Elliot Eisner and The Three Curricula

Two or three 'stops' you have in this article

1. "One of the first things a student learns - and the lesson is taught throughout his or her school career - is to provide the teacher with what the teacher wants or expects."
This quote reminded me of the reading about grades for our inquiry class. By telling students what is going to be on the test, we are conditioning them to pay attention to these topics and revisit them later when studying. This type of school culture is persistent throughout an entire lifetime. Children try to find out what they parents want and expect, they then try to give their teachers what they are looking for and often ask other students or former students such as older siblings what that particular teacher's tests are like and what they need to do in order to get a certain grade. As the reading points out, students spend an awful lot of their lives in school exposed to this culture and it continues throughout their lives. Whether they go on to post secondary and try to do the assignments so as to please the professor or if they go into the workforce and do whatever is necessary to please their boss and maintain their employment. Students are stuck in this very survivalist culture of trying to make it to the next course with a particular grade, or trying to get into university.

2. Implicit Curriculum
One thing that really stood out to me was the message that is conveyed immediately to the students by the physical set up of the classroom. If the desks are separate and in neat rows, the students know that it is an individualized learning environment with little opportunities to talk with others. On the other hand, if the desks are grouped together, students know to expect more group work and collaboration. This was less surprising to me than how the scheduling of classes affects how the subject is seen by a student. While I was in high school, our blocks were rotated throughout the year so that each subject was experienced at different times of the days. It was different in elementary school where art was typically reserved for afternoons. Many times while I volunteered at a kindergarten class the students were working on art or play in the afternoons while they had reading and math lessons in the mornings. This type of scheduling definitely contributed to the status of art and reading in the classroom. When a lesson was not finished on time, the math class or reading class would carry into the art class cutting it short. Certain students were unable to begin their artwork until after they completed their math/reading assignments. However, if an art activity was not finished it was seen as acceptable to just leave it for another day or the student could finish if they were able to complete the math/reading activity early. I was surprised that none of the students questioned why the math/reading was prioritized over art. Sure they were disappointed and complained but they never argued that art was as important as math/reading. It is amazing how early these subtle messages take affect.

3. Null Curriculum
As a high school student I always wondered how the duration of the subjects was determined (e.g why we needed 5 years of ELA, 4 years of math, and no mandatory art/music/dance/film studies etc.). What was so special about ELA, math and science and so dispensable about art and music?Having this conveys the message that ELA and math and science are superior subjects to art and music. Only students who are interested in pursuing art or music will immerse themselves in those subjects or enroll in special programs so as to get into a post secondary program for these areas. However, this implies that students other students will not benefit from having these types of experiences or classes throughout their schooling. Likewise, students entering art or music programs will see no need for math and science and determine it as a hurdle to jump over rather than something that could assist their studies and improve their learning. 

Another aspect of the null curriculum that struck me was the omission of certain topics within a subject. For example, conics was a section that was taken out of the curriculum while I was in high school yet it was something I encountered during my university studies. Why was this topic removed and what was put in its place (if anything)? What about conics did the curriculum decision makers feel was so unimportant that it was removed entirely?

Ways that this might expand our ideas about what is meant by 'curriculum'. How does the mandated BC Provincial Curriculum connect with Eisner's ideas?

Before this reading I equated curriculum with the explicit curriculum but I realize there is much more to curriculum then simply a list of requirements. Curriculum also encompasses what is left out, how the material is presented and how the environment is set up for the students among other things.

BC is helping to connect with Eisner's ideas by providing more opportunities for other types processes for students such as increasing collaboration, increasing ways of knowing such as Indigenous ways of knowing, using different modes of instruction, different modes of assessing. 
It also focuses on decreasing the null curriculum by adding financial literacy to the math curriculum. Students will leave high school with some basic understanding of finance such as knowing how they will be taxed and how to calculate their hours when completing a time sheet.

Curricular Micro Teaching Reflection

The lesson went better than expected. It was a good experience because we had a little set back and had to do some last minute adjustments. We had planned a fun, hands-on activity that would require the students to assemble a 3D object from a net so that they could see how the net is connected to the 3D object. Unfortunately the nets were left behind and we were unable to bring this activity to the students. We had to adjust our plans before going into the presentation by having the students draw out the nets by looking at the 3D object. In addition, we had planned an extra activity for showcasing different nets of the same object and showing what a correct net looks like compared to an incorrect net. This activity was planned to be supplemental in case we had extra time left over after our planned lesson. Although this activity worked out decently well I think letting the students physically hold and try to fold a net would be a better way for them to experience and understand how the nets are related to the object and why some nets do not work. It was a little difficult to figure out how loud to be during the lesson because of the other lesson going on, however I noticed that while teaching the lesson I completely forgot about the other group presenting and was entirely focused on communicating to my "students" and paying attention to my team mates so that we could effectively deliver our lesson and segue well so that the lesson felt cohesive. My main takeaway from this lesson was the importance of preparation. It is a good idea to have a plan for the lesson, have activities/experiences lined up, have extensions in case the lesson goes faster than anticipated and to be prepared to change the plan in case something happens.

Group Micro Teaching Feedback

Curricular Micro Teaching

Geometric Puzzle

What process did you use to work on and solve this puzzle?
This puzzle came a lot more naturally to me than the other before. Since there are an even number of points, each point would line up with another on the other side. Knowing this, I found the angle each segment would be and found that from the first point (1) to 7 is 84 degrees. Since we want the point exactly opposite, this point would be 180 degrees from 7. Doing some simple math I found the answer to be 22. I drew a picture to confirm my answer but it was not executed well (my compass broke) and it was difficult to follow the lines to their counterparts. If the circle had been perfectly drawn, it would have been easier to see. Also, if the number of points was smaller, say 6, one could easily find the diametric by simply tracing the lines back to the number.

Could you create other extended puzzles related to this one -- some possible, some impossible?  (Is there any value to giving your students impossible puzzles?)
This problem could easily be turned impossible by making the number of equally spaced points an odd number. Along the lines of geometry, you could present some ancient problems to students such as cube duplication and angle trisection. After students have struggled for a bit, you can tell them how there is no answer and people have worked for years and still have not been able to find a solution. I think there is some value in this because students become discouraged when they cannot figure out the answer. Learning that many mathematicians were unable to find solutions to these problems could be reassuring that just because an answer cannot be found, does not mean you cannot do math. Furthermore, I would bring up the Millennium Prize Problems and other unsolved problems in mathematics. Having some problems that are possible will also be worth exploring in class. In terms of geometry, I would try to bring in some other cultures geometric problems to get students practicing math while also learning some history. For example, bringing problems about volume of irregular shapes, approximations of pi and the Pythagorean Theorem from Ancient Babylonia, Ancient China and Ancient Indian.

What makes a puzzle truly geometric rather than simply logical?
This problem is purely geometrical because one does not need to do any computation. Knowing the properties of a circle and being able to see is a way to solve it. Once the diagram is set up, all one has to do is trace the line from 7 through the center and to the other side which will end up at 22. Problems were students do not need to compute and set up equations and do algebra to solve a problem, helps make it geometric. Although the problems could be solved logically, that is not the only way and typically the geometric way is easier.

Battleground Schools

1. Progressive Reform (1910 - 1940)
I was very surprised to learn that experimentation and inquiry based learning in math is not a new idea but rather a very old one. The idea was brought about by questioning and analyzing the education system and trying to improve it, similar to what has happened in the last few years in BC. This made me wonder how much the curriculum will change throughout my career and the impact I can have on its changing. If there are serious issues students are having with the curriculum, it should be revised in order to help the students. I worry that we will repeat the mistakes of the pass by not implementing the new curriculum and new ideas in all schools because teachers are more comfortable with their older systems and fixed viewpoints.

2. Attitudes toward math are contagious
Reading this part of the article I was reminded of how important a teacher's disposition is to the students. If a teacher does not like their subject or area in the curriculum it will have a negative impact on the students who might already have negative feelings towards that subject. Teachers should also be careful with how they discuss other subjects with their students. If students see teachers talking bad about other subjects, how can we expect them to come into that classroom with an open mind? I also think that math in particular has a bad reputation. Many students feel that math is something you are good at or you're not. Because of how math has been portrayed in the media, past experiences and friends/family experiences, it is almost cool to dislike math more that other subjects such as music or English.

3. The impact a test (TIMSS) had on the math wars in the US
I understand that a country would feel some disappointment in scoring low compared to other countries, however we must inquire why the scoring is what it is. Although it is natural to want to copy what the top ranked country is doing for their education system and pedagogical approaches, it is not that simple. The test does not account for the class size, which schools were selected to participate in the test, cultural differences in the attitudes towards schools, classroom demographics, and even the mental states of the students while they were taking the test are just a few things to consider when arguing for reformation. Yes we can learn a lot from other countries and the techniques they use in their classrooms, but we cannot simply copy them and expect the same result.

The Dishes Problem

Solution:
The dishes problem was a bit easier than I initially thought it would be. After rereading the problem and taking a few moments to think about it, I came to the conclusion that the number of guests must be a common multiple of 2, 3 and 4. I then started listing out the multiples for each and made another list containing the common multiples.

Common Multiples: 12, 24, 36, 48, 60

Using this list, I added the divisors to see if they would add up to 65. After a few tries, I found that 60 was the magic number.

(60/2) + (60/3) + (60/4) = 30 + 20 + 15 = 65

Therefore, there were 60 guests at this dinner.

Whether it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)
I think the selection of puzzles and histories does make a difference to our students. By showing students that math was done by all kinds of civilizations during all time periods and all cultures will help to broaden their minds that math is not just for old white men. I do not want to discredit what these men discovered, but I would like the students to see that they were not the only ones coming up with amazing math. For me, I always became much more interested in a topic/subject when I discovered that there were ties to my culture. I felt like I could relate to it better and I had a deep sense of pride knowing the people of my culture were able to do such wonderful things. At the same time, I was liked to learn from diverse cultures too. Many times I was surprised at how similar they are to mine at time while also learning about the differences. 

Whether the word problem/ puzzle story matters or makes a difference to our enjoyment of solving it?
The context/story make a large difference to me when solving a problem. One of the issues I had with this problem was the context. It made absolutely no sense to me how the official and the cook did not know the number of guests. Did the official not sign off on the guest list? How was the cook able to prepare enough food without knowing the number of people eating? I also wanted to know what type of gathering this was. Was it a celebration, and if so what were the people celebrating? What was life like in 4th century CE China? Knowing more about the story of the problem would have made it more enjoyable for me because I would be able to think of each of the 60 people in this problem as a real person who lived in China during the 4th century rather than just an answer to puzzle.

Micro Teaching Reflection

The planning process was interesting for me since I have been playing this game since I have been playing it for so long with other people who know the game well. I had to really stop and think about how to break down the rules and points system as well as explain the card values and suits to people who were not familiar with Italian card deck. It was difficult to estimate times for these explanations since I wasn't sure what people would find more confusing.

During the lesson I realized I should have left my lesson plan out to reference during the lesson. I was so preoccupied by making sure my group knew the values of the cards and would get a chance to play I completely forgot to state that the objective was for them. Taking that few seconds in the beginning to explain what I was going to present and what they should be able to by the end of the lesson would have been beneficial to my group so that they could know what to pay attention to during the lesson. I also found it difficult to juggle my attention between explaining the object of the game and how to play with how much time was left in class. I wanted to give as much time as possible to playing the game so I skipped giving multiple examples to give the group a chance to play a game with everyone's cards exposed so that they could have more time to play. In hindsight, doing more examples might have been better and made the game play a little easier for them. I also should have written out the rules and points for the group to reference while playing to make it easier for them to do strategic plays.

Micro Teaching Lesson Plan