Every photographer battles with sun shadows, I personally try to avoid shooting portraits on sunny days as much as possible. In an overcast sky you get a real nice soft light with little shadows. However, there is hope.
The first is to use artificial light. You shooting with a D3000 which I don't believe has command (wireless) flash, but you do have a popup flash. This will act as a fill light and fill in the shadows. They're color are corrected for daylight so it should look moderately natural.
Short of this, you can use a speed light. I use an SB-600. These exceed the built in flash in many ways. You can rotate the head on the flash to "bounce" it off walls and things for indoors shooting (which turns out amazing by the way). Plus, it's a heck load more powerful. The ideal thing in this situation would be to use a correctly positioned wireless flash bounced off an umbrella. I know I said the D3000 doesn't have command flash, but I'm sure there is a kit you can buy to convert it to wireless. But that's probably further than you'd like to go with it.
After you've explored these options, there's post processing. One you've done your photoshoot, it's time to edit your photos. I estimate 99.999% of photographers edit their photos (called post processing). Some argue it's one of the most important aspects of the whole process. You can do something that's called "increasing the shadow exposure". This will take the dark (shadowed) ares of you photo a brightened them.
Having said all this, I don't think you photos are that bad. You've got a sense for composition for sure. In these style of photos I'd like to see more depth of field, but that's a discussion for a later time.
Here are some examples of shooting in the sun that I've had to combat:
Not that I like this photo, I feel like I've over processed it. but it does illustrate the power of the aforementioned "increasing the shadow exposure"
Artifical light - SB-600 on umbrella at camera right:
Heavily post procesed so you don't notice the harsh shadows
Sometimes, you've just gotta embrace the sun. These were taken during the "golden hour" - either 1 hour starting at sunup, or 1 hour before sundown:
Another example of artificial light. Same configuration as mentioned above.
Here's an example of what's called a HDR (High Dynamic Range). This is a little outside the scope of this discussion, but I figured I'd throw it in so you could see what might be down the road for you. Give it a few months of playing with your camera and give me a private message and I'll give you some great links to read. Remind me of this conversation when you do because my memory isn't all that good, haha.
Anyway, I hope I helped more than confused. Feel free to retort with any questions.
Oh, and welcome to the forum