instructions, signs, announcements, or service situations.
• It can also mean to invite or to treat someone in other sentences, but here it simply softens the command.

In Chinese, the subject is often omitted when it is obvious from context.

So 请看课程表上的私教课 naturally means:

• Please look at the private lessons on the schedule
• with an understood you

This is very common in instructions and requests. Chinese does not need to say 你 if everyone already knows who is being addressed.

课程表上的 means on the schedule or on the course timetable.

It breaks down like this:

• 课程表 = course schedule / timetable
• 上 = on
• 的 = links the phrase to the noun that follows

So:

• 课程表上的私教课 = the private lessons on the schedule

The whole phrase before 私教课 describes which private lessons we mean.

Here 上 is a location word meaning on.

Chinese often uses 上 with things like:

• 桌子上 = on the table
• 墙上 = on the wall
• 名单上 = on the list
• 课程表上 = on the schedule

Even though a schedule is not always a physical paper in front of you, Chinese still uses 上 for information shown on it.

So 课程表上 is very natural.

的 connects a descriptive phrase to a noun.

In this sentence:

• 课程表上 = on the schedule
• 的 links that phrase to
• 私教课 = private lessons

So:

• 课程表上的私教课 = the private lessons that are on the schedule

You can think of 的 as the marker that turns 课程表上 into a modifier of the noun after it.

私教课 means private lesson or one-on-one lesson/class, depending on context.

It is made of:

• 私教 = private instruction / private coach / personal trainer
• 课 = class / lesson

In different situations, 私教 can suggest slightly different things:

• in a gym: personal training session
• in education: private tutoring lesson
• in a general schedule: private class / one-on-one lesson

So the exact English translation depends on the setting.

These two patterns do different jobs.

1. 课程表上的私教课

   • this is a noun phrase
   • it means the private lessons on the schedule

2. 私教课在课程表上

   • this is a full sentence
   • it means the private lessons are on the schedule

In your sentence, the speaker wants the listener to look at a specific thing:

• please look at [the private lessons on the schedule]

So Chinese uses the noun phrase before the verb’s object position.

Yes. 看看 is often used in spoken Chinese to sound a bit softer, lighter, or more casual.

Compare:

• 请看课程表上的私教课。 = Please look at the private lessons on the schedule.
• 请看看课程表上的私教课。 = Please have a look at the private lessons on the schedule.

Both are fine.
看看 can feel a little more conversational.

It could be understood in a few related ways, depending on context.

看 is a flexible verb. Here it can mean:

• look at
• check
• read over

If someone is directing your attention to a timetable, check or look at may sound most natural in English.

So even though the basic meaning of 看 is look, in real usage it often overlaps with read or check.

Yes, it is understandable and natural in the right context, especially if someone is directing attention to a timetable or class schedule.

It sounds like:

• a teacher or staff member speaking politely
• a written instruction
• a notice telling someone where to find the relevant classes

Depending on the exact situation, Chinese speakers might also say things like:

• 请看课程表上的私教课程。
• 请查看课程表上的私教课。
• 请看一下课程表上的私教课。

But your original sentence is fine.

Nothing unusually tricky, but a learner may want to watch these points:

• 请 qǐng: third tone
• 看 kàn: fourth tone
• 课程表 kèchéngbiǎo: fourth + second + third
• 上 shàng: fourth tone
• 的 de: usually neutral tone here
• 私教课 sījiàokè: first + fourth + fourth

A natural rhythm would be something like:

qǐng kàn | kèchéngbiǎo shàng de | sījiàokè

The 的 is light and unstressed.