Today I shared with you an excerpt from Jo Boaler's short article called 

Mathematics for the Moment, or the Millennium?



Education Week Commentary, 29 (XVIII) March 31, pp 30 & 34.

We will continue to delve into this article next week. Stay tuned........

Thinking Mathematically

Today I showed you the text Thinking Mathematically by John Mason, Leone Burton, and Kaye Stacey. This revised edition takes up the processes of doing mathematics. We discussed the notions of specializing, generalizing, conjecturing, convincing and justifying. 

We also looked at the three stages of a problem:

1. Entry

What do I know? 

What do I want? 

What can I introduce?

2. Attack

3. Review

And remember that being STUCK is an honorable state!

Assessing the Quality of your Blog

Blog Self-Assessment

This is a reminder that Thursday’s class is an independent working session. Your task is to get caught up in your blogging and to revise or edit your work to your own degree of satisfaction based on the following:

• Is my blog free of grammatical/spelling errors?
• Is it easy to read?
• Have I been careful to avoid statements that make sweeping generalizations?
• Have I used appropriate examples to explain my ideas?
• Have I come up with good questions that are interesting, important, or provocative?
• Have I gone further than simply retelling events to trying to unpack and understand events?
• Have I shown evidence of growth of understanding through my reflections?
• Have I been careful to avoid identifying teachers, students, and schools?
• Have I been clear in my writing and choice of words?
• Have I satisfied 4.8.3 MUN University Regulations on Good Writing as described below?

Good writing is characterized by the following qualities:

1. Content
a. critical insight and freshness of thought,
b. clear and penetrating ideas,
c. perceptive, pure grasp of subject,
d. intelligent use of primary and secondary sources, and
e. a sense of completeness about the handling of the topic.

2. Organization
a. effective introduction and conclusion,
b. main idea is clear and logical development follows,
c. smooth transitions, and
d. good use of details.

3. Style
a. appropriate, accurate, precise and idiomatic diction, and
b. sentences varied in kind, length and effect.

4. Mechanics
a. consistently correct spelling,
b. accurate use of punctuation,
c. grammatically correct sentences, and
d. well organized paragraphing.


Please create a brief self-assessment (to be printed and brought to class on Tuesday Feb 17th) of your blog in one paragraph, addressing the following two questions:

1. How is my blog strong?

2. What do I need to do to improve the quality of my work?

Counting Grains of Sand and Painted Faces on Cubes

Over the last few classes you have engaged in individual and collective mathematical thinking as you worked with cubes and grains of sand. 

The following are some of the topics that came up:

• open-ended math problems and what that means
  
• math problems that make you think more than 2 seconds
  
• math problems that allow for multiple entry points - for the diversity of learners
  
• math tasks that don't tell you exactly what to do and how to do it, step by step
  
• math making sense
  
• students using mathematics to determine if an answer is correct
  
• problem solving
  
• working collaboratively rather than hoarding information
  

On Tuesday, Feb 10 we will continue this work. I mentioned how critical chapters 4, 5, and 6 are to your future growth as a primary/elementary teacher of mathematics. Please be ready to discuss chapters 3 and 4 as we look at what it means to think mathematically and teach for understanding.

In class last week we discussed the following best selling children's book, The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger. 

It is a chapter book containing colourful illustrations of various mathematical discoveries. 

It's a best seller, so I think you'll enjoy reading it, and your students - particularly your elementary students - will find it engaging and entertaining. 

I wouldn't limit it to just elementary students at all as it makes a great whole class read-a-loud. It will depend on your students of course!

What is mathematics?

What assumptions do you hold about mathematics? In class we will spend a great deal of time thinking, talking, and challenging what mathematics might be, and the impact that traditional definitions have on us as learners. Using Lakoff and Nunez's notion of the mythology that surrounds math, (what they refer to as 'the romance of mathematics') we will look at traditional notions of mathematics and bump it up against a reconceptualized view. Figuring out our own positioning towards mathematics is critical to becoming a reflective teacher of mathematics. What part of the romance do you believe? How does what you think about mathematics affect how you teach it?

Your next blog entry shall focus on the nature of mathematics. What, for you, are the big ideas? How, if at all, have your beliefs about mathematics shifted? What is it that you will need to know, to read, to figure out, to study to gain a better understanding of the nature of mathematics as something that might be a living discipline, a human activity?

Reuben Hersh is an American mathematician who has written extensively about mathematics. He takes up his ideas from What is Mathematics, Really? in the following interview that I would like you to read: What Kind of Thing Is a Number? A Talk with Reuben Hersh Be sure to click on THE TALK at the bottom of the page to read the entire interview. He delves into his view of mathematics, the teaching of mathematics, and how our stance towards mathematics impacts how and what we teach.

Please also work your way through Chapter 2, if you have not yet done so to help you with your thinking. Put some thought into this blog entry. Remember, this work is not for me to check off a list, but to help you become informed about the discipline that you will be expected to make come alive with children. Looking forward to reading and hearing your ideas.

Important links for you

Here is the site for the WNCP Common Curriculum Framework K-9 Mathematics that was developed and published in May 2006. Eventually, the NL curriculum documents will all be re-written to reflect this document.

Please begin to make yourself familiar with the written curriculum. WNCP is already used in British Columbia, Alberta, Saskatchewan, Manitoba, Nunavut Territory, Yukon Territory, and Northwest Territories.

The Companion Website for our text is also something you need to become familiar with. Please take some time and check out the web links for each of the chapters as we work through them as well as the black line masters.