Assignment, due Monday, 2/14/22: Read the following 3-page excerpt from the introduction of Wu’s text. In it, he is speaking directly to you, pre-service teachers who are working through the secondary school math curriculum. Respond to the questions below by leaving a comment on this post.
- What do you think is the main purpose of the reading?
- What is a quote that stood out for you in the reading? Explain.
- Emotional self-awareness: Name an emotion you felt while you were reading the text. Describe what triggered that emotion. Do you think that emotion was useful? Why?
- Extra Credit. Respond in some way to one of your fellow students’ comments. Do you agree? Disagree? Did their comments make you think or provoke additional questions? Reminder: Be respectful, be kind.
1. What do you think is the main purpose of the reading?
Wu suggests that preservice teachers can learn k-12 math materials 100% if they study three volumes of his while other textbooks can give them only 90%.
Pre-service teachers should study his three books from different perspectives.
The importance of teaching theorem is to ‘know’ first and how to explain to students.
2. What is a quote that stood out for you in the reading? Explain.
The quote that stood out to me was ‘Rather, to know a theorem, for instance, means know the statement by heart, know its proof, know why it is worth knowing, know what its potential implications are, and finally, know how to apply it in new situations.’
This statement includes how math teachers should teach theorem to students. Explaining how to use the theorem will give students more understanding and hopefully they can discover possible applications to certain situations on their own.
3. Emotional self-awareness: Name an emotion you felt while you were reading the text. Describe what triggered that emotion. Do you think that emotion was useful? Why?
‘Confident’
The more I learn about his arguments, the more confidence I get from the relief for how to teach math to students. He explains why and how his textbooks are helpful for preservice teachers. It seems that every mathematical core content for k-12 math is in his books and I feel that I can teach students better after I read his books. (even though I didn’t read a word from his books yet)
Confidence in math education takes away some of my concerns for how to teach math in the classroom. I always get anxious when I picture myself being in the classroom. because I don’t feel I am ready to teach them. However, I know this course will prepare me to be a better preservice teacher!
Hi, Ihn. Here is Charlotte. I quite agree with you that when a teacher teaches a mathematical theorem, he should explain how to use it. I think teachers should try to explain this theorem in different ways when they meet different students because different students have different understanding levels, so I strongly agree that teachers should try different expressions when explaining mathematical theorems! I love the confidence you have in your future studies. I should learn like you get more confidence in what we should learn in the future. Like you say in this class we have many good learning materials.
The main purpose of this article is to convey to us that most textbooks are more or less created for teachers than for students. “ Ask yourself whether a mathematics teacher whose lessons are correct only 90% of the time should be considered a good teacher. To be blunt, such a teacher would be a near disaster.
“This sentence makes me feel a little” excessive “.Of course, I agree that a teacher should fully understand his teaching content when teaching, but people are not perfect. It is very unfair to think that a teacher is a bad teacher because he can’t teach perfectly.
I like the proof of the Pythagorean theorem mentioned in the article very much. It involves the contents of Chapter 5 and Chapter 4 at the same time. As a teacher, we should learn to contact the relationship between them and show them to students.
When I look at textbooks as a student, I seldom thought about problems by linking different chapters together. After reading this article, I think I should learn to look at problems from the “teacher’s point of view”, write different mathematical definitions together, and try to understand them together. In the application of mathematical theorems in our real world, many theorems are usually used together instead of one by one.
Before I didn’t understand why the teacher had to prove the formula written in the book. I don’t think it’s useful. But now, after I have been exposed to a lot of mathematics, I begin to understand that the process of proving a mathematical formula and theorem is a very important process. The process of proving can help me better understand the relationship between formulas and principles and how they work. When I encounter examples, I can have a more intuitive idea and understand the “internal structure” of a topic.
Finally, I want to say that after reading this article, I began to feel pressure about the process of learning mathematics in the future. Because I began to understand that the study of mathematics is not only to do the right questions but also to understand the inner nature of the questions. I found that I still have 99% of the “content” to explore. I feel pressure and expectation!
Every time the math teacher proved the theorem, I didn’t like it. I didn’t see the point. Also, my study in mechanical engineering supported my habit of skipping the proof because engineers use the results, not the process. So I was in the same position as you, however, I am realizing the importance of proof more and more as I study higher math.
1. I think the main purpose of the reading was that as teachers, we should memorize all theorems and definitions in a textbook by heart, so we can teach our students. It is essential that we know reasoning behind theorems, to be able to answer any students questions and teach them our discoveries in appropriate mathematical terms.
2. A quote that stood out to me in the reading was ” these volumes are essentially school textbooks written for teachers, and as such, you should read them with the eyes of a school student.” The author is emphasizing that textbooks are mostly made for teachers rather than students, which surprised me. While reading, you cannot skim because you have to slowly retain and process information the way a student would, which can sometimes be a challenge.
3. An emotion I felt while reading the text was fear. The main thing that trigged that emotion was learning that it is best to memorize the textbooks 100%. I know it is challenging and will take time but what if you cannot successfully answer a students question and they think of you as a bad teacher. This emotion was a bit useful because it made me want to set a goal for myself to improve my memorization skills.
You can always say to students let me think about it or I’ll get back to your later. Answering student’s questions is important yes but realistically you will not know everything about a subject your first go around. Absolutely do not beat yourself up for not having an answer or compare yourself to someone who does. This is a trap a lot of people fall into remember teaching is for the most part communal.
1. What do you think they main purpose of this reading is?
Wu wants pre-service teachers to remember math is built on axioms, definitions and theorems. It is very difficult to teach without them know memorizing all this information is needed but it also needs to be applied correctly. The teacher need to be able to explain the connections between topics they are the bridge that brings their student’s to greater understanding.
2. What is a quote that stood out for you in the reading? Explain.
A quote that stood out to me is “Students’
typical attitude towards a math course is that if they can do all the homework
problems, then most of their work is done.” If students are not given much of an explanation other that this is a formula you need to learn it they will disengage from the material. I have seen this happened time and again in my work as a tutor. I think we can engage students in such a way that lets them see math is really all around them. That’s something I don’t see many students know or care about usually.
3. Emotional self-awareness: Name an emotion you felt while you were reading the text. Describe what triggered that emotion. Do you think that emotion was useful? Why?
I felt wary as I was reading the text yes it is very important to know the content that you teach. However is not even a comparison teacher who has been teaching the same content for say 10 or even 5 years to someone who just started. The level of mastery is miles apart the longer you are teaching the easier it will be to break down, reframe and present the material needed. Throughout the course of our careers we will learn and grow in ways none of us expected. Each year the material will sink in deeper until you won’t be able to even remember a time when you didn’t know the material. By all means use the methods outlined in the text by Wu but do not stress about being perfect at the start. Even when we are 20 or 30 years into teaching we will still be improving.
1. What do you think is the main purpose of the reading?
According to Mr. Wu mathematics is not only about learning new formulas/theorems/axioms or their application because they are just the tip of the iceberg he believes incomprehension and the application of formulas, theorems, but axioms are also much more profound for teachers so they can be passed their knowledge to the next generation without getting limited just by textbook information.
2. What is a quote that stood out for you in the reading? Explain.
“Ask yourself whether a mathematics teacher whose
lessons are correct only 90% of the time should be considered a good teacher” . I know we all can make mistakes or errors which is fine but for me, it’s unacceptable for teachers who make a significant amount of errors over and over. If the educators completely depend on books to prepare for the lesson their explanation will be really limited because those books only have about 90% of the materials on average.
3. Emotional self-awareness: Name an emotion you felt while you were reading the text. Describe what triggered that emotion. Do you think that emotion was useful? Why?
I didn’t feel anything while reading the text but from my personal experiences, I can ensure that a lot of the things he said are valid. most of the time my educator gave me the formulas to apply even though I had no idea about the connection between each variable but as I progress I have to try to understand the formulas, the meaning of each variable, or their conncetions.