October 14, 1998
This past Tuesday, my partner, Nicole, and I officially observed our first lesson in our fifth grade classroom at Lanigan Elementary. The lesson topic was on Mathematics and the commutative, associative, and identity properties applied to addition, subtraction, multiplication, and division. The students were seated in their normal positions ( tables formed as a semi-circle in front of the board and three rectangular tables behind that). None of the students had their back facing the teacher, they were all ready and attentive as the lesson began. At times throughout the lesson it was difficult for us to examine the responses of the students because it was the math class and we dont know the students as well as the ones in our homeroom, but we are having a lot of fun getting to know them as well.
The teacher began by getting out her teachers edition of the math text book. Are you ready, she stated as the students got situated. If you see an n, what does it stand for? she said. Number!, shouted one student. Yes, said the teacher as she wrote on the board: n ( ) n - 4 = 3. This does not necessarily mean that you subtract. Remember, were changing from arithmetic to math. Add or subtract? one student asked? You have to use one of the four operations, explained the teacher. The students all shouted out, add, subtract, multiply, and divide. At this point in the lesson the students seem interested, but not very motivated. About half of them are completely focused, while several of them are still getting situated and are uninterested in the introduction of the lesson.
The teacher goes on to say, you have to do some operation. Is this number going to be bigger? She answers her own question, Yes, the bigger number goes on top, but there are all different ways to write it. She refers to the Iowa test. The teacher again repeats the question, What are the four operations?. She then goes into a discussion on what happens when you add zero to a number. She explains to the class that they can do 4-0, but that they will learn how to do a problem like 4-8 in a higher grade level. She makes reference to word problems and how numbers can be switched around in all sorts of ways. She writes 4 x 3 x _ = 0. Ask yourselves, what makes sense here?. What if we multiply by 1? At this point the students are a little more interested in the topic and are eager to contribute to the discussion. They all yell out answers with enthusiasm.
The teacher first introduces the identity property and explains it by writing
4 + 0 = 4, 4 - 0 = 4, and 4 x 1 = 4. What do these all have in common, she asks. One student replies with, They all end up with the same thing. The teacher continues on by introducing the commutative and associative properties in the same way. The students enthusiasm and excitement soar as she presents a game in which they pair up with a partner and have to think quickly as she holds up a strip of paper. They have to give the answer as well as tell the property. The students really got into this and it really seemed beneficial to their understanding. They also had to think quickly and work with their partner to come up with an answer before they could say it. The winning pair got a prize and the lesson ended with a round of review questions from the teacher and shouts of answers from the class.
We learned a great deal of information by carefully observing this lesson. Our cooperating teacher kept all of her questions brief and used questioning as a way to get the class motivated. Distinct questions were repeated at the beginning of the lesson so that she knew that the students thoroughly understood the previous material they needed in order under stand the new material. Questions like, What are the four operations?, and In which of the operations can the numbers be switched around? were repeated throughout.
Our teachers questions were directly related to the students responses in the fact that after the students would respond to a brief question, their answer, at times, led her to another question that triggered her memory or brought on a new meaning to the original question stated. There were a few pairs of students that dominated the game during the lesson, but before the game began and the teacher was explaining the properties, the whole class seemed to be responding to questions equally, with a few exceptions here and there.
Interestingly, our teacher did not seem to me to direct different type questions to different types of learners. Her questions were broad and continually directed toward the class as a whole. The students didnt normally raise their hands during the introduction of the lesson. It was more like a math talk, in which the floor was open for any random answers and discussion. Answers and comments were varied as far as the level of students learning, but everyone was encouraged to speak up and offer thoughts to the rest of the class.
Several levels of Blooms taxonomy were included in this lesson and method of questioning. Knowledge was used specifically in the beginning of the lesson when our teacher checked to see the background knowledge of the students. She repeated several questions and encouraged the students to tell, choose, group, label, name, etc. The level of comprehension was used through questioning after she began defining the three properties and translating them into a language that was at the level of the students, but at the same time, still challenging. The students were asked to comprehend the material by converting, translating, expanding, restating, etc. They were also asked to interpret the information by redefining the information that was being taught. The level of application was demonstrated in the game where the students were expected to use what they had learned and apply it to something useful. The math properties were put into action and the students were asked to exercise their minds during this activity. As they played the game, they analyzed the information they had learned and were asked to break it down into smaller pieces and test their own knowledge. Evaluation was used toward the end of the lesson when the teacher reviewed everything they had learned in a bonus round of the game and reflected upon what had happened. She also awarded the students who applied the material in the most beneficial ways.
Looking at this lesson in comparison to the questioning we observed in the videos of Ball and Lampert, they have several similarities and differences. They all seem to use open-ended questions and implement questioning as an effective way to get the students motivated and excited for the lesson. They all use questioning as a tool in finding out the students background knowledge on the subject area. A difference I noticed was that in the Ball video, she seemed to vary her questions depending on the learners ability (the instance with Pravin). Our cooperating teacher used strategies of broad questioning that seemed to fit everyones learning strategies without singling anyone out. I noticed that once in a while all of the teachers distinctively answered their own questions. Im sure this is useful at times in order for the students to hear the whole thought process without interruption.
Observing this first lesson was a wonderful way to study the different interactions between teacher and students. The tone in ones voice and the level of enthusiasm in the room seem to be important factors in the amount of interaction put forth by the students. Questioning is such a beneficial method to use throughout a lesson. It provides both the teacher and the students with a wealth of information. Wow, we really have a lot to learn from our students before we can teach them in the most effective way possible!
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