Monday, January 25, 2016

Handout for "Want To Help Your Child Learn Math? There Are Apps for That!"

Want to help your child learn math – there are apps for that….

Braefoot Elementary – Jan 25, 2016

Tim Pelton

Who are you?
Tablets, smartphones, screen time?
How do you help your child learn math?

Some theories to support learning:

Big Idea #1 “the purpose of the state is to educate people – to make them virtuous”

Big Idea #2  “Learning is a series of question and answer propositions.”  We need to ask questions, encourage questions, share questions (TPS) etc..

Vygotsky: Social Development Theory

Children learn first through social interaction and making meaning.

Big Idea #1 Set up learning opportunities within reach (ZPD)

Big Idea #2.  Reciprocal teaching and peer tutoring are powerful tools to support learning. 

Big Idea #3. Focus on summarizing, clarifying, questioning, predicting.

Big Idea #4 Children raised in environments where there is more cognitive and linguistic stimulation have a developmental advantage.

Piaget: Cognitive Dev. & Constructivism

Children naturally try to make sense of the world

We are all seeking equilibrium, (assimilating and accommodating). 

We develop through stages (continuous progression):
1.Sensorimotor (0-2)   
- Object permanence
2.Preoperational (2-7)   
- Egocentric
3.Concrete operational (7-11)
- Conservation
4.Formal operational (11+)
- Abstract reasoning  (~1/3 of adults reach this?).         

Big Idea #1 Children progress through stages - no point in pushing new ideas before their time

Big Idea #2 Learning happens through disequilibrium.  Children need time to conduct independent explorations.

Bruner: Constructivism
The learner transforms their experiences into knowledge

Big Idea #1  A child of any age is capable of understanding complex information (!) – But not by rote – by discovery

Big Idea #2 - We present new ideas in a sequence:  Concrete/action –> Visual/iconic/descriptive –> Abstract/symbolic

Big idea #3 Spiral Curriculum with Scaffolding (teachers, tutors, parents, peers) is the way to go.

Big Idea #4 Radical constructivism is difficult to follow through on – perhaps a more pragmatic version of constructivism intermingled with instructivism, objectivism, cognitivism & behaviourism.

Papert: Constructionism

Big Idea #1 – We learn best by creating something tangible.

Big Idea #2 – Project-Based learning (PBL) with teachers as coaches and facilitators

Big Idea #3 – discovery learning rather than teacher led learning

van Hiele

The van Hiele model – students progress through a series levels of understanding in geometry
Affected by experience rather than by age. 

Big Idea #1  If students learn by rote and without understanding they will not be able to apply it in new situations.

Big idea #2  We progress through Recognition, Description, Definition, Deduction, Rigor

Big idea #3 Pushing ideas earlier may be possible – but not very efficient.


Bloom’s taxonomy describes the types of learning objectives.  The domain that gathers most of the attention is cognitive: Knowledge, Comprehension, Application, Analysis, Evaluation, & Synthesis.

Big Idea #1 

Questions for audience
  How many of you have downloaded apps to help your child learn? – What did you discover?
  What concerns do you have about using iPads
  What makes a useful App

What we look for in Apps
  No ads, clean, not too distracting
  Intuitive to get started - easy to use
  Can be shared
  Immediate feedback (but not immediate answers)
  Substantial educational component
  (see Bloom’s objectives)
  Resources for parents/teachers
  Some support provided (to help figure out the problems)
  Mastery before fluency (not time bound)
  Tracking of progress

Some Apps we have created (most MathTappers are free) and recommend)