The Teaching Gap by James Stigler and James Hiebert is one of the foundational books in math education. It grew out of research done in response to the Third International Mathematics and Science Study, more commonly called TIMMS. TIMSS, now Trends in International Mathematics and Science Study makes much of their data, materials and resources available for free at timss.org. It's really about systemically improving any kind of teaching, but lucky for us, it's in the context of mathematics teaching. Google Books has a pretty extensive preview.
We ask our student teachers to read The Teaching Gap and have tried various ways to have them read and discuss it. This semester, instead of using BlackBoard, I made a Facebook page for the course. BlackBoard is... okay. Lots of structure. But the discussion threads have never gotten much reading from other students. In the fall I gave Edmodo a try, and it was more functional. I wasn't using the assessment tools there, though, and had no other colleagues using it to share with. So the best features of it were the parts that were like Facebook. Except the students only checked it when they were posting their responses. Facebook has worked pretty well. I use links to Google docs instead of attaching files. Primarily, though, the TAs interacted with it more, had more comments on others' posts and recommended/shared more stuff than they ever did with Blackboard. A lot of our discussion of the Teaching Gap was on Facebook, so I thought I would share the highlights. All of their comments are on Google docs, if you're interested in the whole schmegagy. Dave Coffey, Rebecca Walker and I have developed these assignments over many semesters of working with our novice teachers.
Introduction and Chapters 1 and 2
Focus: Questioning to Make Connection
- Effective readers ask questions that will activate relevant, prior knowledge before, during, and after reading text.
- For example, as you read The Teaching Gap you might ask:
- How does this reading remind me of my personal experiences related to assessment?
- How does this reading relate to other things I’ve read regarding assessment?
- How will this reading connect with my efforts to be an effective teacher?
- Use these questions or develop your own in order to actively engage with the content of The Teaching Gap as it relates to the concept of assessment.
- Read the preface and chapters one and two in text.
- Keep track of examples in the text where you make connections to your experience, other readings, and your vision of effective teaching as it relates to the concept of assessment.
- Jill Beauchamp:I loved the way the "The Teaching Gap" set out to examine teaching across various cultures. It surprised me to find out that teaching varied little within a culture and drastically between cultures. The text spoke about how Japan focuses so much on conceptual understanding and solving challenging problems opposed to spending time practicing procedural steps. This reminded me of what I learned in my COE seminar. We focus a lot on making a distinction between "what are the students going to do" verses "what are the students going to learn."
- Zack Weber: I have heard from other professors that studies of this sort cannot be trusted because the US has the only true random sample of students while the other countries put forth their best students, it makes it difficult to know then if the study really drives these recommendations or not. But I think with them using the video research they have a more solid case for their ideas.
And how can we assess teaching? I think the best way is to have someone assess you. Either have your CT, another TA, or a professor observe your lesson and keep track of what you did, said, explained, etc. I think if you then have a good discussion you will see things you like about your own teaching and things you don’t like about it, and that is from someone else’s viewpoint. I also think a good way to evaluate is by student’s work. Do they seem to understand or are they constantly questioning? Have you changed your class to fit their learning styles or are you using the same teaching style with no changes? I think answering simple questions like this can also help you assess your teaching because you have to provide for the students and unless you adapt then they will always be behind and stuck.
- Abbey Foster: There is constant talk about the good and bad ways of teaching in the classroom, but there never seems to be a consensis about it. I am hoping from this book I learn new ways of what works and what doesn't. The first couple of chapters have talked a lot about how the methods are so different, but I hope they give specific examples of how the US is lagging behind the other countries. The books talks about how important it is to have quality teachers in the classroom. This is interesting to me as I look back on the past professors and teachers I have had. Most of the time, there is some sort of an evaluation, but are these 'quality' teachers really taking into consideration our feedback?
- Allison Behr: I was a little apprehensive about reading this book because I was under the impression that the book would undermine the teaching profession. However, I was pleasantly surprised when the book's preface spelled out the lack of recognition and the hard work that is involved with teaching. I also agree that the problem with education is how it is being taught. Using the same techniques that were used 75 years ago fails to address the current needs and capabilities of our students and ourselves as teachers.
Chapters 3 and 4
Activity: The Teaching Gap
- Read chapters three and four. Keep notes on your reading, in a journal, in the book or on stickies.
- Bring your notes to seminar to discuss.
- Steve Suzio: Based on the reading, I found that the typical U.S. classroom of defining and demonstrating rules and procedures is exactly the scenario in my classroom. The students are given a worksheet and the teacher will go over a few demonstrated problems with them and at the top of that worksheet there is a suggested solution for them to look at if they are stuck. Then after about 15 minutes of lecture, they are given the rest of the time to work and ask questions. Any teaching the teacher does, requires very little thinking on the students part and they can give answers they have no clue to based on the tone and guidance of the teacher. This is not true learning, but more can you memorize a procedure and rule. The Japanese and German classrooms develop the mathematical ideas that are being presented, and students are asked to discover these concepts on their own. The teacher facilitates and lets them know what is important in their discoveries and then provides them with the challenging question.
Thinking about how I can assess my own teaching, I would definitely try using video to record my lesson so I can go back and see what my tone is like asking questions, as well as what questions I asked. I could also review my lessons and see what types of problems I am giving students and how I am going about teaching those to students. If they are struggling, how am I helping them to solve it? Am I guiding them through it? or am I asking challenging questions. Anything that will get me to reflect and see what I am teaching and how I am teaching it will help me assess myself.- Kevin Squire: Great connection back to our classroom, Steve. I agree, the students aren't engaged during lessons. I hope you see that this is what I was attempting when I made the intro worksheet for Ratios (candy mix). I just wanted them to be doing something, too; instead of just watching me talk about math. And the tone thing...so true, man; so true. I catch myself doing this too often. It's pretty funny (in a sad way) when I am aware of this, though; the kids sit there waiting for something else. I think you do a pretty good job of staying aware of this. Probably why you thought to put it in the response, lol. Thanks for the insight, man.
- Becky Marie: Chapters 3 and 4 of the Teaching Gap compare and contrast the teaching methods used within the Japanese, German, and United State’s classrooms. Personally, I found the most interesting contrast to be the amount of time that is spent on in depth, challenging problems in the Japanese classroom and how much time is spend in the US classroom working on definitions and procedures. In my current placement I find that this is very much the case. Much of the day is spent working on procedures, doing problems over and over again. When students take tests, however, their scores are show that they do not really understand the concepts. I am wondering that if more classroom time was spent on meaningful, explorative problems is they would be more apt to grasp a deeper meaning.
- Kevin Squire: This whole "Quantity over Quality" mindset seems to get a bad reputation in many other areas. Why not in Americas classrooms?
- Amy Lee Pickell: Agreed. In every other aspect of what is taught to American students it seems to me like it is quality over quantity except in math
- Kevin Squire: I think that it is a problem of all subjects. I'll have to ponder whether or not this is most prevalent in math classes. i.e. there are A LOT of topics to cover in a typical science class. How many of those concepts are taught deeply, and how many are taught as memorization of facts. Thanks, Amy!
- Brienne Tingley: I agree with this but the problem is how do we get the students to really engage and change their attitudes to wanting to learn to explore it? I feel like as soon as the answer is not given to them, they don't want to even try.
Chapters 5 and 6
Activity: The Teaching Gap
- Read chapters five and six. Keep notes on your reading, in a journal, in the book or on stickies.
- Bring your notes to seminar to discuss.
- Stephanie Petersen: While reading these chapters I would find myself often agreeing with the observations being made and the things that need changing. I also found myself continually wondering how it is even possible to make these sort of changes. I hope that the coming chapters dive more into this! I really liked how the book described schools as systems and how we cannot change the whole system just by changing one part such as the way class is taught. The issue is much larger than just changing the way teachers present information because education is directly related to culture. Students have certain expectations for what will happen in school and how they will learn which is something very hard to change. I know that many of my students have a hard time with change in the classroom and they perform better when there is more structured, guided time. As I read this book, I find myself wanting to step out and make a difference or make a change but I feel that I wouldn't know where to start. How can we make changes in our educational system that might actually be effective? I also wonder why this type of information seems to be ignored or easily disregarded by our society because we have known for a long time that we are behind other countries in terms of education. I know changes are being made, but we need to really find a way to make an effective change that sticks rather than just trying small things that may make a difference for a little while and then just return to old habits.
- Laura Todd: Chapters 5 and 6 in the Teaching Gap covered many questions that I had from the previous chapters, and from our in class discussion. The different ways that Japan and the US use visuals may seem unimportant, but these ways add to the culture differences between the two countries. In Japan students are scripted to be able to answer these complex questions because that is how they have been taught. The example of the teacher that tried introducing a complex problem, but students unable to solve this problem is a good example of of how both students and teachers need to work together to make cultural changes. As a teacher adopting some of the Japanese scripts of teaching can backfire on you because of the US culture and the way students have previously been taught. The survey on the “main thing” teachers wanted their students to get from a lesson was somewhat appalling. In the US teachers said they wanted their students to learn skills, whereas in Japan teachers wanted their students to think about math in a new way to see relationships. I think that younger teachers including our class would have a different view, than wanting students to learn skills.
Chapters 7 and 8
Activity: read the chapter, with an eye for what you can do personally, or what could be done at an individual school. Both should be practical and sustainable.
Reflection: Do you agree with the principles in Chapter 8? Post to Facebook whether you found anything that you think you could do yourself, once you’re teaching. If you were to recommend PD to principal, what would you recommend?
- Brittney Mohnke: I agree with the principles presented in Chapter 8, but it is still hard to picture changes such as this actually happening in our society. If we focus on gradual improvement over time, I think we would eventually see very positive outcomes. However, would people actually act upon these principles? I agree that the most effective place to improve teaching is in the context of a classroom lesson. I think it makes a lot of sense for teachers to become more involved in the reform effort. Although educational researchers provide many good ideas, teachers are the ones who actually know what goes on in the classroom. I also believe that teacher collaboration and the formation of more professional-development groups would be a great idea. This is something I hope to focus on in my future teaching. I hope to improve and reflect on lessons with other teachers. I do not think that keeping the door shut and keeping teaching private is very beneficial. If I were to recommend PD to a principal, I would recommend maintaining a focus on student learning goals for reform. These learning goals should be shared across districts and focused on student learning in the classroom.
- Steven Runkle: The US has been on a path of gradual improvement since the 80's (probably even early if you talk to some of the old timers). Several sets of standards and more and more HS drop outs later, we're farther behind than when we started. The problem with this idea is that people's opinions about education also change over time, and because of this, we reform our educational policies every 15 years or so.
Say we "adopt" this idea of gradual change (and it wouldn't be the first time) and we set a goal to have a brand new curriculum implemented by 2020. I'm certain our goals and opinions about how to "fix the system" will change by then. I'm of the opinion that if we want to implement real curricular change, it has to be within 5 years. That is more than enough time for ed programs and current teachers to adjust.
Like Kevin said, I think we could do this much quicker than people think. But, teachers and administrators have to be committed 100%. If schools can completely implement a completely new special education program within a year, I'm certain they can do the same with general education within 5 years. But everyone needs to be on the same page.
- Luke Hagan: I fully support all of the principles outlines in Chapter 8 except for principle #5. Teachers are most often thought of as the only person in charge of a classroom. The principle seems to be a means to an end for principle #4 but I doubt that the implication can be made.
As a counter example; A developmental psychologist could sit in on the classes of every teacher. This is an ensured in context type of PD and while highly theoretical, still serves as a justification for why teachers need not be straddled with the responsibility of improving the whole of education. It is a nice way to think about a teacher but some will not take to it.
The Initiatives laid out are also completely understandable as well.
Post a discussion question to Facebook. What do you want to know about what other people thought about this? Alternatively, answer someone else’s question by replying to it.
Write a paragraph for your teaching philosophy about how you will improve as a teacher, or how you feel like you can contribute to the profession, or both! (If you already have such a paragraph, edit it.)
- Brittney Mohnke: Chapters 9 and 10: These chapters stressed the importance of teacher collaboration in improving lessons and subsequent student learning. I completely agree that improving teaching should lie in the hands of teachers, not educational researchers, since teachers are the ones who have experiences in actual classrooms. Thinking about teacher collaboration, though, made me think about the situation many of us are in this semester. Many of us are placed in a classroom with another teacher assistant where we have to team-teach and collaborate almost every day. Have you guys seen this as beneficial? Does it connect with what the Teaching Gap is proposing in terms of teacher collaboration? Also, can the time be found for teachers with such hectic schedules to collaborate and work on lessons together during the school week?
- Jess Alexander: I really feel like having another TA in the classroom has been beneficial for me. Allison and I do collaborate and discuss everyday. I think that it could be connected to what the Teaching Gap says about lesson studies, but it would be a smaller version of that. After most lessons, we usually talk about what whether it went well or we give input on what could have been better. I find it very helpful to have a peer there to talk about my teaching and planning with.
- Abbey Foster: I am not placed with another TA in my placement, but I am constantly collaborating with my CT. She’s wonderful and so helpful! We are always bouncing ideas off of each other and trying new things. Time can be an issue, but this is our job and I feel in order to put our students first, we have to give them all of our efforts. If we don’t, I feel we are only holding our students back from reaching their full potential.
Hopefully you can see why we have found the book valuable. At one point we were going to stop (probably for variety's sake as much as anything else) and the previous students said we should definitely keep it. I also hope you can see the value of Facebook as a discussion forum, and are interested in the book if you haven't read it. Sorry the post was sooo long! Short compared to all the responses, but I probably could have consolidated more.
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