Math Update

I recently completed reading Elementary School Mathematics and am thoroughly convinced that it needs to be required reading for anyone who teaches mathematics in elementary school.  Although my copy is out of date, and Van De Walle heavily emphasized the integration of technology in instruction, Elementary School Mathematics provides a broad foundation and an array of tools and activity types that should be standard operating procedure for both curriculum designers and classroom teachers.

Since my goal was to assemble a mathematics instructional toolkit by the end of May, a goal which I unfortunately failed to meet, I put aside my desire to blog about it as I went, and even took some shortcuts in the write to learn process.  Despite these unanticipated setbacks, I managed to spend an appropriate amount of time to reflect on the discussion questions as I went, noting page numbers where I could find the information for future writing.  Now that I've completed a thorough first reading, I will continue to refer to it as I build upon the foundation it has provided me.

Meanwhile, I am taking an online course at Northern Virginia Community College, Pre-Calculus, which relies heavily on a graphing calculator and technology.  Van De Walle places a heavy emphasis on calculators, which is something that we did not do when I was taking Calculus in High School in 1980 and 1981.  Interestingly, the way I learned how to simplify algebraic equations, which was the long way, allows me to trust and cross-check my calculations.  Van De Walle's heavy emphasis on the use of calculators is his most controversial recommendation -- my brother, a high level systems engineer for IBM absolutely deplores the practice -- is deeply misunderstood.  Moreover, Van De Walle's calculator activities are so well though out, assembling my calculator activities will be a first priority.

The J Factor

What does it take to get someone to pay attention? There is a region in your brain called the reticular activating system (RAS), which switches on whenever you pay attention. Unless your attention is switched on, i.e., until the RAS has been activated, no new memories are created.  Brain research indicates that emotions are critical factors in switching on the RAS, the kinds of memories people retain, and ultimately learning.  Furthermore, the intensity of the emotions that activate the RAS determines the extent to which memories are retained and how easily they are recalled.

Two major evolutionary factors play important roles in activating the RAS, the emotions of fear and desire.  Humans recall things that are useful for their survival.  Positive emotions cause the brain to be flooded with endorphins, which cause people to want more of the same.  Negative emotions cause the brain to be flooded with adrenaline and other chemicals which cause fight, flight, or overload responses.  Fear helps us remember things to avoid, helps us prepare and respond to existential threats, and develop fear-response memories that are critical to survival.  Fear itself can become its own reward, however, and when fear consistently becomes the basis for motivation, fight, flight, and overload responses become habituated, and higher level solution-oriented response capacities can become overwhelmed.  Learning environments where fear predominates tend to shut down higher level processing opportunities.  Elevated aggression rates, ADHD, and other processing deficits seem to be on the rise in our schools and I think I know precisely why.

Two schools of thought predominate in education in the United States, Skinner (Behaviorism) and Dewey (Constructivism).  Behaviorists consciously use rewards and punishments to capture and retain student attention through subtle forms of manipulation.  Constructivists view learning as its own reward, and Constructivists design lessons, activities, and create rich learning environments to maximize student engagement so that each child can enthusiastically construct his or her own brain patterns.  While most educators would claim to be Constructivists, Behaviorism has rapidly gained ground in recent years as politicians have wielded pressure to tie school funding to Adequate Yearly Progress (AYP) calculations in an era of No Child Left Behind.  Many schools emphasize punishments and rewards given or withheld, and I’ve noticed a corresponding increase in the level of fear, primarily the fear of failure, as a motivating factor in our schools.  The increase in the level of external political pressure has led, ironically, to declining High School graduation rates, and a general decline in higher level reasoning capabilities.  If school improvement plans set their sights on minimum standards of achievement, i.e., lower level thinking, a decline in thinking skills is exactly the result one might expect.  Could an increase in the number and scope of standards, ironically, lead to a proportional decline in student expectations plus measurable declines in performance on tasks requiring higher level thinking on a national level?

When students are motivated by an internalized desire to learn, natural curiosity takes over.  Intense desire and joy powers the most constructive learning environments, which is something that every effective teacher knows.  Intense levels of concentration are required for higher level thinking.  Intense desire and joy trigger the RAS to be activated in ways that flood the brain with endorphins, creating a self-sustaining loop where synapses that fire together wire together, relationships are connected, and memories are anchored to an array of sensory inputs, making them widely available for recall whenever any sensory anchor is triggered.  Is there a Joy Factor that can be positively linked to improved performance on higher level thinking tasks?