Analysis of the Bees problem

Because this problem is given to kindergarten children, who don't have a lot of mathematical tools, this problem that would be pretty trivial for a third or fourth grader takes some significant problem solving thought and analysis.

The problem is intentionally simple, so that it can be remembered (not read) and the difficulty is primarily in the mathematics and not the interpretation. To the extent that there was interpretation of the problem to do, however, the interpretation was intentionally left to the students, so there is a reasonable amount of age-appropriate intrepretation of the problem, which helps to build the standard 1 skill  "explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals."

Each child had their own strategy that they used to solve the problem, using tools and strategies that they were comfortable with*.

After solving the problem, the children shared how they solved the problem.  After the children had shared their strategies, the teacher pointed out the strategy that one of the children used of saying how many bees as he counted up to highlight a useful strategy that other children might find useful. One of the things this discussion accomplishes is for children to learn how to "understand the approaches of others" (standard 1)

Problem solving strategies included very concrete: one boy used unifix cubes to direct model showing each of the bees and each of the legs, and more abstract: two children used counting strategies: one counting on fingers and keeping track mentally, and the other counting on the number line. Each of these strategies uses math to solve the problem by converting the problem from the context in which it is given to a form where each child can work with the numbers in a more mathematical way. These more mathematical representations are very early mathematical models (standard 4), and they form a somewhat decontextualized way of thinking of the problem (standard 2). 

 

* These strategies are clearly not ones that students developed for this unique problem, but these are strategies that these children use for most of the problems that they solve.  This is important work is for these children to have lots of opportunities to build on and improve their ability to solve problems with their strategies (practicing a strategy so that you master it and know you can use it in a variety of situations is an important part of becoming a proficient problem solver).

Often pre-teachers tell me that these students must be unusually gifted.  My reading of this clip is that these children are probably some of the more proficient problem solvers, but I suspect that they were chosen for the clip largely to show a variety of strategies rather than to show the most proficient in the class.