Five ideas from OAME

Recently I attended the OAME 2014 conference at Humber College.  Here are five speakers who got me thinking.

1. Jo Boaler: With a Growth Mindset, anyone can learn mathematics
Performance praise like “You’re smart” actually encourages a fixed mindset, a belief that ability is inherent rather than developed.  In contrast, growth mindsets are cultivated by practices of: persistence, learning from mistakes, determination to keep going, and being encouraged by other’s success (Carol Dweck).  Those with fixed mindsets underachieve when compared with those with growth mindsets, regardless of high or low present ability.  She believes that with a growth mindset, all people can learn mathematics, except perhaps those few limited by cognitive disabilities.   I think I agree with her point of view, with the great challenge being that some students have established habits of behaviour and belief that reinforce fixed mindset behaviour.



2. Ruth Beaty: Mathematics is not necessarily about moving from concrete to abstract.  
“Concreteness” does not come from an object itself, it comes from our relationship with the object.  This applies also to ideas.  The more connections we have with a mathematical concept, the more concrete it becomes to us. If we only access a concept through an abstract model, then in remains abstract.  Learners need multiple ways to engage with and represent concepts.

3. Dan Meyer:  Even "boring" math topics can be reimagined.
Instead of teaching the “boring” topic of graph terminology by labeling a diagram and just remembering, try first asking pairs of students to describe a graph to their partner to draw without looking.  It’s both a fun activity, and an illustration of why specific mathematical language is helpful. 

4. Ron Watkins: Illustrate with Input / Output Diagrams.
Essentially a sequence of one operation function machines, Input / Output Diagrams could be used to enhance understanding of graphical transformations in grade 10 and 11.  They also could aid understand solving equations using inverse operations or writing inverse functions

5. Chantal Buteau: Lack of time seen as a key barrier to technology adoptation.
A leading reason that technology is not adopted in the mathematics classroom is teacher concerns about time, both the perceived time that introducing technology requires in the course and the time required for teachers to prepare lessons that involve technology.  Combined time factors rank just behind concerns about how to assess when technology has been used in instruction, difficult syntax, and fears of unexpected behaviours.  Although Chantal Buteau’s research was conducted at the post-secondary level with CAS systems, in her talk she generalized this to other forms of technology and suggested that it would likely apply at the secondary level also.