ED218 Developing mathematics: The early years

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Week 3 Wikipedians (January 30 - February 5)

 

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 Wikipedia-style 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 peer-reviewed 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
Hands-on 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.
Whole-body, 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 computer-based learning (to which kids are used), and non-computer 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
Hands-on 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
Hands-on work
Attention to student interests and engagement
"Math is everywhere" mindset
 
Carolyn Lesser
Learning through play, games
Problem-solving 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)
Hands-on math
Visual activities
Students creating something themselves
 
Carolyn
Explore, compare and contrast, share different routes in problem-solving
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:

Task Discussion


  • Keisha   May 2, 2012, 9:36 p.m.

    The website below is about the different ways you can use your body to learn math. Dance is a great way to get your kids to be active and teach them math. My favorite piece in this website is the counting handshake. Kids these days come up with some creative handshakes. This wil allow them to do that while learning about sequences. (I tried to add this on our wiki page but was having some trouble. maybe someone can do it or explain it to me. thanks!)

    http://www.mathdance.org/html/activities.html

    This next site was introduced to me by Carolyn Lesser (thanks!) and I also used this in another task. It shows teachers learning how to teach math with dance.

    http://www.sciencedaily.com/videos/2008/0503-do_the_math_dance.htm

    And these last few links are showing you kids that are using dance to learn. They're fun and really cute. Enjoy!

    http://www.youtube.com/watch?v=TDNGfKR0nZ4

     http://www.youtube.com/watch?v=5_u_0J_btCc&feature=related

    http://www.youtube.com/watch?v=YAjp5noDVE0

  • Kathy Cianciola   Feb. 20, 2012, 10:44 p.m.

    This site provides a good reference for "kinesthetic" and "hands-on" learning.  The article states that representing concepts in physical ways makes the lesson more memorable, and that movement is great for children who may feel intimidated.  It talks about exploring geometric shapes by stretching long pieces of elastic to discover the relationship of one shape to another, and mapping the solar system through dance.  Instead of simply learning lessons, children can perform lessons!

    Creative movement: A physical language for learning, Susan Griss, Educational Leadership,1994

    www.mindsinmotion.org/creative.html

     

    This is a great article, "Zen and The Art Of Unschooling Math," by Rachel Gathercole, but the magazine, "Life Learning" is also a great source for those who are interested in exploring the subject of "unschooling" or "letting the child lead."  It is based on the realization that math is all around us.

    Zen and The Art Of Unschooling Math, Rachel Gathercole, Life Learning Magazine, Jan/ Feb 2005

    http://www.lifelearningmagazine.com/0502/zen_and_the_art_of_unschooling_math.htm

     

    Great study by Jacob Habgood and Shaaron Ainsworth indicating the value of an intrinsic approach over an extrinsic approach, when designing computer games for kids.  "Two studies assessed this approach by designing and evaluating an educational game called Zombie Division to teach mathematics to 7- to 11-year-olds." (SHU Research 2011)

    HABGOOD, MP Jacob and AINSWORTH, Shaaron E (2011). Motivating children to learn effectively: exploring the value of intrinsic integration in educational games. Journal of the Learning Sciences, 20 (2), 169-206, 2011

    http://shura.shu.ac.uk/3556/

     

  • Carolyn   Feb. 5, 2012, 8:55 p.m.

    http://ezproxy.arcadia.edu:2066/ehost/detail?vid=6&hid=106&sid=d676fb26-024f-41e4-8964-4cf7910a1e02%40sessionmgr114&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=eric&AN=ED504839

    This article talks about the simple importance if play, not specifically in math but across all subjects in early childhood. It explains that ECE has been so influenced by standards and strict curriculum that it is. Negatively effecting the students. 

    http://www.education.com/reference/article/Ref_Mathematics_Through/

    Another article on the positive effects of play and how kids can learn math through play. This article also stresses the idea of "natural play" which follows another one of my themes of finding math in everyday life. There is an activity with milk given as an example of finding math in everyday objects and actions. 

    http://thesingaporemaths.com/stratf.html

    I thought this description on how to solve math problems combined the idea of this weeks theme of art by drawing but also involved my theme of finding patterns. I skimmed through the strategies they posted a d I found that I have used almost all of them, especially the working backwards method that I mentioned in my bio. I am interested in finding different articles that explain why kids choice a certain method because although I have used all of the methods, working backwards seems to be the one that works the best for me. Is this familiar to anyone else?

  • Carolyn Lesser   Feb. 5, 2012, 3:45 p.m.

     

     

    Schools Integrate Dance into Core Academics: http://www.edweek.org/ew/articles/2010/11/17/12dance_ep.h30.html

    By Erik W. Robelen

    This article discusses how integrating dance into subjects like science or math and how it can help students, “Arts education proponents suggest that studying the arts provides a variety of academic and social benefits to young people and can enhance students’ ability to learn other subjects, including the development of skills in reading, language development, and math. It’s seen as a powerful way to promote creativity and critical thinking, among other skills.”

     -  Learning through play, integrating subjects, math and art

    The Effects of Color and Background Information in Motion Visuals on Children’s Memory and Comprehension:                                                                                    http://www.eric.ed.gov/PDFS/ED409875.pdf

    By Lin Ching Chen

    This article talks about how using color visuals while teaching students help memory in children especially at a younger age.

    -Visual activities

    East Feliciana Parish Schools Embrace Place-Based Education as a Way To Lift Scores on Louisiana’s High-Stakes Tests. Rural Trust Featured Project:                         http://www.eric.ed.gov/PDFS/ED463136.pdf

    By: Elizabeth Higgins Null

    This article talks about a project to do hands-on work throughout the community has raised test scores in math and science.

    -Hands-on activities

    Exploring Experiential Learning: Simulations and Experiential Exercises: http://sbaweb.wayne.edu/~absel/bkl/vol05/05ba.pdf

    By: Daniel C. Brenenstuhl & Ralph F. Catalanello

    This is an experiment that shows the effectiveness of different learning styles in three sections: experiential, stimulation, and discussion.

    -Research into effectiveness of learning methods

  • Laura Haeberle   Feb. 4, 2012, 5:42 p.m.

    Okay, I focused my research on this week's theme of math and art. Here are references to scholarly articles: 

     

    An editorial on teachers' roles in integrating art and math:

    Biller, Jerry. Math In Art Or Art In Math. 1995. ERIC. Web. 4 Feb. 2012.

    How drawing can be used to to teach children math:

    Edens, Kellah, and Ellen Potter. "The Relationship Of Drawing And Mathematical Problem Solving: "Draw For Math" Tasks." Studies In Art Education: A Journal Of Issues And Research In Art Education 48.3 (2007): 282-298. ERIC. Web. 2 Feb. 2012.

    Why art connects well with math:

    Kim, Una, and Angela Stabley. "The Art Of Math." Mathamatyc Educator 1.2 (2010): 16-21. ERIC. Web. 4 Feb. 2012.

    PLCs and the combination between art and math:

    McIntosh, Ronald D. "Teaching Art + Math." Schoolarts: The Art Education Magazine For Teachers 107.8 (2008): 64. ERIC. Web. 1 Feb. 2012.

    How understanding symmetry can interest children in math:

    Wilders, Richard, and Lawrence VanOyen. "Turning Students Into Symmetry Detectives." Mathematics Teaching In The Middle School 17.2 (2011): 103-107. ERIC. Web. 2 Feb. 2012.

     

    And then here are some of the relevant Wikipedia articles related to math and art:

    Mathematics and Art     http://en.wikipedia.org/wiki/Mathematics_and_art

    Mathematics and Architecture  http://en.wikipedia.org/wiki/Mathematics_and_architecture

     

    Sample Artists:

    John A Hiigli        http://en.wikipedia.org/wiki/John_A._Hiigli

    M.C. Escher        http://en.wikipedia.org/wiki/M._C._Escher

    Dick Termes       http://en.wikipedia.org/wiki/Dick_Termes

     

    Concepts:

    Mobius Strip      http://en.wikipedia.org/wiki/M%C3%B6bius_strip

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

    Synergetics         http://en.wikipedia.org/wiki/Synergetics_%28Fuller%29

    Optical Art           http://en.wikipedia.org/wiki/Op_Art

    Math and Fiber Arts (Quilts, Crochet, etc.)  http://en.wikipedia.org/wiki/Mathematics_and_fiber_arts

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

     

  • SandyG   Feb. 3, 2012, 10:12 a.m.

    * Bhanoo, S. N. (2011, August 16). In future math whizzes, signs of ‘Number Sense’. New York Times, p. D3. Retrieved from http://www.nytimes.com/‌2011/‌08/‌16/‌science/‌16obmath.html  This is a discussion of recent studies that children as young as 3 have math sense and what that  means for the future.

    * Burns, M. (2009, March/‌April). Win win math games. Intstructor, 23-29. Retrieved from http://www.mathsolutions.com/‌documents/‌WinWin_MathGames.pdf  “Games help to lift math off the textbook pages, and they support students’ learning about Numbers and Operations. They are also

    ideal for students when they have extra time.”

    Article explores 4 different games:

    1) Four Strikes and You’re Out = Fun mental computation practice for a range of grades

    2) 101 and Out = A great game for column addition

    3)Seven Up = It is essential for students to develop fluency with combinations of 10. Seven Up, a game from Scholastic’s Do The Math intervention program, gives students the practice they need.

    4) Target 300 = A game from Teaching Arithmetic: Lessons for ExtendingMultiplication, it gives students the opportunity to practice multiplying by 10 and multiples of 10.

     

    * Differentiated learning. (2012). Retrieved February, 2012, from National Council of Teachers of Mathematics website: http://www.nctm.org/‌resources/‌content.aspx?id=22624 This is a collection of tips for meeting the needs of diverse learners.  It includes links to more complete discussions of topics.

    * NHTI. (n.d.). Math tips for kinesthetic/‌tactile learners. Retrieved February, 2012, from New Hampshire Technical Institute website: http://www.nhti.edu/‌learningcenter/‌mathtipslearnstudy.pdf This is a study guide with 10 ideas for teaching math to kinesthetic learners.

    * The Access Center. (2006). Using mnemonic instruction to teach math. Retrieved February, 2012, from LD on Line website: http://www.ldonline.org/‌article/‌Using_Mnemonic_Instruction_To_Teach_Math

    Discusses 3 basic types of mnemonics (keyword, pegword & letter) and how they translate into math instruction. “ Mnemonics are used in teaching math facts, order of operations, measurement, geometry, problem-solving techniques, and other areas of math. The pegword strategy is used almost exclusively in math because it is designed specifically to help students remember numeric information, especially in a particular sequence.”

    The keyword strategy is based on linking new information to keywords that the students already know. This strategy can be an effective way to teach multiplication facts.

    The pegword strategy uses a consistent set of rhyming words to represent numbers. The rhyming words, or “pegwords,” provide visual images that can be associated with facts, thereby helping students associate the number that rhymes with the pegword. This strategy is useful for teaching many areas of math, especially math facts; however, students must have a firm understanding of the pegwords before the strategy can be introduced.

    Letter strategies involve the use of acronyms or acrostics (sentence mnemonics). One acronym that can be used in math is STAR, which is an effective instructional strategy with students who have progressed in math sufficiently to learn word problems and equations. This strategy cues students to complete general problem-solving steps. Letter strategy for problem-solving STAR =

    Search the word problem

    Translate the words into an equation in picture form

    Answer the problem

    Review the solution

     

    * Wetzel, D. R., Ph.D. (2012). Why use technology to teach science and math? Retrieved February, 2012, from http://www.teachscienceandmath.com/‌2010/‌02/‌12/‌why-use-technology-to-teach-science-and-math/  This is a brief article that includes reasons why technology is important in teaching modern math.  It also includes a short discussion on teacher resistance