Math Poem Reflection

I was really exasperated when I first thought about doing this activity.  I'm not a writer and the only poetry I really know is rhyming poetry.  I did some research on the types of poems that I could try and I ran into some interesting ideas.  I think it's a great idea trying to incorporate other subjects with math, and I don't think you can always please everyone with the ones you decide to use.  I think that including free writing about math does get students to actively think about what they know and are learning.  The poetry writing might allow those students who are very creative in that area to enjoy math more, or it may even help further their understanding.  I do think that it may make math more tedious for others.  I'm not too sure what I would do change or modify this exercise, maybe give a list of the types of poems you could use would make it easier for those who don't have much experience with poetry.  After I figured out how I was going to tackle this assignment I did enjoy it and the chance to do something a little different and had some fun with it.

Division by Zero Poem

Danger in division?

If dividing by a number,

Very often the original is now smaller.

It doesn't always work this way,

Sometimes it can get bigger!

If this is something

On which you are confused

Now lets see what zero will do.

But how could this be?

You may soon be surprised.

Zero and division don't always work out

Every zero divided is zero, 

Reverse this about and we now have a mess!

Oh what do we do with this number?

Kinemalgebratics microteaching reflection

I was very pleased with how our microteaching lesson played out this afternoon.  I think it was fabulous on Mike's part to think of linking physics and math together to create such an interactive lesson.  I was actually quite surprised how willing and enthusiastic everyone was to participate in the lab section of our lesson, which shows that at any age the opportunity to move around and do something active in the classroom is a definite bonus.  

I thought that the structure of our lesson was quite clear as well as the verbal and visual communication by all the group members.  I think we could have made our mathematical ideas a bit more clear, in the sense that it may have been a bit difficult to understand right off that we were learning algebra.  I wasn't able to see Mike teach his part of the lesson so I may be slightly off by saying that.  

I felt that our group did an excellent job in connecting the lesson to other areas of life.  We did not really connect our activities to other areas of math, but we were quite focused on algebra for the time that we did have.

One aspect I feel that we could improve on was managing our time a bit better so that we could connect our two activities better at the end.  Erwin did a great job with the time he was given, but we could have left him more time to better connect our lessons and derive the velocity from out distance and time calculations.

Looking at the reviews other groups gave us, many peers really found the activities fun and engaging.  They liked how we took a real life example and applied it to this math concept.  

Some people found our topic unclear at the beginning, possibly by wacky title created so next time making that more clear may help our lesson go more smooth. 

There was also a comment that suggested we spend more time relating our two activities at the end.  This was a time management issue, and hopefully if this activity was done with more time we would be able to achieve this.

Overall I was pleased with how this activity went.  I found some of the other lessons done interesting, in particular the estimation activity.  This group created a lesson that I would definitely be interested in using for the future.  I especially liked their handouts and group work, as well as a nice introduction and well delivered lesson.

Microteaching BOOPPPS Lesson Plan

INTRODUCTION TO ALGEBRA

BRIDGE:Today in Math we are going to be doing an activity involving a ball and measurements!

TEACHER OBJECTIVES:To teach algebra implicitly using a Kinematics Lab.

STUDENT OBJECTIVES:Basic understanding of algebra and the ability to apply it to real world situations involving simple kinematics (v=d/t).

PRE-TEST:Intentionally none done, as we don't want to "tip our hat".

PARTICIPATION:Two tables.

1)The first table is a "Kinematics Shout-Out", where the students derive the basic Kinematics equations and put them in algebraic notation. We will be using the equation v=d/t and solving for the variables v, d, t using repetition.

2)The second table is a "Mini-Lab" with a ball rolling a set distance against a wall. The students will measure the distance from a line to the wall, and measure the time it takes the ball to get to the wall. This will then later be applied to the equation learned previously.

Required Materials:

• Masking tape
• Measuring tape
• Stop watches
• Balls

POST-TEST:Students will use their measurements and their new equations to calculate the speeds that the balls were rolling using v=d/t

SUMMARY:Surprise... you just learned algebra!

Write down the equation you learned and how you could apply this to another real life situation for next class.

Citizenship and the Mathematics Classroom

This was a very interesting article about mathematics and the attempt to include citizenship in mathematics education.  I found it intriguing to note that the author follows a similar train of thought that we have been learning throughout the course.  That is, that we should not just teach optimal ways of finding ‘right’ answers to problems, but that we should provide them with a deeper understanding.  This deeper understanding will help student’s function better in society.  I had not ever thought of the fact that homework and having right and wrong answers may not be good for citizenship education.  I thought the author brought up an interesting point, that by doing this, we are judging a students’ thought process and not giving them the right to be freely creative in their thought process.  After reading this article I can only hope that I can take aspects of these points and use them in my own classroom.  From as far as I can remember, I have never really been given the opportunity to be entirely free and creative when doing math.  There has always been the underlying right and wrong answer that has affected the way I think about math.  I also liked the suggestion to “build community in the classroom” (Simmt, 5) by making sure students contribute in the classroom.  I feel this is a very important point because student participation will encourage other students to become active participants in mathematics.  I really appreciate how this article has tried to incorporate citizenship in the mathematics classroom, and provides the reader with ways to do this.  It is definitely an aspect I have never really thought much about before, but I will certainly consider from now on.

What-If-Not?

The What-If-Not method is a very interesting technique using a sequence of levels starting with choosing a topic/starting point, listing attributes of that topic, choosing an attribute and thinking What-If-Not, posing a problem and then analyzing that problem. I feel that this may be difficult to use for our microteaching lesson, mainly because we have created a very real-life application approach to our lesson plan. I think that to use the What-If-Not technique we will have to make our topic (algebra) more specific to begin the process.  If we did so, we could generate some characteristics about algebra before the lesson, or even have our students generate or add some characteristics they know about algebra during the lesson.   This would create a great base for understanding this topic. I think if we were able to create some What-If-Not statements it may also help to explore the topic, and allow students to get creative and work collectively as a group.

 Some strengths of this approach are:

1) It really allows students, or even instructors to start thinking of aspects or attributes of their topic they may not have thought of before.  This allows someone to be more creative within the math classroom, something that is often taken for granted.

2) This What-If-Not part of this approach is great because it creates a deeper understanding of the topic, and allows the instructor or whoever is using this method, to generate or pose many more problems than they normally would.

 Some weaknesses of this approach:

1)I think the main weakness of this approach is that it seems very extensive.  There are a lot of steps that involve a lot of time.  Although it points to towards a deeper understanding of the topic, I am not sure whether the amount of time spent generating these types of problems would be a benefit in the end. 

2)I also felt that delving into the What-If-Not’s might be confusing for some students.  Many people have a “math phobia” and I think that this could be potentially confusing for many students and put them off math even further.

 I think with lots of practice and more extensive knowledge of this approach, it could be useful in the classroom to spark interest and go into a deeper meaning of some topics.

10 Questions to the authors of 'The Art of Problem Posing'

1) I would like to know why the authors feel that after we solve a problem we don’t understand the significance of what we have done.  Could they provide an example of this?

 2) I would like to ask the authors how or what ideas they changed in their book for the third edition?  It would be interesting to see how their approach to problem posing has changed over the years.

 3) The Secular Talmund is something I have never heard of and I would be interested in finding out how they came to know this idea and have a little more information on what it is about.

 4) I found the fist chapter interesting from the point of view of the first question asked.  You could see the difference between the more simple to more complicated and relational thinking, making it more clear how we can begin to improve on problem posing.

 5) I would like to know why, when asking a question about isosceles triangles, those with ‘weak’ skills or knowledge come up with more robust questions?

 6) I was unclear about the discussion on ‘challenging’ the given’.  Why would you not accept something like a geoboard as is?  How would you change it?

 7) I liked how the authors used observations to create or pose new problems.  This seems like a useful tool, make observations about what you are looking at and only then begin to pose problems.

 8) Does the author find that by posing a problem that requires an approximate answer, the problem solver becomes more creative?

 9) I thought it was interesting that the authors suggested inquiring about the history of some of the problems.  This seems like a great way to become more familiar with the concepts and be able to have a better knowledge base for posing problems.

 10) I would like to ask the authors for more examples of internal vs. external exploration.  I was a little unclear how to go begin exploring this way in terms of mathematics concepts.

Letters from future students

Dear Miss Landon,

I wanted to write to you to tell you how much I enjoyed you as a math teacher, you were my favourite teacher throughout highschool!  Your classroom inspired me so much I have gone on to become a mathematician and I have been nominated for the nobel prize!

I really felt that you were so well organized that I could easily follow all of your lessons and this organization kept me in check.  I always knew when a test or quiz was, or what we had for homework.  I think this showed me that being organized is key for a future outside of school.

I appreciated that you were very approachable as well.  I never felt that I was going to be punished for giving a wrong answer, or that I couldn't come to you for help.  This has been so important for my career!  As a superior mathematician I can take risks and be creative, it doesn't matter if I don't end up with the right solution, I just go back and try again.

The thing that placed you apart from my other teachers was how you taught your lessons.  You didn't just sit at the front of the class and write down notes and algorithms and expect us to copy them down and do homework.  We were able to ask questions, talk to our neighbors about problems you gave us and even try learning things on our own.  

I especially liked the weekly problems you posted on the board.  I loved to go home and work through them on the weekends, no wonder I'm such a great mathematician! Those math books that you kept in the classroom were so interesting as well, no one else did that!  The time you read flatland to us was so much fun, it made the class go by so fast!

Well, I just thought I'd let you know how much of a difference you made in my life.  I promise to include you in my speech when I accept my award!

Sincerely

Peye Thagorus

Dear Miss Landon,

I needed to tell you that I hate math and that you were the worst math teacher I ever had!  You made tests too hard and all your lessons were so fluffy.  Why did we have to work with other students so much?  I just wanted to do the lesson and work on my homework so I could go home.  Your lack of notes caused me to fail tests and now I am in a prison trying to calculate how many more years I have to be here.  This is all your fault!  I hope you learn to teach math better someday.

signed

Jr. i

Hopes and worries.

I really hope that I will become a teacher like the one in my first letter.  I hope that I will be well organized and be able to create a balance between relational and instrumental understanding in my teaching.

I am worried that I won't be able  to create new ways to teach math other than just giving notes for students, or that I will fall into one category of teaching and not be able to combine methods.  I am also worried that I won't give good enough notes for my students to succeed in their studies.

Reflection of "Teaching the Marked Case" video

Teaching the marked case was a very interesting video.  For a while in many of our classes we have discussed engaging the students and using a relational understanding teaching method.  We have not however had the chance to see it in action.  I thought that seeing someone teach using a relational method was very helpful.  As a colleague mentioned in class, the instructor on the video was able cover more than one topic using his method.  This would be very helpful on a tight curricular schedule.  I thought that it also gave the students a great way of understanding how the math they were learning worked.  By the repetition and having students speak out loud I think that they would have a better chance of remembering the concepts they were being taught.  I did however have some concerns on the lack of notes.  If the students have nothing to look back on, how are they to remember what went on months ago?  Perhaps this teacher gave notes after his initial lesson.  As well, I feel that it would be important for the students to have a step-by-step method written down for them to practice which I did not see performed in the video.  I did, however, like how engaged the students in the video were and how many participated without fear of being wrong.  During the video it was also interesting to noticed how well managed the classroom was, so this is definitely a great aspect of this method.  I think that the marked case method has many positive features but could be used along with a more instrumental way of teaching to create and an even more effective lesson.