H. Wu is a professor at UC Berkeley and is the author of the books on which this course is based. He coined the phrase “Textbook School Mathematics,” or TSM, to describe the mathematics curriculum commonly taught in grades K-12 in this country.
[T]here has been a de facto national mathematics curriculum for decades: the curriculum defined by the school mathematics textbooks. There are several widely used textbooks, but mathematically they are very much alike. Let’s call this de facto mathematics curriculum Textbook School Mathematics (TSM). In TSM, precise definitions usually are not given and logical reasoning is hardly ever provided (except in high school geometry texts) because the publishers mistakenly believe that intuitive arguments and analogies suffice. Thus, fractions are simultaneously (and incomprehensibly) parts of a whole, a division, and a ratio; decimals are taught independently from fractions by appealing to the analogy with whole numbers; negative numbers are taught by using patterns and metaphors; the central idea of beginning algebra is the introduction of the concept of a variable (which implies, wrongly, that something is going to vary), when it ought to be becoming fluent in using symbols so as to do generalized arithmetic; solving equations is explained by the use of a balance to weigh variables on the weighing platforms; etc.
H. Wu
Assignment, due Monday, 2/7/22: Watch the following video of Wu speaking about TSM and the way we prepare teachers (16 min). Respond to the questions below by leaving a comment on this post.
- What do you think is Wu’s main objective in this talk?
- What is something Wu said that you agree with? Explain.
- What is something Wu said that you disagree with? Explain.
- What is a question you have after watching this talk? Your question should have the form:
“I’d like to ask _____(person) the following question: ______“
It can be a question for Prof. Wu, or a question for your classmates, or your professor, or yourself. - Extra Credit. Respond in some way to one of your fellow students’ comments. Do you agree? Disagree? Do you have a response to their question? Did their comments make you think or provoke additional questions? Reminder: Be respectful, be kind.
Video
Wu on K-12 math teacher preparation:
“Stop selling what you have; start selling what they need.” (16min)
BONUS: If you’re interested in more detail, here are the slides from a longer version of this talk that Wu gave around the same time.
1) Wu wants to highlight that the state of math education on the whole is subpar for many reasons. Quite a few of them have no easy solutions either such as teachers who are already in their careers know only TSM and maybe aren’t at retirement age yet.
2) I agree with Wu that TSM is very difficult to learn from there are barely any definition or explanations and students are expected to somehow understand. I remember my own confusion going through middle and high school questions as why something worked out a certain way quite often. No one bothered to answer covering the topics that were on the regents were more important than really understanding the material
3)I do not agree that all students who are studying to be teachers go on to perpetuate TSM or that all universities are trying just “to sell you what they have”. The more professors and other staff who have worked in schools and DOE school willing to partner with colleges the more grounded (hopefully) the degree program is
4) Do you ( classmates) believe the system is improving as a whole?
Hi, Irina.
I agree with your answer for #2. Math is hard without a clear definition or explanation. I had difficulties in elementary, middle, and high school.
Regarding #4, which system are you referring to? DOE school system?
I was referring to the implantation of common core standards
Hi Irina – thanks for being first-to-post. I know your question #4 was aimed at your classmates, and I’d be very interested to hear what they have to say. But for my part, I have a lot of optimism about math education — and you all are part of the reason!
1.What do you think is Wu’s main objective in this talk?
TSM is not learnable.
University must help prospective teachers appropriately.
2.What is something Wu said that you agree with? Explain.
I agree that the university should help prospective math teachers. For example, the math education department should have a curriculum that math teacher candidates can success in the future as teachers.
3.What is something Wu said that you disagree with? Explain.
I disagree with Wu’s argument that prospective math teachers should learn from every subject such as chemistry, biology, history, English etc to get better understanding.
4.What is a question you have after watching this talk? Your question should have the form:
I would like to ask everyone or peers who went school in NYC if they have a math textbook and the definition was clear and easy to understand.
1. The main objective of Wu’s talk is obvious: He criticizes TSM for not having and not providing enough definitions in Math Textbooks, proofs, and precisions. He demonstrates it on four randomly chosen examples for 8th grade, namely fractions (although he had much more to show and say).
2. I am not a product of any Middle or High School here in the U.S. so I can hardly judge or agree with Wu’s points. Certainly I am witnessing how and what they teach my daughter in 7th grade; they used Eureka as the textbook, and it gives me positive impression to say that there is little of what I was not taught back in Europe.
3. All examples that Wu used to scandalize the gathered auditorium by were so horrendous that my brain froze. Are the school on the West coast really so bad? Here in New York, as much as I could witness, the students who decided to teach Math are well prepared for their profession, smart, and charismatic. The Textbooks, as much as I can judge, are well written and enough explanatory. The quality of teaching depends, in my view, in particular schools, if it is, for example, Stuyvesant HS or some lost HS in The Bronx. Unfortunately, we are creating opinion that ,in many educational institution ,”if the education is not good, it is always a fault of the teacher”. When would we start realizing that in many schools is defective, or poisonous, atmosphere?
4. Prior to the class’ beginning, I exchanged four emails with Professor Wu. I did not know him and did not see any video of him. Now I would like to ask him a question: Dr. Wu, do you speak for the entire community of Math educators? Don’t you see any light in the darkness you are criticizing? Do we ALL use bad-written textbooks lacking definitions, proofs, and precision?
Qing Chen MEDU 3000 -D200
Hi, Jaroslav. I am Charlotte. I feel sad about this sentence in your reply, “If the education is not good, it is always a fault of the teacher.” Teachers play a very important role in my life. I think whether education is good or bad is not the responsibility of the teacher alone. I’m not always a student who loves studying. Before I didn’t like learning, I didn’t understand the teacher and even feared communicating with them. I study very difficultly, so my grades are very poor. After that, I began to study on my own initiative. I began to love learning, and I enjoyed the sense of accomplishment brought by learning. And I began to understand teachers, and I gradually realized that teachers are just like us (I used to regard teachers as “special beings” outside human beings). I began to understand that teachers just want to help us learn new knowledge so that we can better understand why the world works like this. I think that in education, the actions of both teachers and students are equally important. No matter how good a teacher is, he will encounter “students who will never study”. Education should be a mutual achievement rather than a unilateral responsibility. I wonder what you think of my thought?
Dear Charlotte, you totally misunderstood my point I made: I wrote about the management of the school and/or students who made the teacher feel bad and guilty for everything. Why should I cut off the branch I sit upon? I also want to become one of you teachers. I certainly value all GOOD teacher that have been influencing me.
I’m fascinated to hear that you have corresponded with Prof. Wu! I’d like to know his response to your questions also…
Qing Chen MEDU 3000 -D200
I think the main purpose that Wu conveyed to us is that the mathematics textbooks used by K-12 students are not created for them to learn mathematics better, but more like the research products of universities. Those who write mathematics textbooks for junior and senior high school students don’t consider whether students can understand the real relationship between numbers and calculations, it just tells us how to get the “right answer”. I agree with Wu’s statement: many math education students want to do “better” than TSM when they become teachers because they realized many unreasonable situations when they studied TSM in high school. When I was in high school, my math scores were not very stable. When I was in the first grade of senior high school, my math scores were OK, because I just moved to the United States from China, and the progress of math learning in China was faster than in the United States, so I had a clue when other students were still in the introductory stage. However, after my second year of high school, my math scores began to drop rapidly, because my English was not good and my eyesight was poor. I couldn’t understand what the teacher said and couldn’t see the notes written by the teacher on the board, so I had to try to teach myself with a textbook. Unfortunately, I’m not a smart student. I can’t understand the knowledge points in textbooks by Self-study, it has not improved my math scores.
Now my math scores have made great progress. First, because my English is better than before, I can understand what the teacher said, and when I am troubled by what the teacher said, I will also ask the teacher about my confusion. Secondly, I began to wear glasses and am no longer shy to sit in the front of the classroom. I found that the notes written by the teacher on the board can help me understand the content of the subject very well, and reviewing the teacher’s notes during the exam is more understandable and effective than reviewing the knowledge in textbooks.
I am very interested in the question presented by Wu in the article: “Why not get rid of TSM by writing reasonable textbooks?” I don’t quite understand this problem. Is it difficult to rewrite more rational textbooks? I want to know how it works more. Dear Professor Reitz, What do you think of this problem? Please share more about “How the unreasonable textbooks were made and what kind of people made them?”
Thank you.
I agree with you that most textbooks are not written with students on mind. A decent textbook that is not following TSM is available. Distributing and selling that boom is much harder since the decent textbooks need to compete against established companies like Pearson.
Your description of your challenges in learning math struck home for me – it’s important when looking at students to think about what they might be dealing with & struggling with (in addition to the math concepts you are trying to teach).
As far as textbooks are concerned, I think there are smart folks out there working on this problem – although we still have the challenge of finding the good textbooks and, as Irina pointed out, of getting them to be used in our classrooms!
I agree that ESL students are at a greater disadvantage than American-born students. I was born and raised in America, so I had no difficulty understanding the word problems, and what was being asked. However, many of my friends were in fact ESL students, and word problems were difficult for them (especially my friends who moved to the US later in life vs when they were younger), so they understood what was going on, but they had difficulty explaining their reasoning since it wasn’t their first language. I also remember some teachers being anal when it came to explaining the problem in words so this also lowers the scores for many ESL students
1. I think Wu’s main objective in this talk is that math teachers need a correct version of mathematics. However, they have not been given the proper materials. Instead they have been handed what they have. Wu feels TSM is not learnable because it lacks in definitions and precisions.
2. I agree that TSM is not learnable because I feel it is more effective for a physical person to explain something to you rather than read from a book. There would be times when class would be focused on a textbook, and I would get bored and lose interest in the topic.
3. I disagree that school of educations is a service department. Meaning educators must have expertise in all other departments.
4. What negative/positive effects do you think TSM would have on a child’s learning?
I like the question you raise of “how much should educators know about subjects outside their specialty” (and thanks to Ihn, as well, who raised a similar point above). I don’t have a clear answer, but I sometimes think about “how much Math do we need our English teachers to know?” We don’t need them to be experts. But on the other hand, our students are better off if our English teachers don’t treat math like a “foreign country,” a place they dare not go. I feel similarly about math teachers and other subjects (English included), but I’m not sure where to draw the line between the “minimum you should know as an educated person” and “deep knowledge of a subject”. This is a tough one!
I think TSM will have a mostly negative effect on children’s learning and also if TSM continues like a cycle as Mr wu mentioned it will never change.
Wu’s main objective is to talk about the weaknesses that lie in how mathematics is taught today. How it puts students at a disadvantage from understanding what mathematically is about abstractly, whereas many students are taught algorithmically. I agree that universities should better prepare math teachers. I agree that TSM is ineffective. It is also important to consider where Digital technology has evolved since many of us were in school. I remember lugging around these textbooks that were used by 10 students before me (If you remember those textbooks where you had to record your name inside the jacket itself). While math has changed so has the applications of mathematics. And that is the advantage of digital advancement. Students today don’t need to rely on textbooks. They can look at simulations that demonstrate topics, resources like Kahn academy that show step by step and provide practice problems. So this shows that TSM is in fact ineffective. Some of the examples I didn’t agree with. These problems weren’t great examples. They were too specific instead of showing a broader detail (to be clearer, it’s easier to evaluate understanding through the thinking process rather than just a problem with no solution), also I would appreciate seeing some graphs to further prove his point.
So I was a SPED student in remedial classes for Math and English despite my IEP listing me as high performing. For those in either remedial classes or GFT programs, did you feel your math education made it too difficult or too easy to understand based on biases?
ie… if you are in remedial math you don’t understand complex topics. If you are a GFT student you can advance faster than others?
Also on an unrelated note, that may further help his argument this might be an interesting video to watch concerning math education post secondary
Many college students struggle to pass remedial math. Do they need to?
Mathematics is one of my favorite subjects because it can be learned or taught in so many different ways. However, sometimes some school and teachers design their lesson plans based on the textbook definition and textbook problems. consequently, students will have limited knowledge about the topic and they can’t properly think outside of the box when the classes focus too much on the textbook which does have enough information with precision. Mr wu. also mention how the education system keeps repeating the cycle and that limited textbook knowledge has been passed from generation to generation.
I am agreed with Mr wu the TSM isn’t ideal for learning mathematics and it can be a huge problem for future mathematics teachers because from k12 to college they are also learning TSM and as they progress to mathematics education classes they learn how to teach students about TSM. So the process doesn’t change over time.
I just don’t want to degree anything he said to me his ideas are really logical and well thought out.
What will be the best way to modify TSM and continuously improve mathematics education over time?
Belatedly, I am just now becoming aware of this discussion. To the question of “What will be the best way to modify TSM and continuously improve mathematics education over time?”, I will propose an initial segment of an answer. I have written six volumes that traverse the complete K – 12 mathematics curriculum; please go to my homepage, https://math.berkeley.edu/~wu/, for their titles. They provide a blueprint for the mathematical professional development of elementary, middle, and high school teachers.
Hung-Hsi Wu
Dear Dr. Wu,
What a wonderful surprise to see your message – welcome to City Tech! This is the course website for our MEDU 3000 MATHEMATICS OF THE SECONDARY SCHOOL CURRICULUM course from Spring 2022 – we used several of your texts in the course, and your work always inspired lively discussion and debate. While the current state of things is frustrating and can be depressing (as you illustrate very well), in the end I have a great deal of hope for the future of mathematics education – in no small part due to the passion and creativity of our up-and-coming math educators of tomorrow.
Best,
Jonas Reitz