TPI Profile

 Below is the teaching perspectives inventory profile that I obtained. This is a really interesting analysis. At first I was surprised by the result, but it all make sense after reading the interpretation of the result.

From all 5 categories, I scored the lowest in terms of all of beliefs, intentions and actions in the "Social Reform" section. This perspective is recessive for me. It is totally true that me myself, a math lover and a future math teacher, do not see how math can fit into social actions. I acknowledge that there are tons of real life application of mathematics, and our community would be better if the general public receive more math education. However, I still can not explain to students how exactly math will benefit them. This is the part of math education that I didn't receive as a student, and I definitely want to change.

I scored the highest on "Transmission" and "Nurturing", which is consistent with my own practice in teaching math. I usually follow curriculum very well to avoid missing any content that may cause students difficulties in future learning. I also wholeheartedly want to help all students with mathematics skills.

Some of the internal inconsistence is expected, as I don't have much teaching experience yet. Once I have my own class, I probably would be more explorative and try raising that "action" score. 

Overall, this is a great assessment of my teaching. Being able to adjust and change is critical for becoming a good teacher. 

Response to Textbook and Math Education

This is a very interesting article. It brings up  a lot of details that I never paid attention to (both as a practice teacher and as a student), but worth to think about. 

Firstly, I was attracted by the impacts of pronoun usage in a textbook. Take the usage of the second person pronoun "you" for example, it can be interpreted differently under different context, and thus position students in relation to mathematics differently. While phrases such as "you find", "you know" tells the readers about themselves, other phrases such as "the equation tells you.." portray mathematics as activities independent of human. 

I agree with Morgan that "the absence of first person pronouns obscures the presence of human beings in a text and affects not only the picture of the nature of mathematical activity but also distances the author from the reader, setting up a formal relationship between them." While the second person pronoun also involves the reader in its context, as a student, I did experience some frustration with it. When the textbook assumes "common knowledge" by saying "you know" but I actually don't know it, I always feel bad for not knowing it or for being "stupid". I also find myself more engaged when learning in a community, where the textbook uses "we .." to team up with me. 

The role of a textbook to students largely depends on the teacher. I have experienced many classes where no textbook is required. I have also been in some math classes where I learn the most from a textbook. Now as a teacher candidate, I rely greatly on textbooks to provide me with ideas. At the same time, I also learn the "language" used by textbooks and reflect on the language that I use in class. 

Textbooks definitely have their roles in math education as we can not make sure the quality of every teacher out there, and it's always good to provide students with supplementary materials. At the same time, I also doubt whether the language of a textbook will make such a difference on students' math learning experience, since most of the time, it is a human being (or a human being inside a screen) who is teaching math, not the textbook. 

Micro-teaching Lesson Plan

 

Lesson Topic: Introduction to the slope of a line                                       Grade Level: 10

Length of Lesson: 20 minutes
Presenting Group: Roya, Amrit, Yiwen, Chloe

Stage 1 – Desired Results                     Ccde   Determine the slope of a line segment and a line.
Bi           Big Idea(s):                      Constant rate of change is an essential attribute of linear relations and has meaning in different  r                 representation and contexts
Curricular Competencies:              Students will able to do: Use mathematical vocabulary and language to contribute to discussions in the classroom. Develop, demonstrate, and apply mathematical understanding through inquiry and problem-solving. Reflect on mathematical thinking Explain and justify mathematical ideas and decisions in many ways		Content(s):              Students will able to know: slope: positive, negative, zero, and  undefined
Stage 2 – Assessment Evidence
Formative Assessment(s): Observing each student should be participating in the activity and understanding the concept. Were students able to identify the different types of slopes by looking at the pictures? Were students able to connect the concept of rate of change to slope?			Summative Assessment(s): None
Stage 3 – Action Plan
Materials: Worksheet with pictures of hills for the activity. Worksheet with questions corresponding to the activity. Worksheet to determine types of slopes.		Preparation(s):   Prepare worksheets for the activity, and questions correspond to the activity.
Time	Teacher Does:			Students Do:
Introduction:              (5 minutes)	Start with a warm welcome and introduce yourself to the class. Ask students that How many of you went hiking this summer? Ask students whether they notice something when they hike to the mountains? Tell students that they will learn slopes using the steepness of the hills today.			Students respond to the questions that the teacher asks.
Activity               ( 10 minutes)	Hand in the worksheet of pictures with hills to the students. Tell students to look at the pictures and think about the difference in all photographs. After some time, distribute the worksheet that has questions corresponding to the activity and tell students to answer those questions. Tell students that some hills are steeper than others. Steeper hills are more difficult to climb. After five minutes or so, provide another worksheet that has a graphing grid on the pictures of hills and tell students to draw the straight line according to the steepness of the mountain. Think of a strategy to calculate a number to represent the steepness of each line  Tell students to discuss their answers and discuss with other students. Tell students the steepness of a hill is measured by calculating its slope. Slope=rise/run			Students work on the worksheets that are provided by the teacher. Students answer the questions on the worksheet using their knowledge. Students discuss their answers with other students.
Extension:	Distribute the practice worksheet to determine different types of slopes.			Students work on the practice worksheet to check their understanding.
Closure:               (5 minutes)	Ask students How they feel about the activity? Summarize the concept by asking open-ended questions from students. Ask students if they have any questions.			Students give their thoughts about the activity. Students answer the questions to summarize the activity. Students ask questions if they have any.

Scale Puzzle

Here is my thinking process:

For the 1st weigh, it can only represent 1 weight.

For the 2nd weigh, it can represent 2*1+1 = 3 different weights.

For the 3rd weigh, it can represent 2*(1+3)+1 = 9 different weights.

For the 4th weigh, it can represent 2*(1+3+9)+1 = 27 different weights.

And what's nice is that 1+3+9+27 = 40, so the 1st weigh should have a weight of 1gram,  2nd weigh is 3 grams, 3rd weigh is 9 grams, and the 4th weigh is 27 grams. There should be only one set of solutions, otherwise, some weights are skipped while the maximum possible weights are still 40. 

Extension: Say you want to buy x grams of herb, what is the minimal number of weighs that you need? 

Soup Can Puzzle

Based on research on the Internet, we can assume the height of the bike is around 140 cm. 

I use the height of the letter "U" as a reference because it does not span over a curvature, thus more accurate. 

The height ratio of the letter U and the bike is: b : a = 3.3 : 7.1 (height is measure with a ruler, the unit or the scale of the image doesn't matter here)

As a result, the actual height of the letter U is b = 140 cm * 3.3 / 7.1 = 65 cm

Then I measure the ratio between the height of the letter U and the height of a normal size can, it turns out to be b: c = 1.5 : 16.

The ratio between the height of the letter U and the width of a normal size can is b:d = 1.5 : 10.

Thus, the height of the tank is  65cm * 16 / 1.5 = 693 cm, and the width of the tank is 65cm * 10 / 1.5 = 433 cm.

As a result, the volume of the tank is:

$V = \pi \times {\frac{d}{2}}^2 \times h= 3.14 \times {\frac{4.33}{2}}^2 \times 6.93 = 102 m^3$, which is equivalnet to around 102,000 L of water.

Based on some research, around at least 400 L/min of water is needed to put out a regular house fire, although this number can increase largely is the fire department arrives late. Generally speaking, this is enough water to put out a fire. 

My puzzle: 

General Sherman is a giant sequoia tree located in the Giant Forest of Sequoia National Park in Tulare County, in the U.S. state of California. By volume, it is the largest known living single-stem tree on Earth.

Read more info about the tree online, based on the image below, how tall is the lady standing in front of the tree? 

Response to "Flow" by Mihalyi Csikszenmihalyi

This talk is very related to my experience with mathematics. Due to the fact that I majored in math at university, oftentimes people assume I really love math. I definitely don't hate math, but my passion for it doesn't come from the actual "content". The speech given by Mr. Mihalyi Csikszenmihalyi makes me realize that my motivation for math comes from the "flow", which is the ecstatic state when I solve challenging math problems. 

There are problems or puzzles to be solved in every aspect of life, but what I like the most about math is that it presents problems in the simplest and purest form. A pen and a piece of paper usually suffices for a math problem. I feel the "flow" of programming after learning about coding knowledge, but I wouldn't be able to concentrate on it when there is no functioning computer. I also feel the follow of painting when I practiced it for years and finally mastered it to some degrees. However, I experienced the ecstasy of doing math as early as when I was in elementary school, and this ecstasy appears almost every time when I do math, regardless of the complexity of mathematical knowledge or the material preparedness. 

As an educator, I want my students to experience this ecstatic state as well. They don't need to aim for becoming a mathematician, but while they are spending time on math (whether voluntarily or not), I hope to prepare them for challenging problems and let them gain sense of achievement from doing math. During my my short practicum, I have seen a lot of "Ah-ha" moments from students and their joy of understanding or solving math. It is the educators' job to bring this feeling to more students.