* I am at Hillcrest Elementary School, with Mrs. Sanders in 1st grade. Her classroom is very warm and established, you can tell that she has been teaching for some time now. She constantly has the students move from one place to the other, knowing that 1st Graders need any opportunity to move and stretch. It is such a joy to take part in the classroom; the school, upon entering is very student oriented with their artwork on the walls and in the ceiling. The school has a neat feel to it. Different awards, posters, parent information, and the like fills the walls. Generally, the school is fairly noisy, but not so much so that it is out of hand. The adults always say, "Good morning," to anyone that is passing by and gently reprimand the students that are not doing what they are told.

* During math in Mrs. Sanders class, she begins the period with a warm-up word problem on the overhead. She'll read the question once or twice and have the students represent the problem in two ways: through drawings and a math sentence. I love the way she does this because it allows students to do the math their own way, but also recognize that a number sentence is something that is relatively "universally" understood. She and I will walk around the room and ask students to show us how they decided to represent the problem. She'll then ask the class what they got at the answer and ask them how they decided to do it. Once this is over, they will pull out a number chart to 100 and unifix cubes. Each day, Mrs. Sanders will tell the students to cover certain numbers. For example: Cover the numbers between 54 and 62, cover the odd numbers from 3 to 17, etc. She will give them a couple of minutes to complete this and then she'll put up her overhead number chart. Mrs. Sanders will pull sticks with students' names on them and say a number and ask the student if the number is suppose to be covered or not. She'll ask the class to give her a thumbs up or thumbs down if it is covered. Both of these activities keep the students engaged and actively thinking. After the overhead work, Mrs. Sanders has the students go to the carpet for calendar time. Each week, one student is in charge of leading calendar time. Mrs. Sanders has the class spell the month of the year, sing a days of the week song, followed by a months of the year song. The students then tell each other what the day of the week it is, followed by the number date. The most tricky thing for them being adding number sticks for the number of days they have been in school. Mrs. Sanders continues to draws sticks so as to choose students equally. After that, the student will go up to the number chart on the wall and pick a number. The students will have to say the number that goes before or after the picked number. Several numbers will be picked until the calendar leader will pick two numbers and the class will have to select the number that goes in between the two numbers. This part of carpet time allows students to draw on math terms that will be useful for everyday life. After calendar time, Mrs. Sanders calls them back to their desks. Today, she introduced the concept of subtraction to them by comparing. When the students went to their workbook pages, there are two sets of objects. For example, the students had to match up the number of birds to bird nests and find out which object has more or less and compare the two sets. In my opinion, this is a difficult way of teaching subtraction because the students continually wanted to add both the sets rather than compare the two and count what is left over. Most students grasped the concept of "more than" but not "fewer." They felt comfortable enough to ask questions; so I grabbed two different colored dots; 3 yellow and 2 red. I then instructed them to compare; so I wrote "3 yellow dots" and "2 red dots." We compared them as a class. "Which one has the most? The least? How many less red dots are there than yellow dots?" I think this helped the students grasp the concept a little better to do it again as a class. This objective requires a small amount of reflective thought, simply due to the fact that most students can simply count the number of birds and bird nests and compare.

* To be honest, when it came down to the actual math lesson, the students struggled and most shut down. Most of their concerns were expressed in frustration, with an "I can't do this" attitude. Comparisons are difficult for students to grasp. The workbook the students are using give examples, but the students couldn't really understand the examples. While Mrs. Sanders and I walked around the room, most students had to have us continually showing them how to do these types of problems.

* Because of the difficulty of this lesson of comparisons in regards to subtraction, most students were capable of showing which grouping had more than the other; however, the idea of something having "fewer" objects than the other grouping was demanding for them. As educators, how can we effectively teach this method through another avenue? Why was it so strenuous for students to calculate problems in such a way? Based on the differences and dynamics in the classroom, how many different ways should a teacher present a problem or mathematical concept?

* Extra credit: Comparisons within the CGI Problem Types are difficult for students; however, I believe that if the students were given multiple ways of approaching this problem, they would feel more successful while learning this concept. As an educator, I should show my students that they can think of multiple forms of solving this problem. Thinking of subtraction as "think-addition" may be helpful for this comparison concept.

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