During the day the stars are still there, you just can't see them because the sky is so bright. For example, it's a lot easier to see the glow of a candle in the dark than in the light.
It is always hard to sense small changes to something that is already big to start with. For example, in a noisy room you probably can't hear a dripping faucet, but when everything else is quiet then you can hear the drip, even though the dripping hasn't gotten any louder. Its just easier to hear something soft in a silent background, than it is to hear something soft in a noisy background.
In the same way it's easier to see the dim starlight with a dark background than it is to see the same dim starlight on a bright background.

Try noticing the sky at night during the next month.Compare how many stars you can see now, when the moon is not up (until around midnight or later), to a few weeks from now when the moon is full again. Now imagine having the sun in the sky instead of the full moon. How many stars do you think you should be able to see?

You could also watch the sky as the sun is setting. As the sky begins to darken, when can you first see stars? How bright does the sky seem to be at this time when compared with daytime? Once the sky is fully dark, how bright are the first stars you could see compared to the rest of the stars in the sky?

The reason that you cannot see stars during the daytime is that the sun's rays overpower the faint light we see from the stars. During the night, when the sun's rays are blocked by the other side of the earth, it is possible to see the faint light of the stars shining in space. You can watch this transition if you watch the sunset on a clear night, as the sun's rays become fainter and fainter (and it becomes dawn on the other side of the earth), you can begin to see the first hint of the brightest stars. You will also notice that, generally speaking, the first stars to appear will be those farthest away from the setting sun (where the sky is darkest at that time).

Hope that helps!

This question can be partially answered by several effects. First, the human eye is sensitive to light over an enormous range of intensities. Typical "bright" stars are actually very dim compared to the brightness of the sun -- about a trillion 10^12 times dimmer. The brightness of objects illuminated by the sun typically 10 to 100 times dimmer than it is -- but that still makes the an enormous problem for the eye. (It has at least two mechanisms for light accommodation-- the iris which simple stops a fraction of the light like a camera lens, and chemical changes which enhance the cells particular to night vision. -- this takes some 10 to 20 minutes and unless you walk rapidly from dim to bright or vice versa you won't notice it.) So the first problem is that your eye -- to allow you to see, will reduce its sensitivity when there is bright light present.

Secondly, the atmosphere of the earth has lots of fine particles of dust which are so small they never settle to the ground. These dust particles scatter a small part of the light from the sun in random directions, and the mechanism for scattering works better for shorter (bluer) wavelengths. This is why the sky is blue and why the sun seems to redden as it sets -- it has a longer path in the air -- so more of the blue light is lost, then green ... etc.
By the way, clouds are made of much bigger bits, so they scatter visible light fairly evenly -- making them appear white. (But not to even longer light like infrared -- which can peer through clouds).

Both processes make seeing stars in the daytime very hard. However, if you happen to be in a deep well, with dark walls so that you only see a small bit of sky, and the rest of you visual field is dark, you might see some bright stars during the day.... So, do you think that the astronauts can see the stars during the day from the moon?

The reason we can't see the stars during the day is because when the sun is up, it is so much brighter than the stars that our eyes can't pick them out of the sky. You might think that you could see stars during the day if you looked AWAY from the sun, but the sun's light is spread out all over the sky by our atmosphere, which is part of the reason why the sky is blue during the day (it's clear at night, right?)

Here's a question for you. Stars, just like the sun, tend to rise in the east and set in the west. Why do they do that?

If that's too easy, here's a much harder question. The sun rises in the east and sets in the west. But in the summer, the sun rises in the northeast and sets in the northwest, and in the winter the sun rises in the southeast and sets in the southwest. (In the spring and fall, the sun rises and sets more or less directly in the east and west.) How or why does this happen? (Drawing pictures may help.)

In the day the stars are still there, but you cannot see them because they are so much fainter than the sunlight that is scattered by our atmosphere. If the Earth had no atmosphere, then our daytime sky would be black like at night, except the sun would be a huge spotlight shining down at us. In such an unpleasant world we might see stars during the day. But since we have an atmosphere, the sun's light scatters and gives us a beautiful blue glow from all over, not just from where the sun is. In other words, even if you look away from the sun you are still seeing the sun's light that has bounced off of some particle in the atmosphere, and that light is much brighter than the light from the stars.

Maybe your teacher can help you try to find out what the particles are in our atmosphere that scatter the sun's light and why the scattered light is blue!
WHY IS THE SKY BLUE?

It is possible to see a few of the brightest stars during the day. In fact, there is one star that can sometimes be seen during the daytime, but can never be seen at night! Can you guess which one? (Hint -- it's the closest star.)

There are at least two problems with observing stars during the day time. First, stars are very faint compared to the light from the sun (the nearest star). Our eyes are adjusted to sunlight during the day, and much less sensitive. Not only does the iris of the eye contract from the high intensity sunlight, but the retina becomes much less sensitive to light as well. A clear sky is transparent to starlight, but the blue color from scattered sunlight is bright enough to overpower feeble stars.

The other problem is that your eye has difficulty focusing to infinity when you are looking at a featureless blue sky. If you are trying to see small, faint things like stars it is critical that your eye be focused precisely. However, if you look at a blue sky there is no reference object for your eye to focus on and it is difficult to correctly focus on a star.

Nevertheless, it is possible to see some stars in daylight. The stars must be bright, such as Sirius, Arcturus, Vega, Capella, Rigel, etc. You also need to know exactly where to look, in advance. Finally, it helps if there is some very distant object right next to the star that you can focus your vision on. Aldebaran is a good star to try to see because it lies near the plane of the ecliptic, and the moon passes very near it once every 28 days. (Often the moon occults Aldebaran, that is, it passes between the Earth and the star.) If the moon is very near Aldebaran during the day, you just might be able to see it if you have good eyesight.