Draft Unit Plan

Truncated Cube and Isosahedron: Drawing

This is a picture of my truncated cube and my attempt at the truncated icosahedron. I found it hard to draw icosahedron because I wasn't able to draw an accurate pentagon. I did find the instructions on how to draw it easy to understand and follow. 

Proofs

GeoGebra was used to explore proofs of some geometry concepts such as chords, angles, and tangents. I found it interesting to be able to work out these proofs in various ways. I think this would be beneficial for high school students that find it difficult to understand the concepts and visualize them. It also allows students to explore any other questions they may have. For example, our group worked on lesson one which explored the chords of a circle and we were able to play around and move with the endpoints of the chords. GeoGebra is also able to quickly and accurately produce geometric objects. As Mason mentions, exploring proofs and being skeptical allows students to be involved and understand the reasoning behind the math (Mason, 2001). I think the use of GeoGebra is a great technological tool to explore and analyze math concepts.

Homework Reading: Math textbooks

The example in the article on the use of first person pronouns in math textbook was interesting. As a student I didn't realize the importance of having these pronouns. I now see how the use of 'I', 'we' and 'you' can be used to connect students to the textbook. It also includes students in the mathematical content rather than the author just simply stating the information. As a teacher, I will spend time to ensure using these pronouns in my notes and other information I give my students. It is important to have students to form a connection and in thier developmental of mathematical thinking. Another example used in the article was on the use of picture along with the text is a great point. As a student, I always tend to enjoy and understand the question more when there was a picture provided. The article also mentioned the importance of  the use of colour in a textbook. As a student, I also enjoyed textbooks that provided colour it and it made the textbook stand out. I will do my best as a teacher to provided students with lot's of picture/visual examples as well as the use of colour. 

I think there are many advantages and disadvantages for using textbooks in schools. Some positves include that they provide many examples that model how to solve the problems. Another positive is that they include lot's of sample problem which is excellent for students that want or need more practice. Most textbooks also had a great layout and is very well organized. Some negatives would be that students can be overwhelmed with the amount of information in the textbook. Another disadvantage is they don't take in account to student's background information. There may not be enough background information or higher level thinking questions. Another disadvantge is that students may just do the homework questions by looking at the answers in the back rather than spending the time to solve it. I would personally use the textbook as a resource since they do provide lot's of detail and information. However, for my students I wouldn't always rely on the textbook instead, I would try to use a mix of other resources such as videos and other online math interactive resources. 

Dave Hewitt Teaching

One-stop I had on the Dave Hewitt video was his introduction to integers. He was able to get students' attention and engaged in the activity even though they didn't know why they were doing this. I think it's a great hook to start talking about integers. Another stop I had while watching the video was how Dave had the entire class participate. I like how he was able to get students to be active participants in the lesson rather than just telling students the information. Guessing the number and use of the order of operations activity was another stop I had. I liked how students had to process what the teacher was saying and work backward to answer the question. Students can do this to intuitively problem-solve and find the answer without much assistance from the teacher. 

Arbitrary and Necessary: Reading Reflection

I would like to plan and teach lessons without solely providing arbitrary information so a lot of time isn’t spent on memorizing. I would like to incorporate more awareness rather than giving students information to memorize. This can be done by providing students the necessary amount of knowledge and giving students the time to work out and discover mathematical properties and relationships. Students are then aware of the information and are more likely to remember it than if they were to purely memorize it. I would prefer to help students develop their mathematical awareness through providing activities. Students can also use the information they have to then apply and extend their knowledge. I would provide students with a variety of tools and methods that they can then apply to any given problem. I also think that allowing students to develop new concepts on their own would be very beneficial in a mixed ability class. It would allow students that already understand the concepts to challenge themselves and apply it in ways that would expand their knowledge. For students that are unsure and uncertain of their math skills, it provides the opportunity to test and understand the new concepts. Teachers can also provide some guided instructions and scaffold information where students would then gain and develop a greater understanding. 

Flow

Czikszentmihalyi’s TED talk on flow referred to it as an experience where the skills a person has are being used in a way to allow for greater enjoyment and fulfillment. I have had many experiences being in a state of flow where I was very engaged and focused on completing my work. It usually involved more creative work rather than any mathematical experiences. However, there have been times while solving math problems I have felt very focused and eager to finish the problem. I think that the key aspect to having flow in the class is that it should be something enjoyable. It is important to have this flow to increase student engagement and participation. I think it is possible to achieve a state of flow in a math class. During the two practicum, I found there was an increased flow in work when I used various types of activities during the lesson. For example, when I was working with the grade 8s for Math, I allowed students time to have discussions, activities that involved moving out of their seats, and time to do work on their whiteboards. I found this helped the students stay engaged and focused on their work. I also think that from the list of characteristics of flow, the one on people knowing the task is doable and there is a balance between skill level and the challenge presented is a very important characteristic. One thing that I did during my two practicum, was having a variety of concept check questions throughout my lesson which would range from easy questions to more applying the information type of questions. I found this allowed various types of students to participate during the lesson. It also allowed students the opportunity to challenge themselves and possibly improve their skills and abilities.

Pro-D Day Reflection

For Pro D Day, I joined the virtual Beaty Biodiversity webinar. I had the opportunity to learn so many wonderful things and resources that the Beaty Museum provides. The most interesting thing I learned was that Beaty had over 2.2 million artifacts. I also learned that the museum allows teachers to rent out Beaty boxes to take and show to their classes. I found this quite useful information as I think it would make a wonderful lesson to show students and to have them experience some hands-on learning. I also found this presentation provided great resources such as online exhibitions, YouTube videos, knowledge webs, and many more online websites.