Homework reading: Arbitrary and necessary (updated version)

I found this article to be a great source of inspiration and advice for my lesson plans. My SA gave me a lot of similar advice.

For the subject of Math, there is a lot of knowledge that is arbitrary, that is not regular in terms of what needs to be helped for students to memorize. For example, the author uses the example at the beginning of the book to give examples of naming shapes, defining units, units of measurement, etc. This information is unfamiliar to all students and needs to be told. The teacher's role then is to help students find ways to remember these meanings and content that work for them.

However, the "necessary" parts are the ones that students can work out by their own exploration and thinking (for some able students), and these parts do not rely on memorization/ or partial memorization, but more on understanding. For example, the author gives conversions of formulas, solving triangles, etc.

"Necessary" does not mean memorizing facts, but rather logically deducing or intrinsically understanding from some given mathematical property. It would be helpful if students could explore certain aspects by reasoning from what they already know. The sense of achievement of successful pushback will bring great interest in maths to students.

When I was in high school, there were some so-called "formulas" that I had to memorize. My teachers didn't tell us that we needed to memorise all of them, such as the Pythagorean theorem, which students need to memorise in order to solve triangles. However, if this formula is memorized as "arbitrary", it will be easily forgotten. I think this can be deepened by showing the derivation process of the theorem, which not only makes students remember the theorem more deeply but also consolidates other related mathematical knowledge.

(e.g. using this proof of the area of a triangle to derive it)

As stated in the text, a careful explanation will improve students' ability to use their prior knowledge and experience to understand why this "accepted fact" is correct. This will shift the way they think about learning maths from memorizing and reciting mathematical formulas and facts to possibly trying to understand why these formulas and facts are correct. This will help them in their future learning of maths and, because they can understand, their interest in learning maths will be greatly enhanced.

Giant Soup Can puzzle question

 

The information we can derive from the picture is:

The size of the Campbell's soup can (normal size).

The height of the bike in the photo.

Observe that the water tank is in the same proportion as the Campbell's soup can.

Speaking as a teacher, I think this question can be solved by firstly examining the dimensions of a standard Campbell's soup can. This may include its diameter and height.

After obtaining the dimensions of the soup can, use the information about the height of the bike in the photograph to determine the ratio between the soup can and the water tank. Apply the proportions to find the dimensions of the water tank.

Based on the cylindrical shape of the water tank, use the formula to calculate the volume of the water tank. I would then go on to assess whether the volume of the water tank is practical for firefighting purposes.

As a student, firstly I think I would have problems finding the proportions. However, I would ask my teacher for advice on how to find proportions and I realized that later on I might not quite know how to calculate the volume of a cylinder and I would seek help from my teacher.

Extension of this puzzle:

Calculate by estimating the volume of the calculated tank: how long does it take to fill a standard fire hose from the tank? Should the specification of the fire hose be considered? If the tank is used to extinguish a fire, is the time taken to empty the tank adequate for a typical fire?

Pro D reflection

I participated in the Introduction to SOGI in the K-12 Context workshop, Building Resilience, which I felt was important to me through my previous internship experience. My previous SA discussed this with me during my practicum. In the course of our daily work, we teachers have to face many students with 100% energy, care for them, and help them solve their problems. It is possible that this process will also face a lack of understanding from family members, friends, students, or their parents. All of these things can drain the energy of our teachers. In the long run, it is easy to lose our passion for our careers and our life. It is therefore important to learn how to de-stress and build resilience. The facilitator Michelle Lim introduced the sources of stress, what stress is, and how to deal with it. What struck me the most was that to build resilience we need to complete a stress circle. This requires physical activity, breathing, positive social interaction, laughter, affection, creative expression, and a big cry to complete. Especially for me, I am a very emotionally exposed person and many times my emotions need to be released with tears. Crying is a good process to release emotions, we can let go of our restraints and have a big cry to complete this last part of the circle.

Group teaching reflection

During the preparation of the lesson, because it was a lecture done together as a group, we had a lot of disagreements and discussions about what we chose to present and how we would present it. In the end, we finally discussed a common solution by combining the ideas of all three of us. We used demos in our classroom to generate interest and introduce the software to the group, which will help future students learn maths. Through everyone's feedback, I realized that I need to incorporate body language and eye contact more in future classes, it is easy to just look at the board or stare at the projector when explaining maths problems. Lastly, I also need to improve my ability to deal with when things happen in the classroom that are not at the time or situation I planned. For example, if our class is going faster than expected, how to add new and useful things or summarise the gaps in time better is something I need to prepare for. Overall, this group teaching experience not only allowed us to experience the ability to collaborate with our "colleagues" in the classroom but also to experience how to use the classroom's resources to enrich our own classroom.

Elliot Eisner, Three curricula all schools teach (updated version)

The first 'stop' that stopped me from thinking for a while is the sentence from the first paragraph "But schools teach much more---and much less---than they intend to teach."(p.87). I began to think about what it means to teach more and what it means to teach less. I think this is because there is a gradual increase in the number of courses involved in schools today, with school professors developing more and more courses, and a lot of social skills, time management, and life issues. And the ability to communicate with elders and peers. But what is less taught in schools is that, as mentioned in the article we read last week, the overly formal and rigid way of teaching can lead to a gradual loss of interest (especially for maths). There are also problems that students will encounter in life or later in life when they go out into the community, etc. that schools cannot cover completely.

Another stop for me came from the bit in the article about schools fostering submissive behavior. Before reading the article, the examples the author gave in the article, the so-called incentives, etc., had not occurred to me as a way of being a way of fostering submissive behavior. Suggestions or rules and regulations made by the school when implemented in this way become a way of fostering submissive behaviours. This kind of reward system is likely to make students lose interest in what they are doing and become overly concerned with rewards. In the long run, this may lead to a sense of "routine" in their future work. I think it is difficult to avoid using rewards while achieving the goal of regulating students' behavior and cultivating their interests, and schools can't avoid "asking" students to do something. The way I can think of to avoid this at the moment is to allow students to reward themselves, i.e. instead of setting a common "reward" each student writes down how they think they should be rewarded. They can then reward themselves when they have done it.

Due to the significant amount of time students spend in school, the habits developed during this period may continue to affect their future lives. In the past school education, I agree with the article that schools emphasized more interdisciplinary knowledge and proposed many aspects of "implicit curriculum". The reward system may weaken students' interest in learning, cultivate their increasing competitive awareness, and the arrangement of art classes may make students believe that subjects such as mathematics and science are more important. But nowadays, classrooms in BC schools are increasingly giving students the right to choose. The new British Columbia curriculum also places greater emphasis on communication, innovation, and other aspects.

October 20 - Pro-D day Conference

I will attend 

UBC Faculty of Education

Introduction to SOGI in the K-12 Context

Group teaching lesson plan

The lesson plan

The whole lesson plan

The handout

handout