Low crystalized intelligence- failure to transfer skill from Hippocampus to cortex? We know that when we process some information or solve some problem, we need to pull information from long term memory to working memory. There are few factors known to me that can cause a failure during retrival:


Working memory shortage
poor temporal context
The memory was never transferred to long term memory to begin with


Low working memory is something that can be easily diagnosed with Dual n-back tests.

A study on anterograde amnesic patients have shown that they do not appear to have poor temporal order (5), which indicates that maybe temporal context is not to blame when people forget things. However, it is possible that this does not apply on all cases.

This leaves the third possibility: that short term memories do not always get transferred to long term memories. Is this a possibility? If yes, then why does it happen?



Sources: 


Types of memory
Role of working memory
Temporal context
How is information transferred into long-term memory?
Anterograde amnesia and temporal order
Dual n-back test
First we need to establish the link between crystallized intelligence and the types of memory. Long term memory can be divided in two parts: Procedural and declarative. 

Episodic memory is recollection of events, semantic memory is recollection of learned facts, and procedural memory includes priming, classical conditioning, skill based learning etc and does not require intentional or conscious recollection of an experience (1).

Among these types, Howard and Kahana's model of temporal context theory is only applicable to the declarative branch (2). 

The answer to the question depends on which type of problem solving we are talking about. All three types of memories get used during learning. Problem solving requires skill based learning. But we must also remember a lot of facts in order to solve certain real world problems. Practical experiences also come in handy. However, if we can recall all the related facts but still fail to solve a problem, that indicates poor skill-building. According to Cattell‘s (1971, 1987) Gf-Gc theory, fluid intelligence causes crystallized intelligence (5). therefore, low fluid intelligence might be a reason behind poor skill based learning.

"failure to transfer skill from Hippocampus to cortex" is not likely to happen because skills do not seem to have any short-term and long-term phases. Excerpts from a recent study (6):


  We have shown that when people adapt to successive and opposing sensorimotor transformations, they fail to consolidate learning of the first even when the two transformations or tasks are separated by 24 hr.


From a meta-analysis (4): 


  This implies that a procedural memory may never become fully stable and instead remains vulnerable to interference. When exposed to task B, participants may have retrieved the procedural memory associated with task A and modified it, ‘overwriting’ the memory for task A with information relevant to task B............ It implies that learning a new skill leads to the automatic destruction of another skill. It would never be possible to have skill in more than one task! Our ability to acquire multiple skills may depend upon having contextual cues available to signal the switch from one task to another. 


This theory proposes that our procedural memory has a completely different type of contextual cue system, one that cannot differentiate between multiple skills as efficiently as episodic memory can. This theory also explains why ADHD is such a barrier in learning.

Now we can guess what type of memory is involved in skill learning: When a new skill is being formed by Gf, it is likely utilizing the info available in short term memory to do so. When a skill is being recalled, It goes to working memory for utilization.

In conclusion: Forgetfulness indicates inefficiency in declarative memory, while poor skills might indicate low Gf and/or poor attention span. 

Questions remaining:


What causes inefficiency in declarative memory?
How to strengthen our procedural memory? Can practice help?
Why do people who find it easier to learn through practical and struggle to grasp abstract concepts?


But these questions deserve new topics.



Sources: 


Green REA, Kopelman MD. Neural organization of memory andmemory impairments. In: Trimble MR and Cummings JL, eds. Contemporary behavioural neurology. Boston: ButterworthHeinenman, 1997; 139–152.
https://pdfs.semanticscholar.org/5b83/58754a92cf648f3c5ccea7f34df62bba1e74.pdf
https://www.cambridge.org/core/journals/journal-of-the-international-neuropsychological-society/article/interdependence-of-episodic-and-semantic-memory-evidence-from-neuropsychology/1A97EFA24F2CDED16D12964AD5EE67F9
http://www.cell.com/current-biology/pdf/S0960-9822(04)00937-6.pdf
http://ir.uiowa.edu/cgi/viewcontent.cgi?article=2639&amp;context=etd
http://www.cns.atr.jp/~kawato/Ppdf/CaithJNS04.pdf