This week, I hope to aggregate the first draft of a Wikipedia article on modern elementary mathematics out of examples you proposed during Week 2. We have good content already, but need some Wikipediastyle references.
The task

Find references about modern elementary math for our Wikipedia article

Say what aspect(s) of modern elementary math your reference illustrates. Choose aspects that relate to your favorite themes, this week's theme of math+art, or lists below
You can refer to anything you consider a good quality source. For our article to survive, it really needs links to other Wikipedia articles, as well as what Wikipedians consider "reliable sources"  such as peerreviewed sources or writings of established experts.
Aspects of modern elementary math from Week 2 tasks
SandyG
Using psychological tools such as mnemonics and rhymes
Integrating learning into daily routines in little chunks
Handson work, manipulatives
Using technology to spice up routine work and make it interactive
Different presentation options, based on individual student's information processing features
Using interactive tools for focused training, such as scanning games (vision therapy)
Using computers to provide prompts (random numbers, for example)
Open activities that allow modifications by ages, levels, etc.
Wholebody, kinesthetic math
Learning through play
Laura Haeberle
Math in art
Helping children be more aware of their learning processes
"Learning from the comfort of an iPhone"
Using statistical analysis of learning success (Laura's example was both about technology itself, and analyzing its results)
Using videos in lessons (purposefully, with planning)
Tension between computerbased learning (to which kids are used), and noncomputer math tasks
Using technology (cameras, computers)
Content aggregation from many people (you can do it with thousands online)
Involving families in school projects
Dinesh Tantri
Use of grand stories with characters, being on a mission, and roleplay
Julia Brodsky
Modern statistics  all the modern visual methods of representing it, ahh! (think http://www.gapminder.org , etc) (and yes, you can do it with kids now)
Modeling processes (system dynamics)  previously that could be done on paper only; now you can model those in computer games, etc.
Science modeling (physical processes, etc) and games based on physical models (Universe sandbox, etc)
Mathematical physics (like lattices by S. Smirnov)  it should be easy enough to introduce lattices and fractals on them for the kids
Sets and functions (they are fun to play with; computer allows for more visual interpretations)
Boolean logic (again, easy programming and fun puzzles will do)
Tropical math (nice to introduce new arithmetic signs! Kids love that! And they can come up with operations of their own)
Kathy Cianciola
Active participation of everybody
Kinesthetic learning through the whole body, moving around
Handson activities
Using computers and technology in general
Letting the child lead
Attention to extrinsic and intrinsic aspects of learning
Open activities, math improvisation
Multiple representations
Keisha
Ability to modify activities to accommodate different ages and abilities
Handson work
Attention to student interests and engagement
"Math is everywhere" mindset
Carolyn Lesser
Learning through play, games
Problemsolving and its parts (e.g., attention to math language)
Research into effectiveness of learning methods
Using visuals to help understanding and memory
Integrating subjects (e.g., math and science)
Dynamic, interactive links among multiple representations (stretching rulers)
Handson math
Visual activities
Students creating something themselves
Carolyn
Explore, compare and contrast, share different routes in problemsolving
Quest for better tests, and the question if the best test is no test
Learning through play, math games
Introducing deep math concepts (such as patterns) at very young age
Seeing mathematics everywhere, in daily objects and activities
Creativity, open tasks, student discovery
Teacher as researcher, observing student thinking and expecting the unexpected
Amanda Graf
Kinesthetic learning
Team work
Visualization, visual learning
Use of signs and gestures for babies, sighted older kids, everybody (we did baby signs as a family, too)
Using catchy, edgy, cool content, especially catchy songs
Modifying your auditory environment to suit your preferences and needs (silence, background music, white noise, nature sounds, etc.)
Visualization of data (spreadsheets, graphs)
Data students collect on their own, and then aggregate as a class using technology
The lists come from these tasks: