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ITL 516 Fieldwork National University Michael SuzukiPre-ObservationI observed a third grade classroom at Highlands Elementary school with Kylie Collins, the teacher. The classroom was very large and contained demonstrations of student work around the walls. The amount of work around the classroom seemed potentially distracting. Singapore classrooms tend to have fairly clear walls so the students can focus better; it’s very different than what American classrooms typically display on their walls. The class composite included 15 girls and 14 boys. 13 whites, 2 blacks 5 Hispanics, 5 Asians, and 4 others comprised the composite of the classroom. The lesson started when Kylie asked the students to get into their math rotations. Students knew what to do and started getting into their groups. Kylie told me that the students were rotating through 3 groups which included learning the lesson, independent computer practice, and doing worksheets. Whole group instruction didn’t work well because the students were all at different levels. In addition, the student-teacher ratio in the small group setting helped the teacher give more attention to student needs. Going on, groups were separated according to skill level so that the high achieving students could be challenged more and the ones that didn’t understand the material as well could receive extra help. Before the lesson, students received a card to fill out which contained the level of understanding the students thought they had before the lesson and after the lesson. Next, students sang a song involving multiplication before the actual lesson began. Also, students wrote down on a piece of paper what the objective for the lesson was that day and gave a thumbs up when they were ready to start the lesson. Students would repeat to their partner what they were learning for the day. Kylie was using a pro-wise smart board to teach the lesson which is essentially a touch screen computer that is very large. This board provided visuals that were very easy to see and understand in the small group setting. Observation DescriptionKylie did an amazing job teaching the lesson. She repeated to the students how they should be focusing by sitting up straight, having distractions away, and eyes up front. Within the google slides on the board, she reminded the students that it’s her time to teach and that they should be quiet when she’s talking. However, collaboration was encouraged. Kylie started teaching about what multiplication is; it’s repeated addition. She then went on to explain the commutative property of multiplication. Throughout the lesson there was a lot of classroom management. Students from other rotation groups would complain about other students, be unfocused, and start talking. Kylie had to periodically separate some students and talk with them after the lesson for disrupting other students. She did a good job of explaining how interruptions and talking isn’t helping them learn or their fellow peers. Next, Kylie showed arrays of multiplication demonstrating rows. An array displaying cars of 2x5 was displayed on the smart board. Students would right down how the visual model was represented in multiplication; they would also draw arrays when 5x7 was shown on the board. The group also had dry erase boards to interact with the material and write down their answers while they were learning. Next, the students would solve word problems containing array problems and demonstrate different ways of solving the problem. One example problem was “Mrs. Roberts baked a batch of bagels. She arranged the bagels in equal rows of 4 bagels on the cooling rack. How many bagels did she bake?” A model was displayed on the board as well so the students could visualize three rows of 4. This model was represented as 4+4+4=12, 3x4=12, and 3 rows of 4 is 12. Going on, Kylie explained the commutative property of multiplication by telling the students it’s the flip flop rule. Essentially, 3x4 = 4x3. The product of switched numbers in multiplication is the same. Lastly, Kylie asked some closing questions pertaining to the material so that the students could understand the big picture and what the were learning. Observation in relation to the 8 Mathematical PracticesMake sense of problems and persevere in solving themStudents- The students were able to understand the meaning of the problem as demonstrated by their dry erase boards. Students analyzed relationships between the array model and how it can be expressed as a multiplication equation. The students also were able to evaluate their progress as the correct answer was given. If a student wrote down an incorrect answer, they would reevaluate and try to think about how to get the correct answer. Teacher-Kylie involved the students in rich problems including word problems, visual representations of models, and writing multiplication equations based on the arrays. However, there weren’t many opportunities to solve problems that have multiple solutions. The problems presented had one solution but many different ways to solve it. Student’s thinking was apparent on the dry erase board while problem solving. Attend to PrecisionStudents-Students would communicate to their neighbor explaining the definition of certain terms. When drawing the arrays, the students would check in with the teacher to make sure it was drawn correctly. Although some students didn’t draw it precisely, they were able to persevere and ask their neighbor to arrive at the right answer together. Teacher –Kylie encouraged precision by correcting students that didn’t draw the array models precisely on their dry erase boards. Some students were drawing different models that weren’t arrays. Although the students arrived at the right answer, Kylie made sure the students were drawing arrays because that was the lesson for the day. Reason abstractly and quantitativelyStudent- Representations of the problem at hand were demonstrated by drawing models of arrays. In addition, flexibly using the properties of operations was shown through the communicative property of multiplication. Students understood that 3x5 is equivalent to 5x3. Teacher- Kylie facilitated opportunities for students to discuss or use representations by encouraging collaboration and modeling the arrays on the white board. She also encouraged students to solve problems in multiple ways which engaged their thinking and reasoning. Construct viable arguments and critique the reasoning of othersStudentStudents defended their mathematical reasoning by articulating why their answer is correct. Modeling, adding, subtracting, and checking in with others confirmed their answer. In addition, students could use the communicative property of multiplication to see that they can draw two types of arrays to further confirm their answer. TeacherKylie provided a collaborative environment in which students could listen to the solutions to others and confirm their others. Engaging and challenging questions were asked throughout the lesson that further enhanced students learning and critical thinking skills. Model with mathematicsStudent Students were able to model with mathematics on two fronts. First, the students represented a visual model as a mathematical equation and drew an array when presented with a mathematical equation. Having this diverse skill set will enable students to draw and represent models in various ways. TeacherKylie used visual representations of arrays including bread, frogs, and other 3rd grade appropriate visuals. Use appropriate tools strategicallyStudentThe students used technological tools in conjunction with the teacher to solve the problems. Students were able to write on the smart board to express their answers. TeacherKylie used the smart board and helped the students use the appropriate tools which included their dry erase boards. Look for and make use of structure StudentsThe students understood that quantities can be represented in different ways. For example, 12 can be expressed as 3x4 or 4x3. They also understood that multiplication equations can represent different arrays that arrive at the same answer. TeacherFlexibility in demonstrating mathematics in a number of ways was present including models and equations. In addition, word problems were presented so that students could conceptualize and understand the problem as it pertains to their own life. Look for and express regularity in repeated reasoningStudents Students were able to look at general patterns of multiplying the array by the horizontal and vertical units to arrive at the answer. In addition, students were able to compare their answer from the model and the mathematical equation to ensure accuracy. TeacherKylie was able to engage in student discussions and take the students step by step through the problem so that they could arrive at an answer backed by mathematical reasoning. Post Observation Reflection I think that overall the lesson went very well. I like how Kylie used the smart board, dry erase board, demonstrated models, expressed multiple ways to solve the problems, included music, and related arrays to the students’ lives through word problems. In addition, the communication through collaboration was an excellent way to promote understanding and engage. The students seemed to understand everything in the lesson. The only weakness the students had was creating other models to solve the problem. Although using other strategies can be beneficial, students also need to be able to read the directions and model an array which is what was asked for. Kylie did an excellent job overall. I think some areas that could be improved on is highlighting what a row is. A column was not discussed and I think that this can be confusing for some students. In addition, I think that a concluding problem for homework would be beneficial. For example, requiring students to create an array of their choice on a blank piece of paper and express it in multiple ways using the communicative property would help many of the students. In addition, I think a hands-on activity such as creating arrays from legos might have been more engaging for the students. However, I also understand that she has a limited amount of time so this approach may not have been optimal. Additional questions: How did the teacher:Created a safe and positive?learning space.Kylie created a safe and positive learning space by encouraging student interaction, using positive reinforcement, and valuing questions asked. Students would be praised when they wrote down a correct answer and be encouraged to persevere and struggle through problems when they were having trouble. Set clear expectations and connected students' prior knowledge.Kylie set clear expectations by establishing learning objectives at the beginning of the lesson. Student’s prior knowledge of multiplication was implemented in constructing arrays. Engaged students in higher-order thinking? Students were engaged in higher-order thinking by the questions Kylie asked them. If the students didn’t know the answer, they were encouraged to think about the problem and discuss ways in which they could obtain the right answer. Monitored and/or assessed student learning.??Student learning was monitored and assessed through questions asked during the lesson. In addition, students marked on a form how they felt about their knowledge of the material before the lesson and after the lesson. Lastly, Kylie would assess how she felt the students understood the material after the lesson as well. What I learned I learned a lot through this observation including how to use the technological smart board, representing visual model, classroom management skills, and how students can assess themselves before and after a lesson. I saw first hand how math can be represented in multiple formats and solutions answered in multiple ways. Connecting math to music and the student’s lives was engaging and relevant. I also learned that classroom management is going to be challenging but doable. I’m excited to teach math and challenge students so they can learn, engage in thinking, and provide a foundation so that they can have a better chance at succeeding. ................
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