1. Describe two similarities between the traditional lesson and the constructivist one as described above. What are two differences?
The traditional lesson and the constructivist lesson were similar in that they were both using measurements in their lessons and they both were looking for the measurements of a certain object. The purpose of either lesson was to understand how measurements work and visually see how long measurements of the objects were. There were many differences in these two lessons despite the fact that they were both dealing with measurements. In the traditional lesson, the teacher provided the measuring tools and the measurements of the whale. The purpose of this was to allow the students to experiment with the yard sticks and to see how long a whale actually is. When performing the constructivist lesson, the teacher only provided the students with the ship template and the orders from the king. The students were not given any hint as how to measure the ship and were not given any help from the teacher as they tried to solve this puzzle. In all, the differences between the two lessons were instruction and no instruction.
2. What are two benefits and two drawbacks of the constructivist approach as described above? Why? In your opinion, are the benefits worth the costs? Explain your response.
The constructivist approach is beneficial in that it gives students the opportunity to experiment. By experimenting the students are engaged and they are more prone to finding a solution. Another benefit is that they can learn by trial and error. When measuring the ship with their hands, they realized that all hands are different sized, therefore, forcing them to rethink their method. Though it seems that allowing for students to use discovery learning, it has many drawbacks as well. This approach took up a lot of valuable time and if it had been taught differently, the concept could have been taught and learned within one class sitting. Another drawback to this approach is that students were not catching on very fast and were creating many misconceptions that were not being cleared up or addressed by the teacher. This can lead to confusion down the road for the students. It would be difficult to be learning how to do something one way, only later to find out that it was incorrect. I believe that this approach is only worth the costs when the teacher is using guided exploration. This way, the students are still able to experiment and explore concepts for themselves, but the teacher is there to offer any aid that is necessary to ensure quality student learning.
3. How does the constructivist lesson described above promote critical thinking? Give specific examples of critical thinking from the case study and include a definition of critical thinking to support your response.
It promotes critical thinking by forcing the students to create methods of measurements without having much knowledge of why we measure things. This then leads to greater understanding of why it is important that we are consistent when we measure and the students will retain that information for a very long time. The first instance I noticed of critical thinking is when the students used the boy to measure out the ship. They realized that they now had some measurement to work with and took the opportunity to explore this new idea. To the students this made perfect sense, but when the teacher presented them with the idea that the king had never met the boy and would not know how tall he was, it cause the students to think critically again to solve for a new way to measure the ship.I believe that with prior knowledge of measurements, this could have been an authentic activity. Originally, I do not think that this activity is authentic because it did not teach the children the proper rules of measurement. If the teacher would have used the same scenario and offered a ruler or a meter stick, I then think that the children would have learned a lot more and would have been able to understand how to use measuring tools. The teacher needs to focus more on how the activity is going to benefit them in their lives. I'm afraid that she spent too much time worrying about students engagement. She could have engaged the students just as effectively if she used the same activity where the children were provided with measuring tools.

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