My favourite math jokes

 

Unit Plan - Grade 10 Function and Linear relations (Final version)

Please use this link to get to google doc.

Response to "Arbitrary and Necessary: A Way of Viewing the Mathematics Curriculum"

The author brought up an interesting point about the mathematics curriculum,  which we have probably all encountered before. 

Arbitrary: All students need to be informed of the arbitrary by someone else. It belongs to the realm of memory. 

Necessary: Some students can become aware of what is necessary without being informed of it by someone else, and it belongs to the realm of awareness.

I believe most people would agree that the fun of mathematics lies in the "necessary" part, where we have to potential to discover on our own. However, not "all students have the awareness to be able to work [necessary] out, only that someone is able to work this out without the need to be informed it", so the duty of math teachers are to guide students into the process of mathematical awareness. 

When designing the unit plan for my long practicum, I paid lots of attention to the order in which I introduce new concepts. In the exponent chapter, I re-arranged the teachers' notes and put "negative exponent" before "quotient rule of exponent". My rationale is: if students are unlikely to discover $a^{-n} =\frac{1}{a^n}$, at least I can guide them to prove $\frac{a^n}{a^m} = a^{n-m}$, which builds on what they have just learned about the negative exponent. Being able to prove this instead of memorize it, should be the focus of our mathematics curriculum. 

The author is concerned with "the amount of classroom time given over to the arbitrary compared with where the mathematics actually lies". There is no perfect solution to this problem. I do believe that students need a certain amount of "math facts" before they can really become aware of something. What we can do it to be direct about the arbitrary side of mathematics, and teaching in an educating awareness way whenever we can. 

 

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?