Hewitt Arbitrary vs Necessary

 After reading this article, issues that I ran into during my practicum were voiced. I was tasked with teaching the equations of lines, but ran into difficulties quickly. I thought that I would have been able to just share my knowledge with my students. However, I ran into needing to know a bunch of different forms of the lines. For example, I needed to teach that "General Form of a line is 0 = Ax +By +C where A B C are all integers and A is non-negative."

I marked tests and found that many students did not exactly follow these rules, and felt bad that I had to take marks away for these mistakes. I am happy that I now know that these rules were arbitrary, and this exemplifies why there was so much friction between me and this issue.

The most annoying aspect of this experience is that students were so busy learning these arbitrary rules, that they did not understand the necessary concepts of lines being a relationship between x and y. Students would remove x and y just in order to make the equation look more like General Form.

When I teach my classes, I am going to focus on necessary knowledge and prioritize it. After students understand necessary concepts, I will teach them the arbitrary rules.

Oct 20 Pro-D Day

Last Friday I attended the BCMAT conference in Surrey and it was an amazing experience.

My first session was about a teaching style called argumentative thinking. Using this routine, students are pushed to argue their thoughts in front of the class. I like this routine because it promotes the competency of explaining ideas through mathematical language.

My second session was about Group Quizzes. This idea aligned well with my ideas of how teaching should be done. We have been taught that students learn well from each other, and when group quizzes are used they can supplement each other's knowledge. The only downside is that assessment becomes complicated because you are not assessing the individual. I think that a classroom breakdown should be group work at the start, then individual work to be assessed on afterwards.

My final class was about culturally relevant material. Unfortunately, this session did not teach what I was expecting from the summary. It did talk about the idea of a warm demander, which happens to be an idea that I had already researched myself individually. 

The best thing that I took away from this conference was the interactions I had with other teachers. I did not feel like a lesser person there. I asked questions that were relevant and did not stick out. My confidence increased drastically after this conference, which is perfect for the start of my short practicum.

What is curriculum

 Before this article, my definition of curriculum was confined to the explicit curriculum. This article has expanded my view on things, and connected ideas from many of my other classes.

These new definitions of curriculum were something of which I had a comprehension, but never such an articulate understanding. We have learned about the historical and societal role that school has had on our world. Many have argued that as a social institution, schools reinforce standards that reinforce society. A society of artists would prioritize art. A society of dystopian oppression would prioritize those that sat still and kept quite. A society of of invention would prioritize innovation. These hypothetical societies are examples of the three types of curriculum, and how each can be used to shape the society's members; Explicit, Null, and Implicit.

By explicitly stating curriculum, students are forced to choose between a handful of futures. I have learned that the majority of electives offered by many rural BC communities are trades. This rural society has determined that trades are important, so trades are offered.

Null curriculum is where I think things become interesting. In the above example, by not offering a fine arts degree these communities steal that potential future from their youth. It's unfortunate that there are finite resources to provide programming. I like to imagine all the potential societies that could exist if no knowledge was off limits to students.

Implicit curriculum made me think of all the little things that need to be taught to citizens in order to have a functioning society. In this category of curriculum would be molding of their personality. We now live in a world where everything is so connected and optimized that we could not exist without punctuality. What I like most about implicit curriculum is that this is where I will have the most agency to teach students. I think that collaborative problem solving is an important skill, so I will set my classroom up to implicitly teach this.

I think that BC's shift from content to competencies also indicates their shift in priorities from explicit curriculum to implicit. The soft skills that we teach are often so much more important later in a students career, and I am excited to work under a government body that understands this.

Cambell's Can

 This was my work estimating the volume of the can as well as it's effectiveness for fighting fires. I could not find the water required to fight a fire, but was able to estimate how long the water would last in a fire fight.

I also wrote a question that I remember thinking of years ago while camping in Squamish.

Micro-Teaching: Estimating Percents

I am so content with how this lesson worked out. I feel like we improvised a lot, but did it in a very professional way. It was strange to me, that some members of my group were unhappy with how much improvisation we did. This is strange to me, for I feel that all of teaching should be more improvisation than structured lectures. My strategy has been to learn the material enough that I can just talk about it with those in front of me, and I feel that it has been paying off.

Lesson Plan

 EDCP 342 Coteaching Lesson Plan

 

Subject: Estimating Percentages

Grade: 8

Date: Oct 16, 2023

Duration:  20 minutes

 

Curricular Competencies   https://curriculum.gov.bc.ca/curriculum	Estimating reasonably Using multiple strategies to solve problems Communicate mathematical relations
Big Ideas	The principles and process underlying operations with numbers apply equally to algebraic situations and can be described and analyzed Similar shapes have proportional relationships that can be described, measured, and compared

Core Competencies

Critical/Reflective Thinking: Using logic and reasoning to evaluate thinking Communication: Knowledge, skills, processes and depositions we require to interact with others Personal awareness and Responsibility: Understanding our strengths and catering to them

Materials and Equipment Needed for this Lesson

Markers for whiteboard

  

Lesson Stages	Learning Activities	Time Allotted
Warm-up	Assess understanding and connect to their previous knowledge of percentages by giving an easy “fraction to percentage question” Ex: 5/20 -> 25% Present this warm-up as review (because we did this last class) Present hard fraction as an intro to this lesson: 27/43 -> 62.79%	4-5 mins
Middle	Evan- multiply both top and bottom by a number to get the denominator as close to 100 as possible	3-4 mins
	Jessica- add or remove some amount from the numerator until the fraction is simple and can be simplified	3-4 mins
	Jacky- Use a calculator  *Con is when stuff is simple*	1-2 mins
Recap	Discuss pros and cons of strategies and which they prefer. In what situations will some estimates be better or worse? Encourage them to make up their own strategy All of class has to tackle 27/43 -> 62.79%	6-8 minute

 

Assessment/Evaluation of Students’ Learning

Exit Slip: What makes an estimation a good estimation? How would you judge the “goodness” of an estimation method

Was Pythagorous Chinese

By framing a knowledge as your own, it creates a perceived superiority over others. During the cold war, the ability for the USSR to put a satellite into orbit did not rouse cheers from the Americans, but despair. Cultures often compete with each other over which is more advanced, and this is often measured by which has the greater academic knowledge. We are now living in a global culture, which means that there should be collaboration, not competition, between nations. If we continue the false narrative that knowledge was only developed by "our" culture, then we lose the ability to work together. In competition there is no sharing of resources between sides. If our global culture is to overcome the challenges faced in the upcoming years, we must work together and recognize that all cultures have knowledge to bring to the table.

I am torn about the naming conventions of certain theorems. On one hand, I recognize that calling it "Pythagorean Theorem" emphasizes a the competitive approach to knowledge I mentioned above. However, I do believe that if it is taught with the emphasis that it was not only discovered in western society we can acknowledge that a name is only a name. Many cultures have discovered the concept of a chair, and thus many cultures have different words/names for the concept. It would be problematic if western students were taught that only their culture were smart enough to invent chairs and that is why they call it chairs. Hence, calling it Pythagorean is not a problem as long as the concept is introduced through an international lens.