student #1
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 an 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.
student #2
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 semmester.
student #3
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.
student #4
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. Im 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.
student #5
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.
student #6
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.
student #7
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 alot 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.