Aug 21 Discussions (Read from Bottom to Top)

Posted at Aug 28/2018 06:36PM by Stu 2:
Stu 9 Hello

Posted at Aug 28/2018 08:25AM by Stu 4:
@Stu 10, Thanks for letting me know there is a formal name for my American frontier speculation. I'll have to read more on that.

Also, could you explain what you mean by the pot calling the kettle black? I'm not sure your meaning and would like to understand.

Posted at Aug 27/2018 06:30PM by Stu 7:
Stu 2, I agree with you and I did find myself asking those questions. My biggest question is when did we begin to take out the conceptualization of math in classes and why?

When Stu 9 and Stu 3 mention how they internalize, I did the same thing. However, it also gave me some insight into why things weren't working when teachers would attempt to change or implement new methods. I had never really thought about how throwing students into a different type of learning environment where they don't know there role could be hard on them too.

From a personal experience, going from calculus to my intro to proofs class I struggled really hard. I wanted to know "Where did all the math go?" It wasn't until later I realized I only knew procedural math, I never took the time to conceptualize why equations or formulas looked the way they did. I just took what the teacher gave me and did the homework. Then going into a class where I had to take concepts and relate them to one another I felt I was thrown to the wolves. Basically making that transition wouldn't be as scary in my opinion if we were to embed more concepts and methods from the other countries as we are in Pathways. (This was my thought process into trying to understand my learning from the U.S teaching system) I really like the questions you brought up as well Stu 9, I want to know those answers!

Posted at Aug 27/2018 06:01PM by Stu 9:
@Stu 10, thanks for the reminder to reframe our thoughts towards the goal of understanding education. I think that is important, if sometimes easy for me to forget, to keep the goal of understanding (not judging or shaming) in mind when reading the Teaching Gap and discussing our perceptions of the reading. I agree with you that it was hard to read certain ideas in the text. Like Stu 3 said, it is hard not to look internally and begin to critique myself and my own teaching.

@Stu 3, I think you bring up a great question. How do educators in other countries perceive a discussion on improving their teaching. To extend that, I wonder how policy reform directly affects educators in other countries. Do these policy changes in curriculum cause added stress on teachers as it does in the US? Are there even these sorts of reform based curricula to be followed in most countries?

Posted at Aug 27/2018 05:59PM by Stu 2:
To Pat's question and after reading everyone's comments. My view of the differences in teaching, is how did it come this far in the cStu 10-cultural differences? How did a common mathematical language become so diverse in its teaching and routes of learning? Or how is it that Germany and Japan have learned a "different" mathematics from the U.S.?

I just wondered if anyone else possibly asked themselves maybe similar questions?

Posted at Aug 27/2018 05:14PM by Stu 3:
One thing that stuck out to me was how they responded to the teacher from Japan who was shocked about the interruption to the lesson (where he asked what the announcement was and they responded that it wasn't important and he had to insist that it was). I think this shows how important it is that they were looking at cStu 10-cultural teaching and included instructors from the different cultures. I would never have thought that the allowance of interruptions of lessons might be a distinction. Like the authors I would have ignored the disruption. I was also quite intrigued by how much the interruption seemed to disturb him. The teacher from Japan seemed very upset that the lesson was interrupted.

Something else that struck me was how hard it is to not ‘judge’ my years of teaching while I read the book. I acknowledge that the purpose of the text is to highlight the similarities and differences in the teaching in different cultures to help us understand why US students are consistently underperforming in comparison to many other countries and not to judge the quality of the teaching. It is, however, difficult to stop my mind from thinking through some of the things I have tried over the years critically. I imagine that is why many US educators might have seen this study as an attack rather then an attempt to analyze the (then) current situations. In discussions about education reform at the Community College I taught at (some of which is being required based on new legislation in California) any suggestion of a change was met with resistance and faculty feeling that their teaching was being judged. Administration would bring in data to show low success rates (as a motivator for reform) and were only met with ‘reasons’ why they were low (the students came unprepared, placement, …) and faculty who felt under attack. I wonder if faculty resistance to change is the same cStu 10-culturally (or even in other areas within the US). Does a discussion on how to improve teaching make teachers in Japan or Germany feel judged and attacked?

One last thing that struck me was that the depth of the content being taught in the US was so different then in Japan and Germany. I have been to many conferences that have talked about US math education being a mile wide but an inch thick but the book really expanded how I think about that.

To Stu 4: I would also say my experience teaching has been students who wanted only to be given specific instructions on how to do each ‘type’ of problem – complete with an almost identical problem to follow. When I would give problems that were not ‘the same’ they would sit there and say they were waiting to see an example of ‘that type of problem’. I would expect that in Japan we would encounter a very different attitude in terms of students approach to new situations.

Classes I have taken have definitely influenced my teaching. Its hard to imagine how to run a class that is completely different then the ones you have experienced. I have recently attended a lot of conferences that talked about activity based learning. Many of the teachers in the room seemed very uncomfortable about teaching that way (specifically about how to manage the classroom and still ‘cover’ the content that they want to cover).

Posted at Aug 27/2018 05:05PM by Stu 1:
In response to Pat's question, I would like to reiterate what Stu 9 said. Oftentimes, new instructors are told to teach how they have been taught. Even if they are not directly told this, many instructors unconsciously do this because it is what they know. I feel this is definitely a possible reason for the vast difference in teaching between the U.S., Japan, and Germany. From my understanding of this book, it seems as though Japan and German teachers may have been taught early in their experience as students to think about why the mathematics works. It's also quite possible that they were exposed to conceptually based mathematics teaching throughout all of their education. Thus, when it becomes their turn to teach, they are far more accustomed to and comfortable thinking and teaching this way.

Posted at Aug 27/2018 05:00PM by Stu 5:
I have experienced conceptual curriculum (Pathways and DIRACC) as a student, so I might have an interesting perspective to bring to this.

As an undergraduate student, I took two different math education classes about the Pathways precalculus material. The classes were treated as though we were students and teachers of the precalculus material. We did all of the assigned homework, had hours in the tutoring center, and presented problems for critique in class. For about the first month of class, we all kind of hated it. Most of class was discussion based. So, rather than answering questions in a few words, we were asked to explain a method of thinking or a particular concept to the class. (e.g. As x and y change together, explain what it means for y to change at a constant rate with respect to x.) This was a radically different environment to anything any of us had ever experienced in a math class. We quickly realized that we didn't know how to talk about mathematics in a clear way which made some class sessions very frustrating.

In response to Pat's question, if I had experienced conceptual mathematics throughout my K-12 education, I think that I would have learned a different mathematics. I never thought of math as something you could talk about before these classes. Math felt like something you just did. I thought I understood all of college algebra and trigonometry. But, I didn't know what it really means to understand mathematics. If I had learned K-12 mathematics in an environment where mathematics was something to talk about, then my approach to thinking about mathematics would have changed long before working on an undergraduate college degree.

Posted at Aug 27/2018 01:42PM by Stu 10:
I had trouble reading. Every other sentence made me want to re-structure my classes to try out one idea or another. Although I'm a physics teacher instead of a math teacher, I strongly suspect that many of their conclusions apply to my physics too.

@Stu 4 - It sounds to me like you're referencing Turner's Frontier Thesis ( ).

@Stu 4, Stu 1, Stu 9, et al - This is totally the pot calling the kettle black, but remember that Pat said the point of reading this is not to shame but rather to understand teaching.

Posted at Aug 26/2018 08:51PM by Stu 7:
To also answer Pat's question, Yes I do believe Japan's teachers learned a different math than the Teachers from the U.S. They learned that a type of math where strange formulas weren't given to memorize and practice over and over. Instead they learned to create methods of solving problems through guidance. They would experience the struggle that the challenging problems provided and learned more effective ways to go about them next time. The way that Stu 9 went about being a TA is exactly how I would have done it as well. Had it not been for the Pathways Seminars for this program.I would have taken my favorite things from each Teacher I had before and used what they did since I was successful in their class.

In chapter 5 it discusses the different systems of each country. In every system, the teachers were once students in the system and learned how the system worked subconsciously. Then when each country's teachers stepped into their career they did what they knew best: the system. Therefore I do believe that Teachers from Japan teach as they were taught just as the U.S. teachers did and still do.

Posted at Aug 26/2018 03:56PM by Stu 9:
In answer to Pat’s question, when I was getting ready to become a TA for the first time, we had no formal training. We were told to mimic a favorite teacher's style and incorporate it into our own. As such, I began teaching the recitation sessions for Honors Calculus using only my own personal understanding of the material, the way I had been taught and the way it was presented to the students. I never had a formal explanation on how to create a useful lesson plan, effective classroom management, etc. For me, how I learned how to teach was vastly impacted by the educators who have impacted me ever since I began my education in the sciences. While this is certainly not the case for everyone, I would think that anyone teaching a class will incorporate tips, tricks, ideas, and concepts that they picked up from someone/somewhere else. Regardless of whether this person is a previous teacher, colleague, friend, youtuber, etc. In that same vein of thought, I agree with Stu 6 that comparing the teaching styles of teachers in the United States to the teaching style of teachers in countries whose teaching methods differ drastically from that of the United States’ provides a useful metric to summarize the US teaching style as a whole.

Posted at Aug 26/2018 03:50PM:
Pat: My question seems to have gotten lost in Stu 6's flurry of posts. I'll ask it again:

Might it be possible that Japanese and German teachers "teach differently" than is broadly the case in the U.S. because they learned mathematics differently and learned a different mathematics compared to teachers in the U.S.?

Posted at Aug 26/2018 03:29PM by Stu 6:
For me the cStu 10-cultural study was like the fish getting out of the water. A fish doesn’t know it is in water until it gets out. By looking at teaching in other cultures the investigators were able to see things they may not have seen staying in the U.S. The same can be said for Japan and Germany. I have read this book before (many years ago) and it is still relevant. However, I have had the privilege to work with some great teachers that have changed the U.S. paradigm presented here. They took a scary leap and learned how to change their teaching. When I talk with them they still say they have more to learn. They don’t fear the failure of a lesson. They look at how to make the lesson better. Either by making changes or by starting over. They focus on the concepts and the connections within the mathematics. They let students follow interesting paths in their thinking and guide them to the correct mathematical thinking. I continue to follow in their steps. It allows me to be okay with doing something wrong. It doesn’t mean I am incapable it means I need to pay attention to what happened. Persevere, not quit.

Posted at Aug 26/2018 03:27PM by Stu 6:
The environment and behavior expectations greatly impact learning. Teachers can create this in any classroom. Not all collaborative learning environments look like Japanese behaviors of bowing to the teacher. I develop this through my behaviors and clear boundaries about my expectations of their behaviors. Students know that I expect them to tell me about their thinking. This is discussed on the first day of classes. I have trained myself to never answer the question “Is this right?” I tell students I am a process checker not an answer giver. I ask them to explain their process and we discuss how and why they think their answer is right. Students are the ones to share their thinking and make decisions about correctness together. It is very difficult to do this. Most students don’t want to do this because it is “hard”. It’s only hard because no one has ever expected it before. And, learning is hard. Practicing is easy. Learning a procedure and practicing it is learning. But it is a learning exercise in memorization. Lacking mathematical connections. It has taken me over 10 years to get to a place where I’m comfortable not giving answers and students are comfortable not getting them. And I still have many things that need refinement. Now, I’m working on how to get students to the concepts and connections. It is hard learning for me because it makes me face my mathematical weaknesses. Don’t be surprised if you find me following some common mathematical misconceptions. I’m still discovering my misconceptions.

Posted at Aug 26/2018 03:26PM by Stu 6:
Differences in content and the way students are asked to engage in mathematics in the U.S. as described in the book is about giving brief responses to specific teacher questions. I call this “teacher bingo”. It’s like guessing what is in the teacher’s head rather than gaining insight into the student’s own thinking. The Japanese teachers invite students to do more of the mathematical work. They want to see and hear what the students are thinking. As a collective. It is their feedback loop for their teaching practice. My understanding is that Japanese teachers also debrief their lessons with senior teachers to improve on their lessons. To get better at teaching. I’ve worked in professional development at the county and state level. This reflection with a mentor is a rare occurrence. Most professional development is a one-shot generalized experience. Teachers are asked to take the information back to their own teaching with no supporting work afterwards. Many teachers expressed that they were afraid for the lesson to go “wrong” calling it a disaster and never wanting to try again. Failure is not seen as a learning opportunity. Thus, they teach with this same feeling. They rarely, if ever, let students fail and then support them in learning from the mistake. I think the teaching will change when the learning experiences of teachers within their profession changes. A Professional Learning Community is supposed to be this way but often the implementation lacks fidelity and teachers are still experiencing the same-old same-old. They miss the opportunity to create real change. They fear failing. WE fear failing. When was the last time you felt comfortable not already knowing the answer to the problems being solved in class? How about now knowing exactly how to solve the problem right away? This is the cycle. Teachers experienced learning this way so they teach this way. Japanese teachers also teach the way they learned. However, their teaching and learning experiences were quite different.

Posted at Aug 26/2018 03:22PM by Stu 6:
Thinking about how the Japanese teachers would talk to each other reminds me of a presentation by Phil Daro. He describes U.S. schooling is about “answer getting” and Japanese schooling is about “collaborative learning”. In the U.S. teachers think of lessons as a means to get students to the answer the teacher already has in mind. In Japan it is about developing connections and looking at the answers students give. Why did they say what they said? Is it representing correct mathematics and its inherent connections? He states that for the U.S. it is “How can I teach my kids to get the answer to this problem.” In Japan it is “How can I use this problem to teach the mathematics of this unit.” Conversations among Japanese teachers would be along these lines. They would discuss how to get students to see the mathematics concepts and build their mathematics knowledge. They definitely want students to achieve correctness so teacher collaborations would focus on how to provide a learning experience that allows students to see and develop the mathematical concepts on their own. They would focus on why students did or didn’t “see” the mathematics and how to better get students there.

Posted at Aug 26/2018 03:14PM:
Pat: Another question: Might it be possible that Japanese and German teachers "teach differently" than is broadly the case in the U.S. because they learned mathematics differently and learned a different mathematics compared to teachers in the U.S.?

Posted at Aug 26/2018 02:26PM by Stu 1:
I feel that in Japan, teachers would be more focused on how they can improve their teaching to then improve students understanding of the mathematics they are learning. The Japanese pedagogy is focused on students conceptual understanding, and their ability to solve problems. The Japanese are also very concerned with students making connections acStu 10 seemingly disconnected mathematics topics. Thus, I feel the Japanese teachers’ stories and conversations would be centered around how they can elicit different student ideas, and then how they can use the various student ideas to formalize the mathematics they are trying to teach them. This is very different than the stories one would hear in the U.S. as teachers in the U.S. are less concerned with their own teaching practices and more concerned with student learning. Americans want to see results. Thus, many U.S. stories are focused on the students’ ability to master procedures and definitions efficiently as compared to the process of forming a rich conceptual understanding, which requires time.

Posted at Aug 25/2018 03:12PM by Stu 9:
Echoing what Stu 2 was saying, I find it interesting that many schools in Japan begin by fostering student's manners and respect before they are given exams. I would make the claim that a teacher in Japan would not comment about student behavior at a middle school level as frequently as an American teacher would. Therefore, I would think that many of their stories would instead center around students ability or inability to solve some of the problems they are given in class based on how the teacher believed they should perform.

Posted at Aug 25/2018 03:03PM by Stu 9:
I like how the Teaching Gap draws the comparison between the "story" of the mathematics that can be followed on a completely filled series of chalkboards, and the rapid pace of information that usually flows acStu 10 an overhead projector. It seemed to me that the author was claiming that this was possibly correlated to student's difficulty to focus on more than one problem for a long period of time. Nice connection Stu 7.

Posted at Aug 25/2018 02:58PM by Stu 7:
What stood out to me was how even though this book is dated, it's still relevant to what is happening today. For example, the learning environment I experienced all through out K-12 was exactly like the book described as the American culture. Thus from 1999-2015 our culture hasn't transformed extensively.

I liked what Stu 1 mentioned earlier "The problem is, most teachers teach how they have been taught."

Had I not gone to Grad school and just taught using past experiences, I would have done the same thing. For example in Pathways, we are learning to teach in a conceptual way rather than procedural. This has become more difficult than I thought because I have never experienced teaching or being a student in this type of learning environment. So I am not yet comfortable teaching this way.

It seems like in The Teaching Gap, it references the American Culture of teaching and it seems as if their "System" of teaching is more simplistic in that we only give students the information (formulas or definitions) needed to complete their homework. Whereas Japan or Germany seemed as if they were giving methods to go about solving problems. In the development of each country's curriculum we can see that the U.S.'s teaching methods focuses on different levels of efficiency that are geared towards the school(Just as Stu 2 explains in her situation). Their methods involve using tools or technology such as the overhead projector as an easier way for the teacher to do things in class. It seems as if Japan's Teaching methods are focused on giving students a broader spectrum of knowledge using simple tools, like a chalkboard, to help their students create independent thinking. Here Japan's methods focus on the students rather than the teacher. Then the book sets Germany in the middle of the two in the form of a grey area.

Posted at Aug 25/2018 02:57PM by Stu 2:
In reference to Pat's question, a story I would possibly here from an instructor in Japan is how the environment is more simplistic and structural in the schools than in a classroom in the U.S. It is known that Japan is a very demanding and competitive country within its self, so can that type of atmosphere be projecting into the schools because that is what the students will experience in the outside world.

Posted at Aug 25/2018 02:42PM by Stu 2:
1) The first thing that stood out to me in the book are the variations for U.S. instruction as "additional review" & "learning terms and practice procedures". The setting of a typical classroom (from my experience as a student, being a substitute teacher for Atlanta Public Schools, and a TA for College Algebra at Georgia State) is to practice more procedural problems, rather than conceptual. For example, when they expressed a day in the U.S. classroom with worksheets and going over them, then reviewing similar concepts over and over again. This has been seen in all of the K-16 classrooms.

Now, when I think about the cStu 10-cultural differences, can we also think about prevalent issues within the culture and within the schools themselves?

I wondered why do we teach heavily on the procedural rather than conceptually? Does it have to do with the grades within the program? Not to express any bias against another school, but GSU's college algebra & precalculus students all are in Hybrid courses were most of the lessons are on computer-based program such as MyMthLab. Then once a week, for 50 minutes, they go to an instructor. All of the homework, quizzes, and tests are on MyMathLab. The questions are 90% procedural and 10% of the conceptual questions are missed by most students. As I observed three of the classes (from 3 different instructors) They only work on problems that are "REPETITIVE" to what they see on the online work. If we were to analyze the grades that the students are passing with in correlation to a standardized test, you will see that they do not match. And the instructor of the program stated to me that the "MyMAthLab" computer program is efficient based off of the COST for the school.

This leads to question in my mind, is teaching in the U.S. possibly being affected by other factors, such as money and politics, is why we are more comfortable with teaching at a more procedural level rather than a conceptual level?

Posted at Aug 25/2018 01:43PM by Stu 8:
That's an interesting idea. Are you suggesting that perhaps when America has been around for longer education could become more of a priority? While there are certainly many people here who are struggling financially, I would argue that America is, relative to other countries, no longer really in survival mode. However, the fields other Americans suggested to you--business, law, medicine--do seem very practical, so maybe that does show signs of a survival instinct.

Posted at Aug 25/2018 06:55AM by Stu 4:
This is not Japan, but I remember that when I was a missionary in South Korea and told people that I wanted to be a college professor someday, they were always very impressed that I wanted such a prestigious and respected position. Upon returning to America after my service, most Americans that I talked to felt like I was wasting my potential going into education. They felt I should get a "real" job for smart people like business, law, or medicine. The only positive reaction I remember receiving from Americans who were not in education already were the people who said, "Good, we need good math teachers" like I was giving service to a delinquent program.

This is pure speculation, but I've always wondered if the American cultural opinion of education and its importance is rooted in the early periods of American history and the first European Americans. Although some rich and educated Europeans cStu 10ed the Atlantic to the Americas, most early Americans were either poor or fleeing religious persecution or both. In those days, the poor were very uneducated. As America evolved, New England became cultured and educated, but it's poor moved West to escape the slums of New England. This cycle continued as the United States expanded westward. Only in the last hundred years or so has the entire country been geographically stable in such a way that people have to survive where they are instead of moving to a new, unsettled land.

When people first enter a new land, they don't think about education because they are worried about physically surviving first. Thus, education is a much lower priority then farming, manufacturing, trade, and other industries. I wonder if this historical pattern has contributed to a general feeling among the population that education is secondary to the basic needs of survival. This perspective helps me to frame some of the current American feelings toward education, especially among those in poverty and those in rural areas who feel that education is a hoop they have to jump through until they're old enough to live without it.

Posted at Aug 24/2018 10:11PM by Stu 9:
The first thought that popped into my head when I was reading the Teaching Gap, was whether or not the comparison between German and Japanese schools was truly fair. Surely a teacher in a Japanese school would never have to deal with the level of disruption that an American classroom experiences. In fact, in the Teaching Gap, one of the Japanese researchers commented on how incredulous the PA system was. He could not imagine interrupting the learning process of the students in the classroom. Do German teachers have to deal with gaps in student knowledge due to a change in the new curriculum? However, I think that the use of the other countries as a metric to generalize the American education system was quite interesting. I cannot help but think that the presence of the camera in the classroom helped mitigate some of the behavior issues that an American teacher deals with on average during the year. I simply cannot imagine the stories of a Japanese and German school teacher aligning with what I have heard from some of my friends who are currently educators in the American public school system. Several of whom have left education due to the impact of local legislation on their day to day lives. While I cannot exactly imagine the stories from a German or Japanese teacher, I can give an anecdotal reference to the words of several of the European Mathematics professors (Germany, Hungary, Russia, etc.) I know. Many of these professors who taught me upper division math while in Grad school believed that they were teaching a beautiful subject to students that were too stupid to understand the most basic concepts. I cannot help but think that this level of apathy could only be a detriment to the success of their students in lower-level University math classes. They each spoke very highly of the education they received in their home countries. For example, my Master’s Thesis advisor told me of a “basic” math problem in a German middle school was to prove that the sum of any three consecutive integers is divisible by three. However, I am sure that we have all spent time showing students how to find the set of three integers that satisfy this condition. Even this comparison of mathematical understanding paints a clear picture of the gap described by the authors of the Teaching Gap.

Posted at Aug 24/2018 10:08PM by Stu 9:
I started teaching developmental mathematics to at risk students at a community college housed in a state university. WKU forced the at risk populations to pass a certain number of “cornerstone” courses before they could join their peers and afterwards were labeled “college-ready” by the University. WKU was an open admissions University, so it was not a surprise to have students in your class that had scored a 5 on the math portion of the ACT. The issues endemic to “South Campus” barely scratch the surface of the socioeconomic issues that plague the American school system.

Posted at Aug 24/2018 08:01PM by Stu 8:
Whoops. I meant avoidance of spending too much time in curriculum meetings.

Posted at Aug 24/2018 07:53PM by Stu 8:
I would think Japanese and German teachers have very different perspectives about developing curriculum than American teachers do. Maybe having a meeting to discuss curriculum would be considered strange. Guessing what kind of stories Japanese and German teachers would share is hard because I know almost nothing about either of those cultures, but I might guess that Japanese teachers discuss some of the solutions students presented to problems or what they would consider teaching in their next lesson. In Germany, I could imagine discussion and stories about individual students because the German lessons presented in the Teaching Gap showed examples of students being called on to answer questions or present ideas.

On the one hand, having a curriculum meeting makes sense to me, Stu 4, because the main priority of the teacher would hopefully be getting to know and providing learning opportunities for the students. On the other hand, collaborative meetings with teachers and curriculum developers seems good because it allows the teachers to establish a consistent framework for how and what they teach.

On the other other hand, a meeting like that could go awry if no one has evidence-based information about what would best benefit students' learning and what material is important for them to know.

Posted at Aug 24/2018 03:14PM:
Pat: What stories might you hear from teachers in Japan and Germany (according to the Teaching Gap)?

Posted at Aug 24/2018 01:59PM by Stu 4:
When my sister started teaching middle school biology at the beginning of last school year, I remember telling her that if she had a good department they would feed her assignments and assessments throughout the year so that she didn't have to spend hours and hours planning every day.

Most of the time (in my experience) one teacher will spend hours of unpaid time developing a unique curriculum that is then used for years by the department. Otherwise, teachers/districts buy into professionally developed curricula (e.g. textbooks, online homework platforms, etc.) to save themselves time.

There was a move a few years ago to develop PLC's (Professional Learning Communities) among teachers, but I believe that program was cut in my district because administrators and/or state officials (I don't remember which) felt that educational time should be spent with students in classrooms, not teachers collaborating and developing curricula.

This may be isolated to the district I taught at, so I'd appreciate other viewpoints here as well.

Posted at Aug 24/2018 01:47PM by Stu 1:
What stood out most to me is the focus on teaching compared to the teachers. Oftentimes when you hear about education reform in the US, the focus is on more qualified teachers and better standards. The problem is, most teachers teach how they have been taught. Thus, the cycle of procedure and definition based teaching persists among old and new teachers. I also agree with Stu 4. During my teaching experience, it was very obvious that teachers lack the resources (time, materials, professional development) to effectively change their teaching. This then results in them continuing to teach how they were taught, or how the senior teachers in their building are teaching.

Posted at Aug 24/2018 12:20PM by Stu 4:
I know that I started my teaching career trying to engage students in higher level thinking and activities. However, students resisted my efforts and I found that I had to create most of my activities from scratch. I finally gave up due to lack of time and resources and fell into the traditional American teaching model after my first year. At this point, I felt my classes become smooth and the students seemed to respond better, leading me to think I was figuring out how to teach well.

I fully agree that the culture of American mathematics is to model a procedure and then have students mimic it. I occasionally presented proofs in higher level classes if they were easy to follow, and I rarely asked for student input or direction as I completed the proof. The retired math teacher who was unofficially mentoring me when I began teaching precalculus summed it up best when he said, in effect, "The smartest kids may want to see the proof, but most students just want you to show them how to do the math so they can start the homework."

I assimilated into this culture and eventually even adopted the teachers' attitude of "Yes, new programs and methods are discussed by the elite. But we teachers just jump through the hoops, making token changes to appease the administration, while never really making any fundamental changes to our thinking or practices."

This book is definitely making me rethink these ideas.

Posted at Aug 24/2018 08:18AM by Stu 9:
Hey friends! I was hoping to get the discussion board started off. Maybe if everyone commented with what stuck out to them the most while reading the first five chapters of The Learning Gap. Hopefully that will give us a few discussion threads to follow based on what everyone wants to discuss.