Teachers should focus elementary mathematics instruction on understandings. In the classroom, the teacher is a facilitator and designs hands-on experiences through real-world problem solving. Students are engaged in mathematics by constructing their own knowledge of mathematics, talking and sharing their strategies and thinking creatively, not by the teacher guiding students step-by-step through a process. Elementary mathematicians should utilize concrete, pictorial and abstract representations to explore mathematical ideas.

As bob is driving on an exit off the freeway, he comes to a stop light and sees a homeless man asking people for spare change. “see, he’s a perfect example of why we shouldn’t be giving welfare benefits to the homeless,” bob mutters to his wife. “he’s too lazy to get a job, but he’s healthy enough to beg people for their hard-earned money all day long.” what are the sample and the target in bob’s argument? are there any inductive fallacies present in bob’s reasoning (bias, hastiness, appeal to anecdotal evidence, self-selection)? if so, explain why. if not, explain why not.