Information Age Education Blog
Home and School Environment—and Games—in Math Education of Kids
Recently my close friend and co-author Bob Albrecht shared with me examples of a category of math problem used in some elementary school math classes. We are currently co-authoring a book on the use of games to enhance math education for K-8 students. (Note added 12/2/2012: See Moursund & Albrecht in Reference at the end of this entry for the title and a link to download the book.)
Add to 15: List as many ways as you can to use the numbers 1 through 9 to add up to 15, without repeating any of the numbers in a single equation. If you can, try to list all possible ways.
Example 1. 3 + 4 + 8 = 15
Example 2. 1 + 2 + 3 + 9 = 15
Here is my response to Bob's suggestion:
A math-oriented person may well take joy at and have fun with the Add to 15 activity. But I don't see anything in it that is intrinsically motivating, or that would make it a challenging and fun game for children to play.
This type of math activity suggests to me a significant challenge faced by math educators, one that we are trying to address via a games approach. The challenge is that “situated learning" and the context of a problem are very important.
Here is another way of looking at this. The human brain is designed to learn to solve problems that are relevant to survival of the individual and the species. Learning oral communication provides an excellent example of a survival skill, as does learning one's culture and "appropriate" ways to interact with others in one's immediate community.
We move beyond this when we introduce reading, writing, and arithmetic beyond simple counting and very low level number facts. We move beyond this as travel and long distance communication bring us into contact with people who are "different" from us. We also move beyond this quite quickly in science.
From my point of view, this often creates a struggle between what learned adults want kids to learn and "what comes naturally" to kids growing up in their current society/environment.
Kids who grow up in a home environment in which the home (and perhaps immediate community) has a strong orientation toward a particular area (be it sports, math, science, music, religion, computer or non-computer games, etc.) will adsorb a lot about and gain a strong orientation to this environment, in the same way that we learn our own culture and natural languages.
Somewhat similarly, consider a kid growing up in a neighborhood in which other kids have a certain culture and "home-built" orientation. Kids pick up music listening interests from each other as well as from radio and television. The human brain has a strong orientation for a person to be a member of a culture/society of peers, parents, and others who are strongly involved in their lives.
Some aspects of this transfer of learning (transfer of culture) transfer much more readily than do others. Thus, I suspect few if any of my friends absorbed a math-oriented culture from playing with me when we were young children. However, some of my math-oriented culture may have rubbed off in games such as Monopoly that we played together.
The typical parent and the typical elementary school teacher are not strong representatives of a math and/or science cultural environment. (Enough said?)
What You Can Do
You know that the message sent is not necessarily the message received. You, for example, have “constructed” a personal meaning to my message given above. My overall intent is to provide you with some information and ideas that you will act upon in a manner that leads to improving our informal and formal education system.
So, pause for a few seconds and think about the meaning you have constructed from my message and some possible action that you might take based on that meaning. What occurs to you that you, personally, will try out in your quest to improve our education system?
As a personal example, I have a reasonable level of addiction to games, and I now observe myself as I deal with this addiction. At the same time, I made sure that my children learned to play a wide variety of board games card games, and other types of games as they were growing up. I had benefited considerably from this type of activity. My children also got introduced to computer games back when the games were first becoming popular. The effects on their lives have been both positive and negative. The steadily growing addictive qualities of computer games bothers me and is certainly a major challenge to our informal and formal educational systems.
Spend a bit of time reflecting on what you have just read. How does the information fit in with your current knowledge, beliefs, and activities? How can you make use of the information to help improve our informal and formal educational systems? Who do you know that might benefit from reading this IAE Blog entry?
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Suggested Readings from IAE and Other Publications
You can use Google to search all of the IAE publications.
Then click in the IAE Search box that is provided, insert your search terms, and click on the Search button.
Click here to search the entire collection of IAE Blog entries.
Here are some examples of publications that might interest you.
David Moursund Books. (A number of free books of possible interest to parents and teachers.)
Information, the Information Age, and the growing totality of information. IAE Newsletter - Issue 4, October 2008.
Joseph Renzulli, a world-class leader in TAG education. Issue 19, June 2009.
Key ideas from the book by Christensen, Horn, and Johnson (2008). Disrupting class: How disruptive innovation will change the way the world learns. The book explores how Distance Education is changing our schools. IAE Newsletter - Issue 26, September 2009.
Levels of depth of ICT educational uses. IAE Newsletter - Issue 8, December, 2008.
Moursund, D. (2008). Introduction to using games in education: A guide for teachers and parents. Eugene, OR: Information Age Education. Access at http://i-a-e.org/downloads/doc_download/19-introduction-to-using-games-in-education-a-guide-for-teachers-and-parents.html.
Past, present, and future uses of computers in education. IAE Newsletter - Issue 3, October 2008.
Tutor, Tool, Tutee, Toy. IAE Newsletter - Issue # 42 May 2010.
What is the Information Age? Two brains are better one. Becoming more responsible for your own education. IAE Newsletter - Issue 1, August 2008.
Moursund, D., & Albrecht, R. (2011). Using math games and word problems to increase the math maturity of K-8 students. Eugene, OR: Information Age Education. Free download available at http://i-a-e.org/downloads/doc_download/211-using-math-games-and-word-problems-to-increase-the-math-maturity-of-k-8-students.html.
Written by Dave Moursund, November 10, 2010.
By and large, humans are social creatures. Survival of the species required this. Think about this in terms of schooling.
Imagine a school setting in which students are required to sit quietly doing "seatwork" exercises based on "the" book for a particular unit of instruction. This model of education has a very long history and in some sense can be used as a baseline model against which to compare other approaches to education. Moreover, it tends to fit well with a goal of preparing students to work in a factory-like environment in which they perform repetitious and routine types of tasks without complaint.
Contrast this with a classroom environment in which children are interacting, doing project-based learning, helping each other to learn, sharing the learning experiences, and so on. This type of environment can be designed to encourage individuality, creativity, and higher-order thinking. From my point of view, it is a far more humane approach to education. Moreover, I think it better prepares children for responsible adulthood in today's complex and rapidly changing world.
Written by Dave Moursund, November 10, 2010.
I recently read the following article:
Rothstein, Richard (10/14/2010). How to fix our schools. Economic Policy Institute. Retrieved 11/10/2010 from http://www.epi.org/publications/entry/ib286.
The topic under discussion was what president Obama said or did not say about the role of teachers in student learning. The article attempts to clarify that, with respect to what schools do, Obama stated that the quality of teachers is the single most important ingredient. However, with respect to overall education of a child, the single most important ingredient is the parent(s).
The article indicates that:
Decades of social science research have demonstrated that differences in the quality of schools can explain about one-third of the variation in student achievement. But the other two-thirds is attributable to non-school factors.
The quote is both encouraging and discouraging. It is encouraging in that, as our overall educational system and the general level of education of parents improves, we can expect an improvement in the education of children. It is discouraging in that it is proving to be a very long and very difficult challenge to improve our total informal and formal educational system via this approach.
Written by Dave Moursund, November 14, 2010.
Here is a suggestion of what one teacher can do to help improve math education. It has two parts:
1. If you are not a math teacher, think about what math is used in whatever discipline you teach. Then think about what aspects of this math you integrate into the courses you teach. Presumably you have figured out ways to engage your students in the discipline. Thus, you have an excellent platform to demonstrate the roles of math in that discipline.
2. If you are a math teacher, strive to create environments that will help create and bring out intrinsic motivation. Your goal should be to make continual progress in this aspect of your math teaching. Perfect is not possible. But even the progress of helping one student to "see the light" in one math topic is a useful thing to accomplish.
Written by Dave Moursund, November 15, 2010.
The following is quoted from:
Health Day (11/12/2010). Early intro to math seems to improve kids' skills later. Retrieved 12/15/2010 from http://consumer.healthday.com/...AID=645812.
Talking to young children about numbers can boost their success in math once they're in school, researchers say.
Children whose parents talked more about numbers were much more likely to understand the cardinal number principle -- the size of a set of objects is determined by the last number reached when counting the set, the University of Chicago researchers found.
In the study, the investigators recorded in-home interactions between parents and preschoolers and analyzed the link between parents' talk about numbers and their children's subsequent math performance in school.
"By the time children enter preschool, there are marked individual differences in their mathematical knowledge, as shown by their performance on standardized tests," study leader and psychologist Susan Levine said in a university news release.
She also noted that previous studies have found that a child's level of math knowledge when they begin school predicts future success.
The new findings "suggest that encouraging parents to talk about numbers with their children, and providing them with effective ways to do so, may positively impact children's school achievement," Levine said.
The study was published in a recent issue of the journal Developmental Psychology.
The Ontario Ministry of Education outlines how parents can help their children learn math. See http://www.edu.gov.on.ca/eng/d...earlymath/.