I personally agree with the latter. One needs to capture an understanding of how the problem is solved, rather than solve for the sake of meeting the end-product requirement (finding a solution/solutions). If a child is taught to approach solving with the perspective of solving the problem without understanding why, then the process spent on solving problem is not meaningful and constructive, without a purpose for learning.
As Van De Walle, Karp, and Bay-Williams (2009, p. 33) suggest, "Teaching through problem solving requires a paradigm shift... she is changing her philosophy of how she thinks children learn and how she can best help them learn." The presentation of preparing content for children to experience problem solving experience/experiences should be planned purposefully so that children are engaged meaningfully in the process. With this, the teacher plays a great role in facilitation the process, by providing opportunities for the children to develop a gradual continuum of assimilating and accommodating their prior and present knowledge.
The class was tasked with the responsibility of creating an "environmental task" where we were asked to create the teaching of a mathematical concept through the environment. My group had decided to focus on the concept Units of Measurement, by expanding the children's experience on the topic through the use of non-standard units of measurement to measure the length/circumference of objects/structures in the environment.
The children are involved in problem solving opportunities with the teacher's facilitation by:
1. Asking the children Open-ended questions
- "What do you think can be used to measure this object?"
2. Involve children in brainstorming ways of measuring the objects/structure
- "Asking children to brainstorm on the different ways of using their bodies to measure the circumference/length of the objects/structures.
The following are some of the places we have visited, and the intended teaching content pertaining to Units of Measurement:
1. Getting the children to count how many arm lengths are required to measure the length of the structure.
2. Counting how many foot-long is a stretch of step on the stairs.
3. Counting how many children are needed to go round the different structures.
"No problem can stand the assault of problem solving." ~Voltaire