In my training, I was shown how to do the geometrical form of multiplication (see math album 1 on albums page.) A couple of months ago I had some students who were struggling with division using the Stamp Game. They were not struggling because they didn’t understand it. They just didn’t like using the materials – they thought it slowed them down. Yet, they were unable to do long division purely in the abstract. If these were 2nd graders, I would have simply insisted that they continue with the stamp game. However, these are students brand new to the Montessori setting in 4th grade. So I worked through the Stamp Game with them making sure they understood each step, querying them at the right moments. Once I was sure they understood the logic behind it, I introduced them to the Geometrical Form of Long Division. Maybe this is already out there, but I have not seen it. I created the following lesson using graph paper, green, blue, & red pencils.
The next type of case study topic is the deviant case. This is completely different from what the former two talks about. Here, the purpose of the research is to unravel some facts about exceptional, unusual and untypical things and situations. This is more difficult to determine, but also attracts more people because of its unique nature. The crucial case study topics are ones that receive great commendation, but are rarely put into any use. The core points of the crucial study topic is to determine that propositions or solutions that work when put under the least favorable conditions will actually do better when they are tried under other circumstances. The last is the archetypical cases, and here, we talk about the cases that generate the categories of which they are erroneously taken as representatives in comparative analyses. These defining cases that should be treated as defining cases are erroneously classified simply as earlier models. They are not prototypes, but archetypes. You have to examine how the models are also archetypes that spur the others and not just as parts of others.