Something from nothing,
Is it really possible?
Not from our human perspective.
Infinite, unending, beyond us
Division, splitting, separation
Why do we have to be divided?
Sometimes pain is necessary for growth.
Still it is painful
Zero to worry about,
Why do we worry about what tomorrow will bring?
There are infinite possibilities
He is in ultimate control
Something from nothing,
It is really possible,
Beyond our human perspective
Infinite, unending, forever
Monday, October 18, 2010
Saturday, October 16, 2010
Group Microteaching Reflections
Summary of Comments
The comments we received were mostly positive in nature. The majority really liked that we attempted a Jigsaw approach to this topic. One comment I really liked is that the approach made a potentially dry topic more fun. The class felt that we did a great job of organizing the groups and having something different and interesting for each group to do. The biggest critique we had was the lack of time at the end for the original group of three to report back to each other. On a personal note, my voice was too quiet at one point when I was attempting to not talk over my teammates.
Personal Reflection
I really enjoyed doing this micro-teaching lesson with Michelle and Debbie. It was very interesting discovering the different historical applications of the Pythagorean Theorem. I really wanted to be a part of each of their groups to learn more about what they had discovered. I would absolutely use an approach like this with a class of my own to make the learning of the history and modern applications a fun activity. I would probably extend the activities at each station so that they would expand on the information we only briefly touched on. The one thing I would make sure to improve would be the amount of time that the original groups of three had to debrief with each other. I would also include a longer time of class debrief. Overall an enjoyable activity.
The comments we received were mostly positive in nature. The majority really liked that we attempted a Jigsaw approach to this topic. One comment I really liked is that the approach made a potentially dry topic more fun. The class felt that we did a great job of organizing the groups and having something different and interesting for each group to do. The biggest critique we had was the lack of time at the end for the original group of three to report back to each other. On a personal note, my voice was too quiet at one point when I was attempting to not talk over my teammates.
Personal Reflection
I really enjoyed doing this micro-teaching lesson with Michelle and Debbie. It was very interesting discovering the different historical applications of the Pythagorean Theorem. I really wanted to be a part of each of their groups to learn more about what they had discovered. I would absolutely use an approach like this with a class of my own to make the learning of the history and modern applications a fun activity. I would probably extend the activities at each station so that they would expand on the information we only briefly touched on. The one thing I would make sure to improve would be the amount of time that the original groups of three had to debrief with each other. I would also include a longer time of class debrief. Overall an enjoyable activity.
Thinking Mathematically Chatpers 2 & 3
I first started reading these chapters online from the posting and found them difficult to follow for two reasons. First some of the content was cut off by the scanning and second because I felt as if I was missing some important aspect that had been introduced in chapter one. So once I had an actual copy of the book I read chapter one before proceeding to chapters two and three. This was much better and my insights follow.
Phases of Work
I particularly like how the authors set out the three phases in this chapter and spend most of it focused on phase one. Even though we subconsciously realize we often walk through the three aspects of the entry phase it was great to have it put into words. I appreciated how each aspect was expounded on and more ideas and examples were given to help develop them. I think students would benefit from spending some time pursuing this as well. It may formalize it in their understanding better than anything else we could do.
The review phase is something that we often overlook, even as teachers. How often do we ask our students to look back over what they've done and justify their solutions. We rarely spend any time actually teaching them how to critically look back at what they have done. This chapter gives me some ideas of how I could focus less on the answer and more on helping students justify their work.
Responses to Being Stuck
I really identified with this chapter. Recently in the Problem Solving class we were given a set of five problems to solve, of which we had to hand two in. There was only one question that I felt at all capable of doing on my own. It was very difficult to admit that I could not do the rest of them without help. I was hopelessly stuck and felt extremely defeated. It was only through this experience that I could identify with students who may often feel the same way about any math questions. This chapter showed me that it was okay to be stuck and that being stuck is perhaps the best place to be to truly learn something.
Phases of Work
I particularly like how the authors set out the three phases in this chapter and spend most of it focused on phase one. Even though we subconsciously realize we often walk through the three aspects of the entry phase it was great to have it put into words. I appreciated how each aspect was expounded on and more ideas and examples were given to help develop them. I think students would benefit from spending some time pursuing this as well. It may formalize it in their understanding better than anything else we could do.
The review phase is something that we often overlook, even as teachers. How often do we ask our students to look back over what they've done and justify their solutions. We rarely spend any time actually teaching them how to critically look back at what they have done. This chapter gives me some ideas of how I could focus less on the answer and more on helping students justify their work.
Responses to Being Stuck
I really identified with this chapter. Recently in the Problem Solving class we were given a set of five problems to solve, of which we had to hand two in. There was only one question that I felt at all capable of doing on my own. It was very difficult to admit that I could not do the rest of them without help. I was hopelessly stuck and felt extremely defeated. It was only through this experience that I could identify with students who may often feel the same way about any math questions. This chapter showed me that it was okay to be stuck and that being stuck is perhaps the best place to be to truly learn something.
Thursday, October 14, 2010
Group Microteaching
EDCP 342A October 15th, 2010
Group Micro Teaching – Apprenticeship and Workplace 10
Michelle, Deb, Nadine
Bridge: 2 min
Catch interest by having students form groups of three and numbering themselves 1,2,3 for jigsaw activity in which they will become the expert on some aspect of the history or modern use of the Pythagorean Theorem.
Learning Objective:
Students will be able to demonstrate an understanding of the Pythagorean Theorem by describing historical and contemporary applications of it.
Ø To learn a historical use for Pythagorean Theorem and to understand where Pythagoras' inspiration came from.
Ø To understand that this theorem came about from a practical application, not pen and paper theory.
Teaching Objective:
Ø Learn and improve our methods in conducting an engaging and educational lesson that will reach everyone.
Ø To interactively show the motivation for the Pythagoras Theorem, introduced to Pythagoras by the ancient Egyptians.
Ø To try out the Jigsaw strategy.
Pre-test: 1 min
Ø Who can tell me what we already know about the Pythagorean Theorem?
o Looking for formula, triples, and to see if anyone might already know where it comes from.
Participatory Learning: 7 min
Ø Split groups into 1’s, 2’s and 3’s.
o 1’s at Egyptian Station (Deb)
o 2’s at Babylonian Station (Michelle)
o 3’s at Modern Application Station (Nadine)
Station 1 – Egyptians
Ø Explain how ancient Egyptians used a right-triangle to redistribute fields after yearly flooding.
Ø Explain how they made a right triangle using rope and knots
Ø Explain how Pythagoras became involved/interested
Ø Make a right-triangle with a piece of string and ruler. Make a 3, 4, 5 triangle and see if they can find a right angle in the classroom with it.
Station 2 – Babylonians
Ø Explain Babylonian Mathematics and history of Pythagorean Theorem.
Ø Teaching Babylonian numbering system and ancient tablet.
Ø Briefly cover other ancient cultures in which Pythagorean Theorem was known and used
Station 3 – Modern Uses
Ø Talk about how surveyors use their equipment to set up right hand triangles in order to calculate distances etc…
Ø Have students using laptops research other possible modern uses for Pythagoras.
Ø If they cannot find any, have them brainstorm a list of possible fields that they think may use the Pythagorean Theorem.
Materials Needed:
o String and rulers
o White board, diagrams of tablet and Babylonian numbering system
o Laptops, paper to write ideas down on, pens
Post-Test: 3 min
Groups of three re-form and students teach other members about their area of expertise. Only have 1 minute each to share.
Summary: 2 min
Students complete the statement: The one thing I learned today that I didn’t know before was _______________________________________________________________________________. (Orally if time allows.)
Feedback and Reflections on the Jive Mini-lesson
The feedback I received on teaching the Jive was overall positive. My group members appreciated that I was actively involved in correcting their technique as I walked around. They said the pace was good and the instructions were very easy to follow. Finally they appreciated that I used the history and origin of the Jive to create interest in the lesson. A few of the critiques were that I needed to perhaps explain the proper partner position ahead of time and maybe add some extensions that the professional dancers do.
This mini-lesson was very fun to do. I have taught a ballroom dance class before as an option for my students and it brought back good memories. I did adapt the way I have previously taught this type of lesson as experience has taught me that a slower introduction to the basic step is very important, especially for the gentlemen. I needed to have a little bit more prepared for the students I had as we got through it much more quickly than I expected. In the future I would make sure that I have the proper music with me so that the students can try it with a regular tempo Jive song. Unfortunately all of my ballroom music is currently in Prince George.
Wednesday, October 6, 2010
Timed Writing
Division
Take a group of things and split them up into smaller things, a process kids have difficulty with, trying to teach long division with grade tens of polynomials and the difficulty they have with it, what's the point, hard to think of splitting things up, ummmmm, not sure what else to say, fractions, decimals, being separate from my family here in vancouver, divisions in politics, no one can agree, divisions in the church, humans need to be right create divisions, divisions in families when not everyone agrees exactly with each other, this is a very difficult exercise in and of itself, how does it relate to life outside school, how to reconcile deep divisions, have nothing else to say really about this, hate being divided from those I love, gonna happen again on Tuesday...
Zero
Place holder, not a new concept, took a long time to develop a symbol that meant nothing, do we really understand the meaning of nothing, division by zero is impossible because you cannot take something and turn it into nothing unless you are God, there is zero to worry about because He has it under control, is often forgotten about in mathematical context, running out of things to say about zero, had more to say about division, is it an easy concept for kids to truly understand...
Take a group of things and split them up into smaller things, a process kids have difficulty with, trying to teach long division with grade tens of polynomials and the difficulty they have with it, what's the point, hard to think of splitting things up, ummmmm, not sure what else to say, fractions, decimals, being separate from my family here in vancouver, divisions in politics, no one can agree, divisions in the church, humans need to be right create divisions, divisions in families when not everyone agrees exactly with each other, this is a very difficult exercise in and of itself, how does it relate to life outside school, how to reconcile deep divisions, have nothing else to say really about this, hate being divided from those I love, gonna happen again on Tuesday...
Zero
Place holder, not a new concept, took a long time to develop a symbol that meant nothing, do we really understand the meaning of nothing, division by zero is impossible because you cannot take something and turn it into nothing unless you are God, there is zero to worry about because He has it under control, is often forgotten about in mathematical context, running out of things to say about zero, had more to say about division, is it an easy concept for kids to truly understand...
Mathematics and Citizenship
I enjoyed reading this short article about mathematics and its role in developing good citizens. It continues to surprise me how prevasive mathematics is beyond the classroom. I would never think that things we hear on the news on a nightly basis are linked to math concepts. It makes sense now, but I would never think that, we as humans, have assigned numbers or mathematical concepts to most things we come across.
As far as the classroom is concerned, I have found that students find it very difficult to explain how they arrived at their answers. I think this is largely because the climate of mathematics education does not put enough emphasis on expecting students to be able to justify their solutions. Mathematics is considered very black and white; it is right or it is wrong. This article made me think back to the video where the teacher didn't say if their answers were correct or not. Instead he expected them to know that they were correct without any justification from an outside source. This is a great skill for us to be attempting to instill in our students; the ability to make choices for themselves and know that their choice is the best thing for them.
As far as the classroom is concerned, I have found that students find it very difficult to explain how they arrived at their answers. I think this is largely because the climate of mathematics education does not put enough emphasis on expecting students to be able to justify their solutions. Mathematics is considered very black and white; it is right or it is wrong. This article made me think back to the video where the teacher didn't say if their answers were correct or not. Instead he expected them to know that they were correct without any justification from an outside source. This is a great skill for us to be attempting to instill in our students; the ability to make choices for themselves and know that their choice is the best thing for them.
Saturday, October 2, 2010
The Math Wars
Battleground Schools: Mathematics Education
In the article battleground schools there were two differing schools of thought concerning how mathematics should be taught and approximately three different eras of reform that were considered. The two differing schools of thought are considered conservative and progressive. The conservatives prefer a more teacher directed model of math education while the progressivists prefer a teacher as guide and facilitator model. Each of the eras, 1910-1940 Progressivist, 1960's New Math, and 1990"s Math Wars, seems to favour one approach to the exclusion of the other.
What I noticed as I was reading this article was how driven by societies needs are our math classrooms. Math is not necessarily considered a subject to be taught simply for the pleasure that it can bring. It comes across more as a means to an end. We teach math so that our students can be productive members of society, be that members of an independent thinking democratic society, or a highly scientific, space race populace. Math is to be taught for the purpose of preparing kids for the "real world". To me this indicates that we expect all students to leave school and be the top performers in whatever field of study they happen to get into and if they aren't then we have somehow failed them.. What we fail to realize is that not all students are going to be Einsteins. For me it brings to mind the question, "why do we teach math?" I think we should be teaching math for math's sake. It is a disipline full of interesting things that can be explored simply for the fun of it. Yes, it absolutely has value in the high level careers like engineering and should be pursued for that reason as well. However not all of our students are going to be engineers and to teach all of them as if they will be is doing a disservice to our kids. If we can instill in the students, maybe not a love for, but an appreciation for the complexities and intricacies of mathematics then I believe we will have done our job.
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