My second major: Mathematics

A bit of a swap

Today when we showed up to tutor W, there was another ELL student sitting with him who expressed she needed our help. Her tutor hadn’t showed up that afternoon, and since there are two of us that tutor W, he suggested that he shares one of us with her. As future educators we must recognize that not all things go as planned, so it is important to be flexible. We quickly adjusted to the situation, and since W had history homework that my placement partner was genuinely excited about helping him with, I helped the other student. She was good friends with W, and it was really interesting getting to know her in the first five minutes of talking. She and I immediately realized that we have some of the same favorite singers. She and I worked on her essay in which she needed to use multiple online resources to argue her viewpoint on the Dream Act. Her assignment was to analyze each of the sources she used by identifying the perspective or viewpoint of the article and use it to determine if they are biased or not. She had a hard time understanding what biased means and what this concept of a viewpoint was. I then used our previous conversation about our favorite singers to identify that people have various opinions about every subject. Through this example which she found relevant to her, she was able to grasp this concept a little easier. I thought it was rather interesting working with a different ELL student for a day to see similarities and differences between them and my ELL student. I found that she was stronger with speaking in English then W, and that W is stronger with writing in English than she is.

The most fascinating part of our placement today was witnessing when she and W spoke in another language to each other. I assumed they were speaking in one of their first languages, but they were actually speaking in each of their second languages, which are very similar to one another but are different dialects. It was interesting to watch them have conversations in these languages and laugh about the differences in words when they went to teach us a word in various languages at the end of our session. Overall it was a great learning experience to not only watch such a fascinating interaction, but also to remind us to be flexible and adapt to various situations that may occur in the classroom.

Same subject + different students = different lesson

Today W was starting to learn about exponents, something I was thrilled to hear about! My favorite lesson I’ve taught was last May while subbing in a middle school, and I taught a class of 8th graders exponent rules. There was originally another teacher in the classroom and she told me to stay put and not worry about teaching the students, but then when the kids continued to ask why certain rules existed, she time after time said “that’s just the way it is.” After hearing that a few times I politely asked her if I could say a few words on the exponent rules. I then used the division rules of same base exponents to explain why anything raised to the power of zero is one. The students seemed very engaged and excited to hear somebody explain to them the “why” behind this. After that the teacher asked how I was able to come up with that proof on the spot, and after telling her I’m a double major in mathematics and secondary education, she asked if I was comfortable teaching the rest this lesson without her because she had other work she wanted to go do. The rest of the day I had the best experience working with these exponent rules in a middle level classroom, so I was overjoyed when I heard W was working on exponents.

I was excited to see how teaching W would differ from teaching the same lesson to 8th grade students. It was very interesting to show him new notation of how to express exponents and radicals. He really seemed to grasp that you multiply the base number by itself however many times based on what the exponent is. He had a tough time differentiating between something like 23 and the cubed root of 8 . These are both representing that 23 is 2*2*2, or 8, and that 2 is the cubed root of 8 or 81/3, but he wasn’t sure when a problem was asking for you to find the base, which would be a problem like cubed root of 8 asking you to evaluate that the cubed root of 8 is 2, or when you have 23 and need to find the product of 2*2*2. This was because this notation and language was all brand new to him. I took this hint and took a step back to discuss the language associated with exponents and radicals, and made him a key of which symbols correspond to which math language. This seemed to really help him grasp which process to use when.

It was intriguing to see the differences between teaching this to an ELL student compared to 8th grade students native to Vermont. The biggest factor that makes these two experiences differ so much was in the familiarity with mathematics language and notation. One thing that was helpful to W was when my placement partner made an analogy of exponent notation by drawing a picture. This is something that blew my mind because I hadn’t seen this analogy before, and the visual representation really helped our student to grasp the concept of the notation better. As seen in the picture below, the roots of the tree represents the base number, and the branches represent the exponent. This helped to show the notation and that the exponents is the number written higher than the base. The larger the exponent is, the longer the branch is, so we can think of this to show that exponents with the same base get increasing larger as the exponent increases. In addition, it is good to use the roots of the tree as the base because when you reverse this process you must take the root. For example, 8 is the base, 2 is the exponent, and it shows that 82 is 64. When you reverse this, you take 64 and use the exponent as the root, so that would be the square root 64 which gives you the base, 8. This visual helped to remind our student that in order to find the base you must take the root.

Lesson Reflection

This semester I had the wonderful opportunity of co-teaching a 60 minute lesson on Love and Sexuality within Adolescent Development to my education class of college sophomores. My partner and I had been working on this lesson plan for a few weeks, but what threw me off is that as we planned our lesson more and more it started to be very different than the lesson plan we had originally created. Our activities matched up for the most part, but the content we presented and the means of presenting it greatly differed from our original idea of what we were going to do for this lesson. At first I was very nervous that these didn’t match, but after delivering the lesson and observing the discussion among the students, I was greatly impressed with the topics that students brought up during the class discussions. Even though some comments were tangents from the original topic, there were incredible conversations in the classroom during our lesson in which I’m very glad students had. This made me realize that it’s okay for the lesson to be different from the plan.

The content of this lesson included how types of love and stages of love affects adolescence, the effect of how society views love, and acceptance in sexuality, especially within the LGB community. We began class with bell work of practicing the vocabulary set on Quizlet, with the primary focus of having students review and practice the language associated with our chapter. We found that bell work was a great way to begin the class because it helped to immediately focus the students on classwork and helped them review the chapter they were assigned to read for class. Students were able to use the study guide and Quizlet vocabulary set we provided to review these terms during bell work.

We then jumped into how love and sexuality is unique during adolescent years and how it affects adolescents. In this portion of our lesson we reviewed Brown's Phases of Love and Sternberg's Theory of Love, and discussed how these phases are based on age and development. For Brown's Stages of Love we showed NearPod Slides with definitions and examples of each phase. To show that students understood these phases we had them apply their knowledge of it by creating a visual representation of a phase in small groups. Then, after having students take a minute to jot down the main differences between the first and last phase, we showed the comedy sketch, If Adults Dated Like Middle Schoolers. This video clip is an exaggeration on just how different the first and last phases are, which was followed by a class discussion on how age and maturity directly affects Brown's Stages of Love.

During this portion of the lesson, one group of students got confused on the difference between Brown's phases of Love and Sternberg's Theory of Love, and made a poster on a type of love rather than a phase of love. This moment stood out to me because as a teacher it is of utmost importance to clarify concepts for students, which I do not feel I did well with in this lesson. I focused all my attention to thinking about the lesson going smoothly and thinking about how I rehearsed for the lesson to go, that I did not focus my attention on the students. If I had been properly focusing on students I would have caught the confusion early on when they first started to make a poster, however the many thoughts of what to remember for the lesson consumed my mind. While reading through the chapter and planning the lesson I should have caught that these two concepts are pretty similar and made it a point to show clear distinction between them to help students understand it. I recognize that I should have put more emphasis on the difference between the two concepts, however in the moment when students were sharing their posters it was too late for me to fix it. At this point I had complimented the group on their work and their understanding of that type of love, then proceeded to offer corrective feedback and move on, not to call out too much attention to that group of students. Later in the lesson this error came back into play in a positive way.

To teach the types of love within Sternberg's Theory of Love, we gave formal definitions of the three elements that go into the types of love, which are intimacy, commitment, and passion. We then displayed a graphic organizer of this theory on the board in the front of the classroom while students completed an activity. Students were given sticky notes with each of the seven types of love on them and were to read scenarios that were scattered around the room and match the scenario with the type of love they thought it described. Students used the graphic organizer displayed and the study guides or Quizlet set we provided them with in order to define of each kind of love and match it to an example. This activity went well for the most part. Majority of the sticky notes under each scenario was the correct term that went along with it. There were two scenarios, however, that students got the definitions backwards on, so I used the graphic organizer and definitions to clarify the two definitions and give an additional example to help clear up the confusion. For the scenario that went with the type of love that a group of students accidentally made a poster on earlier in the lesson, every student correctly matched the type of love. I made a point to recognize that because of the amazing job the students did earlier, our whole class had a good grasp on understanding this concept for this activity.

The next part of the lesson we shifted the focus to how society views love and sexuality. We had a guest speaker (one of our classmates) share with the class her experience in tutoring her ELL student. This was extremely relevant to both the class placements and this chapter because her student has mentioned to her on occasion comments about the ELL student's arranged marriage. This began our class discussion on how various cultural attitudes towards love and marriages could potentially affect our ELL students and students of other cultures. Within this discussion the class identified that these students of other cultures are affected socially, academically, and culturally by such varying cultural attitudes toward love. These were the three ways I wanted to point out to the class, however through a very thorough and thoughtful class discussion, the students concluded that before I said anything about it, which I was very proud of and happy to see.

Next, we had students do a gender boxing activity to identify common stereotypes and gender roles of males and females both within relationships and within society. We separated our class into males and females so that a mix of gender would not influence the lists made. After reconvening and making a combined list of these gender stereotypes, we shared the first minute of the comedy sketch Role Reversal: What if Women were like Men and then discussed how stereotypes can influence the actions of adolescents. This discussion transformed into how creating an accepting community among students in your classroom can encourage students to embrace who they are, which brought us to the next part of the lesson.

The final part of our lesson was on acceptance among the LGBTQ+ community, which is important to discuss with future educators, as sexuality is a huge pressure among adolescents. We explained to students that LGB youth are statistically at higher risk of anxiety, suicide, depression, and other mental health issues than their heterosexual peers. Adolescence is a time when you are developing your identity, and the pressure of sexual identity is something many adolescents struggle with. We then shared ideas of ways to support our students in the LGBTQ+ community.

To wrap up class we had our students complete an exit ticket of 3 ways they can support students, 2 new things they learned, and 1 question they have for myself and my partner. This was a great way to summarize what we wanted students to take away from the lesson. At the beginning of class we asked that throughout the class period that students keep a list in their notebook where they would brainstorm how to support adolescents. Throughout this lesson we facilitated discussions of the topics listed above, of which our students had phenomenal contributions to. It was really incredible to see the different connections that students made to current issues, other chapters in the text, our ELL tutoring placements, the community within a classroom, and several other topics.

Though our lesson was on love and sexuality in adolescence, one of our priorities was to emphasize to our classmates the idea that as teachers we are to support our students. This is something I noticed our professor has been really emphasizing to us all semester, so we thought this would be a great way to tie it into our teaching. Adolescence entails great stress as one transforms from a child to an adult, so as teachers we must be aware of the challenges students may face so we can support them both academically and emotionally when needed.

The technology we used throughout the lesson varied from the Quizlet app, to NearPod slides, to poster paper, to YouTube videos, to use of the whiteboard, and more. It was really interesting to experiment with different types of technology accessible to teachers and figure out how to best use technology in a classroom setting. We were excited to play with various types of technology used in varying teaching methods, and figured that using one type of technology throughout the entire lesson may be rather monotonous. We decided that this way of switching things up would grab the attention of the students to help engage them better in the content and corresponding in-class activities.

One way of incorporating our knowledge of WIDA standards and scaffolding instruction to meet the needs of other learners is through our graphic organizer. Our students used this visual to do the scenario activity, which is also a great way to help ELL students by scaffolding instruction, as well as appeal to visual learners. We must keep in mind that there are different types of learners within our classroom, and that in order to effectively present content we must appeal to each type of learner. I am a kinesthetic learner, meaning that I learn best by doing something hands-on. Through the lesson I attempted to appeal to each of the main types of learners. When we had students get up to move around and place one of the types of love under the scenario that it had applied to. This was one way of getting students interacting with the material, and kinesthetic learners may have benefited from this activity, poster making, and the gender boxing activity. In addition, I appealed to the visual learners through graphic organizers, videos, poster making, and having NearPod slides out in front of them. The auditory learners may have benefited from listening to the class discussions, videos, and explanations of content throughout the lesson. Lastly, students had the opportunity to keep an ongoing list of student support strategies they brainstormed throughout the class, so this may appeal to the reading and writing learners. This course has helped me to understand that as teachers we must pay attention to the needs of our students, whether it be academically or emotionally, and it has helped me to find many ways to do such a task.

I got to practice many teacher skills through this wonderful opportunity of teaching a lesson to my education class, of which includes lesson planning, engaging students through activities, using technology to present content, and more. I thought it was very interesting to use the things we have previously learned in class to do this lesson, and I am glad that within our lesson we emphasized how teachers are affected. This is why we had students list ways of supporting students, and through class discussions many topics were brought up relating to how we can build our skill sets as future educators. Overall, I found this lesson as a great opportunity to practice my own teaching skills in more ways than I thought it would.