Tuesday, October 15, 2019

15-min micro teaching lesson plan


Subject: Workplace Math 11 
Topic: 3D objects
Duration: 15 min
Curricular Competencies:
  • Develop thinking strategies to solve puzzles and play games
  • Think creatively and with curiosity and wonder when exploring problems
  • Visualize to explore and illustrate mathematical concepts and relationships
  • Represent mathematical ideas in  concrete, pictorial, and symbolic forms
Content Competencies:
3D objects: angles, views, and scale diagrams
  • creating and interpreting exploded diagrams and perspective diagrams
  • drawing and constructing 3D objects
Big Ideas:
  • 3D objects are often represented and described in 2D space
Materials:
  • 3 sheets of paper
  • pencils/erasers
  • White board/marker
  • Object for introduction
  • Object for drawing
  • Materials for building
Lesson Outline:
Introduction
Teacher-lead, group participation
  • What is a perspective drawing?
  • Why does perspective matter?
  • Do a drawing example with a side-distinctive object
2 min
Activity: Drawing
  • Split into 3 groups. Explain activity and introduce object.
  • Have 3 groups sit around the object, each group with a unique side.
  • Each group will draw the object from their perspective
  • Teachers to walk around, monitor, and assist if necessary
4 min
Activity: Building
  • Take the object away
  • Have the 3 groups rotate their drawings and attempt to build the object with the new drawing
  • Teachers to walk around, monitor, and assist if necessary
6 min
Conclusion
  • Bring object back out
  • Have groups share what their object looks like, see how different the 3 groups are
  • Wrap up: so why does perspective matter? Because look how different all these drawings look, even though they’re all the same object.
3 min

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Monday, October 7, 2019

Mini lesson reflection

On one hand, I definitely like to plan out the material that I intend to cover; I understand that having a hearty lesson plan allows substitutes or successors to conveniently pick up where you left off, and it also helps with classroom discipline in that students can tell when you are unsure of what you are doing. Furthermore, just as athletes have a game plan mapped out so that they can focus on which complex movements are to be expected, having a lesson plan allows you to achieve the pedagogical equivalent of that.  On the other hand, it seems that getting lesson plans done quickly and efficiently in itself seems to be a major skill, and I believe that excessive pedantry results in a certain fragility in your lesson where any student asking a slightly "interesting" question throws you off your course completely.  Still, it seems that striking the right balance can be challenging.

For my preliminary part, I thought I would go into the history of house music- first appearing in Chicago and how it can be traced back to disco. Also, there is patriarchal theme in the language "Oppan Gangnam Style". "Oppa" is a language used by women and girls to refer to their older brothers, giving the kind of domineering vibes when a drill instructor refers to male recruits as "ladies" in order to degrade them on purpose. Also, Gangnam is an upscale area with expensive clubs and apartments, so, in a way "Gangnam Style" actually contains a rather boastful message. Still, most of the lyrics of the song are about what kind of ladies he likes and what kind of guy he is (temperament-wise), so the song can also be interpreted to mean "this is how we party in Gangnam".
As for PSY, PSY himself actually comes from an exceedingly privileged background and received some top-tier schooling in the form of Boston University and Berklee School of Music. So, I took a dance lesson and introduced some social critical elements.

The signature movement has many "building blocks" in it.

https://giphy.com/gifs/vevo-gangnam-style-psy-oppa-nYI8SmmChYXK0

It requires you to hop and drag your feet in rapid succession. Here is how one would scaffold the learning process: isolate them into simpler movements, slow practice until it really "sinks in" your brain, and put the isolated elements together. To that end, I first made them practice hopping on one foot, then dragging the foot that you are hopping on mid-air without moving backwards (a lot of slow, deliberate practice here), then I added the signature hand movement. Also, sharing the source of the inspiration helped greatly too: mimicking a horseback rider. The group members picked it up very well.

Do you know how clumsy you feel when you lift weight for the first time, because your muscles do not have the "practice"? Admittedly, I felt that a bit when I when it came to the choreography part. incorporating the signature movement among many others. I actually got nervous because I thought that the planned choreography did not incorporate the signature movement enough, which then began to affect my recall.. I thought I was running out of time, and then it turns out that I still had two minutes, so I pulled out what I had in mind for "extending" the lesson (just my opinion: it is better to have just a little too much material because you can always cut some in order to meet the time) and then the two minutes flew by. Checking the clock discreetly and quickly, and being able to accurately "feel" how much time has passed all seem to be actually non-trivial skills to develop.

In the future,

  • Be confident about what you have to offer.
  • Speaking quietly with clear enunciation actually requires attention.
  • There is a difference between minor adjustments and disrupting your own lesson stemming from a lack of confidence.
  • Break it down, slow practice, put them all together- scaffolding cannot get any more literal or physical than this, I think.
  • Figure out a way to check time accurately and discreetly. If you can tell time without looking at the clock, even better!






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The cook math puzzle

"How many guests are there?" said the official.
"I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them".  There were 65 dishes in all.  How many guests were there?
Let us investigate some earlier ones.

The first three guests used a dish of rice and a dish of broth; that would be two dishes.
The fourth used used a dish of rice and a dish of meat; that would be two more dishes.
The sixth used a dish of rice, and a dish of broth; that would be two more dishes.
The eight used a dish of rice, and a dish of meat; that would be two more dishes.
The ninth used a dish of broth; that would be one more dish.
The tenth used a dish of rice; that would be one more dish.
The twelfth used a dish of rice, a dish of broth, and a dish of meat; that would be three more dishes.

 I think we can in fact find an iterative summation algorithm here:

  • dishCount = 0
  • numGuests = 1
  • while (dishCount < 65):
    • if (numGuests is a multiple of 2):
      • dishCount += 1
      • Immediately exit loop if dishCount is at or exceeds 65
    • if (numGuests is a multiple of 3):
      • dishCount += 1
      • Immediately exit loop if dishCount is at or exceeds 65
    • if (numGuests is a multiple of 4):
      • dishCount += 1
      • Immediately exit loop if dishCount is at or exceeds 65
  • print("The number of guests is: " + str(numGuests))

 Asking if a given integer is a multiple of n is equivalent to asking if the said integer does not produce a remainder when divided by n. 

 Thus, we arrive at the following Python code:

 dishCount = 0  
numGuests = 1

 while (dishCount < 65):
    print("Current number of guests: " + str(numGuests) + ", current dishes served: " + str(dishCount))
   
    if (numGuests%2 == 0):
        dishCount += 1
        print("Current number of guests: " + str(numGuests) + ", dish of rice served.")
        if (dishCount >= 65):
            continue

     if (numGuests%3 == 0):
        dishCount += 1
        print("Current number of guests: " + str(numGuests) + ", dish of broth served.")
        if (dishCount >= 65):
            continue

     if (numGuests%4 == 0):
        dishCount += 1
        print("Current number of guests: " + str(numGuests) + ", dish of meat served.")
        if (dishCount >= 65):
            continue   

     numGuests += 1
print("The number of guests is: " + str(numGuests))

 The program prints 60:

Current number of guests: 1, current dishes served: 0                                                                          
Current number of guests: 2, current dishes served: 0                                                                          
Current number of guests: 2, dish of rice served.                                                                              
Current number of guests: 3, current dishes served: 1                                                                          
Current number of guests: 3, dish of broth served.                                                                             
Current number of guests: 4, current dishes served: 2                                                                          
Current number of guests: 4, dish of rice served.                                                                              
Current number of guests: 4, dish of meat served.                                                                              
Current number of guests: 5, current dishes served: 4                                                                          
Current number of guests: 6, current dishes served: 4                                                                          
Current number of guests: 6, dish of rice served.                                                                              
Current number of guests: 6, dish of broth served.                                                                             
Current number of guests: 7, current dishes served: 6                                                                          
Current number of guests: 8, current dishes served: 6                                                                          
Current number of guests: 8, dish of rice served.                                                                              
Current number of guests: 8, dish of meat served.                                                                              
Current number of guests: 9, current dishes served: 8                                                                          
Current number of guests: 9, dish of broth served.                                                                             
Current number of guests: 10, current dishes served: 9                                                                         
Current number of guests: 10, dish of rice served.                                                                             
Current number of guests: 11, current dishes served: 10                                                                        
Current number of guests: 12, current dishes served: 10                                                                        
Current number of guests: 12, dish of rice served.                                                                             
Current number of guests: 12, dish of broth served.                                                                            
Current number of guests: 12, dish of meat served.                                                                             
Current number of guests: 13, current dishes served: 13                                                                        
Current number of guests: 14, current dishes served: 13                                                                        
Current number of guests: 14, dish of rice served.                                                                             
Current number of guests: 15, current dishes served: 14                                                                        
Current number of guests: 15, dish of broth served.                                                                            
Current number of guests: 16, current dishes served: 15                                                                        
Current number of guests: 16, dish of rice served.                                                                             
Current number of guests: 16, dish of meat served.                                                                             
Current number of guests: 17, current dishes served: 17                                                                        
Current number of guests: 18, current dishes served: 17                                                                        
Current number of guests: 18, dish of rice served.                                                                             
Current number of guests: 18, dish of broth served.                   
Current number of guests: 19, current dishes served: 19                                                                        
Current number of guests: 20, current dishes served: 19                                                                        
Current number of guests: 20, dish of rice served.                                                                             
Current number of guests: 20, dish of meat served.                                                                             
Current number of guests: 21, current dishes served: 21                                                                        
Current number of guests: 21, dish of broth served.                                                                            
Current number of guests: 22, current dishes served: 22                                                                        
Current number of guests: 22, dish of rice served.                                                                             
Current number of guests: 23, current dishes served: 23                                                                        
Current number of guests: 24, current dishes served: 23                                                                        
Current number of guests: 24, dish of rice served.                                                                             
Current number of guests: 24, dish of broth served.                                                                            
Current number of guests: 24, dish of meat served.                                                                             
Current number of guests: 25, current dishes served: 26                                                                        
Current number of guests: 26, current dishes served: 26                                                                        
Current number of guests: 26, dish of rice served.                                                                             
Current number of guests: 27, current dishes served: 27                                                                        
Current number of guests: 27, dish of broth served.                                                                            
Current number of guests: 28, current dishes served: 28                                                                        
Current number of guests: 28, dish of rice served.                                                                             
Current number of guests: 28, dish of meat served.                                                                             
Current number of guests: 29, current dishes served: 30                                                                        
Current number of guests: 30, current dishes served: 30                                                                        
Current number of guests: 30, dish of rice served.                                                                             
Current number of guests: 30, dish of broth served.                                                                            
Current number of guests: 31, current dishes served: 32                                                                        
Current number of guests: 32, current dishes served: 32                                                                        
Current number of guests: 32, dish of rice served.                                                                             
Current number of guests: 32, dish of meat served.                                                                             
Current number of guests: 33, current dishes served: 34                                                                        
Current number of guests: 33, dish of broth served.
Current number of guests: 34, dish of rice served.                                                                             
Current number of guests: 35, current dishes served: 36                                                                        
Current number of guests: 36, current dishes served: 36                                                                        
Current number of guests: 36, dish of rice served.                                                                             
Current number of guests: 36, dish of broth served.                                                                            
Current number of guests: 36, dish of meat served.                                                                             
Current number of guests: 37, current dishes served: 39                                                                        
Current number of guests: 38, current dishes served: 39                                                                        
Current number of guests: 38, dish of rice served.                                                                             
Current number of guests: 39, current dishes served: 40                                                                        
Current number of guests: 39, dish of broth served.                                                                            
Current number of guests: 40, current dishes served: 41                                                                        
Current number of guests: 40, dish of rice served.                                                                             
Current number of guests: 40, dish of meat served.                                                                             
Current number of guests: 41, current dishes served: 43                                                                        
Current number of guests: 42, current dishes served: 43                                                                        
Current number of guests: 42, dish of rice served.                                                                             
Current number of guests: 42, dish of broth served.                                                                            
Current number of guests: 43, current dishes served: 45                                                                        
Current number of guests: 44, current dishes served: 45                                                                        
Current number of guests: 44, dish of rice served.                                                                             
Current number of guests: 44, dish of meat served.                                                                             
Current number of guests: 45, current dishes served: 47                                                                        
Current number of guests: 45, dish of broth served.                                                                            
Current number of guests: 46, current dishes served: 48                                                                        
Current number of guests: 46, dish of rice served.                                                                             
Current number of guests: 47, current dishes served: 49                                                                        
Current number of guests: 48, current dishes served: 49                                                                        
Current number of guests: 48, dish of rice served.                                                                             
Current number of guests: 48, dish of broth served.                                                                            
Current number of guests: 48, dish of meat served.                                                                             
Current number of guests: 49, current dishes served: 52                                                                        
Current number of guests: 50, current dishes served: 52                                                                        
Current number of guests: 50, dish of rice served.                                                                             
Current number of guests: 51, current dishes served: 53                      
Current number of guests: 51, dish of broth served.                                                                            
Current number of guests: 52, current dishes served: 54                                                                        
Current number of guests: 52, dish of rice served.                                                                             
Current number of guests: 52, dish of meat served.                                                                             
Current number of guests: 53, current dishes served: 56                                                                        
Current number of guests: 54, current dishes served: 56                                                                        
Current number of guests: 54, dish of rice served.                                                                             
Current number of guests: 54, dish of broth served.                                                                            
Current number of guests: 55, current dishes served: 58                                                                        
Current number of guests: 56, current dishes served: 58                                                                        
Current number of guests: 56, dish of rice served.                                                                             
Current number of guests: 56, dish of meat served.                                                                             
Current number of guests: 57, current dishes served: 60                                                                        
Current number of guests: 57, dish of broth served.                                                                            
Current number of guests: 58, current dishes served: 61                                                                        
Current number of guests: 58, dish of rice served.                                                                             
Current number of guests: 59, current dishes served: 62                                                                        
Current number of guests: 60, current dishes served: 62                                                                        
Current number of guests: 60, dish of rice served.                                                                             
Current number of guests: 60, dish of broth served.                                                                            
Current number of guests: 60, dish of meat served.                                                                             
The number of guests is: 60                                                  

      
I think I can whip out a formula at this point:

d/2 + d/3 + d/4 = 65
6d + 4d + 3d = 780
13d = 780
d = 60
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