Unit plan

 Math 9 Chp 4 polynomial

Homework reading for textbook

 From a teacher's perspective, the examples provided emphasize the role of examining how textbooks connect students to mathematics, their peers, teachers, and the world. At the same time, textbooks have a certain structure, and the form of language and images in textbooks influence students' mathematical understanding. Also, considering the students in the class, if there are ELL students in the class, then the textbook is a good resource for them to learn some specialized mathematical language. Teachers may use other words to explain specific definitions in order to make it easier for students to understand, so it is easier for students to associate those easy-to-understand words with specialized mathematical vocabulary.

From my own point of view as a student, I would not use the textbook too much, but it is a good resource for me to prepare and review. I would use the examples in the textbook to preview what we were going to learn and to review if I forgot them afterward. Through reading this article I have found that indeed when I see specific language in a textbook I will recall a specific situation that it introduces.

Perceptions of textbook use and role change:

Regardless of how updated textbooks are, textbooks are a resource that can be referred to for maths learning. Textbooks are constantly evolving, the applications to the real world may change, the variety of examples may change, and there will be plenty of additional information and hands-on activities afterwards. What I have learned through my short practicum is that my SA will choose examples from different versions of textbooks to present through knowledge of the students' classes. I also think that textbooks are a resource for us and we can use them flexibly.

“Flow”

 I have experienced such a state of "flow", and I believe that for me, it is the combined action of environment, inner drive, interest, and focus that drives me to reach this state. I have reached such a state in my mathematics studies. The last time was when I was completing my university math game theory assignment. I really enjoy this class and I really like my professor. I also know that as long as I spend time researching the problem, I can definitely solve it. During the process of researching the topic, I greatly enjoyed the process of trial and error and solving the answer.

I think it is possible to achieve such a state in high school mathematics classes. As teachers, we need to help students build mathematical confidence, so that they are not afraid of difficulties, enjoy the feeling of solving problems, and cultivate a comfortable learning environment, so that students feel at ease and can ask questions at any time without being disturbed. This requires a lot of classroom management skills. As future teachers, the most important thing is to create an environment for each other, which is not only between students but also between students and teachers.

Dave Hewitt & mathematical awareness

 

The first "stop" comes from the joke Hewwit shows at the beginning and the question he raises. For many students, they only know very similar problems that they've been taught, even if they don't know them under a different name. This means that, in the teaching of mathematics, many students do not understand the logic of learning but rather memorize. How to get students out of the mode of teaching maths as rote learning and develop more ways of thinking is something that we new teachers need to reflect on.

My second "stop" is that Hewwit gave more examples of 2+3. How do you think Hewitt developed the 2+3? I was very inspired by this, and in my short-practicum my SA also talked about the need for teachers to be flexible and use a variety of examples in their lectures to help students understand the content. This is a skill I should develop.

I also realized that in the videos we watched in class, the point that inspired me was that we shouldn't just leave the maths classroom to books and paper and pencil, we can use the environment to engage the students and get them involved.

When developing the fraction problems, I think Hewwit developed them step-by-step according to the difficulty of the problem, starting with answering the question for specific numbers, moving on to more general answers, and finally getting to the mathematical laws. It is important to develop mathematical problems step by step, with simple thinking to further think of deeper and more mathematical problems that will exercise the students' mathematical thinking.

Based on these two videos I feel that in my teaching I should be more interactive with my students, where they can start to think actively, exercise their sense of mathematical thinking, and understand how mathematical knowledge works in concrete terms.

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?