Reflection two

Context

Jess and I were assigned to the ELAMS middle school. We were teaching a math lesson to the fourth graders. We are currently working with Kristen Crawford who has been teaching there for a while now. Previously, Jess and I went to ELAMS to teach a lesson about fractions. The lesson went pretty well last time and the students learned a lot. This time we wanted to be even better than the last time we went, so before creating the second lesson plan, Jess and I contacted the Ms.Crawford to assure the plan aligned with what the students were learning at that point. We learned that the students were now working on decimals. We created a series of activities that were checked by Ms.Crawford, and learned that some of our ideas were slightly advanced for the students, so we cut out some parts of our activities to fit the needs of the students.

Objectives 

Our objectives primarily focus on math. The objective focused on understanding of decimal placements, and we focused on visual and numerical representations. There were four learning objectives that guided our lesson:

  1. Students were able to demonstrate visual understanding of decimals notation.
  2. Students were able to indicate the numerical value/equivalence of decimals based off of drawings.
  3. Students converted fractions to decimals
  4. Students were able to compare decimals and order themselves from smallest to largest.

These objectives were made based off the standards that the activities were meant to meet. The lesson meets the key objectives because the common core standards expect students to extend understanding of fraction equivalence and ordering. Students should be able to use decimal notation for fractions with denominators 10 or 100( CCSS.MATH.CONTENT.4.NF.C.6 ), understand decimal notation for fractions and compare decimal fractions by comparing two decimals to hundredths by reasoning about their size (CCSS.MATH.CONTENT.4.NF.C.7 )(this standard includes “recognize that comparisons are valid only when the two decimals refer to the same whole”). Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.( CCSS.MATH.CONTENT.4.NF.C.7) We formulated these objectives based off of our planned activities and the standards listed above. 

Activities

Jess and I wanted to create activities that grow on their previous knowledge. We were aware that the students were now working on decimals. We started out with having the idea of students working with tenths, hundredths, and thousandths. At first glance it seemed like a great idea, but with advice from both Jack and Ms.Crawford, Jess and I decided to stick to tenths and hundredths. We realized that it was not only not fair to the students because Jess and I had a hard time demonstrating the decimals pictorially, but it was also advanced for the common core standards. We created cards that either had a pictorial or numerical form of a decimal with tenths or hundredths; enough for the class. At the beginning of our lesson we connected the topic, decimals, to something the students are familiar with, money. They students were encouraged to use the idea of money to help them at any time if they needed to. This got them excited and prepped them for the first activity. The first activity, students get a card and identify where to be seated whether it is at the hundredths or tenths table. The second activity was students working together to see decimals in different forms, promotes teamwork and expands the students’ knowledge. The third activity, one student from each table (hundredths or tenths) shares out loud what they learned and shows it on the class white board. The fourth activity had students get up from each table and order themselves from smallest to largest. The very last activity involved two students standing up with the decimals and the class told Jess and I whether the decimal was greater than, less than or equal to.

students ordering themselves from smallest to largest based on their given decimal.
This is an example of a student’s card that has a decimal represented pictorially, and this student sat at the “tenths” table.
This is an example of a card a student got that was in numerical form. In this case the student sat at the “hundredths” table.

Jess and I organized five solid activities that were sequenced in a particular order to not only cover the standards, but to also help students build upon what they already learned.  The activities required white boards, group work, and a change in perspective. Based on the topic and standards listed above, students’ creativity were incorporated to the best of our ability in each activity. Most of the creativity was during the second activity when students were working together to demonstrate the decimals visually or numerically. The students would draw different graphs to portray their decimal. This also forced students to think deeper than what they normally see, and its also significant to mention that those students had a guide on their table. Jess and I established that we did not want learning to be difficult but rather a guided process because the students have a better experience and want to learn more. Because that idea is behind the activities we assigned the students, the activities aligned with what they already learned and more.

Equity 

This lesson was equitable. I came to this conclusion because the activities more mostly student run. The students were working together to understand the material better. No student was left behind because they all knew that in order to move on the next activity they needed to actively contribute to their group. In addition, we made sure to relate the topic to something all students from different backgrounds could relate to, money. This helped students see the significance of math in the real world and how that relates to themselves.

Assessment

The students were assessed informally for the most part. The assessments began from the moment the students started finding what group they belong to after getting their slips at the beginning of class.  Jess and I both observed the students’ initial ability to accurately determine the place value of their decimal (does the student sit at the appropriately labeled table). Formative assessments continued after they found their groups and were instructed to create an alternative form (numerical or pictoral) from whatever was on their slip. When each student figured out their alternate form from what was on their slip, they were responsible for showing that on their whiteboard to move on to the next student till they were done with everyone at their table.This was assessed formally (and is our only summative assessment) because it was a way to see if the table was on track and kept students at around the same pace.

Another formative assessment occurred as  Jess and I evaluated student understanding when one student from each group was randomly chosen and explained an example to the class. This was another opportunity for us to assess whether or not they grasped the material. Additionally, when students were attempting to order themselves in front of the class according to their decimal value, we and the rest of the class observed and noted their success or lack thereof with comparing decimal values and ordering them from smallest to largest. This was another example of a formative assessment.

Our last form of assessment for this lesson was building off of the previous one in that we will be assessing students’ ability to use the correct symbol that reflects the relationship between the decimals, both pictorial and numerical. This happened when two students were standing in front of the class and the rest of the class is responsible for telling Jess and I which symbol to use. At this point we were be able to see what progress if any has the class made between the beginning of class and this last activity, and we added clarity to their confusion with the time we had left.

Sources

Resources that we have used in order to help us prepare for lesson 2 are the Common Core State Standards Initiative website (CCSS.MATH.CONTENT.4.NF.C.6CCSS.MATH.CONTENT.4.NF.C.7), Eureka Math Grade 4 Module 6 (lesson 10), Kristen Crawford who provided us with the Eureka Math Module website in order to see the content they are learning, and Kyle. We used the Common Core State Standards in order to ground our lesson and ensure that it would be following the course of what skills these students should be learning. We used the Eureka Math Grade 4, Module 6 in order to get a better idea of the content that the students will have just recently gone over by the time we teach. Eureka is the platform that the classroom we are teaching in gets their curriculum from. Once we saw the concrete content that the students are expected to learn, we created our own activities and lesson. Kristen Crawford was a helpful resource in that she gave us access to the Eureka Math Module, and Kyle was a helpful resource by allowing us to meet with him and give us feedback on our lesson.

Reflection

I thought this lesson went very well compared to the last lesson. The students were engaged and willing to learn. The students weren’t spending a lot of time asking me questions, instead the students were communicating with each other to get their answers. I thought it was great that the students gave each other encouragement when the work became difficult. There was also a moment when there was a challenge posed to the class, and the class was split as to what the answer was. The students handled it well. They did not tell their peers that their ideas were wrong. They challenged the opposite ideas by creating graphs to prove or agree with their peers.

For the most part, everything went smooth. The only unexpected event was when one student from the group refused to do work. It was the weekend before their spring break so Jess and I were warned about the students have a difficult time paying attention. The student ended up doing the work because the other students respectfully held him accountable. The other students would encourage him to do the work so they can move on to the other activities. Because each table had about the same number of students, Jess was able to moderate about half the class while I did the other half.  The other unexpected event that happened was more technical. The camera stopped filming multiple times which interrupted some of my time that I was supposed to be focused on the students. As a result, I took care of the problem to the best of my ability and communicated with Jess. Then I went straight to the table and checked in with all the students to make sure they were on track.

The students were constantly learning. The activities were created to follow the objectives which were based on the state standards, so as the students were doing the activities, the idea was that they could not move on to something new without “meeting” the objectives from the last activity. This is why the activities were put in a specific order so that students are building their knowledge. An example of students having to meet one objective to get to a new activity was the third activity where the students from each table (hundredths and tenths table) would order themselves from least to greatest in front of the class which covers an objective (extend understanding of fraction equivalence and ordering and understand decimal notation for fractions and compare decimal fractions by comparing two decimals to hundredths by reasoning about their size). Once the students demonstrate proficiency in that activity, they can then move on to the next activity which is comparing the decimals. This now covers a new objective (Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model) but still reinforces the previous ones. I am proud to say that all the students made it through all the activities and they met all the objectives because Jess and I had to check their answers to let them move on to the next activities. Few students need a challenge and would actually ask me for more work to do, but most importantly absolutely no students back out of doing the work.

Students were very vocal about what they enjoyed and didn’t enjoy. Most of the students would just yell out that they needed help and I would address the question for the group because I did not know who else had the same question. I only had one student who did not talk at all and would draw other figures on the white board to distract himself till everyone was done. Of course the rest of the table noticed this along with me and we encouraged him and guided him through understanding how to get to through the problem. On small occasions I would catch one or two students asking their peers for help more privately, but I didn’t see that as a set back on my part because it shows the students are being more comfortable with asking for help which is something that they struggle with because of their age and class size, so it was progress that I appreciated.

As a teacher and being part of this class, I there are moments where I feel like my head is still at Trinity. Now, this doesn’t mean that I am incapable of giving the students my full attention.  It means I feel like I am being graded rather than enjoying the time I have with the kids to the best potential. I think as a teach people must learn from their experiences and appreciate the larger aspect of things, and apart of that process is “just doing.” This means that as much as my grade matters at Trinity, I want to just be able to think about what the students need. In the future I want to have a recording device that doesn’t remind me that I am being graded when it fails to record. I also hope that Jess and I will continue to have strong class activities that involve groups but we would rotate around those groups. I think its best that if there are more teachers in the room, then students get used all the adults present.

I think this lesson really tested my patience. I am normally a patient person, but the hour felt long and the students were energetic (its great they love the activities). Additionally we had more technical problems so it was a difficult session for me. I learned that day the importance of professionalism and keeping my emotions out of the way of my work. Its important that I stay calm and give the students they attention they deserve to be successful because I already passed my time in fourth grade.

Proposal/Reflection

Our first workshop will take place on Friday, March 1st at 2-3pm. During this session, the curriculum topics and standards we will be focusing on are “Extend understanding of fraction equivalence and ordering (recognize come up with equivalent fractions), “use the four operations with whole numbers to solve problems” (including word problems), and “generate and analyze patterns” (found on School Standards Slides).

In workshops 2-3, we plan to expand upon these standards and topics using larger numbers, while also bringing in division of fractions. The key learning objectives will be as follows: students will be able to multiply fractions while understanding the concept and grasping patterns when solving problems, and students will develop understanding of equivalence of fractions . We choose to focus on more hands-on activities to help students learn. Our first activity will refresh the students’ memory of basic concepts that help them understand larger ideas of multiplying fractions. In this activity, we will use cubes and start with smaller numbers and cubes to ensure that we lay the foundations regarding the basic elements of multiplying fractions, so that we have a sound starting place. This will consist of a guided class demonstration in which the person leading that portion of the session (either Jess or Anne) will verbally and visually guide students on how to conceptualize what the process of solving “one half times one half.” We would do this through manipulation of the cubes.

A second guided activity in which student groups would follow along as the facilitator worked through another problem would involve the multiplication of the fractions 4/8 and 1/2. We would have the same set-up as before, but this time would be using larger fractions of equivalent value. The students would be encouraged to slow down and notice patterns within this new problem, such as 4/8 is the equivalent to ½ , and they would understand this by seeing the process of how many halves are in 4/8. This is crucial to the understanding of fraction equivalence and its importance and relationship to multiplication of fractions. In addition, by being able to see and physically manipulate the cubes, students would develop a more conceptual understanding of what happens when they multiply two fractions. This would be on a level beyond the simple memorization of a procedure.

A third activity would serve as our main and final assessment. This activity would be an exit ticket that includes a short problem similar to the first one we worked through as a class, as well as a reflection question that would indicate to us whether or not they grasped the alternative method we were trying to get them to understand. The problem on their exit ticket would be ½ times ⅓, and the reflection question would be “What is something new that you learned today? Did working with the cubes help you understand this?” These exit ticket responses would be a good gauge for us to determine if they actually grasped the concepts we taught as well as if they could apply them in future problems by themselves.

Besides Jack and Kyle being great resources for articles and sites that provide you with inspiration, the cubes are the main resource of our first workshop. They will be the central component in our workshop to help students refresh and grasp the material.

Jess and Anne will be communicating with each other and the teacher at ELAMS (Ms.Crawford) periodically throughout all workshops to ensure that everyone is on the same page. During workshops, Anne or Jess will alternate roles between active facilitator and classroom support. Due to the addressed behavior issues of this particular class, the teacher, Ms. Crawford has indicated that herself and possibly another teacher will be in the class as extra support. We will remain in contact with Jack and Kyle if any changes or needs arise.

Reflection 

On March first,  Jessica Semblante and I went to Moylan Elementary School (ELAMS). Our lesson plan was to help students learn to multiply fractions by using cubes any way they feel comfortable. We started the lesson by understanding where students as a whole stand with the topic. Everyone was separated into groups of four. We handed everyone one cube stick, and within the group everyone had a different color stick. We put a problem on the board and asked everyone to work within their groups to solve the problem using the cubes. Overall the lesson went well. Jess and I walked around to different tables to see what the students were thinking about. During the lesson all students were making the attempt to solve the problem, and the students were using interacting with each other to solve them. Going to different tables, allowed me and Jess to see which students are having a harder time than others. Of course, not all students were fully focused, but when we told them to focus and provided some guidance, the students started to pay attention. There was one table at the back that was not very corresponding with instructions. It was very unexpected, and so I took a step back and I observed their behavior. I saw that the students were influenced by each other. They found comfort in what would be considered mischievous behavior. My immediate reaction after seeing this was working with students individually within the group, and it worked. As the one, then two people started to understand what they were supposed to be working on, the goal at the table was not to avoid solving the problem but getting the right answer. I could see that students were learning. Before we asked for the answer to the problem, they were yelling it out. Each table had at least one figure made from the cubes to represent their answer. When I walked to the tables, I was interrupting arguments about how to start solving the problem. When it was time to come together as a group, every group shared a different way to solve the problem which was not only shocking, but it was proof that the students weren’t passing the answer around. They actually understood the material just in different ways. This idea of variety in thinking was also present when students were expressing their mathematical thinking and confusion. Some students were more direct with how they were feeling about the problem than others. There were some students that raised their hand to say they didn’t understand the purpose of the cubes or even how to solve the problem in general. There were some students that would just stare at me as a form of communicating that something is not working, and they need help. Other students that did not communicate to me that they needed help either isolated themselves or turned their cubes into toys. Having this understanding of how the kids learn and express their progress, lets me have a wholistic view of my teaching. I think we could use some improvement on explaining the material more thoroughly to the students and being more patient with students. In the future I think that we should take more time to really break down how we will present the material to students that makes it easier for them to understand what they are. This lesson demonstrated personal growth from the past.

3.7.2019

Classroom Observation & Teacher Needs report

I went to ELAMS on a Thursday afternoon. When I entered the classroom, students were sitting in their assigned seats and were focused. The students were at the end of one of their scheduled events. At the beginning of the math lesson, I was asked to join the circle with the students. The students seemed very excited by my presence. They were moving around and chatting a lot. I was introduced to the group as Ms.V. The students reviewed their work from the previous class. The teacher announced the answers aloud. I noticed a fraction chart on the white board. The class was very excited as they got the right answers for different problems. This also showed which problems the students had a hard time with because they wouldn’t say much for those difficult problems. The students then moved to the tables and pulled out their laptops to work on math problems. The teacher used this time to tell me about the group. The teacher called the students the “hot group” which meant that the students have the tendency to get very excited and out of control. I was told that during Trinity math sessions, there would be multiple adults in the room facilitate the group. As for academics, the teacher said that the students were working on fractions and multiplication. At the end of the conversation, I walked around to observe what students were doing and if they needed help. All students showed interest in the content, the students were handling it differently. Most students were trying to solve the problems, others were spaced out, and a small few were engaging in conversation as a distraction. I started talking to the students. I helped them understand a small part that was keeping them from solving the problems. At the end of every conversation that had with the students, I told them how great they did when solving the problems. The students seemed to be shocked, and other students saw their peers understanding the content, they wanted to be more engaged too. Many students had a hard time asking for help. In fact I was looking for faces to know whether students understood. By the end almost everyone was understanding and comfortable. The teacher in the meantime was pulling students aside to a round table in the far back of the room. One of the students was sleeping and I was told to avoid bothering the student because it was a sign of a personal issue. When the time came, the teacher called the attention to all students to put their work away and head to the circle. At the circle I was asked how I would like to be called. We settled with Annie and transitioned to another subject.

2.14.19