Week 2: Learning Theories and Math

Have you ever wondered why some people have the uncanny ability to spit out numbers they've just heard once, or perform simple math operations in their head within record time?  Were they born with a special aptitude, do they learn (process information) differently, or were they taught by different teaching methods?  Recent research in how people learn numbers and math purport that those viewed to succeed in the above areas exhibit the ability to dual code; i.e. the ability to associate numbers with words and images (Bell, 2003).  Much of the information presented below comes from articles and research posted on two websites:  LD OnLine and Ohio State's Ed Laughbaum. 

Gersten and Chard, in their article "Number Sense:  Rethinking Arithmetic Instruction for Students with Mathematical Disabilities" (2001) state that research from neuropsychologists and cognitive psychologists agree that disabilities in math include three items:  high frequency of procedural errors, difficulty in retrieval of arithmetic facts, and inability to symbolically represent or code numerical information for storage in the brain. Looking back to the way I was taught basic mathematics, the methods used were primarily memorization and recitation.  I recall being graded on how many problems I could solve in 60 seconds, which emphasized memorization of the addition and multiplication tables.  This turned basic math into declarative knowledge, which researchers agree that the retrieval of declarative knowledge is often slow and conscious (Ormrod, 2009). This sentiment is echoed in both Gersten & Chard's work as well as Bell’s work.

After all these years, why is the memorization and recitation method in math now being proved as not adequate?  I do not have an answer for that, except that the brain and learning theories is still an emerging topic.  What we know now is that for humans to place items into long-term memory AND be able to recall it quickly, we need to create connections to words, sounds, experiences, and emotions (Ormrod, 2009).  Laughbaum (2010) posits this theory by stating, "Teachers must create connections to improve the memory of mathematics taught."  He goes on to explain that processes need to be connected by relationships to personal experiences and emotions.  The more connections, or associations, you have to the data, the easier it becomes to recall, even if you don't have all the data upfront.   

If you agree with the current research and theories, what remains is to establish is the best way to teach math to create the most connections possible.  Laughbaum has done extensive research on this topic and has information available on his website: http://www.math.ohio-state.edu/~elaughba/ .  He has several presentations and published papers on his site that explain methods used to help retain math data and procedures, including pattern building, generalization, and technology such as software.  What is important to note is the order he recommends using the methods.  He generally recommends letting students generalize and formulate their own processes and procedures before demonstrating a preferred method to students (Laughbaum, 2008). 

For me, drilling basic math through memorization wasn’t the most effective, in part because I am a very visual and relational type of person.  Current research in the field recommends associating words, colors, patterns, and experiences to numbers, which is something I was never taught and never formulated on my own.  Did it hold me back in school or my profession?  Not at all!  Could it have the potential to hold others back?  I believe so, since those who may be slow to recall math information may be incorrectly labeled as “slow” and lacking understanding to move on to higher forms of math.  Can being slower to recall basic math operations help create test anxiety, causing students to “blank out” during exams and being incorrectly labeled?  You bet, and research by Higbee (1999) validates this theory by correlating the time to recall information with test anxiety.  
 

The authors, researchers, and websites cited in this article are making valuable contributions to the world of information processing and retention in a often overlooked discipline - math.  As an instructional designer, whether within education or corporate training, the theories and methods presented will help you create and present material that will be retained long after the students have left your class.  LD OnLine (http://www.ldonline.org/) has a wealth of information on how learning theories relate to memory retention, especially for those with learning disabilities.  For more information on how the brain processes and retains math, Laughbaum has an extensive work published on his website at http://www.math.ohio-state.edu/~elaughba/.   

I’d like to open this blog to readers to share experiences of how they learned or teach math; what methods work and which didn’t? How do you form connections to be able to recall the information later? How does research in cognitive factors help or change the way math is being taught?

References

Bell, N. and Tuley, K. (2003). Imagery:  The sensory-cognitive connection for math.  Retrieved January 16, 2010 from: http://www.ldonline.org/article/Imagery%3A_The_Sensory-Cognitive_Connection_for_Math

Gersten, R. and Chard, D. (2001).  Number sense: Rethinking arithmetic instruction for students with mathematical disabilities.  Retrieved January 16, 2010 from: http://www.ldonline.org/article/5838

Higbee, J. & Thomas, P. (1999).  Affective and cognitive factors related to mathematics achievement.  Journal of Developmental Education, 23(1), 8.  Retrieved January 16, 2010 from Education Research Complete Database.  Permalink: http://ezp.waldenulibrary.org/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=2256674&site=ehost-live&scope=site

Laughbaum, E.D.  (2010).  The neuroscience of connections, generalizations, visualizations, and meaning.  Retrieved January 16, 2010 from: http://www.math.ohio-state.edu/~elaughba/

Laughbaum, E.D.  (2009).  Generalizing patterns in algebra for long-term memory understanding.  California Math Council, ComMuniCator, (34, 2), December, 2009.   Retrieved January 16, 2010 from: http://www.math.ohio-state.edu/~elaughba/

Laughbaum, E.D. (2008).  Implications of neuroscientific research on teaching algebra, Int. J.

            Continuing Engineering Education and Life-Long Learning, Vol. 18, Nos. 5/6,

            pp.585–597.   Retrieved January 16, 2010 from: http://www.math.ohio-state.edu/~elaughba/ 

Ormrod, J., Schunk, D. & Gredler, M. (2009). Learning theories and instruction (Laureate  custom  edition). New York: Pearson.