FETC -- Rethinking How We Teach Mathematics with Technology to Struggling Learners

In the featured session, Rethinking How We Teach Mathematics to Struggling Learners with Technology, Ted Hasselbring discussed how we can use technology to address the recommendations of the National Mathematics Advisory Panel for all students, including those with special needs and at-risk for school failure. The following are notes from his presentation:

•Math proficiency 2009 – About 2/3 of our students are performing at basic or below. By race, Black and Hispanic students are performing 78% to 84% at basic or below. The 2006 PISA Math Results show global competitiveness. The NCTM Curriculum Focal Points and The National Math Panel Report titled The Foundations for Success provides suggestions. How can technology provide target intervention for students?
•We are born with the ability to develop language and math (number sense) – it is a hard-wired capability.
•Approximate number sense – basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants, and animals. (Halberda, Mazzoco & Feigenson 2009) ANS Acuity http://literacyencyclopedia.ca/index.php?fa=items.show&latest=true
•Participants enjoyed participating in a quick ANS Acuity assessment with flashcards. Children that do well with this typically do well in math. http://www.nature.com/nature/journal/v455/n7213/full/nature07246.html
•Subitizing might be a pre-requisite for kids learning math. In a dissertation study by Forde, we found that a high percentage of special education students were unable to subitize. Is this the root of their problem? Subitizing doesn’t have to be done visually, it can be done with audio.
•Sensory register>Immediate memory>working memory>long-term storage
•Working memory is important. We can only process a certain amount of information at one time. How you go about a task you will use more or less of your working memory. If you are able to subitize, you use less of your working memory. We want to reduce as much cognitive load as possible so we can do better at high level tasks.
•There is a 7+2 Rule – Miller, 1956 http://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two
•Kids between the ages of 5 and 14 don’t have as much working memory as adults. Working memory is typically minutes vs. hours or days. For adults, we can devote about 20 minutes. With a book, we can read a phrase and internalize it and then read another phrase and make a connection.
•Empirical evidence suggests that using physical manipulative models during instruction can enhance students’ conceptual understanding of math concepts without impeding their ability to complete algorithmic procedures. However, they can be expensive and difficult to store. They become unusable if pieces are broken or missing. The amount of time for setting up, sorting, and cleaning is also an issue. Benefits can be nullified if not enough time is allotted for exploration.
•Why use technology? There are a lot of advantages. Deliberate Practice – In the simplest sense, expert-level fluency of any skill is developed through a significant and specific type of practice called deliberate practice. Targeted practice in which one is engaged in developmentally appropriate activities. Real-time corrective feedback that is based on one’s performance. Intensive practice on a daily basis that provides results that monitor current ability. Distributed practice that provides appropriate activities over a long period of time (i.e., 5-10 years), which allows for monitoring growth towards expert performance. Self-directed practice for those times when a coach, mentor, or teacher isn’t available. As educators, we want to provide as much deliberate practice as possible.
•The FASTT Model (Fluency and Automaticity through Systematic Teaching with Technology) The product FASTT Math follows this model. http://www.tomsnyder.com/fasttmath/overview2.html When introducing new information it: builds on existing performance level, small instruction set, requires recall from memory, and offers feedback.
•With special education students, we can develop high levels of subitizing up to place values of 100. No evidence yet that this will transfer to mathematical problem-solving.