During problem solving, do you use primarily algorithms or heuristics? What are the advantages of each? Both have advantages and are useful for different situations and each relies on different type of knowing. Objective knowing, which uses systems and logic, is better paired with algorithmic problem solving.This includes formulae and theorems that have been tested and proven to work. Algorithms are used when there is a clear, systematic pathway to solving the problem.
Heuristics, which incorporates both objective and subjective knowing, is useful when solving issues that do not require a fomula. Heuristics uses both objective and subjective knowing, including historic background, research and other knowledge and also includes what appears to be an intuitive sense. This last sense usually is a reflection of knowledge gleaned through other sources but contributes to finding solutions to problems in a way that cannot be quantified in a set formula. Heuristics allow the mind to apply all it knows from different sources and sometimes seems like a shortcut to the solution when different ways of knowing come together through thoughtful process.
These are two different routes to solutions, and you are correct when you state that you use them both for different problems. There are problems which require a systematic, logical and step by step method towards the solution, such as math. This could be referred to as "objective knowing (Frager & Fadiman, 2005)" which tests hypothesis, follows a concrete-sequential logic to the solution. In order to solve a math problem, you must use mathematical functions to find the answer. The ability to use a tried and true formula to answer the problem is an advantage and in many cases, necessary. ...
There are two different pathways to problem solving: heuristics and algorithms. Algorithms are better applied to quantitative problems that are best solved by formulas, such as math and some science problems. A heuristic approach is suited to solving problems that are broader and interpersonal. Both methods are useful but represent different ways of knowing. Algorithms use systems and heuristics apply a more holistic approach.