Interesting concept, odd execution.
First, the control choices were odd. Having jump be space and shard functions enter is too much of a distance. I had to use my right hand, the hand i'm using to move the character, to also use the shard. On the keyboard, I would recommend making z and x jump and shard.
Second, I can't see enough of the levels. It felt wrong teleporting above spikes I couldn't see. This can be fixed by having a fixed view to see the entire level or designing the levels so you'll never have to throw the shard somewhere you can't see.
This idea can work, with tweaks to the controls, level design, and other little things. If you're looking for ideas, I recommend a time limit or time record, using the shard and teleportation to get through the level as fast as you can. Overall, you have a good concept, criticism, advice, so please, build off that.