Entrance Slip # 9: TPI Results

 1)

From my results, it seems that nurturing is my dominant perspective while social reform is the perspective I identify with the least. The perspective with the most inconsistency is transmission, where it seems that I apply and believe in it, but don't really intend to. 

2) I was most surprised by the height of the developmental perspective because, although that is one of my goals as a teacher, I don't think I have done enough to achieve 12 points for action (my highest action points across all categories) - I would have expected it to be closer to the transmission range, with apprenticeship and nurturing being my top two perspectives. I wasn't too surprised at the results for social reform because it is one I am still grappling with. 

 3)  Considering that for my top two perspectives, my beliefs/intentions are higher than my actions, I wonder how I could bridge this gap and align them so they are more or less on the same level. In encouraging us to look into the reason for these differences, the TPI website asks if it's a matter of job constraints, philosophical inconsistencies or lack of clarity about departmental expectations. At this stage, only having taught a few lessons in a school setting during my practicum, I think it's partially due to the fact that I haven't experienced the full job yet. For instance, if I wanted to raise my nurturing actions to the same level as my intentions/beliefs, I could implement certain assessment strategies that facilitated learning instead of causing students extra stress with standardized tests. Similarly, I would have more opportunity to explore apprenticeship as I was in charge of more lessons.

Leaving social reform to the side because I still need to struggle with that perspective and find out where I stand, my second lowest is transmission, which I intend to work on over the years anyway so there also isn't much for me to say about that. However, for the developmental perspective, I think I need to work a lot at effective questioning. I would like to follow Asha's advice in this regard by taking simple questions and taking out information to make it more interesting, but I would have to try my hand at it before I could say where my skill level on that lies.

Entrance Slip # 8: Thinking about math textbooks

Image source: https://edcp34220.blogspot.com/2020/11/your-homework-reading-for-sunday_16.html

As a former student, I don't know that I necessarily thought a lot about the language used in terms of using first/second person in problems. However, I do think the way problems were structured as absolute fact (such as the equations for the male/female height-femur relationship) shaped my attitude towards math. In contrast, I remember complaining about physics problems that told us to "assume friction is negligible," because I thought it was silly for us to be doing a "real-life problem" in a vacuum setting. I admitted I understood it was for simplicity in calculation but it still bothered me. Now I realize math had the same problems, but because the questions were stated as fact while the physics questions admitted their modifications, I hadn't questioned it. I think it also influenced the way I viewed math as more stable than physics or other sciences because we focused more on math "rules" and less on the experimental and uncertain aspects surrounding the situations in the problems we worked on.

As a teacher, I think textbook questions are often manufactured to fit a lesson instead of finding an application of the lesson content and modifying it to fit the skill level of the class. Of course, as mentioned on page 12, textbooks have to make certain assumptions of student knowledge and can't completely cater to a class, but they could still try to base their examples in real-life applications, or give better context. Going back to the femur/height example, I don't know a lot about proportions of the human body and these examples seem like generalizations made up for the sake of tests a math skill, which either should have been stated as such so students knew this wasn't some steadfast rule, or if it is, then that rule should have been explained more to spark interest in students.

In my opinion, textbooks are good for skill building questions, but less helpful in meaningful word problems or activities. In my opinion, word problems should be formed by the teacher so that the teacher can tailor them more to the students, make the problems more applicable to the environment around the students (i.e. where they live, what their context is with respect to the world etc.), and bring some of their own interests and ideas to those problems as this will likely spark more interest and inspiration in students than if the problems seem to come from a faceless source. The textbook may also offer further/alternative explanation to math ideas but I believe students generally turn to the internet for video explanations and easy-to-follow explanations instead of reading through the textbook, which may contain information that is either not being covered in class or is more difficult to follow. However, from what I have observed in classrooms and from my own experiences, workbooks with answer keys are almost better than textbooks because they provide the student a means to make sure they are on the right track. Thus, I think textbooks or workbooks can be useful for testing basic skills and as an additional source of knowledge, but I think classrooms can survive without them if the teacher is able to provide students with strong notes, their own problems that are more applicable, and perhaps use something like Khan Academy as a supplement to skill building problems from the textbook. One of the disadvantages to using something like Khan Academy is if students don't write their work down in a notebook, then they won't be able to refer back to their process at a later date.

Homework: Scale Problem

Solution:

At first, I tried to use numbers without including 1. I thought if we had some x, we could take the next number, x + 1, and get 1 by subtracting the two but I realized that this created issues when trying to create numbers later on that may have required subtracting 1, but x and x + 1 were also needed in the construction of the number, so this wouldn't work (e.g. When trying 10, 11, 13, and 17, I couldn't achieve 22 because 22 could be taken by adding 10 + 11, but in order to get the extra 1, I would need 11-10. Of course there are more options, like 11 + 11, but each required doubling up on a weight, which is not possible in this situation):

Then, I tried using 1 and working up from there. I chose 3 and 9 because they resulted in consecutive numbers from 1-13. Then, I subtracted 1, 3, and 9 from 40 to get 27. I checked to see if this worked and it did:

Thus, the weights are 1 g, 3 g, 9 g, and 27 g.

Are there several correct answers?

I tried to do a bit of an analysis based off of my findings. I realized if the numbers were a <  b < c < d, then a + b + c + d >= 40 to reach 40, and d <= 2(a + b + c) + 1 to bridge the gap between the highest number a + b + c  could achieve before d would have to be used. However, I was unable to determine if there were any other correct answers. 

Extension:

I think it would be useful to have students try to make all combinations of weights with a lower number by using a smaller total number and real weights and scraps of recycled paper to avoid wastage of herbs. For example, if we took 1 + 3 + 9 = 13 to be the total grams achievable, this would cut the table down to:

p = 1g -> 1 = p

p = 2 g -> 3 = p + 1

p = 3 g -> 3 = p

p = 4 g -> 3 + 1 = p

p = 5 g -> 9 = 3 + 1 + p

p = 6 g -> 9 = 3 + p

p = 7 g -> 9 + 1 = 3 + p

p = 8 g -> 9 = 1 + p

p = 9 g -> 9 = p

p = 10 g -> 9 + 1 = p

p = 11 g -> 9 + 3 = p + 1

p = 12 g -> 9 + 3 = p

p = 13 g -> 9 + 3 + 1 = p

where p is the amount of paper, in grams and the numbers represent the 1, 3, and 9 gram weights.

If weights from 1 - 13 g were available, students could spend time trying to see if other combinations worked and tangibly grasp why or why not. I myself could probably benefit from an activity like this because I had trouble disproving other combinations to the four weight case.

I think it might be a bit excessive for students to do a five weight case. However, if the pattern of 3^0 = 1, 3^1 =3, 3^2=9, 3^3=27 continued, the next weight would most likely be 3^4 = 81. It might be worth having students guess what they think the next weight would be and justify their answer to show that they recognized a pattern.

 

 

Group Microteaching (Grade 8 Percentages) Reflection

 I definitely thought timing was a problem with our presentation. I was guilty of going over my time for sure. Part of it was to do with not being comfortable enough with the technology (i.e. I wasn't planning on doing the slides, and then I also wasn't prepared for the lag in annotation from the audience/students). I was thankful to our classmates for really participating and answers questions enthusiastically during our project, but that may have not been the case with grade 8s. I definitely think shortening the introduction would have helped create some more wiggle space for students to take time and digest the material, as well as answer. Specifically, I would have cut out the example with 5% of $10, just because it was very similar to the previous example and the rest of the presentation was already covering more interesting examples. We also could have gone through the fractions to percentages a bit quicker but I think with some more experience with technology, we would eventually stop running into as many problems with pacing between co-teachers. 

In terms of positives, I thought the examples that Jeff and Zach presented were relevant and seemed to keep the audience interested. A few people mentioned liking the annotation function (credit goes to Jeff for that addition!) and I think it would be good to give more time for annotating/whiteboard functions. I noticed students in schools often like writing on real whiteboards because they are using a different medium. Similarly, in previous Zoom tutoring session I have done, students (as long as they can easily write on their screen) liked being able to have some control and options during a lesson by replying through chat, annotation, and/or by verbal response.

Group Microteaching Lesson Plan

Image source: https://www.tes.com/sites/default/files/tes-resources-prim-maths-percentages.png

Here is a link to Zach, Jeff, and my lesson plan for an introduction to Grade 8 Percentages/Ratios:

https://docs.google.com/document/d/1WGeIS-LlCwqy_kapq5hjuNyWVA_2IZ_NzCwWujDtadI/edit?usp=sharing

Here are the slides:

https://docs.google.com/presentation/d/1ePmaC04-iKjv7NsQsBiYgXVRmSYQqhXCfV-oSeBic8s/edit?usp=sharing

Soup Can Puzzle

I have started with my student bird observations by describing my process and wrong turns:

When I started this question, I decided to check the sizes of the picture as well as the actual and soup can dimensions:

  I measured the bike height from the bottom of the wheel to the top of the handle because I believe the picture is taken from a slight angle. I wasn't able to measure the length of the tank accurately so I didn't fill it in the table. I measured the tank from the ground up and rounded up slightly because the tank is partially in the ground:

	Bike Height (cm)	Length (cm)	Diameter (cm)
Picture	3.5	--	7
Actual	H	L	D
Soup Can	--	10.1	6.2

Then, I researched the bike size and after analyzing Norco bikes based on the Stack height and wheel diameters, I estimated that the bike was about 0.95 metres, or 95 cm high and used this as my H.

Because I wanted to relate the bike height with the diameter, I at first thought H + x = D, where x was some number, but didn't find this very helpful. Then, I decided to use the picture relation and real dimensions to get the following:

3.5	=	95
7		D

D = 190 cm

Then I used the soup can dimensions to get the actual length of the can:

190	=	6.2
L		10.1

L = 309.516129 cm

Thus the diameter of the actual tank is around 1.90 metres while the length is about 3.10 metres long. 

As a sanity check, assuming my bike height estimation is correct, this makes sense because it means the diameter of the tank is about twice the height of the bike.

To calculate volume, the equation is V = π*r²*h, so (using the cm for simplicity) we get V = π*(190/2)²*(309.516129)

V ≅ 8775671.713 mL

Most statistics about putting out fires were in gallons so I converted this amount from mL to gallons and got 1930.37791 imperial gallons. From the sources I found, most listed gallons per minute, ranging from 100 gpm - 2000 gpm needed for fires depending on how severe they were, how long it took the firefighters to arrive on scene etc. (Quora question answered by firefighter, Firehouse.com).  There were also too many variables to determine how many minutes were needed for the fire to go out. As one firefighter said, most house fires could be tackled with the 500 gpm power (Quora question answered by firefighter), so if the average house fire could be put out in less than 4 minutes, this tank would be enough.

My teacher bird thought this would make a very interesting project for students to flesh out and find more information on for different scenarios (e.g. research water tanks in the areas they live and determine what range of fires that tank could handle). It seems like a simple question at first but once it is attempted, there are many questions to consider. I started with a chart because I couldn't just jump in and start solving - I needed to figure out where I was and where I wanted to go. The topic of putting out fires is also a good one because all students would be familiar enough with the concept to have an understanding of what was going on, and the application of ratios was a little more interesting than simply enlarging an image or determining the full size of a building given a scale drawing and one of its dimensions like we usually see in textbook questions.

Extension Question:

Image source: https://ship-photo-roster.com/ship/cosco-prince-rupert#1

The Prince Rupert Port container ship, Cosco, is 334 metres long. The photographer of the above picture closed their right eye and aligned their thumb with rightmost edge of the ship. Then they closed their left eye and opened their right to see that their thumb appeared to have moved 1/4 of the ship's length to the left. Estimate how far the photographer is from the container ship. How far away would the photographer have to be to just see the entire ship in their peripheral vision if they were standing directly in the middle of the ship, lengthwise? Hint: On average, humans have 120 degrees for their field of peripheral vision.

Solution: For the first part, we use the distance estimation method to get 334/4 * 10 = 835 metres away. 

Next, we use tan(60 degrees) = 167/d, d = 96.42 metres away.