While not nearly as sexy as iPads

and definitely not as lucrative as Khan Academy

I for some reason made the choice to lead a 90 minute session this morning on

**student posed problems**. By this I mean creating a culture where students are producers of mathematics, not just consumers of mathematics.
I began by talking about classroom values that I try to instill which foster students creating good mathematical problems of their own. I'm sure there are more, but I highlighted the following:

- Promote collaboration
- —Focus on process, not just answers
- Build comfort with unfamiliar problems
- Start with good problems
- Create intentional vagueness
- Assess as check-ins, not evaluations

We unpacked each of these values and did some math. I then tried to make a pitch for why it is important to let students create their own math problems. I first reached out to the romantics, claiming that we make music in music class and art in art class, and math should be no different. I then gave the non-romantics a list. Non-romantics love lists.

- Checks for deeper understanding
- —Differentiate
- Model mathematicians
- Teach higher order thinking
- Determining parameters is oftentimes the “real” mathematics
- Meaningful sharing

We unpacked these ideas and did some more math (a pattern you see?). If this was the skin and bones and hair of the talk, we now delved into the meat.

**How do you get students to ask good mathematical questions?**

Of course, this can be simply answered with a list.

A. Creates variations

B. Creates generalizations

C. Creates extensions

D. Looks at simpler examples when necessary

E. Looks at more complicated examples when
necessary/interesting

F. Creates and alters rules of a game

G. Invents new mathematical systems that are innovative,
but not arbitrary

Ok, not actually simple. Required unpacking. And math to keep it fun. And most likely lots more practice long after this session. Finally, I talked specifically about

**The "Invent Your Own" Project**, a 5th grade project we do at the end of the year where students deeply explore a topic of their choice. If you're interested in the nitty gritty details of the project, feel free to explore what we hand to the kids. Please use this! All I ask is that you cite where it came from and let me know what worked, what didn't work, and what you made better. For example, I'm planning on completely revamping the rubric I used for this project so if someone else chooses to do this before I get around to it in the spring, whippee.
I next did a little student bragging and some examples of past projects. Here are three.

Model of a hypercube |

Fractal made on a laser cutter |

Exploration of cuts made from different paper folding |

People were just begging for one last list, so I shared some non-visual examples of past topics:

- A variation on RSA Encryption
- Workbook to teach Egyptian Fractions
- Scaled Barbie
- Map projections
- Efficiency of product packaging
- Different ways to calculate pi

With the last list out of the way, we spent the last 25 minutes brainstorming ways people could start to incorporate

**student posed problems**into their curriculum. Good times. Good times.
To those of you visiting here for the first time, welcome. Please continue the conversation in the comments. To my long time reader(s), I'm back from a pretty
long break...errr, hiatus...actually, I like sabbatical. Yes, let's call
it a sabbatical. So to you, welcome back.

It's amazing what happens when students begin to realize the creative power of mathematics.

ReplyDeleteI recently gave a very similar talk at a Math for America workshop here in NYC. Our bullet lists are virtually identical.

The only other thing I have in the "Why?" list is the value of becoming a good technical writer. If you can learn to express complex mathematical ideas clearly, you can write clearly about anything.

I, too, am often asked for lists of starter projects, but it almost defeats the purpose, which is for students to find something unique to them.

Great Article

DeleteIEEE Projects for Engineering Students

Final Year Projects for CSE

Great Article

DeleteProject Centers in Chennai

JavaScript Training in Chennai

JavaScript Training in Chennai

Patrick: Thanks for the comment. If you have anything you think would be worth sharing, I'd love to see how you've been both conceptualizing and implementing this idea.

ReplyDeleteHi Avery-

DeleteAs a follow up, I've put together a few "Math Research Project Outlines", which are really just sets of questions built on a particular seed question. For example, here's one on Grid Walking.

As loose as they are, this is pretty much how I mentor student projects: I help them construct interesting, relevant questions, and then help them put the pieces together. I'd love some feedback, if you're so inclined.

I've put these together as an attempt to get more teachers and students involved in the Greater New York Math Fair, a student math research/writing event: http://www.nycmathfair.com.

Hopefully these can shed some light on how students might start an investigative project.

The paper folding mobile reminded me of a beautiful theorem that some of my math circle colleagues in SF showed me: the "one cut" theorem. What it says is that if you draw anything on a piece of paper -- even a concave thing -- even a disconnected collection of things! -- there exists a way to fold the paper such that with one straight cut all the way across, precisely the region(s) you outlined will fall out. Well, it doesn't quite exactly say that, but I'll leave it to your students to find out what kinds of things might be uncuttable, and what the rules might be for folding.

ReplyDeleteIn my own practice, I often present a situation that leads to a sequence or pattern, and then ask the participants what they see, what they wonder, whether what they wonder is always true, and how we might find out. So there's some of the feeling of creating their own questions but within the framework of a shared mathematical context. Sometimes the context seems to push people to ask pretty much the same questions, but every once in a while I'm really surprised by the patterns people see and the questions they ask!

A talk by Erik Demaine got me into the one-cut challenge a few years ago. I put together a few resources like this:

Deletehttp://mrhonner.com/2011/05/09/one-cut-challenge-triangles/

It's the perfect problem in many ways--easy to state, easy to get into, something you can explore physically, and surprisingly deep!

I've posted some thoughts about your wonderful session on my math education blog:

ReplyDeletehttp://blog.mathedpage.org

Who knows, I may start blogging regularly!

however as a general rule this authorization is only every once in a long while given.best essay services In the ten years I have functioned as an instructor in Australian government schools, I have just observed one instance of this.

ReplyDeleteYou are gentleman and you need to be duty bound to deposit the amount help with essay writing in the bank for the education of your children.

ReplyDeletethank you for a great post.

ReplyDeleteDissertation Examples

There are also a few privately-owned companies which offer loans to students.MUT This certainly increases the options at your disposal.

ReplyDeleteAdvancement for our kin with incapacities was difficult to find UNIVERSITY IN KENYA as of now with thusly of reasoning pervading our general public, writing and considering.

ReplyDeleteA Positive social change and its related monetary development are accomplished as the general population apply the abilities they learned while they were in school. https://www.ngscholars.net/jamb-registration/

ReplyDeleteBuild up a technique, stay with it for a couple of months, at that point reassess and correct your costs appropriately. comic

ReplyDeleteThanks For sharing this Superb article.I use this Article to show my assignment in college. sd jain modern school suratit is useful For me Great Work

ReplyDeleteI read this article. I think You put a lot of effort to create this article. www sscollegeonline com I appreciate your work.

ReplyDeleteI love the way you write and share your niche! top 10 schools in north delhi Very interesting and different! Keep it coming!

ReplyDeleteThe academic guidance of students at their home is called Home Tuition. The service providers of home tuition are generally evening academies of varied types. These academies are organized by educators and non-educators. this link

ReplyDeleteHi, This is a nice article you shared great information I have read it thanks for giving such a wonderful Blog for the reader.

ReplyDeletetree trimming greenacres

Excellent Post! For more information Visit Here.

ReplyDeletetree removal gibsonton

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..tree removal services dover fl

ReplyDeleteThis is a great article thanks for sharing this informative information. I will visit your blog regularly for some latest post.

ReplyDeletetree trimming companies apollo beach

I have read your article, it is very informative and helpful for me.I admire the valuable information you offer in your articles. Thanks for posting it..

ReplyDeletetree trimming wesley chapel

Thanks for the wonderful share. Your article has proved your hard work and experience you have got in this field. Brilliant .i love it reading. tree trimming services tampa fl

ReplyDeleteThanks for the wonderful share. Your article has proved your hard work and experience you have got in this field. Brilliant .i love it reading. residential tree services miami dade county

ReplyDeleteThanks for the wonderful share. Your article has proved your hard work and experience you have got in this field. Brilliant .i love it reading. tree services near me in palm beach county

ReplyDeleteHello, I have browsed most of your posts. This post is probably where I got the most useful information for my research. Thanks for posting, maybe we can see more on this. Are you aware of any other websites on this subject?

ReplyDeletetree care companies broward county

I think this is one of the most significant information for me. And i’m glad reading your article. emergency tree services kendall fl

ReplyDeleteExcellent Post! For more information Visit Here.palm tree services miami dade county

ReplyDeleteGreat article and a nice way to promote online. I’m satisfied with the information that you provided commercial tree services miami springs

ReplyDeleteThis post is good enough to make somebody understand this amazing thing, and I’m sure everyone will appreciate this interesting things.stump grinding west miami

ReplyDeleteExcellent Post! For more information Visit Here.stump removal golden glades

ReplyDeleteI read your article, It really gives me a very valuable informatiom.

ReplyDeleteGood morning Images

I found so many interesting stuff in your blog. as we provide online research paper writing service at affordable prices. for more info visit our website.

ReplyDeleteThis comment has been removed by the author.

ReplyDeletenew york city escorts

ReplyDeleteThank you for sharing the blog love it

I can set up my new idea from this post. It gives in depth information. Thanks alot.

ReplyDeletegai goi da nang

Nice Article Thanks For Sharing For More Info Visit: gai goi ha noi

ReplyDeleteA lot of our goal is to keep up your clinic or clinic so you can focus concerning running your internet business! Our advertisement cleaning team insures every detail to assure your clinic maintains some clean not to mention professional appearance for a employees not to mention customers. Aside from commercial vacuuming services, this site offers regular good inspections for helping prevent any sort of issues; but, should a desperate arise, you can easily respond to all your needs fast. In virtually all cases, you can easily follow up with our clients’ requests inside an hour. cleaning company in dubai

ReplyDeleteOur skills will help to increase the productivity of the company.iso 9001 washington

ReplyDeleteWONDERFULL. iatf 16949 louisiana

ReplyDelete