I put together themes you suggested for the course in this mind map: http://mind42.com/pub/mindmap?mid=994691af-7ac0-42ac-b297-0279be4568fa It was a fun task, and of course it's not the only way to summarize themes - questions and comments and versions are welcome. The whole task took about three hours, but comments may be much faster. Here's the bird's eye view on the map (too small to read).

This week's topic, "Scope of modern elementary mathematics," is "meta" - it fits with all our themes. This task is about us building a definition of what good modern elementary math is, with current examples. 

1. Find six blog posts, forum discussions, videos, articles or any other online content that goes with your themes from last week, AND are examples of "modern elementary math." You can spread examples over themes (two per each) or distribute them any way. 
2. Limit your search to fresh, current content - either something posted within the last few months, or something still currently under active discussion. Use time limits in your blog or web searches to do so. This will raise the chances of dialogues happening.
3. Leave comments at places where you find examples, adding something to the theme (as expressed there).
4. Copy all your comments and links to their web pages in one comment to this thread. You may want to copy comments and links into a document as you go along, because some places moderate comments (slowly!) and you won't see them for a while.

We will end up with something similar to a blog carnival, but not limited to blogs, and with our comments in it. Here is an example from the latest, 46th issue of "Math Teachers at Play" carnival by our Denise - the part about math puzzles:

• Gary shares a few puzzles that elementary-age children can understand but adults can enjoy exploring as well: Numberplay: Tanton Wordless. [Errata: Moving your mouse over the second picture will display solutions for four of the six puzzles shown, implying that two are impossible --- but really, only one is impossible. Can you find the missing solution?]

• MathCounts is a great source of problems for middle school and older students. Mrs. Lin offers Mathcounts competition preparation strategies I, along with a blogful of questions and solutions.

• My entry for the carnival is the 2012 Mathematics Game, a terrific puzzle for middle school and beyond.

• Fawn offers a series of challenges in Puzzles and Brainteasers, Set 3, Set 4, and Set 5.

• Can you solve Pat’s Interesting Rectangle Partitioning?

• John presents A Renaissance math puzzle. Intrigued, Thony digs into history in The story of a problem.

Here is another example from the themed Mathematics and Multimedia carnival, by Murray Bourne and featuring Bon and Denise:

(1) Bon Crowder of Math is not a Four Letter Word has written an interesting thought piece on the difference between motivating and inspiring students, in:

Are You Teaching Math Through Motivation or Inspiration?

(2) Denise in Let’s Play Math! says “Let’s look at two common mental models — partitive division and measurement division — to see how the sister could have divided her pie…” in:

How to Understand Fraction Division

(3) Colleen Young (who has a “keen interest in how new technologies can deepen the learning experience for students”) has begun a new blog aimed at students. She’s right – most math blogs preach to the choir – it’s about time there were more blogs addressed to students.

Hello Students!

(4) And finally in this section, here are my suggestions (right here insquareCircleZ) on:

How to make math class interesting?