Learning Environment

I think that I have mentioned in an earlier post that I find the articles in Teaching Children Mathematics (NCTM) very valuable. They are very relevant to learning in elementary mathematics classrooms.

The most recent issue arrived today and the focus is "Learning Environments That Support Mathematical Understanding" - sound familiar!

I've only had time to read one of the articles, Learning to Think and Thinking to Learn. I seem to always set the goal to leave more lesson time for discussion and continue to fail to make the time. I will say that using the new Investigations program has helped me immensely because it is built into each session - yippee!

This article provides classroom examples for using incorrect solutions to facilitate discussions, encouraging students to question each other's solutions, and allowing time to develop understandings. The author also talks about extroverts and introverts and providing for both types of thinkers. There is nothing earth shattering in the article but it reinforces strategies I have used and has given me some ideas for tweaking what I do so I can be more effective. If you have a learning community/study group with a mathematics focus at your school this article has a reflect and discuss page that is a good way to guide the process of self-observation and self-reflection.

Have you used incorrect solutions to facilitate discussions in your classroom? Do you have the students share (as in the article) or do you share the errors anonymously?

Dates Please

Maggie, could you post some specifics about our upcoming Webinars?  We are wondering about locations and if we need to bring anything.

My principal today was asking about the October Coach Training, Administrative Support and Muster, so we will be looking for details about those events as well.

Thanks!

Accelerated students

I would be interested to know what other districts do to provide math instruction for accelerated students. Our teachers have developed a variety of activities, extensions, etc for kids who welcome and can handle more expanded math experiences beyond the curriculum, but what about the extraordinarily motivated and accomplished rare student who masters the curriculum, standards, extensions, etc? We currently have 2 such students in our elementary school, and with no GT program or other support, per se, have accelerated them to the next grade level in math, and both are at the top of their math classes. Was that the best solution for them? What have other districts done?
Thanks,
Debbie

Speaking of Master Teachers...

Our very own Debbie Butterworth has been recognized with an award by the Parents Foundation of Cape Elizabeth for her work in the K-2 Math-Lab!  

Debbie, perhaps you would take a few minutes when we next meet to share with the rest of the group so we can better understand your work there.

Congratulations... we are proud of you!

Ethnomathematics Talk at Bates

Hi everyone... a reminder that Ubiritan D'Ambrosio (Bonnie introduced us to his work in ethnomathematics this summer) will be a guest speaker at Bates on Thursday.  There will be a lecture at 4:30 and a public talk at 7:30.  Copy paste the following link into your browser address bar for specifics:  www.bates.edu/x182781.xml 

I will be driving down for the event - hope to see you there!

Maggie

Ethnomatematics and time

The additional article from Bonnie that highlights an interview regarding Ethnomathematics is quite weighty, a lot to think about. After reading it I decided to begin thinking about one small part of the article as it relates to my classroom. An earlier area of exploration in our blogs encompassed creating a math climate. On page 99 of the last from Bonnie article Milton speaks of “a broader view of mathematics, which embraces ideas, processes, methods, and practices that are related to different cultural environments.” When I read this comment the word embraces rang in my head. The math climate or, for that matter overall classroom climate is optimal when the students thinking, ideas, processes are embraced. When we meet student where they are with prior knowledge we create a culture, yes, a community of learning in which children feel valued, therefore safe to take risks and share their thinking.
We, all at some point in our teaching careers, struggle with the demands of insuring that the curriculum benchmarks (MLR’s) are met, and that we expose our students to the concept strands of our math programs. After reading this article and reflecting on my various experiences teaching, includes those experiences with ELL’s, I found myself thinking about time and how it can be used to enhance a math lesson (any lesson). There was another comment in the article by Ubi that I found myself thinking about. “It is natural, in the view of many educators, that by making children happy and at the same time building a recognition and respect for other cultures, there is a concern for losing ‘precious’ instructional time, which could be used [for] teaching mechanical techniques.” I wish I had some profound insight to share about the use of time and building an embracing community that supports a positive learning climate for all areas of learning including math. What I can say is that creating an embracing environment is one of the professional growth areas to which I feel strongly committed at this point in my life as a teacher. Sylvia Ashton-Warner said it best, “But I must do what I believe in or nothing at all. Life’ so short.”
There are several books that guide my thinking and planning in my classroom, and support me on my journey:

TEACHING CHILDREN TO CARE Management in the Responsive classroom
By Ruth Charney

SERIOUS PLAY IN THE PRIMARY CLASSROOM Empowering Children
Through Active Learning Experiences
By Selma Wasserman

MORAL CLASSROOMS, MORAL CHILDREN Creating a Constructivist
Atmosphere in Early Education
By Rheta DeVries & Betty Zan

DEVELOPING CROSS-CULTURAL COMPETENCE A Guide for Working
With Young Children and Their Families
By Eleanor W. Lynch & Marci J. Hanson

THE MIDDLE OF EVERYWHERE Helping Refugees Enter The American
Community
By Mary Pipher
TONGUE-TIED The Lives of Multilingual Children in Public Education
Edited By Otto Santa Ana

It is a juggling act for sure balancing time with the diverse needs of our students. How do you approach diversity in your classroom as it relates to math and beyond?

Document Camera Possibilities

I was searching for ways to use document cameras on the web and came across an interesting application for them:  this particular teacher uses it to document student work as they move through investigations.  She created a digital folder for each student and when a project was finished, the students used the documentation to help explain to their parents what the project was about and how they were thinking.  At the end of the year, she burned each folder to a CD and added it to their portfolio.  She recommends going to Reggio Emilia sites for more information about the power of documentation.  Here is a link for you to start with:

http://en.wikipedia.org/wiki/Reggio_Emilia_approach

Reggio Emilia is a small place in Italy  - you can read how the approach was birthed there.  One thing that stood right out is, although they are saying it in a different way, it's all about eating mangoes!!

The explanation made me think of so many things you could do with this... what about using a bulletin board to post photo series taken as pairs or groups of students worked on an investigation, and getting others to imagine what each pair/group was thinking and all the ways that thinking might be recorded.  

For RTI... imagine the applications!  What a wonderful reference for them to return to - reminding them of their thinking path... could create a small album with chapters (concepts) and, again, have them think of ways to record their thinking path.  It seems the possibilities are endless.  

Happy reading! 

Posing or asking the right questions can be crucial to learning, esp. for the challenged students.

When we are teaching new concepts, the way that we ask a question can create clear or murky understanding. Posing a quiding question that is open is essential, so that there is room for inquiry and student exploration into the answer. Students
need to search out the answer by creating connections, adding vocabulary, and collecting their own data. Using the data and discussing their understanding will lead them forward. But it is up to us, as educators to create the "right" questions, questions that leave room for student thinking and lead into the concept that is to be discovered.
There is a text titled, "Good Questions for Math Teaching" by Peter Sullivan and Pat Lilburn.
I think that if we want students to investigate and learn the what and why of math before we introduce the symbols, than we need to be very careful of our language and the questions we ask in math. Students need to gain confidence in inquiry and dare to make mistakes along the way to be stronger thinkers and problem solvers, "math thinkers", who can take the challenge as we teach new concepts throughout the year.