Micro Teaching Lesson Plan

Lesson: How to fold shuriken (throwing stars)

Objective:  Students will be able to fold a throwing star from a sheet of paper

Practical details: 10 minute lesson, 4 students

Materials needed: one sheet of paper for each person (I will bring an extra sheet for everyone in case they finish early and want to make another); 10 sheets total

Structure:
Introduction (1 minute):
Gauge prior experience with origami and ask if anyone has made a throwing star before (if most of them have, ask about if they have made cranes.  Whichever has more people learning something is the one we will do)
Pass around papers

Instruction (5 minutes):
Lead the students through the origami folding process.   
The first step (tearing the paper in half) is precarious so they need to make sure to crease it very well
Step two: fold one of the halves in half both ways (note we generally keep the color on the outside)
Step three: fold one side up at the half and the other down (note that you need to remember which side you have folded up and which you have folded down) to make a Z-like shape
Step four: repeat steps 2 and 3 with the other half paper, but this time we need to fold the sides in the opposite direction (will make sense with a demo)
Step five: place them back to back in a cross shape such that the sides with openings are facing out (will make sense with a demo)
Step six: fold in the end triangles (it can be a bit finicky) and we are done!

Practice + Closing (~4 minutes):
In this time, students can make a second shuriken with the backup paper (to test if they can do it on their own).  They can also (if there is space in the room) try to throw them.
If there is excess time, students will be asked if they know how shuriken were used, if they think this is the only shape they came in, what they are typically made out of.
If instruction runs over, this section can be dropped

Note: if we end up making cranes instead, the instructions take longer so it will likely fill the ten minutes more fully.  Should there be excess time there, we can talk about how cranes are a symbol of peace and hope due to an atomic bomb survivor who folded 1000 cranes to make a wish for health.
 

Math Art Write Up (Individual)

This project was very interesting to me.  I have done a lot of origami growing up and I find the way that we can twist one single sheet of paper into so many shapes to be fascinating.  I have made the icosahedron that we made in class before by myself in high school, but the artwork by Neel Shrestha caught my eye because although it was a similar shape, I couldn't quite figure out how it all attached.

After we had selected the piece, I told my group that I would help them learn how to make it since I had the most experience with origami and I found Neel's instructions online of how he created it.  I haven't done anything complicated with origami in years so figuring out what each part of the instructions meant was a little satisfying puzzle.  In particular, there was a part where we had to use creases to "twist" two triangles shut which was immensely gratifying to have click into place.  This piece also quickly showcased the math built into origami- the first step was folding a square into an equilateral triangle which was super cool.

Figuring out that first piece took me over half an hour and while we were making the rest of them as a group, we realized quickly that there would be no way that we could teach the class how to make that particular piece in five minutes because the base unit was too difficult for a beginner.  This was obvious from the fact that it took me several minutes to help Doreen and Yikang with their first pieces, and that was a two on one instruction ratio.  Based on this restriction, we decided to go with showing the class the Sonobe unit, which has a much simpler folding process.

Doing the demonstration for the class taught me a few things very quickly.  For one, using descriptive language is very important and will help everyone keep on the right track.  I hadn't fully thought through the fact that students wouldn't be able to simultaneously look at my paper and their own, so coming up with analogies such as the double doors or precisely describing which point on the paper we were folding from and to was key.  In addition, emphasizing points where it would be easy to go wrong was important.  The thing about teaching origami is that every step is important and needs to be executed with a fair amount of precision in order for the whole piece to fit together.  I can see how this could be a problem with classes that aren't listening as closely.

I really wish that we had been able to have a bit more time for the demo so that we could've asked the class to start playing around with the pieces that they made and see what they could create.  The Sonobe units can also be put together in structures of 3, 6, and 12 before you need the 30 to make our icosahedron.  It would've been very interesting to see if they could've made them and I think that this would be an awesome exercise to do with actual classes as well.  It gets them thinking about geometry, but in a way that's almost like playing with legos.

Overall, I think that making this art piece and doing origami in general is a fun (and cheap!) way to get students thinking about geometry.  You can scale the difficulty of what you're doing to ensure that everyone is capable of contributing.  I believe that this would be a fun activity to do in the first couple of days of class, where you end up with an icosahedron with everyone's names on it.  It creates a sense of community and reaffirms that everyone is one part of the whole class, as well as creating a memento for you as a teacher to remember your class by.

Math Art Write Up (Group)

Group: Doreen, Minami, Yikang
Original Artwork: Neel Shrestha - Origami Snub Dodecahedron

Remake & Issues:
We aimed for a complete replica, but with more colors to better demonstrate the number of shapes required to enclose the volume. One major issue in our process appeared on our first few attempts at assembly, the dodecahedron required a very specific orientation of each piece, where mirrored or chiral pieces would not fit in. In the end we realized all pieces require the same orientation, and remade several to complete the assembly.  Below are pictures of the two mirrored pieces.

One interesting aspect of making this structure was seeing how the 2D papers linked together to form the final 3D structure. The folds we made needed to be precise and creased thoroughly, otherwise the locations of connection wouldn’t align with each other perfectly. You can see this in the pictures below. With just two pieces, the origami still lies relatively flat. When we begin to link them all together, it introduces the curve that we see.

 

 

Alterations:
After the snub dodecahedron was finished, we realized that this piece would be too difficult for the class to make, both in individual making and the assembly stages. So we decided to use another polygon as the class activity topic for demonstration. During planning phases, we believed that adding names to everyone’s own pieces would be a nice addition to encourage group work spirit, so it was added to the plan.
This second structure that we made was an icosahedron, which was an interesting counterpoint to the dodecahedron that we had previously made, since their faces and vertices were swapped. Additionally, it had faces that rose up in pyramids as opposed to being empty space like the snub dodecahedron. Below is an example of the icosahedron we made. Another interesting observation about this second creation was that it was structurally quite sound. This is actually common for origami, but it can be strange to think that all of these pieces of paper interlock to form a ball that can be handled more roughly.

 

Interactive Activity:
We decided to use our interactive activity as our alterations to show the class what they might be able to do with their own classes in the future. This included a walkthrough of how to fold the basic piece of a Sonobe unit, as well as a little exposition on how they might talk to their class about playing with origami. When designing the activity, we tried to make sure that it would be fun and accessible to both beginners and experts, as well as creating a sense of community by contributing a small part to end up with one cool structure. If we had more time, it would have been nice to give the class a chance to try and explore to put some structures together themselves.
 

The Locker Problem Notes

 

Sorry, not sure how clear this picture will come out.  Essentially, I started with the facts given to me and tried to reason with the first few lockers about if they would be open or closed.  That led me to thinking about how primes would be open.  Then I started thinking about primes being primes because of their factors and realized that even factor having numbers would be open.  So I tried to think of what would have an odd number of factors and realized it would actually only be the perfect squares.

 

My Favorite and Least Favorite Math Teachers

 Among my favorite math teachers must be Ms. W, Prof H, and Prof A.  Ms. W's class I enjoyed because she worked really hard to make the class fun.  It was my senior year of high school and so she treated us as adults, but she also worked games into her class framework.  It was a class that I could say without a doubt that I wanted to attend every day.  Prof H and Prof A, whom I also liked just from their personalities, pushed us harder in class.  They were the profs who gave us all the pieces and asked us to put it together ourselves in class, which was difficult but ultimately I felt like I had a much better handle on the material because of the practical experience in class.  

On the other side of the spectrum, my least favorite math teachers all share one quality— solely lecturing without interaction with the class.  I find that listening to a lecture for an hour or more gets extremely tiring and I lose focus.  I don't learn the material very well nor do I end up finding it interesting.  This is absolutely something that influences me as I teach and I try to educate in a way that is more engaging than a straight up lecture.

Three Curricula

What Eisner says early on in the reading about schools offering more than simply class material brings to mind something I learned in my EDUC 401 class last year.  In that class, we discussed three different instances of students who were not necessarily acting like "good students" in that they often did not follow school rules nor did they do much work in class.  However, we were given context to their situations and in multiple cases, we rationalized as a class that those students were actually acting in ways that would give them the skills they might need for the future (e.g. social relationship building).

Something else this reading brought up for me was the discussion of implicit curricula, which teaches the values that the society values.  I've attended school in both the US and Japan, but they're very different.  For example, in Japan, the teachers move between classroom as opposed to the students.  The students are also expected to help serve lunches as well as clean up the classroom every day.  Culturally, doing things for the community is important in Japan and those values are reflected in what students are expected to do.  On the other hand, a more extreme example of parents/community getting involved in the US can be seen in legislature such as the bills to try to put the Ten Commandments into every classroom or the bills that try to ban schools from mentioning LGBTQ+ matters.

The explicit curricula that Eisner mentioned is most prominently connected to the BC curriculum through the content learning standards and the big ideas.  However, I do think that BC is trying to address the implicit curriculum and some of the values that we are teaching students through their curriculum by including the curricular competencies and the core competencies, which focus much more on what students are expected to do.  As for the null curriculum, there are some things that were previously ignored that are now trying to be incorporated (such as First Nations perspectives), but I have heard from current math teachers that actually managing to include First Nations perspectives in their lessons without it feeling cheap is quite difficult. 

Relational & Instrumental Understanding

    When Skemp defined the two different kinds of understanding, there was an instant connection in my mind to how I've approached mathematics over the years.  When I'm learning, I quickly gain instrumental understanding, but in order to feel good about the subject I need to reach relational understanding.  I find that one of the best ways to do this is to try to explain it to someone else- thus my tutoring over the years has pushed my relational understanding.  Skemp's descriptions of potential mismatches between students and teachers also caught my eye- although in high school, all my teachers looked for was instrumental understanding, university finals caught me off guard with questions that pushed beyond exactly what we had been taught and it forced me into relational understanding if I wanted to succeed.  One last thing that arose for me during reading was about the BC curriculum.  Although I don't know too much about it yet, I believe that a teacher I worked with last semester mentioned that they had switched from having content expectations to having "curricular competencies" where they are able to do all sorts of things like explaining and reasoning as opposed to knowing specific content.  However, she also mentioned that this made it a bit of a struggle, since the content is so closely tied to the competencies.

    Overall, I agree with Skemp that relational understanding serves us better.  Understanding the material instead of simply regurgitating rules not only helps making connections within math class, but also might help students think about math out in their own lives and to be able to apply lessons they've learned.  Many students don't continue in math past high school, but it can still help them adapt to whatever is happening in their lives.  While a certain level of instrumental understanding makes math speedy, relational understanding gives a much more complete picture.