Many websites like Lumosity.com claim to improve cognitive function and memory with a science based understanding of "brain plasticity". This however, is not true. Brain plasticity is a true quality that the human brain posses, there have even been studies showing that new brain cells form after death. This is only an effect of a cause however. The source of why brain plasticity is occurring is never addressed on the website.
The theory I have of late is based around the idea that attention is the source of action.
What sites like Lumosity seems to try to accomplish is training the ability to concentrate on novel problems. This may seem like you would become better at paying attention to novel problems. However, In reality your just becoming better at solving those specific individual pre-encountered problems with less of a load on your own cognition, but creating more of a load on solving broad, novel, un-encountered problems.
For example, When first learning to drive a vehicle or ride a bike, It can be difficult in the beginning, but after repetition it becomes so easy that it is like breathing. This is because you have put brain power into creating a fatty sleeve over each synapses that is connected to the neurons responsible for driving, therefore the neuron becomes much more conductive.
Eventually though, you will reach the point of not having to be cognitively aware while still performing said action. When this moment occurs for the first time, you experience it in the form of a distraction. When this occurs, you stop forming a sheath around the neurons responsible for driving. You also have a small feeling of boredom which is what induces the distraction. This feeling of boredom is induced by the ability to no longer need cognitive awareness to perform the current focus of attention.
If this feeling is acted upon, then the attention shifts. This is caused by the myelin sheath around the synapses connecting the neurons responsible for driving and motor function, together, being more conductive than the myelin sheath around the synapses connecting the neuron that is responsible for attention to the one responsible for driving which happens to sit higher in the cognitive hierarchy.
When this happens, you start trying to form a fatty sheath over a synapses that is connecting the neuron responsible for attention to neuron that is responsible for the new thing your paying attention to. In the mean time, each instance this happens, the myelin sheath around the synapses providing energy to the neuron responsible for the direction of attention degrades and causes the said synapses to become more insulative.
If you wanted to work on being able to solve novel problems before ever encountering them then you probably want to work on the fatty sheath that supplies energy to the neurons that are responsible for direction of attention.
This is possible by holding attention on said task, driving in this case, even when boredom occurs. It forces the brain to form a fatty sheath around the synapses next up in the hierarchy of energy flow.
This is why attention to the breath and bodily sensations is the best form of meditation for creativity and preparing for any unforeseeable cognitive demands. Because it very quickly induces sustained cognition to have a higher energy demands higher up levels of the cognitive hierarchy, which also puts a demand on the synapses to have a higher conductivity up the cognitive hierarchy.
Basically, to bring this whole article together in somewhat layman's terms, sites like Lumosity keep you in a state of creating myelin sheaths around lower level forms of specified cognition by constantly attending to novel problems which makes it easier to solve those many specific novelties but worse at solving actual novelty. While the ability pay attention to highly expected and predictable cognitive tasks creates myelin sheaths around the synapses of higher and broader forms of cognition to actually ease the cognitive demand of performing novel or broadly understood tasks and solving novel or broadly understood problems.