H.W.
Hi there,
Years ago, I was a lead teacher of an older toddler group at a daycare. Our rule of thumb was that attention spans last about 1 minute per year old for the child. If your daughter is playing at something for two to three minutes, which can seem like an incredibly short time to us, she's actually doing fine. Some people might give you anecdotal advice on this, such as "My child at this age could do such-and-such for ten minutes" and that's fine, but bear in mind that the child is probably not doing *everything* for ten minutes. (and watching television doesn't count!)
Children will engage for longer in things they are interested in than those they aren't. Some of this has to do with where they are developmentally. It sounds as though your little one is going through a phase of gross motor development, and it can occupy just about every minute of their time because even as toddlers, children are hardwired to work toward mastery. It is very common for little ones to "not hear" when we yell Stop or No because they haven't developed the executive function skills in the brain which facilitate multi-tasking, and when a child is engaged in running, etc., ALL of their senses are focused on the task. This can be misconstrued as a child willfully not listening, when in fact, they truly 'don't hear' us. I've learned over time that it's best to catch up with an active child and get their attention physically first (through either gentle touch or joining them in,say, hopping or other activity) and then to give a direction. If it's a safety issue, be prepared to stay close and run after them, catch them physically and then calmly say, "Stop those feet now." Young children need to actually have their attention physically drawn away from their activity and over to you before they can hear what you are saying.
(At this point, some might suggest that I am too lenient or am not respecting a child's intelligence. This is far from the case. I have worked with children for 19 years come Novemeber, and these conclusions come with years of trial and error. They are also supported by research as well as hands on application.)
In regard to your question about activities, "will they sit and color", what I found was that each child played in the way they were needing to. When I presented markers to a group of toddlers, more of them were interested in playing with the caps than coloring with them. Give them 3 markers and two containers and the markers were treated as manipulatives, to be dumped out and rolled around! If you want to introduce art opportunites, more gross-motor friendly activities like those big 'dab-o' type sponge-tipped markers work well, because the toddlers love to pound them. Soft playdough for punching and pushing, along with some popsicle sticks and other items to press into it (don't worry about rolling pins, cutters, etc. at this age) is fun. Big paint work with big brushes is fun, and so are activities like "painting the house" with a paintbrush and water, where the child can use those big brush strokes and not make a huge mess. Dump-and-fill activities are par for this age, so if you have a sandbox, or even a bin of rice or dry oats, use it--just add some containers and scoops. I introduce a lot of fine motor skills practice around three years of age, and can give you a list of these for later on if you need. Just send me a message.
And to answer your last question: children will do/play whatever they are needing to learn without micromanagement, if given the opportunity and the setting. Some children engage in puzzle and block play or dolly play much earlier than others--it's a huge spectrum. If we keep distractions to a minimum (television off), a child will find what they are needing to do.
Children do not need to be talked into playing, and they learn through play. Bruno Bettelheim wrote a great book (The Good Enough Parent) and discusses how different kinds of play all help the child to work through what they are ready and needing to learn (especially in the social/emotional realm) , and children come back to tasks that they haven't successfully mastered, if we give them the chance. Be patient, know that your daughter sounds very typical, and if it were me, I'd let her play outdoors every chance she gets. Toddlers are exhausting, and if we give them room to move (and happen to have a fenced-in yard), this can help tremendously. She doesn't need you to over-engage, either...she knows what she needs to be learning, and will do it if she can!