How to test effectiveness of a children's museum in improving cognitive function? For those who have never heard of a Children's Museum before, there is a national association in the US with some information.  The basic idea stems from Vygotsky-like paradigms of learning through play.

My first impulse was: write a GUI that presents a series of standard cognitive tests in a fun way, put the software on a computer in a kiosk during the museum events.  Finally, compare child performance on the test to the number of visits to children's museum.

Of course, there's some considerations: if somebody takes the test multiple times, they're probably going to get better at it, so this might give a false-positive (rising with the number of visits).  So, for instance, only the first test taken by each person would be considered for analysis.

But that is a rather inexperienced shot in the dark.  Any other ideas?
General literature on training and educational program evaluation

In general, you would want to read up about program evaluation in general, and educational program evaluation, and training evaluation in particular.
With regards to the educational context I found this article online. 
With regards to training evaluation, you could check out Kraiger et al (1993) or Sackett and Mullen (1993) or any number of other textbook treatments of training evaluation.

Specific comments on evaluating a "children's museum"


What design will you use?: is it going to be a pre-post design where you compare knowledge before and after exposure to the program? Are you going to have a control group who does not experience the program or experiences an alternative program? How will you allocate participants to conditions? random allocation is better.
Decide on the constructs of interest?: What is the program meant to improve? You speak about quite general learning goals, but training programs are much more likely to have more specific effects. E.g., if you have a program that teaching addition, then students are likely to get better at addition, but their general intelligence is likely to be unchanged. You may also want to think about the time frame that benefits are meant to persist after exposure to the program. You can also look at Kirkpatrick's framework of training evaluation which talks about different kinds of outcome variables.
What will measure your constructs of interest?: Are you going to use existing measures or develop your own measures? If the content is highly specific to your program, then you will probably need to develop your own test items. 
Determine your sample: How are you going to recruit your sample? How many participants will you need to ensure reasonable statistical power?
When and how will measures be administered? I think you would want to do this in a controlled setting. A kiosk would probably be problematic from a measurement perspective.


Rough starting point

Of course there are a whole range of issues related to program evaluation, and dealing with children introduces many additional issues.
The following might provide a rough starting point:


two groups: control and intervention; about 100 participants per group
three time points: before intervention, immediately after intervention, a few months after intervention
Use some general measures of ability related to the program as well as some highly specific measures that tie in closely to program content. 
Also measure other factors like child and perhaps parent reactions to the program including both quantitative and qualitative evaluations.
Perhaps link in with some surrounding schools or day care facilities to recruit participants or use some form of waiting list system for admission to the program. Administer tests in a controlled environment (e.g., in a supervised room). 


References


Kraiger, K., Ford, J.K. &amp; Salas, E. (1993). Application of cognitive, skill-based, and affective theories of learning outcomes to new methods of training evaluation.. Journal of applied Psychology, 78, 311. PDF
Sackett, P.R. &amp; Mullen, E.J. (1993). Beyond formal experimental design: Towards an expanded view of the training evaluation process. Personnel Psychology, 46, 613-627. PDF