People's problem-solving ability is functionally like a bicep. If you exercise it, it will grow. Lately, this has been rediscovered in the context of "Growth Mindset." Two professors in England, Michael Shayer and Philip Adey, developed a series of lessons in the 1990's that develop problem-solving ability. This is not like that Lumosity nonsense. Shayer and Adey's Cognitive Acceleration curriculums are as effective and reliable as penicillin.
I've done some work implementing Shayer and Adey's "Cognitive Acceleration through Science Education" (CASE) materials. Here's a written overview, here's a talk I gave online, and here's an example exercise on proportional reasoning (and coffee beans) that uses Shayer and Adey's Curriculum Analysis Taxonomy (CAT). Adey gave me personal permission to distribute the CAT "as widely as you like," so me sharing it with the web isn't copyright infringmment, so far as I understand.
Philip Adey was far more eloquent than me on the subject. Here he is giving a talk at an ICOT, a few years before he died.
Shayer and Adey used a "Science Reasoning Task" (SRT) to assign a student to a (modified) Piagetian category. That measure isn't widely used in the US, and it seems like Lawson's Classroom Test of Scientific Reasoning (CTSR) should describle (more or less) the same student ability. I made a small study of this relationship, and from the data I have, the link between the two measures is probably there, weak, and noisy. Here's a summary. If you'd like to contribute student data to this study to improve the study, send me an email and I'll share the assessments.
Nathan Moore, 2015-August-13