Teaching Episode: Mini Lessons

This week in our education classes we had the opportunity to prepare and teach back-to-back mini lessons to our classmates. We chose a topic within our unit, drafted lesson plans, edited and revised them many times, gathered materials, set up technology to use to present the material, created assessments, and more. After giving our first mini lesson on Tuesday we went back through and revised our lesson plan for Thursday based on how much we were able to cover in the first lesson. This teaching episode was very unique not only because we had to figure out how to teach, engage, and assess in just 20 minutes, but also because we taught these lessons to our classmates in our education classes.
In my group there was one other mathematics major and three English majors. This was an incredible opportunity to teach to learners at a variety of levels, as there were some students who were rather lost in the math content (after not doing this type of math since middle school), and others who thought it was far too easy for them (the other math major). After each lesson, we exchanged feedback with one another. This was perhaps the part where the most learning happened. Not only did we learn about ourselves as teachers and about how to time a short lesson, but we learned from others about how we performed from the students' perspective. The feedback included things like our classroom presence and teacher language, clarity in how we spoke and presented the material, getting students interested and engaged in the content, organization, and more. This was incredibly helpful when editing our lesson plans between Tuesday and Thursday classes and figuring out the areas which we should focus on improving.
On Tuesday I did not have enough time to introduce slope triangles, so I had to edit my lesson plan so that I could have enough time to do this on Thursday, and sift out what was necessary for Thursday and what material would have to come in the following lesson. I recognized that I tried to fit far too much content into these two mini lessons than what was possible within this time frame, while still doing the activities I had set up. I edited the learning outcomes from the lessons, what pieces of standards the lessons pertained to, the timing for each of the parts of the lesson, the assessment for after the second class, and the accommodations for students. I had never had to edit lesson plans based on the timing of back-to-back lessons. I hadn't before thought about how if students have an important question related to the content that needs to be addressed, then that could throw off the timing of the lesson that I originally intended.
Attached here is a folder of my materials for these mini-lessons, of which includes my first and second draft lesson plans, a screenshot of the NearPod presentation slides, a detailed outline, some examples of vocabulary discussed in the first lesson, assessments from each of the lessons (exit task folders), feedback from my classmates and professors, and a few images from the activities.
In my lesson, I used NearPod to present material. The first lesson started with having students draw any picture using only straight lines, then setting this aside. We reviewed what we previously knew about graphing points on an xy-plane, then jumped into the relationship between two points. I wanted for students to spend some significant time on the language associated with this lesson, especially because there were three English majors in the room. We discussed how we have heard the word slope before in other contexts, and then talked about the words "rise" and "run" and the directions we associate with those words. The idea of this is to help students remember the vocabulary to better understand what slope is. After defining slope, we looked at types of slope, and I gave students examples of these through hiking. After this we dove into an activity where we used m&m's and graph paper to see that there is not just one specific line within one type of slope, but instead that there are an infinite amount of lines that classify as each type of slope. This activity also served as an introduction to proportional relationships, and students observed one defining quality: that these lines that are all proportional relationships all go through the origin. After this we were almost out of time, mostly because I hadn't factored in time for the questions that students had, so we moved on to the exit task. Students were asked to define slope, draw a picture of each type of slope and label it, and to write down one question they have.
I think this first lesson went very well for the most part! I could have been more clear with the directions for the activity, but I quickly caught onto it when my students seemed confused. Though I do wish we could have had time for the last few things I wanted to do in this first mini lesson, I am really pleased with the clarifying questions that students asked. They seemed to respond well to hearing something explained a different way in order to understand something if they didn't get it the first way I explained it. The feedback I received indicated that students liked my explanations, the activity, the pacing, and my classroom presence. My professor indicated she liked the clarity of my instruction, strong sense of my audience, use of NearPod features and ability to connect with students' knowledge and experiences. Some areas to focus on for the second lesson were to provide more clarity with directions for the activity, ore clarity on what students are learning, and that with a real group of students I may need to slow down and check for understanding more often. Another piece of student feedback is to come back to the pictures we drew, as it was clear we ran out of time and students may not have known why we drew those pictures at the start of class if we didn't do anything with them. This helped me to recognize that this activity could be a great way to start off the next class by reviewing types of slope. This feedback helped me to recognize what I should and should not focus on for Thursday's lesson.
The second lesson was on Thursday, and we began by going over the exit task from the last class to review what we already knew so we could jump right into the content for the day. One student was absent last class, so I created a note sheet for her of notes from last class, so she was able to follow along. This note sheet could serve as a good tool for differentiation for students who need help with organization or students who need assistance in note taking. To review from last class, students took the pictures they all drew and labelled each line its the type of slope. Then, we discussed proportional relationships by looking back at the m&m's activity, and then talked about what a constant of proportionality is and why it is important. Afterwards we reviewed that slope was the ratio of vertical change to horizontal change (or rise over run) and went into the hallway for an activity. I had x and y axes taped onto the floor, and using the floor tiles as one unit each, we did a graphing activity to help students visualize graphing slope and proportional relationships better. There were two pairs of partners, and each round one student would stand on the origin and the other would stand on where they think a second point on the graph would be. After agreeing on where the second partner would stand, students would look over to the other graph to compare. We did a few rounds of this, where I would either give them a slope or an equation for a proportional relationship (in the form y=mx). After this activity, we discussed why we did this activity and what students got out of it. Finally, students took an exit task to wrap it all up.
This second lesson I don't think I did well with timing. I ran out of time at the very end and students didn't have long to complete the exit task. In the feedback I received, students and my professor agreed that I should have left more time for the assessment at the end of class. My assessment was much longer than it should have been, especially given that I only left 2 minutes for it. The feedback I received for this lesson included issues of timing at the end, and that I should have focused some more time on defining the language associated with proportional relationships the way I did for slope, rise, and run. Another piece of advice I received was to not pack as much content into one lesson, which is something I found myself struggling with throughout planning these mini lessons.
The assessments I had students complete showed that they retained a significant amount of information. I saw there was some confusion about zero slope and undefined slope. I also noticed that some students had a hard time looking at a line and figuring out what the slope is numerically. This lesson focused more on positive and negative slopes and the skill of graphing using a given slope. From viewing the results of the final assessment, I saw that each student seemed to understand that a proportional relationship is one that goes through the origin, which answered a part of a common core standard I was hoping to address. (CCSS.MATH.CONTENT.7.RP.A.2.A). The other standard I was hoping to address was to have students identify slope (or unit rates) using graphs and equations, (CCSS.MATH.CONTENT.7.RP.A.2.B). I think students were able to do this well during some of the activities, but besides that students did a much better job being given a slope and then graphing it or writing an equation, rather than the other way around, as this standard is looking for. I believe that a lesson following these mini lessons would have to move forward in helping students to learn this skill so they can effectively meet the standard completely.
Through this lesson I worked on performance criteria 3.1 Active Engagement, 4.2 Making Discipline Accessible and Meaningful, and 7.2 Knowledge of Learners by the activities I planned for each mini lesson. I recognize that there are different types of learners and multiple intelligence's, so I try to do all I can to keep all students engaged in the content. Looking at our accommodations matrix alone, (link in my lesson plan drafts), you can see that many students have attention span and distraction issues, as well as some students who have language barriers. The lesson I planned used activities to help those students, as well as get all students to be able to better visualize concepts and to help students who need more hands-on learning to keep them engaged. I showed performance criteria 9.1 by the practice of creating and revising lesson plans, receiving feedback and adjusting instruction based on that, and most of all learning about what I'm like as a teacher and how I can improve and grow further.

1:1 Technology Letter and Contract

In our Curriculum and Literacy classes we discussed how technology is becoming more prominent in classrooms as a tool for learning. Though 1:1 technology initiatives give students the ability to access a wide variety of educational resources, we as educators must also be aware of the risks of each student having devices. In groups, our education classes created a letter for parents informing them about implementing a 1:1 initiative in our fake school, and a contract for students and parents to read and sign that they understand the guidelines. You can view our letter and contract here.
Through this project we considered all the pros and cons of technology in the classroom. The pros were quite obvious about how technology can enhance student learning and understanding, especially through educational apps, access to online databases, and knowledge of digital citizenship. There are a variety of ways that technology can help personalize students' learning as well, as discussed in this article here.
Some of our arguments against 1:1 technology initiatives is directly related with our concern for students' internet safety. It is outlined in our letter and contract that students are not to reveal any personal information on the internet and that students are to use the technology for anything related to academics but not for personal reasons such as social media or gaming. In addition, this gives us as educators an opportunity to teach students about digital citizenship and have class discussions about the dangers of the internet.
This meets performance criteria 9.1: Continuous Professional Learning and 10.1 Collaboration to Ensure Learning. Through a thoughtful examination of technology in the classroom, we learned about the most useful ways for technology to help support student learning. One thing that we established was to teach students research skills and how to evaluate if a source is valid. If students are researching, we want them to understand that not everything on the internet is true, that way the use of technology is not counterproductive to their learning. Considering the depths of a 1:1 initiative helped us to become more equipped to work with students using technology at our placements and prepare us for technology use in our future classrooms. It is also extremely important for teachers to be on board with technology assisting students to become more independent learners and for their learning to be personalized. Teachers must use technology to collaborate with students and help guide them in personalized learning in a way that students can explore their interests through various school subjects.
As a future math teacher, one thing I'm concerned with about technology is students building a reliance on calculators. At my placement, I've seen many students have MobyMax math homework open on one tab and a calculator on the other tab. Sometimes this is okay, for example when students are doing problems on unit conversions or word problems. This is not okay, however, for the students who are working on long division problems, where they must learn the process of long division, but instead they pull up a calculator and plug in the numbers. Students can build a reliance on calculators because it is simple to plug numbers in and let a machine do the work for you, however it is counterproductive when it takes away from them remembering basic operations they need for everyday use. As a math tutor to students at Saint Michael's College, I have worked with many college students who have relied on their calculator to compute basic multiplication for them. Calculator reliance is a bad habit for students to get into because when they use it as a crutch, they lose their fluency in basic computation and basic graphing skills. Sure, calculators are an excellent tool in math classrooms in many ways, and they should be used for math exploration and problem solving and reasoning skills. My main concern I have about technology integration, however, is that students would rely on their devices to compute for them, because they have easy access to it with the 1:1 initiative.
One thing that would better prepare me for technology integration in the classroom would be professional development about when and when not to allow students to use calculators as well as learning about math education tools. Throughout the past few years, I've accumulated many math education tools through my education classes, placements, and keeping in contact with many local math teachers. I'm very excited to continue to grow this collection of technology resources and learn how to best integrate technology into math. When many people think of teaching math, they tend to think writing out your work in paper and pencil, so learning technology tools for math is a great way to keep math exciting and appealing to students.