In class timed free writing on Zero and Division

We were asked to do two consecutive in class "free" writings, each 4 min. long in duration. We were supposed to write continuously, writing "I can't think of something to write" repeatedly until we had a new idea/sentence to write. In transferring my writing from class, I have marked those instances by replacing the above statement with "..." for brevity.


Timed "free" writing on Division (4 min):

Making something big small. Making distinctions. Individualizing or categorizing. Dividing a room. ... Making tasks simple. ... Breaking to smaller chunks. What does it mean to divide a number by itself? What does it mean to divide a number by zero? What about dividing zero by any number? Dividing zero by zero? Making a long journey into smaller segments. Making shapes into smaller parts.


Times "free" writing on Zero (4 min):
Looks like a circle. Is the first integer, the middle point between negative and positive numbers. It is elusive! How many zeros can you fit in a zero? How many zeros can you fit in one? What is the size of zero? Why do you get zero when you multiply another number by zero? You get the same number when you add it to zero. A number minus itself is zero. ... Zero is complex, yet so simple. Its whole, yet empty. Can God be zero? ... Zero is in the shape of a circle. 0! (zero factorial) is one, why? ... Zero means focus: zeroing on things, narrowing down. Zero is nothing, nil, nothing, zilch, notta.

Assignment #2b: Group microteaching feedback and reflection

Feedback

Clarity
Structure was clear - 4.14
Verbal & Visual were clear - 4.07
Math ideas were clear - 4.14

Active Learning
I was engaged in learning - 3.57
A variety of activities offered - 3.64
Instructors showed engagement was valued - 3.93
Offered activities connected to other math areas - 3.93
Connected to other areas of life and culture - 3.43

Some comments included: good classroom management, very engaging, clear instructions, good humor, clear review, concise, fun activity,good easy examples, it's good to have a real life problem at the end, very well organized.

Also on the not so positive: bit much time in review, short on time, the board was blocked (couldn't see), wait for students to respond, little long and drawn out, the pace is too fast, needed examples of geometric series at first, define terms clearly, relax when speaking.


Reflections
I felt a bit of planning and practicing with the group prior to our teaching would have proven instrumental. Just as any group activity/project, communication, planning, coordination, and practice are essential. We did not get a chance to do this because of scheduling conflicts and due to the sheer amount of work for other classes.

I liked the interaction and question/answer session with the students during the review session. This allows for the teacher to touch basis with the students and find out what and how much they remember from the last class/topic (arithmetic sequences/series) before moving on to introducing the new topic (geometric sequences/series in this case).

Developing informed, active, and critical citizens in my math classroom

Reflections and ideas based on reading
CITIZENSHIP EDUCATION IN THE CONTEXT OF SCHOOL MATHEMATICS"
by Elain Simmt

Undoubtedly, mathematics plays an important role both in terms of numeracy and logic in not just today's society but throughout ages and in varied and diverse societies all over the world. Once sees applications of mathematics in nature, art, science, technology, business, economics, sociology, health, meteorology, sports, politics, architecture, transportation, spirituality, ... This is in form of numbers & figures in quantitative measurements, shapes and geometry, probability and statistics, and diagrams and graphical representations. Examples of applications range from describing natural phenomenon through mathematical modeling and devising multi-parameter models to predict reality to using power law to explain growth/decline rates and fractal geometry for image compression, Mathematics also forms the basis for decision- and policy-making, economic and financial transactions. We even use mathematics in our day-to-day lingo: weighting one's options, trends,

Mathematical thinking, through the processes of posing questions, discussing and devising different approaches to solving problems, using critical reasoning to making sense of conceptions, analyzing current events which quote or use mathematical results, recognizing patterns, making connections, making estimations and educated guesses, communicating and describing results, offering explanations, ..., enable and empower students to apply these tools in other aspects of life and outside the classroom.

I believe individuals should not be accepting the so-called "facts" at their face value. They should instead be constantly asking questions like: "does it make sense? Is this right? What does this mean? What is this trying to tell me?, ..." I intend to instill this belief in the students I cross paths with.

Assignment #2a: Group microteaching lesson plan

Topic: Geometric Series
Time duration: 15 minutes
Group members: Mina, Rory, Sam

Bridge/Pretest: Recall arithmetic sequences and series, and geometric sequence (consecutive terms have a constant ratio).
Recall that a series is the sum of a geometric sequence. Give students the bouncy balls for initial investigation.
Learning Outcomes: Understand connection between sequences and series. Be able to compute finite and infinite sums. Begin to formulate an understanding of series convergence.
Teaching Outcomes: Incorporate multiple teaching modes. Prove the formula for calculating a geometric series.
Participatory: Have students bounce different balls. Investigate how successive bounces decrease in size. Lead into the idea that the heights of consecutive bounces form a constant ration = geometric progression. Discuss how to add the total length of 20 (or so) bounces. Prove formula for sum of geometric series. Raise the question: ‘what if the ball never stops bouncing, but continues forever with each subsequent bounce scaled by the same ratio?’ Discuss how powers of r, for r ric progression. Discuss how to add the total length of 20 (or so) bounces. Prove formula for sum of geometric series. Raise the question: ‘what if the ball never stops bouncing, but continues forever with each subsequent bounce scaled by the same ratio?’ Discuss how powers of r, for r Post-Assessment:Have students break into small groups (3-4) to collaborate to complete a problem set. Make some problems tricky by manipulating indices.
Summary: Recap relationship between sequences and series. Discuss infinite series, and the issue of convergence.

"Art of problem posing" by Stephen Brown & Marion Walter

How would you use "Art of Problem Posing" in micro-teaching?

By composing and posing a series of questions on a new topic, one is able to introduce the concept without "telling" what the concept is. In a sense, it becomes a process of search and discovery; exploration and illumination and therefore more meaningful. Learning and teaching becomes more collaborative/cooperative.

What do you think of the "what-if-not" approach?

The "what-if-not" approach stresses how things should not be taken at face value. This type of questioning opens doors to other paths of solving/analyzing problems and another way of thinking about them. In a sense, there is more generalization of a concept going on. More in terms of relating the problem/issue to other similar ones. This approach also helps us get out of a rigid, single minded mentality. We open ourselves to other ways of doing and seeing things.

Top Ten questions/comments to Brown & Walter

The Art of Problem Posing by Stephen I. Brown and Marion I. Walter

1. What is the problem asking?
2. Can it be generalized?
3. What are the givens?
4. Are there any exceptions to the rule?
5. What are the parameters and what are the variables?
6. What are some applications?
7. What if the number of parameters was varied?
8. What are the constraints on each parameter/variable?
9. Can the problem be represented graphically?
10. What tools can I use to solve this problem?

In-class timed writing (6min.) My greatest and worst Math teacher ever

Oct. 2, 2019

A) DrMina, my best Math. teacher:
Without doubt, DrMina was my greatest Math teacher. She is the one who inspiredme to pursue a career in science. She simply made Math make sense. Instead of introducing us to concepts, formulas, and equations, she helped us "discover" them as a class ourselves. We had so much fun! We worked on problems together as a team. She read us excerpts from books on Math, told us stories about "i", "0", the history of Math, and Mathematics behind Music, Sports, ... To be able to relate mathematical concepts to everyday life experiences, to see the beauty in the relationships, to be able to make connects, ..., all helped me appreciate Math. and recognize its importance/relevance. I remember feeling comfortable and at ease in class. Discovering the solution of a puzzle or solving a Math. problem was such fun.


B) DrMina, my worst Math. teacher:
I still remember being bored in her classes. I just didn't want to be in that class. I didn't want to take part in group activities she would have us do. I didn't know what the relevance of what we were being taught was to my future. I didn't really care to learn the material.

Aspirations for my future teaching career:
My aspirations are to be able to reach as many kids as possible. To be able to teach effectively and clearly. I would want to be able to convey the message to them that it doesn't matter whether they'll be pursuing higher education or go into careers in math. science, or technology. That learning math. will help them develop their minds and creativity. That it will help them develop problem solving abilities.

Worries/fear for my future teaching career:
That I would not be able to reach as many kids that I would like. That the education system would not allow me or limit my ability to teach the way I would like to. Another worry is that I would not be a creative teacher.

Comments on "Mathematics Education" by Susan Gerofsky

Comments on Battleground Schools: "Teaching Mathematics" by Susan Gerofsky

In This paper, Susan gives us a historical perspective on mathematics education ideologies in North America in the 20th century. She discusses how math. education has oscillated between two polarities: "progressive" and "conservative/traditional". She points out three major reform movements in the 1900s, responsible for shifts between the above two ideologies in math. education:
1- The progressive movement for mathematics through activity and inquiry (circa 1910-1940)
2- The New Math reform movement of the 1960's
3- The NTCM (National Teachers Council of Mathematics) "Math Wars," standards-based math. reforms, from the 1990s to the present.

I find it interesting how questions like "why math.?", "how much math.?", and "how to teach math.?", "how to assess mathematical knowledge and understanding', etc., have been debated and revisited throughout the history. Somehow, I would feel with the age of industrialization, and technological advances, it would go without argument that learning mathematics is essential to function in today's society. Perhaps "how much", "when" and "how to teach" math. are relevant questions to be revisited from time to time, especially in this rapidly changing society.

The assumptions and stereotypes associated with math.and mathematicians is somewhat alarming. Presumptions such as "mathematics is hard, cold, distant and inhuman", or that "it is only necessary and appropriate for a small elite to understand mathematics". As someone who pursued a PhD in particle physics, I admit that the subject material becomes more complex and people pursuing a higher level of education in any field become mainly focused on their area of expertise; however, this does not mean high school math. needs to be difficult to understand and that all mathematicians or physicist are nerds. I think the main reason behind peoples' misconceptions about math. is because math. is not taught well in schools. The reasons behind this as Susan points out are a few: teachers who are math-phobic, teachers who learned math. the conservative way, finding teaching math. in any other way than the conservative way not practical or possible, and unqualified teachers.

The fact that there is not separation between the government/politics and education (as elaborated on in this paper) is not news to me since I know first hand how governments' choice in funding certain projects and not others changes as the political parties in power change. I am not surprised to know how the curriculum in schools is also influenced by the above. I think government's involvement in
setting/shaping the curriculum (in any field in schools) is wrong. Focus has to always be on producing informed, independent thinkers with critical problem solving abilities through the education system and constantly coming up with and implementing methods proven to improve students' understanding and comprehension of concepts based on results from research.