When kids learn through discovery, they build their own knowledge, on their own. For that to happen, however, learning opportunities must be provided for.
Thus, whole group participation should be limited. Usually when a student answers a teacher's question, in front of his classmates, he is one of the brightest in the class. Quiet students, on the other hand, need to be exposed to learning situations in small group settings.
Those classroom events help kids come up with their own conclusions, after observing, recognizing, or putting things together. Such process may be driven by a single question. Pre-schoolers in a math class may be asked, for example, "What happens when three red blocks are joined by two blue blocks?" Many activities, to go further, may center on this kind of question. After kids find out that 3 plus 2 is five, they can discover what happens when two elements with the same attributes join four of other traits.
However, teachers should be able to identify those students who are not making discoveries, that is, when kids are told to do something that proves they have made the expected connections. In my example, a kid is given 10 circles and 10 triangles so he can pick a total of 7 shapes according the instruction given: "Show me 7, using both circles and triangles." In the end, he or she must realize that 3 and 4 makes 7, 5 and 2 makes 7, or 6 and 1 makes 7.
That assessment must be ongoing. Kids do not discover or gain knowledge at the same pace. Some of them need extra learning opportunities in different contexts. A struggling kid may not be able to learn about adding by putting objects together, but he may do it by drawing two different types of vehicles inside a boat and stating that when you put them together you get a total. Nevertheless, we must know who are those struggling students, by assessing their findings on a regular basis.
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