The Giant Soup Can of Hornby Island

NEW EDIT:

As for an extension, we can consider the process of building and constructing the giant soup can. To do so, we need to find the surface area of the soup can, and we can do using ratios.

Supporting Students with Exceptionalities Pro-D

 Having worked as an SEA for half a school year, this was a very insightful pro-d. One of the things the speaker, Hazel, emphasized was to respect the child by giving them the right to self-identify. For example, the child might self-identify as a student with autism rather than autistic. If that is the case, that is what we should call them. Another thing she emphasized is terminology, like IEPs or the tiers of funding. She stressed the importance of not using these as adjectives to directly describe a child, because it is dehumanizing to do so. For example, we do not want to be calling a child an IEP or a tier 2 child. I think this is important because as teachers, we need to watch what we say. What we say has weight and can be mistaken the wrong way. 

The other main thing I took away from the Pro-D is Hazel's mention of Shelley Moore's principle of inclusivity, as seen below. She was talking about how our society has progressed throughout the years from exclusion of students with exceptionalities to segregation and now integration and inclusion. Our goal as teachers is to provide all students with a sense of belonging in the classroom. We want to make them feel included. However, what I find interesting is that Shelley Moore takes it a step further and has a category called teaching to diversity, where we as teachers treat every student as unique and different. That way, we see the best and most unique parts of our students and treat them all equally. I really liked the idea and the way she visualized it with dots. Very interesting.

Assignment 2 Precalc 11 Lesson Reflection

Overall, I thought we did an okay job with the lesson. Having been in charge of the demo, I felt that using colored paper and showing the steps by labelling the sides of the squares and rectangles could have helped students visualize it better. If I used colored paper, I could have stuck it on the whiteboard and labelled the sides with a marker. Also, someone put a comment about erasing the board too early, and I have taken note of that. Having taught in a classroom of grade 11s before, I found it actually a lot harder to teach in the classroom full of math students. I found that grade 11s are more interactive with the content because they are there to learn, while teaching it to math students who already know the concepts can be less engaging. When my groupmates explained the algebra part, I felt like they could have constantly linked it to the geometric representation to help students visualise and understand the connection. That is why I spontaneously stepped in to explain the connection to the geometric representation. But having stepped in a little too late, grade 11 students could possibly be confused. 

Overall, I love the ideas we had and thought the geometric representation was unique, but I think that there could have been more organization and communication between the groupmmates on each others part and tying it all together.

342 chess microteaching reflection

Overall, I think that the microteaching went well. There were two stumbling blocks for me in my opinion. One, I was still sick, so I found it hard to talk and hard to catch my breath when talking. Two, I found that it was a lot of content for the 10 minute time constraint, as I ran out of time for the demo which I really wanted to do. However, I found that stopping where I was at instead of rushing the demo in the last two minutes was a good choice, because it allowed the students to absorb and think about the material instead of ruh through a demo that they might be too fast for them to process. After hearing that I have to present in front of the whole class instead of 5 people, I also made last minute adjustments to my presentation to better accomodate the whole class (slides, online chessboard, visuals of different scenarios). The practice of spontanaiety and adapting to the environment is essential in the teaching field. There are times that the lesson may not go according to the lesson plan, and that it okay. As teachers, it is important that we adapt to our students, the classroom, and the environment around us.

 

Assignment 2 Microteaching Lesson Plan

LESSON PLAN PRE-CALCULUS 11

Unit: Quadratics

Lesson: Completing the Square

Big Ideas:

Algebra allows us to generalize relationships through abstract thinking.


The meanings of, and connections between, operations extend to powers, radicals, and polynomials.

Curricular Competencies:

Visualize to explore and illustrate mathematical concepts and relationships


Represent mathematical ideas in concrete, pictorial, and symbolic forms


Solve problems with persistence and a positive disposition

Learning Objectives:

Understand why completing the square is essential in finding the roots of a quadratic equation


Develop a geometric interpretation of what completing the square looks like


Be able to complete the square algebraically


Apply the process of completing the square to solve quadratic equations

Materials needed:


Whiteboards + markers


Paper


Scissors


Pencil/pen





Lesson:

Introduction: (3 mins) - Lisa L leading

Recap: we already learned about quadratic factoring.


Intuition for today’s lesson

Try to find the roots of this: x2+6x-11=0 using factoring. You can't, right?


This leads us to today’s lesson. Many quadratics are not factorable, but still have roots. So how do we find the roots?


Remember perfect squares? We can easily solve for x if we could rewrite this problem into a perfect square, then simply use basic algebra. How can we make a quadratic into a perfect square?

Demo: (5 mins) - Nathaniel leading (others are walking around helping students who are struggling)

Pass out paper and scissors to students. Instruct students how to visualize completing the square with this short arts and craft

Fold the paper along a diagonal to make a square & cut that square out. That square has side lengths x and area x2


The remaining paper is a rectangle with side lengths b and x, resulting in an area of bx. Together with step 1), the total area is x2+bx


Now we want to fold the rectangle in half lengthwise and cut it. Notice how each cut rectangle has length x by b/2, since we cut it. Each cut rectangle has area bx/2. Align one strip below the square and one strip to the right of the square. Notice how we haven’t removed any paper so the area is still x2+bx.


Now how do we make this a square? What do we need to add? The remaining value that we are missing is a square with side lengths b2. So its area is b2/2. This is why when we “complete the square,” we “half n square.” So to make a square, we add the value that is half the coefficient of the x term and then square.

Direct Instruction: (7 mins) - Lisa D leading (Lisa L helping co-teach. Nathaniel walking around & observing if students are understanding the concepts)

Relate what we did in the demo to how we complete the square algebraically with an example or two.

Closure: Exit Slip (5 mins) - everyone walks around helping students

Everyone get into groups of 3 and tries a problem

Assessment (formative):

Introduction & Direct Instruction: Are students paying attention? Are students engaged, asking/answering questions, and participating in discussions? Are students able to follow along with the examples discussed? Are students able to find connections between the visual representation and algebraic representation of completing the square?

Hands-on Practice (group-work): Teacher walks around and guides students in their groups. During the demo, do students understand how to make a square (complete the square) visually with the crafts? Are students able to complete the square of the given examples algebraically?

What is meant by 'curriculum'?

It was interesting to read about the implicit curriculum. This makes me reflect on what I learned as a student. Socialization, professionalism, organization, behavior in class, respect, conflict resolution, and more were all learned implicitly in the classroom. On the other hand, teaching about mathematicians, all who are male, may implicitly make students believe that mathematicians are all male. This makes me ponder about what I want my students to learn as a high school teacher. It also speaks to the amount of responsibility I have in the classroom as a teacher to be inclusive and encouraging to students of diverse backgrounds.

Reading about the null curriculum has got me thinking about how many students leave high school without knowing important life skills like cooking, social skills/ettiquette, budgetting, and doing one's taxes. I guess one can argue that there is not sufficient time in the curriculum or that parents are expecting academic content, but these skills are just as and if not more important than the academic content we learn in school. As a homecook myself, I am noticing that as years pass by, fewer individuals grow up knowing how to cook. It is quite shocking. If not taught in school, who is responsible to teach such life skills? Perhaps parents? And if parents lack the time to do so, how will students learn such skills? I think that schools are responsible for students to learn the null curriculum. Although they may not teach it, they need to effectively communicate with parents about students' well-being and how the null curriculum can be eventually picked up and worked into their set of everyday skills.

Overall, this reading has expanded my thoughts on what "curriculum" actually means. I have always thought of curriculum as the academic content taught in the classroom, but I never thought about the fact that students learn many things implicitly in the classroom and hallways at school. The BC curriculum has been designed so that it is malleable and can give teachers room to teach what they want to teach, as long as they lead students toward the curricular competencies. That being said, teachers have the freedom to teach parts of the null curriculum that did not used to be taught, such as taxes and budgeting under financial literacy. Teachers can design their own inquiry projects for students to explore these important life skills under the context of the subject they are learning. This allows teachers to be creative in instilling the values and skills they want their students to learn whilst in the classroom.

Homework reading and blog post: Battleground Schools

It was interesting to read the various negative views of mathematics. These are perspectives that I often hear from people and even see on media, tv shows, and movies. The media portrays mathematicians and scientists as "nerds" or "eggheads" as the article describes, with the typical glasses, a possible lab coat, and wacky hair. Even my parents and my peers have told me that most mathematicians are socially awkward and have trouble communicating with others in the real world. Looking into the real world and having a lot of friends in mathematics, we see that these portrayals of mathmaticians are not even close to being true. In fact, they discourage many young individuals from going into the field/study of mathematics. As a prospective teacher, I want to dismantle the streotypes of mathematics and make math fun and enjoyable for my future students.

On the other hand, it surpised me that even during the Cold War, the lack of individuals in college studying mathematics was a prevalent issue. This makes me think of why this is the case. How were mathematicians really portrayed back then? The fact that it was a worry and a concern by the United States shows the importance of having mathematicians and scientists in our society. That being said, it is important to continue to encourage gifted students in our educational systems to pursue such career paths amidst the stereotypes in our world today.

Lastly, it was interesting to read about thre NCTM standards. It was my first time hearing about them. I think that their values should be align with how mathematics is being taught in the classroom. As the article mentions, I think that it is important to instill in students an appreciation of the beauty of mathematics. In addition, mathematics should revolve around developing "flexible problem solving skills", not just tmemorizing formulas. However, I think that standardized testing, such as the SATs, ACTs, etc. goes against such standards. Standardized testing creates a more stressful environment for students and demoralizes them to do math. It destroys the fun in math and instead, makes it routine-like. With heavy time constraints, students who memorize short-cuts to solve problems often are the ones who perform better. Hence, it does not actually test one's ability to think, problem solve, and even derive formulas, but instead, one's ability to memorize.

Micro-Teaching Topic: Chess Openings

LESSON PLAN

Unit: Chess Openings

Lesson #: 2 (The Intuition Behind a Chess Opening)

Unit Essential Question: What makes a “good” opening move?

Learning Objectives:

• Know the chess piece value system

• Understand the objective of a successful chess opening

What Students already know:

• The rules of the game

• How the chess pieces move

• The objective of the game

Materials needed:

• Chess Board

• Whiteboard

Lesson:

1. Intro: Has anyone heard of the term “chess opening” before? What is it? Recap the last “lesson.” (1 min)

2. Direct Instruction & class content (5 mins)

1. I will use the whiteboard & chess board

2. Students will learn:

• The chess piece value system

• Development of pieces

• The importance of controlling the center of the board

• Attacking and defending pieces

• Trading & the concept of a “tempo”

3. Demo w/ class (4 mins)

   a. This demo will involve the whole class. Teacher will ask the class questions regarding what  

   they think they should do next and guide them on why or why not it may be a good move.

4. Closing: Ideally, we’d have students pair up and practice for one another, but for the sake of time and the lack of chess boards I own, we will not do that in the allotted 10 minutes. 

5. Hook to next lesson: Next class, we will have you play chess games with each other and analyze how the opening phase affects the rest of your game.

Differentiated Activities:

• If we have an odd number of students, there can be one group of three.

• Some students may need more help than others so during hands-on practice, I will walk around helping/scaffolding those students 

• For students who may be more experienced, I will pair them up with me and challenge them further

• Direct instruction & demo is good for visual and auditory learners. Pairing up to practice is good for kinesthetic learners.

Assessment (formative):

• Introduction & Direct Instruction: Are students paying attention? Are students engaged, asking/answering questions, and participating in discussions? Are students making connections or comments comparing new material learned with material they already know? 

• Hands-on Practice (students pair-up): Teacher walks around and guides students in pairs. Teacher poses questions to help the students think & self-evaluate. Are students able to carry out instructions? Are students asking for help from their peers or from me when needed? Is there growth and improvement from the last time I walked around? Are students reflecting on their experiences and learning from their mistakes? Are particular students finding it easy? Are others getting stuck and finding it difficult?

Teaching Perspectives TPI reflection

Looking at my TPI graph, I am roughly at the average for most of the five teaching perspectives, with the exception of the social reform teaching perspective. My nurture as well as my developing teaching perspectives are high and almost one standard deviation above average. For nurturing, this means that I strongly believe that effective teaching assumes that long-term, hard, and persistent effort comes from the heart, not the head. For developmental, this means that I believe that effective teaching must be planned and conducted from the learner's point of view. On the other hand, my social reform teaching perspective being almost two standard deviations below average means that as a teacher, I focus on the individual rather than the collective. This means that I tend to not take learning into social contexts and challenge students to question their beliefs and values.

Looking at my results, I cannot say that I am surprised. I do believe that all students are capable and can be nurtured to succeed as long as they put in the effort. From experience, the students who have failed the class are the ones who fail to complete the homework, not pay attention in class, and never ask for help. I have also had students who struggled in the early phases of class, but through effort, determination, and persistence, performed better than most of their peers because they were active in their own learning.  

I also believe that teachers should teach content in a way that students can best understand. As each students has different learning preferences, it is important for teachers to study their students and have a grasp of how to accomodate to their learning style. Good teachers can teach the same concept from multiple perspectives in multiple contexts depending on the student.

Lastly, my social reform perspective is low and I can see why. For starters, I tend not to link social issues to math. I often feel like social issues are more relevant in other subject areas, as math focuses more on logic and critical thinking in different circumstances. The other reason why I avoid and am often careful around social issues (especially the controversial ones) is becuase not everyone's values and/or beliefs may align. Some people disagree with certain things that most people agree on, and perhaps they may be sensitive when talking about them. Hence, I am very careful when talking to students or people of various backgrounds and beliefs.

I guess one follow-up question would be that is discussion of social issues really important in the math context?