Malte Winkler

Hand-Held Calculators — What Should the Boulder Valley School District Do?
	•	position 1: ignore the existence of the gadget; we are not interested in technology, but in important mathematical skills; recommendation: do not use hand-held calculators in schools

A problem with this position is that you are ignoring the use of tools. Using these tools will be an important part of an individuals skill set. Also it will be exceedingly difficult to develop advanced math skills if you have to spend time bogged down dealing with the fundamentals all the time. When learning calculus you don't want to spend time doing the long division that the problem might require. 

	•	position 2: keep the curriculum the same, make children learn arithmetic, multiplication tables, long division, drawing square root by hands; recommendation: after they have it all mastered, allow the use of hand-held calculators.

This approach does not take advantage of the utility that the hand held calculator might be able to 
offer in the learning process. Scaffolding as discussed by PEA can be defined as the process of 
aiding a child achieve a goal or solve a problem that they would not be able to do "easily" on their 
own. Properly utilizing technology such as hand-held calculators or more advanced technology 
could help facilitate this scaffolding process thereby reducing the strain on the teachers and 
accelerating learning. Fading being the removal of aids  

	•	position 3: invent/ create new calculators, new curricula, new scaffolding mechanisms that make learning these skills more fun and create a deeper understanding of underlying concepts — recommendation: using these hand-held calculators, the learners would acquire the skills and the knowledge and eventually become independent of the gadget (“scaffolding with fading”)

The Hand-held calculator fail to be faded nor should they be. Position 5 maybe better.

	•	position 4: find new ways to distribute responsibilities between humans and machines such that humans do the qualitative reasoning, use estimation skills, relate the mathematical result to the real world and machines do the detailed quantitative computations recommendation: establish new divisions of labor, rely on distributed intelligence

Distributed intelligence is developed enough or prevalent enough to used in every situation where
it might be needed. 

	•	position 5: invent/ create new calculators, new curricula, new scaffolding mechanisms that make learning these skills more fun and create a deeper understanding of underlying concepts — recommendation: using these new curricula, the learners would acquire the skills and the knowledge via “scaffolding with fading”. Then allow use of conventional calculators as distributed knowledge devises. 

Scaffolding with Fading(SwF) as discussed by Pea seems to be a sticky issues when it comes to calculators in primary and secondary education. In learning to ride a bike you have scaffolds such as training wheels or the steading hand of a parent. These scaffolds are slowly removed dependent on the progress of the child never to be used again once the child has master the bike. One can not approach calculators in this fashion. Calculator if used properly can be used as a scaffolds to learning basic math skills by checking if a correct answer has been achieved for example. However calculator remain important after basic math skills are learned. Why waste time doing long division when learning to solve a calculus problem. Not learning how to use a calculator such as advanced calculators with the ability to graph functions and so forth will hinder the child's further development by wasting their time on uninteresting tasks. As Pea states calculators fall somewhere between SwF and distributed knowledge devises. The best approach might be to create new tools that embody SwF for learning basic concepts and then allow calculators to be used as distributed knowledge devises from which the user is never weaned .  

 Even if the software cannot do an assessment of the learner and then provide adaptive scaf- 
folding on its own, it seems entirely possible that the teacher could do such an as- 
sessment and then be in charge of switching levels of scaffolding that are provided 
by the software.