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Essay: Solving Math Arrays With Construction Paper: Connecting Repeated Addition To Student Learning

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  • Published: 1 April 2019*
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  • Words: 1,815 (approx)
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The video is clip shows a piece of a math lesson teaching about arrays. The purpose of this lesson is to build a knowledge of repeated addition. The students will learn how to group multiplication equations into an array. This lesson will serve as a building block for students to understand and become fluent in multiplication facts while fully understanding the concept behind multiplication. In this clip, the students are using construction paper cut into rectangles and squares to create an array. In my lesson plan, I explained that the students would have the opportunity to practice creating an array before working independently and in pairs by coming to the board and solving four problems as a group. I then dived into the definition of what an array is and how it relates to multiplication being repeated addition. I gave examples an example for them to listen and see on how we break our arrays into columns and rows. After we have broken our equation into an array we count the total number of objects used.

The learning environment is a small resource room shared by two para-educators. There will be multiple adults that you will hear in the background, this is due to the room being shared by the three para-educators. I have my room broken down into leveled groups. Small math groups begin at 12:35, directly after lunch/recess, so students do come in at various times as each re-enter the building at different times. There is not a specific curriculum required of the resource room, but I follow Bridges Intervention and allow for substitution with richer content experience when needed. Students have a strict classroom procedure of entering the room, grabbing their classroom folder, and siting at their tables. On this particular day, you will see me move in and out of the camera, which is caused by one of my para-educators having to leave early and a substitute was not found in time. The group that was missing their para happened to be my lowest group, so it was pertinent that I bounce back and forth to ensure that they have full understanding.

I strive to create a positive learning environment in my classroom. Many of these children are significantly below grade level, so to alleviate some negativity and stress I have set up a  strict classroom norms for myself and the para-educators. If a student gets something incorrect, I gently correct them or ask questions so they can self-evaluate and self-correct. You will notice this in the video clip at minute 5:37. I try to make encouraging comments to the students and lead them to self-correction when they get an answer wrong. I also make it a point to praise students when they get something correct, such as working well together. I work hard at encouraging students to ask questions if they are confused to eradicate the taboo that not understanding is a bad thing, but rather that not understanding creates a path for learning. This is evident when I allow one my student to incorrectly put her answer on the board, but go back and have her ask questions. She knew that her answer was not correct. This is a method I am still working on, but I could see improvement from the beginning of year where she would have just walked away. Instead, she stayed there and asked questions. This is seen in the video clip at minute 10:05. If content perplexes a student give I make sure to stop and clarify anything that is confusing and slowly walk through the steps again.

The interactions between my students are friendly and respectful. A part of my teaching philosophy is giving the students the same respect I would like them to give me. For example, in the video clip you will see how I gently let my student know she needs to move through the problem at a quicker pace. I set high expectations for each student. Many of my students feel as though they are not held to a high standard and I want to make sure they know that is not the case. Students have their objective and success criteria written on the board so they can at any time know how to be successful with any given activity. At minute 16:13 you will hear me praising the student for answering the question correctly that she was confused about. Students follow the classroom rules and routines which are clearly established at the front of the room. My room is set up in a manner where student can access tools needed to succeed, like anchor charts, multiplication tables, dry erase boards/markers, objective, success criteria, visual timer. Students know to respect each other and ideas that are shared, even if they know the answer is incorrect. I strive to create an atmosphere where my students know how to practice productive struggle and questions that facilitate learning and understanding. I remind my students of the “not yet” rule. A lot of students in my resource room come in with an “I can’t” attitude, so in order to change their mindset on the phrase “I can’t” they are expected to say “not yet” afterwards. In the video, at minute 4:40 you can hear a student who had difficulty say “not yet” after saying “I can’t.”

Throughout the lesson I used strategies that engaged and motivated students to focus. I built a context that interests the students, a superhero that puts a city back together. I also related arrays to real life and how they are everywhere. This lesson took place with students having the opportunity to come up to the board and draw – a favorite pastime of theirs. I will randomly ask students questions to informally assess where they are with the content as well as to ensure they are staying engaged. At the end of the lesson, students have an opportunity to earn a star. After two weeks of great behavior, fully body listening, following classroom procedures/expectations they earn a sticker in their classroom folder from myself or a para-educator they can pull a prize from my prize box. At this time, I have an elf on the shelf as well roaming the classroom helping keep an eye on students to ensure they are doing their very best work. Many students do not have the means, living in a low poverty area, to enjoy some of these fun things during the holidays. This has proved to be an amazing strategy to ensure students to stay motivated despite hardships at home. Another way that I support and encourage is by reaching out to parents outside of IEP meetings/reviews. Having a child on an IEP can be discouraging for both parents and students, but I have found that this communication is a huge motivation to help the learners stay focused and engaged with learning. We also use academic language in my classroom which gives students with IEP’s a chance to feel confident and intelligent with their verbiage. I want to allow them to learn the proper way of identifying math equations. I do not allow “this” or “that” as a response.

It is very important to create that link between a student’s life and new learning, so we discuss how many arrays we can see in our city as well as how to successfully know how many cupcakes to bring to the Christmas party. I access students prior learning asking what repeated addition looks like. Before any lesson begins I dive into our learning objective as well as the success criteria in steps. I change the colors of marker to indicate what was taught in the last lesson and what is new. Throughout the lesson I made a point to provide feedback to the students as seen at minute 15:28. The student shared that she was unsure of the proper procedure for creating an array. This was intended to supply verbal feedback after the lesson allowing her to provide feedback to me.

I also worked on promoting self-monitoring. I find the success criteria especially important for self-monitoring . The success criteria are up on the board, easily viewable and reviewed so the students know exactly what steps they need to take to be successful. At the end of the lesson the students do a thumb up, down, sideways check allowing them to self-evaluate on whatever strategy was taught. When the lesson ends the students will change their thumb check card to up, down, or sideways depending on how comfortable they feel with the material. Some students at the end of the lesson still felt confused about creating arrays and left class not fully understanding. In those situations, I reteach the lesson all together. Most IEP students need to restart rather than pick up where they left off. I also will reteach the lesson using a different strategy if the majority have their thumb checks are down or sideways. Supporting the students learning is evident in the video as well. I used materials, instructional strategies in the lesson to support the students toward reaching their IEP goals.

For this lesson, I would do a few things differently. For starters, I would have the students work as partners at the table while my students at the board finished their problems. While watching the video I realized how many times I had to redirect students for not staying on task due to my back facing them as well not being able to see what the students were doing. Another task I may do differently in the future is change my strategy of creating windows for our building. I had students cut out the “windows” to create their arrays to, but some students had fun just cutting up a bunch of pieces rather than being productive with their cutting. This behavior is also due in part to a para-educator being suddenly absent with no replacement. Asking more self-reflecting questions throughout the process of them working on their arrays is an action that I want to see myself do more of in the future. There was quite a bit of quiet time while students were working, and while I was informally assessing, I want to understand the students through process better. I would also ensure that students properly knew what self-reflection looks like by creating a classroom anchor chart. By asking these self-reflecting questions I would have been able to address confusion by my students a lot faster than at the end, seeing many thumbs sideways, down checks. At minute 8:31 the student decided that she was going to just draw on the board rather than try to figure out her problem. In hindsight, I would not have left her there because I believe that much of her confusion later was due to me not noticing that she did not fully understand the lesson in the beginning.

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