Hi,
I bought a box of 12 inch rulers...
Now I'm ready in case I'm asked to teach a 5 year old basic geometry. :)

"First they ignore you, then they laugh at you,

then they fight you, then you win."

- Mahatma Gandhi

I was 5 at the time. We just made squares, triangle, trapezoids and hexagons until algebra made sense.
I remember having a paperboard under the rulers with 1 inch pattern helped our thinking.
We were Hungarian, so it could have been Metric.. but no matter, the concept stuck.
Learned to count volumes and relationships.

... no structured class... just kids playing.. learning from reality.

We used the rulers to draw the shape of roads going into the distance, and houses and roofs, and to scale the size of trees as they went into the distance on the road. Even drawing faces was easier were rulers framing and lining up the features.

Thanks for the reply. I share your thinking about estimation as important as computation, and I think lots of research backs you. I spend a lot of time trying to help teachers understand the balance that needs to occur in a classroom so that students aren't just compliant, but engaged, observing, and learning. They have a tough job, but it's worth the battle.

I looked at your organization's site yesterday. I must say I didn't look that closely, but I'm impressed with the effort (one reason why I made the connection). Like my mother too young to retire but ready for a change in perspective? When she retired she worked for ten years running a small non-profit office. She was the business manager, but had more experience and knowledge than anyone else in the organization. She liked not having the title, so she could make it happen and not have to worry about all the details. (Not saying you are like that, but that's her story)

I'm finishing my coursework this spring and sitting for comps in the fall. I work too much during the summer to attempt to study for August comps. I'm working on my framework for my dissertation. I'm battling one of two approaches to explore problem solving in algebra. It's a pertinent area for immediate impact on a growing field in math ed. I'm exploring providing students a specific model to explore- specifically the Singapore bar model, and use explicit strategy instruction to see how well they are able to incorporate. I'll send you a brief description if you are bored and need some bedtime reading. The other topic is of more interest to me, but has some other issues; using metacognitive reflection and threaded discussions to identify processes and concepts that students are using in problem solving situations in algebra. Connected to the first but separate.

Anyway, thanks for the reply and I look forward to connecting again. Have a good Sunday. I'm going for a ride! It's sunny and not cold in Kentucky today.

Great! I am glad to see you visit our site. I manually confirmed your account, so give it another try. :0)

I'll give you a question first, if I ask you to solve the equation 3x + 5 = -4 using a table of values.

I would then ask that you think about the decisions you made to come to the solution. The process you used, and the decisions you made are what I am interested in helping you organize, develop and expand upon. It's that thinking that students use when solving complex problems (or not so complex problems) that I believe we need to focus on more as teachers of mathematics. I think (and research backs me up on this) that most teachers focus on the simple skills of solving linear equations algebraically rather than allow students to sort throught those rough processes and learn to become more efficient at making critical decisions.

Let me explain by accessing the problem I asked you to solve earlier. Could you look at the problem and rethink your approach so that you could solve it more efficiently next time? or What answer could there be on the output side that would make this method very difficult? Why would it be more difficult?

If you can sort those kinds of questions out after solving the problem then you are more likely to be able to use those processes in a flexible manner in future problem solving endeavors (at least that's the theory I'm using as a basis for my project). So my goal would be to use an on-going conversation with the teacher and other classmates to explore problem solving approaches, to learn to capture them, think about them, make them more efficient/effective.

What do you think?

I didn't realize you had two comments. I actually responded to the second comment first, sorry.

Yes I notice learning styles. It's one reason I like the metacognitive focus. It allows students to analyze their thinking to find efficiencies and faults. It's our job as teachers to present them with multiple perspectives and to provide them opportunities. For instance with the problem below, I would ask students to solve it from multiple perspectives; table of values, algebraically, graphically, and even a group to explain what the solutions represents in terms of some application or to make connections between the input and output somehow. It's interesting, I just used this approach with teachers in a workshop, and I got a lot of pushback from high school algebra teachers because they couldn't explain the solution in words. It just reinforced to me that they weren't trained using multiple perspectives and they don't value them with their students. In my opinion, they don't get it (but that's just my opinion).
I would be glad to share my idea with you. It's not fleshed out yet, but I need to spend some time working on it.

Dear Bob

I am only a classroom teacher in the backblocks of Australia. I might be out of my class but your project might be heading where I want to go. I am worried by a group of boys (mainly) who are 'failing' mainstream school and leave with minimal literacy etc. I am interested in trying to reach these kids in other ways. I have used blogs and web pages and podcasts to teach a seriously ill student for a semester, successfully. So, I dabble.

How did the interview go? Sorry I could not make it. I had a class at that time.

Greg

The radio show is generally available: http://www.blogtalkradio.com/search/zenhausern/

Hi, Bob! Thank you so much for your sharing.

Hi, Bob. Thank you for your generous offer- I'd love to accept. I started to send you a note the other day, but my browser shut down in the middle off it. I've lost the url- do I need to go to the site and sign up?

ThanX~~~ Sharnon

Yes, I am interested in the history of distance education. Are you willing to have your classroom or course of students participate?

Wow! Would you like to be a speaker for the course? I have a timeline of events and early in the course, we will need someone to present on the History of DE.

Wonderful! A panel of speakers would be nice. Please let me know which three dates in January and February work best for you. I will choose one of the proposed dates if that is ok. We would need about an hour to an hour and thirty minutes of your time.
Thank You!

Sincerely,
Aries Cobb

Thank you. I am considering using Google. Google has a video and a chat feature. Or we may use skype. Do you have any other options in mind? I am open to suggestion.
I am putting the final touches on the syllabus this week I plan to have date ready on Friday November 20, 2009. Thank you again.

Sincerely,
Aries Cobb

Hello!
I am unfamiliar with DimDim and Open Meetings. I will explore them as well. Please keep me posted.

Thank you again.

Sincerely,
Aries Cobb

Dear Bob,

Thank you for your time and consideration. I have two dates in mind for the panel discussion:
(a) January 19, 2009-Scope and Definition of Distance Education, and
(b) January 26, 2009- Historical Context.
The course meeting time is 5:00 p.m. -8:00 p.m. Please let me know which date and time is best for you. Thank you again.

Sincerely,
Aries Cobb

Dear Bob,

Nice! I am very excited about this project. The panel discussion will take place from 6:30-7:30 p.m. Please, write an agenda for the meeting that I will share with the teaching professionals enrolled in the course.

Thank you,
Aries Cobb

Hi Bob
I teach Media Art and would love to connect my students with others from around the world. Would Morocco have any teachers or students that you think might like to work on a collaborative project?

HI, Bob,
Happy Thanksgiving! I'm heading across the street to help with the cooking for a big gathering today.....would you like to talk on Monday? Or email me at my work email address, and we'll find a time to talk on Monday or Tuesday. Or, I'm doing a webinar about ePals on Wed. at 4:15 p.m. eastern time, if that is helpful.
My work email: roates at corp dot epals dot com (said that way to inhibit the spam bots!)
Best, Rita

Hello Bob,

I am very excited about our project. Have we scheduled a time for our dress rehearsal for the panel discussion? Please let me know when is the best time for use to meet.

Thank you,
Aries Cobb

Hello Bob,

December 11, 2009 at 7pm is great. I look forward to our meeting.

Thank you again.

Sincerely,
Aries Cobb

Hello Bob,

December 11, 2009 at 7pm is great. I look forward to our meeting.

Thank you again.

Sincerely,
Aries Cobb

Bob,

My husband is related to a "Jimmy" but doesn't know his wife's name. Maybe the same person? Possible son of Bill Schutte, my husband's uncle from Indiana.

Finished in early May (whew!), but thanks for the offer. Would have been helpful, I'm sure. I felt like I was wandering in no-man's-land for quite some time!