DLG reviews

• This was literally the best class I have ever taken in my entire life. If I could just take this class on repeat for my entire education I absolutely would. I spent hours outside of class poring over problems with my classmates: at dinner, at the baths, late into the night. I learned so much math from this. It was absolutely fantastic.

• Easily my favorite class, and an amazing professor. Every class period was very fun and made all of us want to work hard to solve all the problems. The structure of the problem solving in DLG also says a lot about Hungarian math education and why it is so successful. This class is a highly unique and worthwhile opportunity for BSM students, and I feel very fortunate to have been able to take advantage of that opportunity and get such a memorable experience from it this semester.

• I have continued to really enjoy doing the DLG problems. As other classes have been picking up and midterms have started, it has been increasingly harder to spend quite as much time thinking about these problems, but that has made me enjoy finding time to do them that much more. Looking back at the problems from the entire term, it's great to think about how many concepts we've covered and how many ideas we have been building up from day one. There were a few classes that have felt pretty repetitive, but looking back on the process, I'm glad we have continued with the same topics. The class the other day where you introduced the 100 piles problem and the magic number problem was refreshing, as those both felt like fresh new problems.
  
  The two player games have been the most difficult for me. For most of the other problems, I have just been able to keep trying solutions until I reach a solution. This has been much harder for me in the two player games because I have to think of two people simultaneously. I need to think about what the best move for me is, and what the best move for my opponent is. It's always just a few too many things to process and I always make a mistake while thinking about my opponents moves. I have been getting better throughout the term, but they are still the problems I have the most difficulty solving, and there are a few class periods during which I have spent the whole time trying to find a solution, unsuccessfully.

• This class has not been exactly what I expected when I enrolled in it, in that it devotes very little time to explicitly discussing how to instruct children. However, I feel that how the course has been structured up until this point has been much more valuable than it would have been otherwise. I realized this the first time one of our problems to work on was simply "come up with interesting questions about ____". This was when I first recognized that, through solving and exploring all sorts of unrelated and engaging problems in class, I now have a much better idea of what it actually means to ask interesting questions. I now have a much greater appreciation for the value of problem solving skills and how I would go about culturing these skills in students. The course has made me all the more excited about teaching students, now that I think I have a much better understanding of how to pose productive questions. The problems we do in class remain interesting, and I am still very fond of the casual structure of each lesson, with most of the time just spent solving/discussing problems. Overall I am enjoying this class quite a lot, and I'm excited to see how it will progress through the rest of the semester.

• I have really started to see myself using some of these problems in my own classroom, which is really exciting. I feel like I am getting more used to the problem solving atmosphere and even asking questions after solving certain problems. I feel like eventually I'd be able to teach a class using some of these problems and other problems, too. One thing I really enjoyed last week was the question about symmetries (points versus lines). It sounds like such an easy task, but being forced to make up questions on your own is actually quite difficult! I know I sat and looked at it for a long time, wondering if I could come up with any thoughtful questions about points and lines of symmetries. I think this would be a good task in a classroom lesson involving symmetries, but is also just such a useful skill for children to use. I think it would be great if students could develop the skill of asking questions on their own about things they are interested in.

• I am really enjoying how we are beginning to talk about how children solve these problems, and starting to think about the methods and modes that they think in. It is probably one of the more useful skills we can learn if we are to be teachers in the future. It helps when explaining a solution to know the most common misconceptions about a problem. I am sure it helps with hints to students as well.
  
  Recently we also have been talking about asking good follow up questions and i enjoy trying to think of good ones. I am also thinking it would be cool if later in the semester we could get into groups and make up problems similar to the ones we have been solving, maybe that is upcoming, but i think thats also an extremely useful skill to know.
  
  I am still finding the problems very fun just for myself as well, its a nice way to end a long day.

• Week 3 was another good week. I was proud of myself for being able to figure out problem #18, though I probably could've done a better job explaining it at the board. I think it's really interesting and helpful when we discuss different ways of solving problems, especially since they can be pretty different. I'm finding that different solutions usually have the same underlying principles, so I like seeing how people approach problems differently. While I'm enjoying the problems and the class, I'm starting to wonder again about the element of us doing things from the "teacher's perspective". It seems that it's slowly coming in (e.g. "What would be a good question to ask next?"), so I'm looking forward to seeing where that's going. Also having the problems in a pdf is really great and will be really good to have.

• So I am really enjoying class so far. I got the problem of 8 weights in class last week, and I'm looking forward to looking at its counterpart for homework. I initially found the problem of finding a product of numbers 1 to 100 which 72 does not divide to be... a bit dull. I'm not a big fan of using properties of divisors, though this problem was simple enough and I can see how it would be extremely helpful in the classroom environment. I am beginning to see how working out these problems will help us understand the student. In fact, I have begun to start some of the problems by approaching it in the way I think the child student would and then moving on from there.
  
  I'm getting the hang of the problems but this set seems particularly challenging :) Im excited.

• In response to our activities in class I am overall happy and excited to continue this course. I can tell over the past few weeks that the style of questions that are asked in this class have become much easier to think about, which is a testament to their place in a classroom. I appreciate the variety of problem as well, I know some people can be much more visual with their problem solving and approach them in a more diagram driven way vs. those students who offer much more proof driven answers. Having these two ways of problem solving in one class is very helpful but especially so when the students get to talk and discuss answers in pairs or small groups. I encourage you to continue emphasizing participation and collaboration in the classroom. I would also like to note that as a more visual and physical learner I find myself putting a lot more thought and effort into the problems where we have materials to work with (like the match box problem and problems with the checkerboard and paper coins.) I'm really glad you have integrated those types of problems into our class time.