Mental Modeling.

Businesses are about solving problems.  Where people have problems, businesses see opportunities to help add value.  The best businesses are those that see what needs to be done, do it, and dynamically adapt to improve solutions. 

But how exactly does one solve a problem?  We can hire people who are good problem solvers.  Intuitively this means we seek people who can define the problem (communications), gather potential paths, plans, and protocols (search analysis), select the most promising plan (prediction), and monitor or oversee the action path (leadership).  We can even begin to state desired qualities - communications, search analysis, prediction, and leadership. 

But what exactly does these mean?  It still does not answer the question. The general rule of thumb is that if we cannot explain a concept well enough to build it or to teach it, then we do not truly understand it.  Seeking these poorly understood qualitites is like seeking love - a case of "je ne sais quoi" but I will know it when I see it.  This is a lottery.  So where are they and how do they operate, these "things" that make the "things" to solve problems?  

As ever, we start at the beginning, with the simplified examples from childhood. 

Willatts (1990) showed that 12 month olds can plan and execute a 3-step sequential plan.  The infants were able to remove a foam barrier, pull aside a light covering cloth, and grab a string to reel in a visible toy.  This demonstrates (internal) communications - I want toy.  This demonstrates search and prediction - I can first remove foam barrier, then cloth, to get to toy.  It demonstrates leadership to keep all resources tied to the task.  Problem solving competence starts early.

Bauer, Schwade, Wewerka, & Delaney (1999) showed that 21 month olds can plan and execute on even nonvisible actions.  The children were shown a toy, then given the component pieces to assemble it.  In up to 90% of successful cases, they performed the actions in the precise correct order, which suggests they planned the solution rather than randomly jamming pieces together until they stick.  This trend increases with the 27-month olds also in the study.

Klahr (1989), and Klahr & Robinson (1981) showed the progression of working memory in 3-6 year olds in Tower of Hanoi.  The Tower of Hanoi problem is famous for requiring intermediate steps away from goal before progressing towards goal.    The results were as follows:

3 year olds could handle up to 2 intermediate moves .

4 year olds could handle up to 4 intermediate moves.

6 year olds could handle up to 6 intermediate moves.

This showed increasing depth and complexity of path analysis with increasing age.

Benson, et al. (1989) and Fabricius (1988) explored physical route planning.  One year olds can journey to unseen rooms to find unseen toys.  5 year olds appear to plan more alternative routes before starting and do less backtracking than 4 year olds.  This showed increasing breadth of planning with age.  Gardner & Rogoff (1990) showed that older 7-10 year olds could selectively plan in advance when given time, which reduced errors.  Younger 4-7 year olds did not do as much planning when given the chance.

Corrigan (1975), Sophian & Huber (1984), and Oakes (1984) explored the development of causal relations.  Their findings showed that contiguity (events close together in time) is present by the 1st year, precedence (the causal event precedes the effect) by the 3rd year, and covariance (the relation is stable and consistent over time) by the 5th year.  The children show that they tend to favor causal information in forming categories and drawing inferences (Keil, et al., 1998).  This shows that children gain more "logical" analytical skills with time.

Siegler (1976) and Case (1985) showed that problem solving development can be surprisingly domain specific.  They tested children of varying ages from 2-17 on predicting motions on an arm balance scale with varying weights and varying distances.  Their findings showed:

2 year olds could accurately solve the balance problem but only on simplified scales (i.e. fewer pegs and weights).

5 year olds appeared to use a simple Weight  rule.

9 year olds appeared to use an enhanced Weight, Then Distance rule.

13-17 year olds appeared to use an advanced Weight AND Distance rule.

Few children of any age group however, used the appropriate weight and distance cross product mathematical rule. 

Oddly enough, even a class of 16-17 year olds who had just studied the cross product mathematical rule - but, and here is the key, they studied it on a pan balance scale rather than an arm balance - did not apply that rule to the arm balance. 

Consistent with the study by Chi (1978) where child chess experts performed extremely well in chess memory but showed little or no improvement in numerical memory, the problem solving skills appear to be highly specific. 

Continuing with this specificity theme, DeLoache (1987; 1995) explored how well children can mentally switch between scale models to a full sized environment.  The task was to openly place a miniature model toy under a miniature model chair in a model room.  The children then needed to find the full sized corresponding toy in a full sized room.  The 3 year old children could solve this problem.  The 2 year old children could not.

Exploring further, DeLoache, Miller, & Rosengren (1997) found that the 2 year old children can do this after all if they are convinced the mini model IS the room.  The research team went through a pantomime act where the room and its contents were miniaturized via a magical miniaturization machine with bells and whistles and flashing lights.  They placed a miniature toy under the miniaturized chair.  Then they put miniature room through the magical machine in reverse and showed the full sized room again.  In this case, 2 year old children had no trouble finding the full toy under the chair. 

Implication: younger children are not necessarily incapable of solving the model problem, only more easily distracted by the mini scale model as novelty toy in itself.  Upon viewing the miniature model room, they appear to want to play with the room itself as a toy. Conversely, if the older 3 year old children were allowed to play with mini model room, they then associate that model as a separate toy itself, and they become unable to find the full sized toy in the problem task.

The takeaway message from this is that problem solving is not based on a canonical set of logical rules, steps, or qualitites.  Instead of young, immature children having no logic module and more mature individuals developing correct logic, it is more the case that even young children can display competence in problem solving with more mature children building upon those experiences.  Capabilities are not absolute.  Rather, they may be experience-dependent.  Chi (1978) demonstrated that memory improves with practice on the task at hand.  It does not derive from an absolute Random Access Memory capacity with MegaByte or GigaByte or ZettaByte chips.  It more appropriately derives from the richness of the spatial relations and temporal chains that exist from experience that a person can leverage and apply. 

The key neurological structures implicated in problem solving are executive and memory functions, notably the hippocampus and the prefrontal lobe - especially the dorsolateral prefrontal cortex.  The above research appears to indicate that it is not hard coded logic, nor pure memory capacity, nor processing speed.  It is not purely nebulous communication, search analysis, prediction, and leadership qualitites.  It has to do with selective attention, working executive attention, and social learning.  In other words, it has to do with spatial focusing and temporal chain filling in to track a series of actions towards a goal that signals to others about our fitness. 

These structures imply that problem solving skills are not absolute.  They will not progress linearly and monotonically.  They are not defining the features or the qualities of a person in and of themselves.  A person can not be a good problem solver - saying such could technically offer a bigoted opinion.  A person can only either have experienced solving problems of this particular form - or be ready to do so.  Any diagram showing problem solving skills as a linear, monotonically increasing function of intelligence over processing speed or capacity is a gross simplification at best and deceptive marketing otherwise.  But neither is problem solving haphazard or random or stochastic.  It is not necessarily age driven.  As both the empirical psychological and the structural neurological research confirm, it is spatially and temporally attention driven with a dose of social learning goal setting.  A child will devote spatial visual attention to understand the problem statement, apply past experienced temporal patterns in a chain to project to a future goal, one that is socially acceptable and maximizes social rewards - be it fun, funny, or impressive. 

At the end of the day, perhaps it is not that business is about solving problems.  Rather it is that solving problems is about business.  People  solve problems to add value.