Directions: Respond to the prompts below (no more than 6 singlespaced pages, including prompts) by typing your responses within the brackets following each prompt. Do not delete or alter the prompts; both the prompts and your responses are included in the total page count allowed. Refer to the evidence chart in the handbook to ensure that this document complies with all format specifications. Pages exceeding the maximum will not be scored. 1. Which lesson or lessons are shown in the clip(s)? Identify the lesson(s) by lesson plan number. [Lesson two will be the focus in the shown clips.] 2. Promoting a Positive Learning Environment Refer to scenes in the video clip(s) where you provided a positive learning environment. How did you demonstrate mutual respect for, rapport with, and responsiveness to students with varied needs and backgrounds, and challenge students to engage in learning? [ My rapport with the students is emphasized in the first clip when the class is taking notes. I always try to promote a positive learning community where students feel comfortable answering questions in front of their classmates. I also try to stay positive and call students by their names. I think acknowledging students as individuals helps to build respect and relationships. In Anita Woolfolk s Educational Psychology she discusses Piaget who believed knowledge construction was not possible as long as there was a learning hierarchy between the teacher and students.therefore it is important to open a dialogue between both teacher and students. Gardner s theory of multiple intelligences argues that children learn in different ways, and teachers can create and adapt lessons to help students learn. By taking notes on an overhead and verbally discussing the rules for the order of operations I am trying to take into account various intelligences like auditory and visual learners. In the second clip, students are broken into small differentiated groups. Each group was given a problem according to their ability, and are working together to solve the problem. The groups will also write an explanation about how they used the order of operations to solve the problem. By differentiating my activity it allows for students to be challenged at the apprioriate level. Students will be able to apply the concept of the order of operations to a numerical expression where they will not feel frustrated. I am also walking around the classroom and meeting with each group to help and guide their thinking.] 3. Engaging Students in Learning Refer to examples from the clip(s) in your explanations. a. Explain how your instruction engaged students in developing understandings of mathematical concepts. [ By presenting the rules for the order of operations and then having the students break into smaller differentiated groups it allowed for students to make their own connections with the material. If I had presented the class with various expressions and then worked each problem out step-by-step I m not sure how effective that lesson would have been. The students would not have been actively engaged and instead would spend the entire period copying notes and examples. I think students learn best when they are interrpreting information and using that information, in this case the steps in the order of operations, to make connections from the material presented in class in order to solve the problem. Working together in small groups allows students to discuss different ideas and work towards a common goal building a learning community. I also think by having a language function and not having students merely find the 1 of 6 6 pages maximum
answer but think and write the steps they took to solve the problem out on a piece of paper helped make sense of the rules. In the second video, you can see students actively engaged and speaking with one another. The first group had come up with their explanation and as I read through their answer another student noticed the group forgot to explain how they worked through the exponent step and wanted to add more information to their answer. Another student jumped in and said 10 to the second power was equal to 10 x 10 making their final answer 100. I told them that was in the right direction and we needed to expand on our explanations. The students then began to make the changes. Woolfolk stated Vygotsky advocated a constructivist approach in which social interactions and a person s culture are important for the construction of knowledge. Like Piaget, Vygotsky emphasized participating in a broad range of activities with others where learner outcomes are produced by working together. The zone of proximal development illustrates the space between what a student is capable of doing independently and the scaffolding of knowledge from the guide. I implement small group work in the classroom so that knowledge can be constructed by participating in activities to help students refine ideas with their peers by working together. Usually when students work on different problems to present in front of the class I usually have the entire group come present to the class making sure everyone was responsible for presenting a part of the problem. Unfortunately, there were concerns of privacy from filming the childrens faces. Even though I had consent forms from all parents, I have to respect the issues from the school and we decided the children should cover their faces. Due to this situation, it was decided it would be easier to film if there was one student who presented the problems instead of the entire group. In the last few minutes of the second clip, I have two students who come to the front of the class to present their problems. I think listening to other students explanations on how to use the order of operations in different ways engages the whole class and although it is not shown all the groups get to present.] b. Describe how your instruction linked students prior academic learning and personal, cultural, and community assets with new learning. [ In the first clip, I am introducing the order of operations to the students. I know from previous grades they have already been exposed to this concept but I was not sure how much they knew. This is why I used questioning to gauge what my students knew and what they could tell me about the order of operations. When we talk about why we write multiplication and division in the same step a student is able to tell me that it doesn t matter which is first you simply work left from right. This part of the step is something that I thought students wouldn t know depending on how their previous teachers taught the subject. When I begin to talk about the order of operations eliminates... and then ask the class what might come next I am trying to connect today s lesson to the previous day s work on parentheses and identifying ambiguous number statements or expressions. I also try to connect today s focus with yesterday s lesson by reviewing key vocabulary like nested parentheses and asking students for clarification. You can not hear it on the video but one of my students near the front of the classroom has trouble reading and writing. The special education teacher will usually begin copying notes if the student begins to fall behind but we always allow the student to try and copy as much as they can. Writing out the steps in detail allows the students to have a resource in which they can refer back to. I think this is important because when a lot of students go home and might be struggling with a homework problem they often ask their parents or an older sibling for help. Some parents might not find math a subject they are comfortable with but a student can show 2 of 6 6 pages maximum
their parents their math notebook and show them step by step what we are learning in class. It can serve as a guide for students to refer back to but also for parents to know how to help their child and learn about what we are doing in class. This is another reason I walk around the classroom to make sure the students are copying the notes because it can serve as a great tool when the special education teacher or myself can not assist them right away. Still Failing at Fairness by David and Myra Sadker and Karen R. Zittlemen looks at gender bias with both boys and girls. Their goal was to encourage parents and educators to help children develop in a world without stereotypes. In the 1980 s trained raters went into classrooms in four states and the District of Columbia where they recorded a dialogue between teachers and students. The raters observed students from different racial and ethnic backgrounds as they attended math, reading, English, and social studies classes. The lessons were taught by both women and men from different races. By the end of the study there was a clear structure of emerged sexism which was largely unnoticed by both teachers and students. From grade school to graduate school, female students are more likely to be invisible members of classrooms. The study found Teachers interact with males more frequently, ask them better questions, give them more precise and helpful feedback, and discipline them more harshly. When I first read the book, Still Failing at Fairness, I was completely shocked. In 2013, we expect gender equalities to be erased from the classroom. Throughout my masters education program I observed in many classrooms throughout Chicago and found that for a large part gender equality still exists in today s schools. I believe many teachers don t realize they are enforcing this stereotype and when I teach I can find myself saying just a simple term like you guys that reinforces this notion.there is also a stigma around math where it is a male dominated subject. I felt this when I was growing up and I do not want the same for my students. I make a conscious effort when I teach to make sure I am asking a variety of students both boys and girls which is shown in this video clip. Although there are more girls in the class, it is important to make sure both males and females excel academically and see the opportunities available to them outside of the classroom.] 4. Deepening Student Learning during Instruction Refer to examples from the clip(s) in your explanations. a. Explain how you elicited student responses to promote thinking and develop understandings of mathematical concepts. [ I promote students thinking and understanding by using a variety of techniques. I use questioning to elicit different responses from students to expand on their background knowledge of a subject or review terms we have covered in class. I also try to make connections from what the class is currently learning to previous concepts we have talked about whether it be from a recent lesson or one that occured several months ago. Through note-taking I try to explain to process of how a mathematical concept works in this case it is the order of operations. By having a written explanation it allows for students to refer to their notes for guidence when they are having difficulties solving a problem. I also have students describe in a written format how they found their answers. This guides students to think about the steps they took to find their answer. When students write out explanations in a logical and understandable format it allows myself or other students to be able to follow along and see how they solved the problem. I first start by trying to elicit responses from the students by first listing the order of operations. When the student states multiplication or division as the third step in the order of operations, I am trying to develop understanding as to why we say multiplication or division and not just list them as separate steps. I try to emphasize that neither multiplication or division has dominance over the other but you simply work from left to right. In the forth step when a student says the next step is addition, I try to make the connection to the previous step that addition and 3 of 6 6 pages maximum
subtraction are like our rule for multiplication and division. I want to emphasize that addition does not come before subtraction but instead work with what comes first left to right. When I refer to how order of operations eliminates ambiguous problems I am trying to connect the learning to the previous lesson. In this lesson, the class analyzed ambiguous number problems and found there could be multiple solutions. The class then learned how you can insert parentheses to make number statements true. By describing the process of how each step works, I want students to develop a further understanding of what must be done in order to solve a number sentence. When you take time to explain how to use the order of operations instead of just stating what the order is it builds understanding of how to implement these rules to help solve problems. In the second clip, I am walking around the classroom meeting with each group. The purpose of visiting with each group is so I can see how they are progressing with their problem but also ask questions to help guide their thinking often asking them to make connections to previous work we ve done in class for example working with exponents. Instead of saying I solved exponents first, when talking with the first group in the video, I ask how they solved the exponents having them further explain their reasoning and process. When students are required to present in front of one another, it makes them reflect on their answers to make sure the rest of the class will be able to follow along. ] b. Explain how you used representations (manipulatives, models, tools, diagrams, charts) to support students understanding and use of mathematical concepts. [ In the video you can see the class taking notes on the steps of the order of operations and also writing out the process for each rule. This is important because it allows students to look back at their notes when they need help with a problem where a parent or teacher might not be readily available to provide individual support due to the nature of the classroom and the home. Unfortunately there are limitations as to how much we can show in the video but I do discuss ways to help students remember the process. For example, we used the mnemonic device Please Excuse My Dear and Sally and also used the short form PEMDAS as an easy and fun reminder of the order of operations that can prove useful for all students. ] 5. Analyzing Teaching Refer to examples from the clip(s) in your explanations. a. How did your instruction support learning for the whole class and students who need greater support or challenge? Consider the variety of learners in your class who may require different strategies/support (e.g., students with IEPs, English language learners, struggling readers, underperforming students or those with gaps in academic knowledge, and/or gifted students). [ My instruction supported learning for the whole class by taking into account the individual needs of the students. With the class, I provided the foundational concepts when learning about the order of operations. I provided the class with this understanding and clarified basic misconceptions that can occur when implementing these rules to a numerical expression. Support was provided to students in terms of writing these notes with the special education teacher and another student was allowed to use a laptop in accordance with their 504 plan. To make sure every student was able to participate and be challenged during this lesson, I decided to implement a small group activity where each group would be given a differentiated problem according to their skill level. I was aware my high students would be able to solve a problem with nested parentheses and exponents and where my struggling group of learners needed a basic number model with multiplication, division, addition, and subtraction. In 4 of 6 6 pages maximum
the second video clip submitted at the end you can see two students presenting their group s answers. The first group was a group of on-level learners who were able to explain their ideas in a precise and clear manner. The second group presenting were my below-level learners but what makes it so empowering is how supportive the entire class is for each group. It is also empowering because one of my struggling students in a variety of subjects was able to get up in front of the class and accurately describe the process they used to solve the problem correctly. In this activity everyone was given the background knowledge needed for the activity and while each group solved a problem they were still able to implement the same concept and present their answers in front of the class.] b. What changes would you make to your instruction to better support student learning of the central focus (e.g., missed opportunities)? [ To begin with, I wanted to emphasize the connection between the previous days lesson and the material we were learning in the clip. When I begin to talk about the order of operations eliminates... and then ask the class what might come next I should have made the connection more explicit. Instead of just asking for the word ambiguous I should have been more thorough in my questioning. I should have asked what did ambiguous mean? What makes a number sentence ambiguous? How does the order of operations eliminate ambiguity? If I followed through with more questioning, I could see what my students were thinking and how they were relating the previous lesson to the material in the segement shown in the video. While I did model the language throughout the lesson I wanted students to use when they went to work on their own problems in small groups I should have done an example with the class. I should have been more thorough in my modelling. I did not initially think I needed to model an example since I knew all of my students had been exposed to the order of operations in previous grades and I wanted to provide an activity where they felt challenged. I think it is important for teachers to set expectations on what they expect from their students and I should have been more explicit by doing an example together. I verbally went over what I expected which is not seen in the clip but I think it should have been more visual and written out on the overhead with student input solving an example together. I noticed in the video at the end of the first clip a student raised their hand and in the middle of the second clip another student had raised there hand. While I did answer the first students question after a couple of minutes, I need to be more active and aware of students hands and look for possible questions students may have. In small groups I would have liked students to practice a variety of questions but there is the constraint of time. I also would have liked each member of the group to talk when presenting their questions of the class. Although this is normally done in the classroom there were constraints with the video requested by the schools administration. By having all the students active participants in presenting their groups answer it holds each member accountable for their work and participation in the group. Also towards the end of the group work, in the video I can hear one of my students say Kindergarten this can imply the students are finishing their work and becoming off task but as I was walking around the classroom I saw the groups were finishing up and knew we should move on to the presentations soon. When I wanted to begin the presentation, I asked group one to start but they were not quite finished so I moved on to group two however before starting in with each group I should have checked with each group to make sure they were finished. ] c. Why do you think these changes would improve student learning? Support your explanation with evidence of student learning and principles from theory and/or research as appropriate. [ In this lesson I tried to take a constructivist approach to teaching where the goal of an activity is meaning making where students internalize the information and make connections. 5 of 6 6 pages maximum
Constructivists believe teaching and learning should emphasize doing rather than exposure to direct instruction unless deemed necessary by the teacher. I felt for this situation while I wanted my students to make meaning to the material in group activities I felt I needed to be guide the students into seeing the connections with the previous days concepts. In Literacy for the 21st Century, Gail E. Tompkins discusses the concept of gradual release. This allows teachers to use the five levels of support: modeled, shared, interactive, guided, and independent. By using the levels of support teachers are able to move from more to less gradually giving the students increased responsibility. For example, when a teacher introduces a new strategy they model how to use it. When teachers want students to practice a strategy they ve already introduced, they guide students through an activity, slowly releasing more responsibility to them. Once students can apply the strategy, they should be encouraged to use it independently because they re applying what they ve already learned. When looking back on my lesson, after I introduced the main concept I allowed students to work in small groups right away. I believe it would have more beneficial if I scaffold my instruction more where I modeled a problem, then as a class we worked on a problem together, eventually allowing the students to work in their small groups.] 6 of 6 6 pages maximum