Assignment 3

Geo Sketchpad

From Natalie's workshop today, I had realized what a powerful tool the geosketchpad could be to bring out mathematics. One amazing feature was that the program did not make us use that much numbers, and had us constructing shapes and questioning basic properties of triangles and such. It's definitely a tool that I would love to incorporate into the classroom.

A few worries from the seminar that I had however were that I don't feel very competent with my geometry and am not sure if I would be able to incorporate the program into the classroom well. Secondly, as a pre-teacher, one of my main concerns would be time and I wouldn't want to stray away from the PLO's too much.

However, I'm very glad and excited that I had the opportunity to experience and play around with this technology. Hopefully, I'll figure out a way to effectively incorporate this into the classroom setting- even if it's just a method to introduce geometry or a way to wrap up the unit and solidify a student's understanding.

Thinking Mathematically Problem Solving!

Had trouble uploading the problem, so I just decided to type it:

Working on Problem: 31

WORK ---------------------MENTAL THINKING

Try it: a) 1 5 7 10 11 15 16 20 24 25 29 31 b) 5 10 15 20 25 30 31 c) 5 6 10 15 29 24 25 29 31

Try working it backwards. To be the person to reach 31, must land on 25 to ensure a win because if not- will end up landing on a number between 26-30. This leads to the other player adding to 31.

Try out hypothesis: d) 1 3 7 8 13 15 19 23 25 29 31 (Eureka, it works!!) (PLUS, this works every time AS LONG AS you start off with the number 1.. and make sure you don't lose count.)

Try working from it backwards with consistent train of thought... If person who lands on 25 is the winner, then he/she would want to land on 19 to ensure a win. And keep doing the same pattern, and realize we're just subtracting six from the number each time. Ending up with the pattern of wanting to hit the numbers 7, 13, 19, 25, 31 in order to secure a win. In other words, we want to touch x = 1 (mod 6)

Question number two: What if 31 was some other number? e) Reach 33: 3 8 9 10 14 20 21 22 27 28 33 f) Reach 24: 4 5 10 15 16 17 22	We can try to work backwards again or can we see if we can incorporate modular arithmetic? For example, if we want to reach 33, should we try x=3 (mod 6) where x is 33? Or if we want to reach 24, should we have x = 22= 4 (mod 6)
Question: What if it goes from 1-6? g) Reach 31: 3 9 10 12 17 23 24 25 31	Well, since it was in mod 6 when it was from 1-5, is it now in mod 7? So let's set up our general equation and check: x = 31 = 3 (mod 7)

Question: What if the numbers were 1,3,5 or 2,3,7?? Ex) 1 2 7 10 13 18 19 22 25 26 31

Try out with 1, 3, 5... Can we still use generality? YES! Why? Because, as long as we start at 1, can always reach x = 1 (mod 6) because of how the numbers work--> at your turn, will be able to chose number that makes it become 7. To make this more clear, if we start with 1, then need to add 6 to become 7. If player 2 says any of the numbers (1, 3, 5), we can find the complement of it that adds up to 6- making it 7. 1&5, 3&3.

** Unfortunately, I got really confused if we extended it to 3 players and came to the conclusion that we can have 2 people gang up on the other player to make sure the 1 person does not win. But I'm not sure if we can have a guaranteed winner.

*** Tried to make a tree (like a probability tree) with testing out 2, 3, 7 to see all the possibilities. But it got really messy and I was unable to figure out the winning strategy if we only use number 2, 3, 7.

Stories of My Short Term Practicum

1.
I had the opportunity to observe a variety of classes- as I am sure many of my peers also had done. However, it was very interesting to note down all the different strategies seen in the various classes, different management strategies and teaching strategies that one can incorporate perhaps into their own teaching style.

In one English course, the teacher had incorporated various teaching strategies that were engaging as well as relevant to the topic. They had worked in groups of four to discuss the topic at hand, with one person being the "recorder". After, each group had a presenter where they represented their group, went up in front of the classroom to speak into a "mic". It gave the students an opportunity to realize how there are various way of communicating. As well, it made me realize the IMPORTANCE in giving students the chance to have an outlet to explore the subject in different manners and to present information in other modes than merely note taking.

In another class, there were three different levels of Japanese in the room- grades 11a, 11b, and grades 12. Though they were learning different material, they had the ONE teacher in the same room. It made me realize the importance of staying on TOP of things, being really organized, and able to be multitask as a teacher.

I had also attended two Social Studies courses, and had realized how teaching styles and management can be different- yet, both teachers had a good control of the classroom. One teacher, a relatively petite lady, had really rowdy kids- however, when they were in HER class, not a peep was heard from them other than when she asked for participation. They were all on task and it was evident that the class as a whole was learning. In the other class, it was the polar opposite- it was a total RUCKUS! However, it was evident that the students knew where the teacher's boundaries were and would not step over the line. There was a lot of banter between the teacher and students, yet, material was still being learned. So from this experience, it makes me reflect and wonder what kind of style would I want to incorporate into my classroom? Which method would work for ME and my students?

Though there was much that I had observed and it is impossible to note it all down at the moment, another fantastic approach that I saw was co teaching. Or having teachers from other subjects (english) come into a science class and help students learn about note taking and how to grasp information from a textbook. It was a great approach to help students realize that learning should not just be ONE subject on its own- it should be interdisciplinary. If possible, I would love to try and combine mathematics with other subjects (such as science or language)!

2.

On my short term practicum, I had taught two classes. One grade 8 science (on osmosis and diffusion) and a grade 11 math class (on graphing quadratic functions). For the latter, I had quite the learning experience...

Though I was into the second week of the practicum, I had not met this particular class yet. So teaching the grade 11 class was a bit nerve wracking as I did not have any idea what to expect. My sponsor teacher started off the class by introducing me and telling them that I would be teaching them for the day - making me realize that the students had no forewarning that I was their student teacher until that day. After the short introduction, my S.A. went to the back of the room to let me start teaching.

With a no bell system at the school, I promptly closed the door and began to take attendance. I had learned from my first class that it was important to not let late comers disturb the flow of my class and that I should wait until I was ready and found a natural pause before I opened the door and let them in. (I had learned this the hard way and found myself being constantly disrupted the first time I taught).

After I had let the latecomers come in, I began teaching students on quadratic functions. I plotted out the basic parabola with them first and then had them explore transitions and transformations. By the time I had gotten to horizontal shifts, I realized that the pace I was going at was much slower than I anticipated. How could I manage to teach everything to the students by the end of the class?

Then, in the middle of my teaching, an earthquake drill went off and we were disrupted for at least 15 minutes.

After the drill, the energy of the class had gone up quite significantly and it was difficult to have the students get back on task again. However, being stubborn and thinking that it was REALLY crucial for the students to learn what I had planned, I sped up my teaching a bit more and finished up the transformation quickly and assigned homework for them to do, and then dismissed the class.

A few things that I had learned from the classroom- or finally realized what my UBC teachers have said is really true... Time is my worst enemy. In the future, I must plan for LOTS of extra time in case students struggle with a certain concept, or just for disturbances such as drills. Secondly, I had not followed up with the late students- and we need to make sure the students know that lates are NOT allowed. And as well- even though I'm rushed for time in teaching, if I ever ask a question, I need give some wait time for the students to absorb my question. Lesson plans are constantly being changed and as teachers, we need to be flexible and find a natural stopping point if we cannot teach all the material in one lesson. And finally, with a no bell system- I must be really AWARE of when to dismiss my students!

Group Micro Teaching Reflection and Summary

Overall, the micro teaching gave a great opportunity for us to try and test out our skills in explaining math techniques. Unfortunately, I was sick and did not get a chance to participate in my peer's teaching, however- it was a great opportunity to try teaching in a safe and constructive environment.

One thing I wished for would be that instead of a 15 minute microlesson, the lessons were 30 minutes long instead. That way, we would have a better sense of what a "true" lesson at school would feel like.

For my group's microteaching lesson in particular, there were quite a few points that we needed to improve on and a few points that went really great as well:

Plus-
- the class was very actively engaged and on topic in general
- it was a nice way to introduce the topic
- it allowed a chance for the students to shine on the stage
- the Mario and Luigi worksheet was humorous yet very applicable

Minus-
- some of the worksheets were not very consistent and at times too challenging and confusing for a grade 8 student
- the students may not understand what the focus of the activity was because we did not introduce the activity well
- our introduction did not go the way I wanted it to and I felt that it may have been confusing for the students
- the students began to dominate the discussions after awhile, and as "teachers", we should learn to facilitate the conversation and guide them in a way that was suitable for all students to understand
- our timing was really off and it would have been much better if we made the worksheet shorter since we lacked time to conclude the activity nicely

Interesting-
It was a great experience to try "coteaching" with other colleagues and I hope that in the future, I will have the opportunity to try this in real life. It is definitely challenging to communicate with one another as we all have our own unique styles and way of classroom management. However, with practice and confidence, I am sure that students will be able to benefit in learning from different teachers.

Group Microteaching Lesson Plan

Topic: Graphing

Bridge: Tell the students that we are going to work on graphing today. Assign them into groups and hand out worksheets for them to work on!

Teaching Objective: To allow students the chance to work in groups to think and hypothesize over graphing. To promote a bit of worksheet guided independent learning. For students to work on their communication among peers to reach a conclusion for the answer. And to facilitate discussion among the small groups.

Learning Objective: Students will be able to create lines of best fit for particular graphs and realize that graphs are not always linear. As well, they will learn that there is a practical reason for graphs!

Pre-test: Ask if anyone knows how to graph data points. Ask if they have seen a graph and know what should go on the x and y axis.

Participatory Activity: Hand out the different worksheets to different groups to have them explore graphing techniques.

Post-test: Have students come up to the board, draw their graph and describe what conclusions they derived from it. The students will explain the answers they obtained from the experience.

Summary: Conclude with we can graph many different shapes and they all explain data in a very visual friendly way. As well, it is important skill for us to be able to graph plots because we can predict the general trend and see relationships. Graphs can be very applicable to daily life. In the upcoming unit, we will focus in more detail on the linear graph.