Unit Plan

Unit Plan 

Textbooks

As a teacher, I learned that I need to be aware of the textbooks I use in class and their linguistic choices. For example, I was not able to realize the difference between exclusive and inclusive imperatives before reading this article. It was interesting to think that these linguistic choices will not only help students reflect on their independent work, but think about their mathematics in the community. This will positively affect their involvement in class and enhance their mathematical thinking. Further, I learned that I need to be aware of the language I use when I give out my own instructions as well. As a student, I believe I will find myself reflecting on my thinking if I am given instructions such as "describe the pattern" or "suppose you use" instead of "make a table" or "graph your data." The verbs such as make and graph are very straightforward and require no thinking. However, describe and suppose are verbs that allow me to expand my thinking process. 

I personally do like textbooks as I believe they offer a guideline for teachers. However, I don't think I will be relying on them too much. Many textbooks that I encountered contain a lot of exclusive imperatives. Further, I think I will be able to allow students to reflect on their mathematics in the community if I give them personalized instructions that contain inclusive imperatives. Finally, I also need to be aware of what textbook I choose to use in class. I would prefer to use textbooks that have a separate section for problem-solving and applications (ex. MathQuest - I examined this textbook last class) as they allow students to make connections and understand relationships between math and the world.

Flow

There were many times when I experienced a state of flow. The model of flow was very relatable and made sense to me right away. When I encountered math problems, I felt all the different emotions that were listed in the model, so I knew what it felt like to be in a state of flow. This was possible when my challenges and abilities were balanced out. It always felt good to be in a state of flow as I was completely involved in what I was doing and I was able to experience a meaningful study session. Hence, I believe that it is possible to achieve a state of flow in secondary math classes. Teachers should implement challenging but not too challenging as well as fun activities. Deciding the difficulty level is challenging because everyone has different strengths and weaknesses. Hence, teachers should also prepare extending or easier questions just in case. Teachers should also know who their learners are in order to implement an appropriate level of difficulty. Lastly, teachers must make the assignments/activities engaging. They must be engaging enough to grab students' attention. Thus, when students are interested and are challenged enough, they will be able to get into the state of flow. 

Dave Hewitt

In the first video, I liked Dave's idea of using the entire classroom as a learning tool. His introduction to algebra and number line lesson was also taught by allowing students to speak in unison. This gave every student an opportunity to reflect on their learning. This made me stop and reflect on my role as a teacher candidate. However, as I was watching the video, I felt like the lesson was dragged on for too long. For example, I would implement more activities and foster group collaboration after a quick interactive lesson. Otherwise, if my lessons are too long, I believe my students will lose focus and interest. Another stop that was interesting was the concept of powers of the mind that was mentioned in the second video. He mentioned that there are different powers of the mind; one of them being memory. As teachers, we need to make sure that memory isn't the only skill that is being taught to the students. This is so common, especially in a mathematics classroom. It was also interesting to learn that we can learn a lot from little. His example of fractions made sense. We need a common name to add fractions and this can be easily explained with the concept of addition. I was able to learn that educating awareness is necessary instead of making students memorize information. I think Hewitt created the fraction problems to support awareness. This problem helped me understand how fractions work and that fractions can be equivalent even when they don't have the same denominator. These examples are crucial for students as they are able to build awareness in them. It will allow them to apply their knowledge instead of using their memory to solve it. Hence, I will need to be definitely thoughtful of the examples I give to my students in my teaching. 

I was able to find fractions between 5/7 and 3/4. Here is the work:

Arbitrary and Necessary

I was always aware of the difference between arbitrary and necessary realms in mathematics. As a student, I never understood why my teacher made me memorize formulas in a math classroom. It did not enhance my learning journey and made me spend less time practicing my logical and critical skills when solving a problem. As a math teacher, I need to make sure I am helping my students to practice their own awareness as this is a crucial skill in mathematics and problem solving. The article talked about a teacher informing their students that the angles of a triangle add up to 180 degrees. This example made me think about one of my lessons during my short practicum. I had to teach my students the quadratic transformations: stretch, vertical translation, horizontal translation, and reflection. However, my SA and I agreed that we did not want to tell our students what a, p, and q does in y=a(x-p)^2+q. Instead, we created an activity where students were able to investigate and play with Desmos, numbers, and tables of values to observe what each variable represents. Hence, this will drive students to use their awareness to come to their own conclusions. This also can be easily done through whiteboards. The day after I taught my students each of the transformations, I made them work in pairs and use the whiteboards to draw the graph of y=a(x-p)^2+q. The process of playing and struggling first before I gave them the lesson enhanced my student's understanding of this specific chapter. When I become a math teacher, I want to implement activities that will allow students to use their intuitive thinking to play and struggle before I give them my lesson. I believe that giving a lesson at the start of a class will allow students to practice developing their awareness instead of memorizing information.

Unit Plan Assignment

 I will be teaching Pre-Calculus 12 Trigonometry for my long practicum

The Giant Soup Can of Hornby Island

We need 1291 liters of water to control a fire, hence there is enough water to put out an average house fire because the water tank can hold around 17,861 L of water. 

This problem allows students to use proportions, estimating, and reasoning. Students may get stuck when they need to find the dimensions of the actual Campbell Soup can and the height of the bike in the photo. They also might get stuck figuring out the diameter of the tank from the height of the bike just by looking at the picture. However, this is a good problem as it allows them to connect to the real world. The problem is realistic and practical. Being able to estimate is a crucial skill because we use it all the time in our daily lives when we go to the grocery store. Further, allowing students to find the information they need to solve word problems is also an important skill that is needed when they become adults. 

One way I would extend the problem is by allowing students to look at the length of the bike in the photo instead of the height. In this case, they would need to figure out how high the tank is when given the length of the bike. This will help them realize that they only need one dimension of the bike to solve the problem when they are given the dimensions of a normal-sized soup can. 

Update November 5, 2023

Here is another extension problem. About one person can fit in between two hedges. What would be the total area of the six hedges at the front not including the hedges at the back. This will allow students to estimate the width and length of the hedges using their knowledge of human measurements. Further, they will need to consider the gap between the hedges when calculating the area.

Update November 7, 2023

This photo was taken at Jeju Island in South Korea when I traveled this summer. This place is called Osulloc Tea Musem and it is a place that shares the history and culture of Korean tea. Osulloc cultivated a farm to create an organic tea farm in Korea. However, it is considered one of the greatest tourist attractions because it was nearly impossible to grow crops on this land due to the rocks. Since it is challenging to see the hedges at the back, only consider the six hedges at the front of the photo and find the total area!