Final Blog Post

I learned a lot from this course on inquiry, the importance of outdoor education, and the different types of math resources available. In particular, I enjoyed some of the readings such as Lockhart’s Lament and the arbitrary and necessary article. I found that learned some new concepts while reading and reflecting on them. I also enjoyed the short Dave Hewitt video and his ideas on how math should be taught. I liked how we were able to reflect on our favourite and least favourite math teachers. I found that it was important to reflect on this as it helped to think about what my teaching style and persona would look like. I also think it’s necessary to think about the teachers that weren’t so great and what are strategies I can use to avoid being like them. I also enjoyed learning some fun games that can be used in a class on our last day of class. I found that they were some great ways to start or end class. One suggestion that I have to improve this course is to include the blog post and deadlines for each one on the syllabus. I found it a little difficult to keep up with the deadlines and due dates using the blogger format. Thank you for a great semester, Susan and Erica! 

Final Unit Plan

 Here is a link to my final unit plan: Final Unit Plan

Opening Up Mathematical Questions

Some closed questions in math are true and false questions, multiple-choice questions, or some that just require simple input of numbers in a calculator. For example, one question from my unit plan is what is the mean from this list of data. One way to open up this would be to include additional conditions. This method will open up the questions and provoke a deeper understanding of the problem. This can be done by having students then think about what may occur to the mean if another data point was added to the set. For example, if the data point was larger or smaller than the mean how would that change the original mean. Another way to open up this problem would be the comparing/contrasting of three. For example with the question on mean, one way to open it up would be to compare the mean of 3 sets of data. Perhaps, here would be a great opportunity to have students think about outliers and how they can affect the answer. A third way to open up a closed question would be to use the always, sometimes, never true method. I like how this method really has students think about the way the question is posed and how the conditions of the question really have an influence on what the answer would be. For example with the mean question, one open-ended question that uses the always, sometimes, never true method would be the odd number mean always has an odd number of data points. This statement also students to explore several different possibilities and to really take their time to understand the question and the content. Another way to open up this type of closed question would be to pose the question where there can be several different possibilities. For example, what are 3 numbers that give a mean of 24? This question allows students to think about the infinite answers that are possible and how general this question is. The method that I like the best is the use of having additional conditions to open up the question. I like this because it allows shows the progression in having a question become more open-ended. I also like how the question can be changed slightly requiring the students to think about possibilities that they may have not considered on their own. The most appropriate method would also be the use of having additional conditions and posing questions where there can be multiple answers. I think both of these methods allow students to explore math ideas and to think about different perspectives and how there are multiple approaches they can take to answer a question. I like how both of these types of questions allow for scaffolding so there is an opportunity for the progression of closed to open-ended questions.

Market Scales Problem

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.

Microteaching Lesson 2: Reflection

I enjoyed having this microteaching lesson as it gave us an introduction to teaching math in front of a class. I think our presentation went fairly well. It was structured, organized and it flowed well together. The class provided us with feedback on how our activity was fun and an engaging way to practice multiplying fractions. One thing, I would like to work on was including the whiteboard more during our lecture portion of the lesson. I also noticed that not many people wanted to come up to the board during our activity. I should have encouraged students more and made them feel comfortable coming up to the board. I could have done this by providing the group with some paper to work on the problem in groups or individually. Then start inviting people to share their solutions on the board. I have also noticed a few of the reflection sheets suggested projecting our voices louder as it was hard to hear. For the next lesson, I would like to work on and improve the projection and clarity of my voice. One great idea that was given in the peer assessment was to use concept  questions to check understanding rather than asking students if they understood the topic. I think this is a great idea and something I would like to use in the future.

Peer and Self Assessment:

Campbell Soup Problem

 Campbell Soup Problem

Solution:

• I first found Campbell Soup cans have a height of 4.25 in and a diameter of 3.25 in (Flynn, 2020). In cm, this is 10.80 cm in height and 8.23 cm in diameter 

• Then I found the average length of a bike which is 175 cm (Ellis, 2021)

• I then estimated that the bike would fit approximately 3 times across the length of the large soup can. So the height of the large soup can is 175 cm*3= 525 cm

• To find the diameter of the large soup can, I use the size of a normal-sized soup can and scale factors: 

Scale factor = Height of large can/Height of small can = 525 cm/10.80 cm= 48.61

• To find the diameter of the large can, multiply the scale factor by the diameter of the small can: 48.61*8.23 cm = 400.07 cm

• So dimensions of the large can/tank have a height of 525 cm and a diameter of 400.07cm

• The volume of the large soup can: 

V=pi*r^2*h = (400.07/2)^2(525) = 65,996,538 cm^3

• I then found the volume of water to put out a house fire is 20,000 gallons (Kiser Construction, 2021)

• 20,000 gallons * 3785.41 cm31 gallon = 75,708,236 cm^3

• Since the volume of the large soup can is 65,996,538 cm^3 so it's not enough to put out a house fire

Extension: 

One way I can extend this problem is by having students solve the problem:

How many average-sized water bottles would be needed to hold the same volume of water as the fire department soup tank?

References:

Ellis, C. (2021, June). Find a Bike Lock that Works. The Best Bike Lock. 

https://thebestbikelock.com/bike-storage-ideas/best-bike-storage-shed/what-size-shed-for-bikes/

Flynn, A. (2020, June). How big is a Campbell soup can? Greedhead. 

https://greedhead.net/how-big-is-a-campbell-soup-can/

Kiser Construction. (2021). How Much Water is Used to Put Out a House Fire? 

https://www.kiserrenovations.com/about-us/blog/entryid/4/how-much-water-is-used-to-put-out-a-house-fire

Micro-Teaching Assignment 2: Lesson Plan

 Here is the link to our group microteaching lesson plan and slides: Lesson Plan   Presentation

Eisner Article Response

This article touches on this idea of “reward junkies”. I found this idea interesting as schools often use rewards such as grades, bonus marks, extra playtime during lunch and recess to motivate students into doing school work. Although this may work, there is the possibility that without rewards students wouldn’t have the desire to finish their tasks. Also over time, the rewards may lose their powers as they may not provide enough motivation. I think that the use of extrinsic motivation in the classroom isn’t the best way to engage students in learning. I would prefer to have students learn with the use of intrinsic motivations. This is when students want to learn about the subject or content because they are truly interested and curious about it. This can be difficult to foster in a class as students won’t be interested in everything a teacher has to teach. One way to accomplish this is to foster students' curiosity, provide them time for questions, and allowing them to follow through on those inquiries. Another point the article makes is the biases schools form towards Art subjects. It’s remarkable how schools have made the subject, Art, seem like a break from doing “actual work”. I think it’s crucial to have Arts in the curriculum as it allows the expression of individuality, creativity, and innovation. Arts education shouldn’t be pushed aside but rather used to build on skills that can’t be gained in courses such as Math, English, Science and Social Studies. This stigma can translate into students beyond high school. For example, students may feel as if they can’t pursue an Arts degree as it won’t provide job prospects and they may settle for something they’re not interested in. I think it’s important to have students realize that they should pursue and focus on their interests. 

A curriculum is a tool and outline used by teachers to teach students content. It involves two processes which are described as intellectual processes and content in this article. The intellectual process involves the development of cognitive development such as working on behaviors, attitudes, and emotions. Whereas, the content is the explicit knowledge that is taught to students and the information they are expected to know. Eisner also discusses the importance of what schools don’t teach. There are some aspects where students learn things just due to the organization and structure of schools. For example, the use of having required versus elective courses and the hidden messages this portrays. It can represent this ideology that taking a Math course is more important or superior than taking an Arts course. The B.C. curriculum has a few big ideas for each subject. It is then broken down into two streams which are the curricular competencies and the content. This is similar to Eisner’s thoughts about the curriculum. Eisner emphasized the need for schools to provide students the opportunity to imagine, invent and innovate. Through the B.C. curriculum, this is possible because the core competencies focus on inquiry where skills such as reasoning, analyzing, interpreting, communicating, and collaborating are given importance. 

Battleground Schools: Response

The Battleground Schools article reveals some key aspects of mathematics education. While reading this article, one thing that intrigued me was the idea of “programming the environment”. I think the best way to learn math is by having students use inquiry and providing them with hands-on material rather than having students sit and listen to the teacher lecture. I was taught math by just having the teacher talk and I would zone out about halfway through the lesson. I was never really engaged with my learning so I think it’s very important to facilitate a class where there is that use of inquiry. Another thing that made me stop while reading was the problems parents faced when helping their children with the new curriculum. I can resonate with this as my parents learned different math techniques which made it difficult for them to help me with my homework. I also found the tables showing the opposing arguments for teaching math interesting. I liked how I could compare the conservative vs progressive for each area of interest. I was able to see in which areas I show more conservative and other areas where I was more progressive. 

Micro-teaching Reflection

 

I learned a lot from microteaching my lesson on card tricks. I learned that I was a bit nervous to present and that is something I should work on. I also forgot to follow some things on my lesson plan so for next time, I should double-check if I miss anything. Something I could improve on was the timing and pacing of the lesson. I didn’t time the tricks properly so not everyone in the group had enough time to try out the card tricks. I also thought the organization wasn’t the strongest. For next time, I would bring in a sheet with rules and I would also have a short wrap-up at the end. I thought the explanation of the card trick went great as the students that tried the trick were able to complete the task. Overall, I enjoyed teaching my lesson. I also enjoyed learning about the aspects of my lesson and delivery I should improve on. 

Teaching Perspective Inventory: Results and Reflection

 

These are the results of my TPI graph. I scored above average for nurturing and developing with scores 45 and 38 respectively. I also scored 35 and 31 for apprenticeship and transmission respectively which were close to the mean. I scored the lowest for social reform with a score of 29 and it was recessive for me. One of the results that surprised me was the score for transmission. I thought I would have a higher score for this as I think providing students with clear objectives and lectures is a key aspect to learning new content/material. One of the results that I wasn’t surprised by was the social reform score. I was expecting to score lower in this due to my teachable subjects. I thought it would be harder to provide students opportunities for social action/reform in a math or science class. However now reflecting on this, I could perhaps use Biology as a way to address social issues such as climate change, pollution, and species at risk. Some questions the TPI results raised for me was “what are some ways I can use social reform in a math or biology classroom?”,  “what are some underlying values I have and can learn from these results?” and “From these results, what are some assumptions that I have about teaching?” 

Microteaching Lesson Plan

 Here is a link to my lesson plan for the microteaching assignment: 

https://docs.google.com/document/d/1ZhxajEgFogescwVh3yxQLG9IeNasZdmiaQwNofCEqXM/edit?usp=sharing