Ch. 7/8 Case Study Analysis
In the article titled "A Constructivist Perspective on Teaching and Learning Mathematics", the author, Deborah Schifter, contrasts two mathematics lessons which she feels offers an understanding of the difference between a lesson based on constructivism and one based on the traditional didactic approach to learning.
In the traditional approach, the teacher has noticed that the students are very excited to find out that blue whales can grow as long as 100 feet so she decides to have the students measure this length in the hallway. Here's how she went about it:
I told the children exactly how we would go about measuring the whale's length. We would take the yardstick, which we hadn't explored, and we would put it down and keep track of where it ended and then place it there and keep counting till we reached where it ended and then place it there and keep counting till we reached 100 feet. (Schweitzer, 1996)
Although the children were quite impressed by the length of the whale, the teacher recounts that the lesson seemed unsatisfying, and wondered what the students had actually learned about measurement.
In the constructivist approach, the teacher had a measurement activity concerning Thanksgiving. She laid out a model of the Mayflower on the floor in the center of the room using masking tape. Then she prepared a scroll or edict for the students to read, telling them that the ship could not sail until they told the king how large the boat was. After the edict was read, she waited for the students to figure out how they could measure the ship and be on their way. Here's how she described what happened after the reading of the scroll:
"Well, what should we do? Who has an idea?" I asked. Thus our discussion of measurement began... or I thought it would begin. But there was a period of silence-a long period of silence.
What do young children know about measurement? Is there anything already present in their life experiences to which they could relate this problem? I watched as they looked from one to another, and I could see that they had no idea where to begin. Surely, I thought, there must be something they could use as a point of reference to expand on. Someone always has an idea. But the silence was long as the children looked again from one to another, to Zeb, and to me. (Hendry, 1996)
After some confusion about the word edict on the scroll (some students thought the boat was three feet long because the E in edict looked like a three) the following interaction occurred:
I felt we were back to square one again with more silence, until Tom raised his hand and said, "Mrs. Hendry, I know it can't be three feet because the nurse just measured me last week and said that I was four feet, and this boat is much bigger than me!"
From Tom's initial observation, our discussion on measurement was basically off the ground. Hands immediately went up. The children now realized that they knew a little about measurement, especially in relationship to their own size and how tall they were.
"Let's see how many times Tom can fit in the boat," someone suggested. Tom got down and up several times along the length of the boat: the children decided that the boat was four
"Toms" long.
"How can we tell that to the King, since he does not know Tom?" I asked. "Send Tom to the King," was their easy solution, while others protested that they wanted Tom to stay on the boat for the trip. I was really hoping that they would relate to the information Tom had already given us about his size. I thought someone might add four feet, four times, presenting us with a quick solution to the problem. But this was not the route they decided to take.
Mark raised his hand and suggested that we could measure the boat with our hands like they do with horses. His neighbor had a horse that was 15 hands. "Then we could tell the King how many 'hands' long the boat was." The children agreed that this might be a better idea.
"All right," I said. "Since it was Mark's idea, he can measure the length of the boat with his hands." Mark was also the biggest child in the class.
At first, Mark randomly placed his hands on the tape from one end to the other, but when he double-checked, he came out with a different answer. The children were puzzled for a while as to why this happened. It took several more tries and much discussion before they came to an important conclusion. The children decided that it was necessary for Mark to make sure that he began exactly at the beginning of the boat and did not leave any gaps in between his palms and his fingers as he placed them on the tape. Measuring this way, he discovered the boat was 36 hands long.
Great! We decided to tell the King this, but just to be sure, I suggested we have Sue, the smallest child in the class, measure the other side. She did and related to the class that her side was 44 hands long. Now there was confusion.
"Why are they different?" I asked. "Can we use hands to measure?" "No," the children decided, this would not work either, since everyone's hands were not the same size.
Al suggested using feet. We tried this, but once again, when someone else double-checked with their feet, we found two different measurements. The children at this time began to digress a little to compare each other's hands and feet to discover whose were the biggest and smallest.
Finally, our original discussion continued, while the children explored various concepts and ideas. Joan sat holding a ruler, but, for some reason, did not suggest using it. Perhaps, I thought, it might be that her experience with a ruler was limited, and she may not have been quite sure how to use it.
Our dilemma continued into the next day when the children assembled again to discuss the problem with some new insights. One child suggested that since Zeb knew the King, and everyone knew Zeb, that we should use his foot. 'Measure it out on a piece of paper and measure everything in 'Zeb's foot."' Using this form of measurement, the children related to the King that the boat was 24 "Zeb's foot" long and 9 "Zeb's foot" wide.
Curiosity began to get the best of them and the children continued to explore this form of measurement by deciding to measure each other, our classroom, their desks, and the rug using "Zeb's foot." I let them investigate this idea for the remainder of the math period.
On the third day of our exploration, I asked the children why they thought it was important to develop a standard form of measurement (or in words understandable to a first grader, a measurement that would always be the same size) such as using only "Zeb's foot" to measure everything. Through the discussions over the past several days, the children were able to internalize and verbalize the need or importance for everyone to measure using the same instrument. They saw the confusion of using different hands, bodies, or feet because of the inconsistency of size. (Hendry, 1996)
Questions:
1. Describe two similarities between the traditional lesson and the constructivist one as described above.Both lessons involved measuring large objects and both lessons used the measurement of feet. One being the English measurement and one being Zeb's foot.
2. What are two benefits and two drawbacks of the constructivist approach as described above?
The benefits of the constructivist approach would be for the student to come up with suggestions and answers to problems because the teacher asks for student's inputs. and it also creates a cooperative learning situation in the classroom because students are being brought into the discussion. The drawbacks to this type of approach would be that the teacher is not teaching traditional facts because the students are asked for how would they do something? and students may learn information that is not correct because the students are coming up with their own answers to problems. Why? In your opinion, are the benefits worth the costs? Explain your response. I believe that the benefits are worth the costs because there is there is much more topics of learning being covered as opposed to just giving facts and information to students. With constructivism students are learning to use creative thinking abilities, they are taught how to work together and in groups, they learn how to work in a community and come up with different solutions, it also helps to bring all students into the learning process and it helps on their cognitive thinking skills.
3. How does the constructivist lesson described above promote critical thinking? Give specific examples of critical thinking from the case study to support your response. Critical thinking is promoted in this constructivist lesson by creating a situation where students have to come up with ideas and solutions on how to measure the boot. The students are also questioned on their methods of measurement, encouraging them to think and rethink their ideas. The teacher points out the flaws of how they decide to measure and this forces the students to think about alternative methods of measurement. Mrs. Hendry also asked many questions while teaching, this promotes the students to think on their own as to how to do something.
4. Would the constructivist activity be considered an authentic activity? Why or why not? Yes, this would be considered an authentic activity because learning how to measure something and why we use a particular form of measurement is an activity that most people will encounter outside the classroom in everyday life.
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