A colleague teaching mathematics at a community college recently asked if I knew of research about "the effectiveness of mass practice in terms of long-term memory." Apologies in advance if you don't have access to an academic journal database and can only view the article abstracts.

There is research about so-called "human calculators" who do mental math with large sets of figures; in every instance these folks have developed their talent by spending countless hours memorizing arithmetic facts and relationships. Seems in the most extreme cases their brains are wired to support this sort of activity.

http://rstb.royalsocietypublishing.org/content/364/1522/1385.short

However, if we are talking about whether mass memorization equates to meaningful learning for the typical person, evidence from the 1950s demonstrated this was not the case beyond the retention of simple facts:

http://www.sciencedirect.com/science/article/pii/S0022101507632996

Learning with connections is far better. Think about early school mathematics books (in the 1700s) that had page after page of formulas to memorize related to commercial transactions involving proportional relationships among different units. The time and effort it took to try to memorize these was inordinate (and drove many away from mathematics). More "modern" textbooks by the early 1900s had students learn about proportional reasoning as a general relationship that could be applied to an infinite number of specific situations - thus by learning one conceptual relationship (which could then be memorized and also re-constructed if learned with understanding), students had a much better chance of both long-term recall and correct application.

Some recent articles related to this idea demonstrate quite powerfully the advantages to conceptual learning.

http://onlinelibrary.wiley.com/doi/10.1002/ddrr.45/pdf

http://www.academicjournals.org/ERR/PDF/Pdf%202011/Jan/Narli.pdf

## Monday, July 11, 2011

## Monday, June 20, 2011

### Technology in Mathematics Education

This week Education Week featured an article about technology in mathematics education where I was quoted a couple of times. The gist of what I had said was the while technology is crucial in supporting mathematics learning, it is not in and of itself a substitute for quality teaching and curriculum materials. Something not mentioned in the article (which I understand does not have room for everything) was my concern that teachers are not being given enough time to for professional development to not only learn about new technology tools and resources but also to learn how to design and implement learning activities with these.

In case you have the time and interest, here are a few articles and tutorials worth exploring about exciting tools to support mathematics teaching and learning!

In case you have the time and interest, here are a few articles and tutorials worth exploring about exciting tools to support mathematics teaching and learning!

- Article titled, "Investigating Algebra with Virtual Manipulatives" from NCTM
- Tutorials on using the National Library of Virtual Manipulatives
- Geogebra Tutorials (25 items) from Mathematics and Multimedia blog
- Interactive Geogebra Tutorials (and geometry lessons!) from Dr. Carol Fisher
- Online book about using Geogebra by geogebra.org
- Wolfram Alpha intro video (amazing tool if you've not tried it)
- ScreenR allows you to record and narrate anything from your screen - easy to use!

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