TPI test results and reflection

 

My TPI results

My TPI test result shows that my dominant perspective is Nurturing. Apprenticeship, Transmission, and  Social Reform are my Back-up teaching perspectives. Developmental is my recessive teaching perspective. My profile is a bit flat and it has a standard deviation of 4.24.

When I look at this result, I think it does show what I look like right now --- a beginner. I have the highest intention score in the Nurturing perspective. I feel comfortable being a nurturer. As a teacher, I think my priorities are providing students support and encouraging them. I have the lowest action score in the developmental perspective. This one is funny.  I am not surprised for this result because I believe in natural development. If students feel safe, encouraged, and are placed in a positive learning environment, development is inevitable. I will not let students know my expectations of them. Instead of that, I hope they can feel that I firmly trust them, and believe they can achieve their goals sooner or later. Everyone is living life at their own pace and vibrating at their own frequency. Expectations, especially from a teacher, may cause pressure since it sounds like a task. Oppositely, trust is an attitude and it sounds like encouragement. 

For the question "In my teaching, building self-confidence in learners is a priority," I strongly agree. For questions starting with "I expect people," I mostly give them "rarely" or "sometimes." Again, I just don't want to give others any pressure. For the question "  I share my own feelings and expect my learners to do the same," I don't know if it is a good idea to share teachers' own feelings with their students, while definitely, I will not expect my learners to do the same thing as I do. I will share some positive emotions with my learners. I think it is not appropriate to show students teachers' negative emotions.

Thinking about math textbooks

As a teacher, when I observe the image of Figure 1: A hand doing mathematics (Lappan et al., 1998, p. 6), I think the disembodied, generic hand is simple enough to help students understand the process. There is no need to draw a person in that image. The unnecessary part of the graph can confuse the readers.  This image is quite detailed, and it positions the students to recall their real-life experience that adding coins to the cup will eventually break the bridge. 

As former students, the figure shows a very interesting scenario that someone is trying to test how many coins a paper bridge can hold when each side of the paper bridge has 1 inch on the books. The ”1-inch“ label is a clue. It will make me eager to figure out the paper bridge's holding capacity. 

No matter as a teacher or as a former student, I think the textbook is necessary for learning mathematics systematically. Not like some other subjects, such as physical education and language, mathematics involves many concepts, theories, theorems, propositions, etc. We need a book to present them systematically. With a textbook, students could learn mathematics in a rigorous and systematic way. I always think learning Math is like building a skyscraper. The final height of the skyscraper will usually depend on how strong and deep the foundation must be built. To build a skyscraper, we need a guide book (Technical Drawings). Moreover, for Euclid's "Elements" and Euler's "Introduction to the analysis of the infinite", we all know how important these textbooks are. 

There is one issue that I concern about. Math textbooks are too expensive to have for most students and schools. Some schools do not have sufficient funds to buy Math textbooks for students. And Math textbooks change versions every several years, so it is another difficulty for school. I observed students in my practicum school are still using Math textbooks in old the version. 

Some people suggest digital textbooks or e-textbooks. I think students need to avoid spending too much time with electronic devices. There are many Apps on their electronic devices, so students cannot fully concentrate on the textbook and learning.

In conclusion, I think textbooks should be essential for Math learning, and they still play a fundamental role in schools. 

Puzzle: The scales problem

The first thing that we need to know for solving this puzzle is weights and herbs could be placed on the same side of the scale. 

When we measure 1g herbs, we need a 1g weight. 

When we measure 2g herbs, let us try to find a weight that could be as heavy as possible. Don't forget we have a 1g weight. We place 1g weight on the same side with herbs. So we can put a weight with a maximum of 3g on the other side of the scale.

Now we have two weights, 1g and 3g. Keep going, do the combination.

When we measure 5g herbs, 3g weight and 1g weight are not enough to balance the scale. We need a new weight and hope it could be as heavy as possible. Using the same logic we used when measuring 2g herbs, we can have a weight with a maximum of 9g. 

Keep going, do the combination. 

By the same logic, when we run out of weights, the new weight will be  27 = 14 + 9 + 3 + 1.

The values of the four weights are 1g, 3g, 9g, and 27g. I checked these 4 numbers for herbs weights from 15 to 39 on my rough paper, and they all meet the requirement.

I think 1g, 3g, 9g, and 27g is the only solution because the total weight of these four weights is just 40g.

Extension:

Since in the above puzzle, the solution can be written as 3^0, 3^1,3^2, 3^3, I would like to ask my students to try 2^0, 2^1,2^2, 2^3,2^4, and 4^0, 4^1,4^2.

I want them to use these weights to weigh out the amounts of herbs from 1 to some number. They need to find out what this " some number" would be. 

Reflection of Microteaching

Reflection:

"The linear equation" is a big topic, we should narrow our topic down into one section of it, such as "graphing linear equation" or "solving linear equation."   

There are couples of things I learned today. 

1. Making the lecture interesting does not mean to cover as much as possible. Covering too much in one lesson will cause students to feel overloaded. 

2. I like the hook activity presented by another group. They taught us how to use a piece of paper to know the volume by making the long cylinder and the short cylinder. This activity is very impressive. 

3. I also like our group's activities. One is an open question--- " Which one does not belong?" Another one is "Desmos". https://www.desmos.com/calculator

Assignment 2: Group curricular microteaching

Title	The Linear Equation	Grade	10	Date	13 Nov 2020
TC	Cheryl, Annie, Ben, Marius	Subject	Math	Time	20 min

Learning Intentions (SWBAT)	Understand (big ideas)	Know (content)	Do (skills)
	Linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.	- Meaning of slope and y-intercept in the context of word problems.	- To create a linear equation for a given situation. - To solve a linear equation with one variable.  - To show a formal check for a solution.  -Identify linear equation
	Essential Questions
	Factual	Conceptual	Debatable
	- What is the graph of a linear equation? - How many solutions can a linear equation have? -What’s the definition of a linear equation? -What’s the definition of a function?	- How to interpret the symbols in a general linear equation? -How does slope and y-intercept affect the graph of the linear equation? -How did ancient mathematicians solve linear equations?	- How many variables can a linear equation have?

Preparation	Materials/Resources	Organization (setup, pre-made things, classroom management, etc.)
	Powerpoint Presentation Internet connection	Google slides Zoom

Learning Engage- ments	Opening (provocation, APK/S, mental set)		Time
	Set the tone for the lesson - Introduction - Share agenda : Overview - Warm-up: The importance of the graph		3-5mins
	Strategy		Time
		Introduction to functions Provide a brief example of how functions work. Provide the definition of a function.  2.       Definition of a line Provide intuition on the definition of a line. 3.       Introduction to linear equations Provide brief examples, introduce y=mx+b and its graph. Solutions to linear equations. Special cases. Quick knowledge check. 4.       History False position and double false position. 5.       Class Activity Playing with Desmos. Get students to explore in real time the parameters “m” and “b”.	15 mins

Puzzle: The Giant Soup Can of Hornby Island

 My solution to the puzzle: 

Figure 1

1. The height of the bike is given. I will determine the length of the bike. That's because I can clearly see the ratio of the bike length to the tank length in the photo.

2. The size of the can is given. Measure the length a on the Soup can in centimeter. 

Find the ratio of length a to the height of the can. 

D

Which is the same ratio of the bike length to the tank length

3. Once we know the tank length, we could figure out the other dimensions of the tank by using proportions. We know that the dimensions of the soup can and the dimensions of the tank are in proportion.

Extension: 

Question: If every two people have to keep at least 2 arms length distance,  what is the maximum number of people allowed to be in an indoor basketball court? What is the max number of people allowed to be in a football stadium? Given the dimensions of the basketball court and Figure 2.

Figure 2

Solution:

We can see each person as a circle with a radius of 1 arm's length.  The first step, figure out the most efficient way to arrange these circles in a rectangle. 

Which way will you choose?

We know the room length and arm length. How many people are there in a row?

How many rows are there in an indoor basketball court? We can figure it out by finding the height of this equilateral triangle first.

Once we know the number of rows in an indoor basketball court, we can find the total number of people. 

Using the proportions and the figure, we can find the max number of people allowed in a football stadium.