Reflection On Chapters 2 & 3 of "Thinking Mathematically"

          I found the reading from chapters 2 and 3 of “Thinking Mathematically” to be quite interesting.  I agree with the argument that too often in mathematics, students are more focused on getting the “right” answer and this often is the their drive behind solving a problem as opposed to truly understanding and reflecting on a problem before answering it.  I think this relates back to the discussion we had in class earlier in the term regarding relational versus instrumental understanding of mathematics.  Do we want students to just be able to come up with the correct answers or do we want them to be able to understand the fundamentals behind the question they’re solving?  I’m sure if you were to ask me when I was in high school, I would’ve thought reflecting on math problems was not only crazy but also a waste of time because the goal for me at that time would be to just come up with a (correct) answer; however, after completing my degree and now as a teacher candidate, I recognize the importance in getting students to think instead of simply just solve mathematical problems and I hope this will be something I am able to show my high school students through my teaching.

Reflection On Group Microteaching Assignment

          Overall I thought our group microteaching lesson was strictly OK.  I found this assignment a bit more difficult than the last microteaching we did because this time we had to teach in groups and thus it was a little tricky coordinating the lesson in a smooth manner; nonetheless, I thought my group worked well together and most of the comments we received back from the class were fairly positive.  The students felt we had good time management as well as a great “hook” to start the lesson and that we were able to successfully relate the fundamental counting principle to aspects of their daily lives; however, some of the students also thought the second example we presented (involving the ice cream cones) was too difficult to be used when introducing this topic.  The question we “assigned” for homework was also thought to be too hard in comparison to the examples presented in the lesson.  I agree with this assessment because I could see the confusion on the faces of some of the students during the lesson.  This is something we should definitely work on for next time.  Other suggestions from the peer evaluations included not having the class around one table next time and relating the lesson to other topics in mathematics.  On the whole though people felt our group did a good job and I too am satisfied with the lesson but at the same time realize that there is still a lot of room for improvement.

Lesson Plan On Teaching The Fundamental Counting Principle

Group Members: Paramjeet, Zhi Song and Mandeep

	Content to be Covered	Time spent	Materials	Modifications
Bridges	Asking whether teacher candidates have ever felt what they learn in math class they don't actually use in real life	30 seconds	Paper-made outfits and ice cream cones and toppings
Learning Objective	To be able to use the  Counting Principle in everyday life
Teaching Objective	To teach grade 12 students the essence of the Counting Principle
Pretest	Ask students whether they know the Counting Principle	30 seconds
Participatory Learning	Get the students in one group and work together to solve the outfit and ice-cream problems	9 minutes
Post-test	Write out problems relative to Counting Principle on board and get students to solve	3 minutes
Summary & Wrap-up	Then restate the key components of the Counting Principle	2 minute

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Reflection On Simmt Article

            I agree with Elaine Simmt's article on how mathematics can play an important role in citizenship education.  We know that society holds this perception that learning math isn’t important for everyone because it has “little to do with the world we live in” but I think Simmt’s article does a good job of refuting this belief.  The article brings up a good point on how there has been a “mathematization” of society and that without even realizing it, people tend to work with or at least encounter math regularly in their day-to-day life.  What I especially liked about the article was Simmt’s argument on how it is important for citizens to be educated in math not only for the sake of general numeracy skills but also because learning mathematics teaches students how to become informed, active and critical citizens by teaching them skills on how to “identify and pose problems” and how to explain and to question.  These skills I believe are necessary to have in order to be a good citizen.  I also feel that learning mathematics teaches people more than just how to work with numbers; it develops the mind and gives students the problem solving skills they will need in their everyday life.

Dividing By Zero Poem

Dividing by zero

Is nothing less than illegal

An operation for which there is no answer

Thus cannot be allowed

Dividing by zero

Just doesn't make sense

For no value times zero

Creates an answer that's anything besides zero

Dividing by zero

Is often referred to as undefined

No matter which numbers zero tries to dine

It just won't divide!

Timed Writing

Zero

Ok when I first think of zero I think of nothing.  Actually I think of a song i heard as a kid that either you're a zero or a hero haha.  I think a lot of people, especially kids, may have a negative conotation attached to the zero.  They may see it to mean you have nothing.  If you play sports, to have zero goals means you didn't accomplish what you set out to do and you probably lost or at the most tied in the game.  I know the concept of zero can be hard to visualize or understand at times in mathematics.  What is zero is a common type of question I remember younger students used to wonder.

Divide

When I think of divide obviously the first thing that comes to mind for me is mathematics.  Division was a topic i at first struggled with in elementary school but came to love once i realized it was just the opposite of multplication.  I'm tring to think of ways it is used outsideof mathematics.  It can be used in daily everyday life when someone refers to dividing up the class, dividing up supplies, etc, etc.   I'm not sure exactly ;what i shold be writing right now, whether i should be writing about the different ways the w ord is used in everyday life or should i focus on the way it's used in math.  I guess another way to think about divide is to think of it as breaking apart.  Divide something for some people amay  mean to break something that is whole apart, like a country.

Fast Forward To 2020 (Fictional Letter)

Dear Ms. A,

Hi, my name is John Smith.  I'm not sure if you remember me but I was a student in your math class about ten years ago.  I'm writing to thank you for all the help you provided me with during that school year.  I began that year with a strong dislike towards mathematics.  It had been a subject that I'd never really understood nor wanted to understand.  I'd always found math to be too abstract and felt that it would never be of use to me in real life; however, my opinion changed after I had you as my math teacher all those years ago.  You were probably my first math teachers to not actually teach straight from the textbook.  You always came up with your own math problems and examples for each topic, which always incorporated something I had learnt in one of my other classes.  I loved how you had the class participate in so many group activities throughout the year instead of you just lecturing us from the front of the class each day.   I also really appreciated how warm and welcoming you made your classroom for all of us students.  You maintained good class discipline and made me always feel like I was in a safe environment, thus allowing me to feel comfortable enough to participate in class discussions.  It was one of the few classes I had in high school where I didn't feel intimidated or afraid to ask what I may have preceived as a "stupid question."  Being in your math class made me decide to pursue mathematics in post-secondary and now be a successful graduate with a mathematics degree.  You were one of my most memorable teachers in high school and I just wanted to thank you for all the help you gave me during that time.

Sincerely,
J. Smith


Dear Ms. B,

Hello, my name is Jane Smith and I am a former math student of yours from about ten years ago.  I am writing to you today to convey some of the less than pleasant memories I had while being in your class. I remember I always felt somewhat nervous whenever I took a math course in high school as math was not always the easiest subject for me; however, I feel that my experiences in your class stemmed from more than me just struggling with the subject.  I feel (and I'm trying to say this in the nicest possible way) that you taught that math class quite poorly.  I didn't find you to be an enthusiastic or motivating teacher.  In fact, you were always spoke in soft, monotone voice that would always put be to sleep.  I could never quite hear everything that you said in class and the things I did listen to were so boring, I regretted listening.  I felt you didn't have enough activities in class, all you did was lecture.  You tended to give too much homework and your tests were way too long.  I did like you as a person, but as a math teacher I'm sorry but you were below par.  Please take my comments as suggestions for improvement.

Sincerely,
J. Smith



At this stage as a teacher candidate, the thing I most fear is not being able to implement all the good teaching strategies I am currently being taught in the Education Program.  Currently, all of my instructors emphasize on how important it is to engage students, be enthusiastic about what you're teaching, work towards instructional as well as relational understanding, etc, but I fear I might be too overwhelmed in my first years of teaching to be able to accomplish it all.  I realize it will take a great deal of experience actually teaching in a classroom before I will be able to achieve all the traits I'd like to have as a math teacher.  This is something I'm willing to work hard towards because I love math and have a great passion for teaching and I hope this will come across once I become a teacher.

"Battleground Schools: Mathematics Education" Article Reflection

            Susan Gerofsky’s article “Battleground Schools: Mathematics Education” discussed some of the conflicts that occurred in mathematics education (and are still occurring) in the past century.  The conflict for the most part has been a clash between the “progressive” and “conservative” or “traditionalist” views on how math should be taught in school.  Gerofsky’s article summarizes the differences these two positions hold in their approach towards math education.  The conservative view emphasizes fluency in mathematical learning and absorbing and applying facts so as to achieve the goal of obedience and a value of precision and correctness; in contrast, the progressive view stresses understanding achieved through inquiry and sense-making, with original thinking and generic problem-solving skills seen as the goal of math education.  The article goes on to describe how the battle between these two viewpoints was played out in public schools in North America, beginning with the Progressivist Reform from about 1910-1940, during which the work of John Dewey, advocating reflective inquiry in education, was accepted into progressive teachers’ colleges and was put into practice in some classrooms.  By the 1960’s, the Cold War between the US and Soviet Union brought on the movement known as “The New Math” which focussed on creating a unified, logical and highly abstract algebraic structure of mathematics based on set theory.  The goal of this program was to familiarize all students in the K-12 system with the mathematical foundation needed for future careers as scientists; however, by the 1970’s it was obvious this program wasn’t working and hence was soon put to an end.  The article ends discussing how the “Math Wars” over the NCTM Standards from the 1990’s to present have brought on both support and opposition from progressives and traditionalists, as well as from sensationalist media coverage in a battle that shows no sign of resolving anytime soon.

            I found this article to be a most interesting read.  Though I was not too familiar with all the curricular reforms implemented in the past or currently are being developed, I’ve always been quite aware of the debate surrounding differing teaching methods and ideologies being used in classrooms.  I agree with Susan Gerofsky’s opinion that much of the debate has been further inflamed by media coverage that has “little basis in fact” and has unfortunately resulted in math education becoming another stage for a left-vs-right political face-off.  I too feel that working towards balance and consensus would produce a more beneficial result than what the “Math Wars” are achieving now.  What else interested me about the article was the history of math education that was presented, especially “The New Math” movement of the 1960’s.  I’d never heard of this program before and it surprised me how such an initiative was started as a result of a space race against another nation.  It’s alarming to think how such political battles can often be fought in our classrooms.