In this paper from Stanford, Menon reviews how brain pathways necessary for multistepped math problem solving take time to develop from early grades into adulthood. It's studies like these that are long overdue.
Children have to drive their procedural and working memory systems much harder when solving path problems because they haven't automatized number relationships or procedural steps. The brain areas involved show that math is difficult because it requires word / symbol recognition, basic number / quantity processing, fact and procedure retrieval, working memory, visual / semantic representations, episodic memory, attention, decision-making, and of course error detection, conflict resolution etc....and the truth is many of these cognitive systems don't come on online until later in childhood, and sometimes not fully into the early 20's. Some implications for educational programming are obvious - are some educational expectations developmentally appropriate? Are teachers sensitive to individual differences in neurodevelopment and can they modify educational expectations appropriately? The conventional school approach is to not advance students to the next grade if certain academic standards are not met. But what of the legions of students who are ahead in some areas and behind in others?
The developmental truth seems to be that brain processes important for math problem solving take time to develop:
"maturation of the prefrontal cortex and development of connections to the
prefrontal cortex increase in children between ages 6 and 14 years"
"posterior parietal cortex and the dorsolateral prefrontal cortex regions that
support working memory continue to mature from the age of 7–25 years"
"the capacity of memory systems, the speed of retrieval and the strategies used to remember continue to develop through young adulthood"
And "Because the prefrontal cortex matures relatively slowly compared to the posterior parietal cortex, children may be slower or have particular difficulties with certain types of arithmetic problems that require reasoning and interference resolution even when computational and retrieval skills are mature."
In our dyslexia clinic, these developmental factor often become huge issues. Though a student may be advanced in many areas, if automatization of tasks such as rote math fact retrieval or handwriting or weak, it may be enough to sink their boat and hold them back a whole grade. But if you follow these kids into high school, college, and beyond, you see their abilities just come online later - suddenly everything is easier and tasks that would have taken them hours to days, now can be done in 20 minutes.
This paper also highlighted another bone we have to pick with the way things are in medicine and education. When a child has weakness in visual working memory, we can't use that as a diagnosis in the clinic (ICD9 codes) or classroom (504 or IEP). They have to be diagnosed with ADD or ADHD or nothing. It's like trying to fix a fine precision watch with a sledgehammer. If a review paper from a reasonable place like Stanford can address children's learning in terms of episodic and procedural memory, visual or semantic representations and decision making, can't some of these same principles be discussed at school? The better we can get at identifying the problem, the better we can get proposing an answer.
Developmental cognitive neuroscience of arithmetic