Reddit mentions of Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom

You don't. When we lie to students and tell them that such and such mathematics relates to their lives, when they know better and we know better, you lose credibility and they lose interest.

Instead, you should be upfront with them. Admit to them that unless they get a job that uses maths, they will never sit down and derive two systems of equations in two variables and solve them. Instead, the act of learning the maths--of thinking about them, struggling with them, and understanding them--will arm them with cognitive tools which translate to all thinking processes in all areas, which is unmatched in studying any other area.

You tell them that you study maths because it makes you a smarter person, physically, through shaping the way neuron connections are eroded into their brains. Convince them that the time they put into studying the abstractions and structures of problems in mathematics will erect a permanent filter in their mind which they will push every thought through for the rest of their lifetime.

And then you prove it to them. You take an idea that you know is just past their understanding--through formative assessment--and you demonstrate to them that they understand it. This part takes work because it is necessarily one-on-one.

Maybe you have a student that doesn't understand a concept. You give him a problem that has that concept and he hits "the wall." This is where you get excited, because you're about to blow their mind. Don't give him the answer or show them the steps, teach him to understand the question. Teach him how to think about the problem, how to reach into what he knows already and put the ideas together to understand this concept. Lead him there, don't take him there.

When this happens you'll get some sort of "eureka" moment from him, and you will have begun a process of successes that you can build off of that will invariably convince the student that he can do it. He'll begin to see that math isn't some magical manipulation, but rather that he can understand it with enough hard work and intentional thought. Most importantly, you've built yourself credibility, and the student has a glimpse into the meaning of what would otherwise seem like idealistic bullshit.

And then, you have built a student who will willingly study maths for the sake of studying maths.

See Daniel Willingham's book Why Students Don't Like School. He makes a much better argument against "making it relevant" and goes through the brain processes to describe what happens in learning and what motivates us to do it.

I can't even imagine how hard writing a blog is, so I absolutely commend you for trying it out!

However, I think mistercow had some very valid points to go along with his cool username. I had a lot of the same thoughts, and almost stopped reading on several occasions even though the subject matter is of immense interest to me (I'm a pediatric neuropsychologist). I don't think mistercow was offended by your blog entry, but I think he was justifiably confused and maybe even frustrated by some of the vagueness and conflation of related concepts in your post (and 'prefrontal visual cortex' doesn't make it any better... I have no idea what you might mean by that? Maybe 'primary visual cortex'? But that doesn't make sense either...).

If you want suggestions, I read a lot of sciency blogs as a diversion from all the usual textbooks and journal articles I read, so I'm happy to give some friendly advice.

The blogs that I find most successful focus small - they only try to tackle one thing at a time, for example. If you want to talk about using visualization to help improve your memory, great, awesome, do it - but only do that. I don't think you need to also go into your views on caffeine, or hydration, or chess, or mentally-effortful series practice, or the use of imagination to solve problems, or your lizard brain, or visual pattern recognition (which is done by entirely different brain systems than the ones involved in active problem solving, BTW - that's what mistercow had a problem with... you can't just "make" a logical problem that requires cortical effort into a subcortical visual recognition problem even if you wanted to, though you can use visualization strategies to help you solve problems, which sounds similar but is really entirely different), or any of the other things you touch on in about one sentence each. You could save all of these ideas for other posts, for example. This gives you more to write about in subsequent posts, keeps your focus for each post laser sharp, and directs your readers' attention exactly where you want it.

Once you've figured out what you want to talk about, get a hook. A lot of popsci bloggers use a current research study, a classic research finding, or an everyday example as the introduction to a topic. So, if you want to talk about visualization in the pegs of loci sense (which I think is where you're headed?), you might introduce readers to the general topic by having them first try to remember something using a verbal cue (e.g., quick - what brand of spaghetti do you usually buy?), and then try to remember it using a visual cue (much easier: what color is the box? where in the grocery store is it located?). Or, briefly describe a classic study on how effective visualization is as a memory strategy. Alternatively, talk about someone who is really good at memorization using visualization strategies, like those people who can memorize hundreds of playing cards at once, or someone like Daniel Tammet.

Then, give your readers what they've come for - explain science in a way that's directly applicable to their everyday lives. That's a lot easier said than done... you've got to get the science right, the explanation right, and the implications of the science correct, all without being too simplistic or going beyond what the science can support -- a delicate balance to be sure!

As an example of why this is so tricky, and I promise I'm not trying to poke holes in your specific post here, but I had a lot of trouble with your assertion that "At some point, people stop using their imagination to solve problems" -- I am literally not even sure what specific scientific findings you might be thinking about.

Certainly people don't "stop" using visualization or imagination or creativity or any such thing. I think you might be thinking about the sort of 'common sense' idea that as kids grow up, they 'lose' their creativity and imagination? However, science doesn't really support this. In fact, somewhat counterintutively, this common 'experience' that adults report results from the fact that we get better at thinking linearly and using useful cognitive heuristics as we age, but this massive increase in problem-solving ability comes at the possible expense of the ability to think in illogical and/or inefficient (and therefore potentially creative) ways. This leads to some strange research findings (that in fact might make a good blog post!), such as that kids are better than adults at not falling into some easy cognitive traps (e.g., together, a ball and a bat cost $1.10 - the bat costs $1 more than ball - how much do each cost?). Ironically, though, you then go on to recommend some 'repetitive' pattern-recognition-y mental exercises, which train the very skills adults have that kids have less of! So, here's an area where I think you might want to tighten up what you're thinking about, and/or your explanation, and/or your understanding of the research base in the area.

In general, while you seem to have great intentions, I think a general cognitive psych book might provide you with some helpful background... a technical but yet understandable one on how people learn to think is Why Don't Students Like School?.