Expectations From The Proceptual Divide Analysis
Expectations from the proceptual divide – two episodes
Raquel, a second year student of Business had some interest about the problem and decided to work alone. Grabbed her tablet a searched (in Portuguese) for similar problems switching to English when she found some articles related to Monty Hall.
Her solution is based on the conditional probability, namely Bayes Theorem using a decision tree as shown in figure 2 bellow:
Figure 2. Sketch presented by Raquel to explain her solution where P stands for “Prize” (“Prémio” in Portuguese) and N stands for “Nothing” (“Nada” in Portuguese).
In this decision tree Raquel explains that the red crosses stand for the time that the host reveal one door. Then she continues her explanation …show more content…
Activity system drawn from Raquel outcomes.
This activity system also evidences a difference on the expected outcome from the two isolated activity systems (student and teacher), the intersection made from this kind of Venn diagram in the middle shows a third object that emerges from the connection of both activity systems.
The next episode with Mariana went up differently. Mariana is a third year student in Education, and she is at ease with the use of technology, so she choose the Monty Hall problem and tried to simulate the solution using a spreadsheet. The next section describes all the steps Mariana made to build the simulation:
On the first cell she wrote =INT(RAND()*3)+1 to generate a whole number form 1 to 3, on the second cell used the same formula to generate a new random number (from 1 to 3) to indicate the door that the contestant could chose, for the third cell the formula was more complicated, but with the help of some spreadsheet cheat sheets she got a conditional formula: …show more content…
As the number were randomized she got values around 67,5% every time arriving to the conclusion that it is advantageous to switch.
This method to find the result is a convincing demonstration and could be found in many web pages around internet, but in this case Mariana didn't just copy the formulas or the demonstration spreadsheets that can be downloaded, she explained to her classmates and replicated the simulation.
Although this simulation isn't a traditional mathematical proof it shows that technological tools could be used to give a new look to mathematics, this outcome was classified as relational in SOLO levels close related to the extended abstract level because, by one hand Mariana makes complex relations, explain the causes, integrates several areas of knowledge, by other hand she goes beyond the topic making generalizations to other concepts.
The activity system is different from the one presented in figure 4 due to although the system contradictions are the same in figure 5.
Figure 5. Activity system drawn from Mariana outcome.
This activity system shows the use of more complex procepts clearly a sign of proceptual thinking due to the use of simulation evidencing a proceptual
Raquel, a second year student of Business had some interest about the problem and decided to work alone. Grabbed her tablet a searched (in Portuguese) for similar problems switching to English when she found some articles related to Monty Hall.
Her solution is based on the conditional probability, namely Bayes Theorem using a decision tree as shown in figure 2 bellow:
Figure 2. Sketch presented by Raquel to explain her solution where P stands for “Prize” (“Prémio” in Portuguese) and N stands for “Nothing” (“Nada” in Portuguese).
In this decision tree Raquel explains that the red crosses stand for the time that the host reveal one door. Then she continues her explanation …show more content…
Activity system drawn from Raquel outcomes.
This activity system also evidences a difference on the expected outcome from the two isolated activity systems (student and teacher), the intersection made from this kind of Venn diagram in the middle shows a third object that emerges from the connection of both activity systems.
The next episode with Mariana went up differently. Mariana is a third year student in Education, and she is at ease with the use of technology, so she choose the Monty Hall problem and tried to simulate the solution using a spreadsheet. The next section describes all the steps Mariana made to build the simulation:
On the first cell she wrote =INT(RAND()*3)+1 to generate a whole number form 1 to 3, on the second cell used the same formula to generate a new random number (from 1 to 3) to indicate the door that the contestant could chose, for the third cell the formula was more complicated, but with the help of some spreadsheet cheat sheets she got a conditional formula: …show more content…
As the number were randomized she got values around 67,5% every time arriving to the conclusion that it is advantageous to switch.
This method to find the result is a convincing demonstration and could be found in many web pages around internet, but in this case Mariana didn't just copy the formulas or the demonstration spreadsheets that can be downloaded, she explained to her classmates and replicated the simulation.
Although this simulation isn't a traditional mathematical proof it shows that technological tools could be used to give a new look to mathematics, this outcome was classified as relational in SOLO levels close related to the extended abstract level because, by one hand Mariana makes complex relations, explain the causes, integrates several areas of knowledge, by other hand she goes beyond the topic making generalizations to other concepts.
The activity system is different from the one presented in figure 4 due to although the system contradictions are the same in figure 5.
Figure 5. Activity system drawn from Mariana outcome.
This activity system shows the use of more complex procepts clearly a sign of proceptual thinking due to the use of simulation evidencing a proceptual