1. children learn mathematics?
How do
children learn mathematics?
Prior to taking a closer look at some of the digital technologies we will be using to enhance your child’s learning in mathematics, let’s take a brief look at learning theory –how it has evolved and what it tells us about how learning occurs.
Fiona Gately

2. Three fundamentally different theories about learning have emerged.
Learning theories
Three fundamentally different theories about learning have emerged.
Over the years, various learning theorists have attempted to explain this phenomenon. Three fundamentally different theories have emerged. These are the Behaviourist, Cognitivist, and Constructivist Learning Theories.

3. Behaviourist theory
Learning is acquired through exposure to external stimuli, and is evidenced by changes in learner’s overt behaviour.
Behaviourist theory looks only at what can be observed. It proposes that learning is ‘acquired through exposure to external stimuli, and is evidenced by changes in learners’ overt behaviour. If no change in behaviour is evident, it is assumed that learning has not occurred (Snowman et al., 2009, p.382)
Snowman et al., 2009, p.382

4. demonstrates new skills Students: practise skills until automatic
Teacher:
makes all decisions
demonstrates new skills
Students:
practise skills until automatic
assessed through Q & A
mathematics:
drill and practice
new concepts
This is very much the ‘old school’ approach where the teacher makes all the decisions about the learning – what will be learned, how much will be learned and how it will be learned. The new concept is explained or the skill demonstrated by the teacher, and then practised by students until they can perform automatic recall of facts or procedures (Mergel, 1998, p.2). This is usually assessed through a question and answer test (Snowman et al., 2009, p.382). While there is room for the drill and practice aspect of the behaviourist approach to consolidate concepts already learned, the Behaviourist approach is no longer recommended for teaching new mathematical concepts.

5. Cognitivist theory Focuses on the
internal mental processes individuals use
in their effort to
make sense of the world.
The next learning theory to gain popularity was the Cognitivist Approach. Unlike behaviourism, which focuses only on observable behaviours, cognitivist theory focuses on the ‘internal mental processes individuals use in their effort to make sense of the world’(McInerney & McInerney, 2006, p.572).
McInerney & McInerney, 2006, p.572

6. The Three-Stage Information Processing Model
sensory register
short-term memory
long-term memory
According to cognitivism, external stimuli first enter the sensory register where they are processed in short-term memory, and then transferred to long-term memory for storage and retrieval (Mergel, 1998, p.7). Although cognitivist theory has contributed to our understanding of how to teach higher order thinking skills such as analysis, synthesis and evaluation (Dell, 2003, p. 4), it is not the learning theory of choice when introducing new mathematical concepts.
Mergel, 1998, p.131

7. Behaviourist theory Cognitivist theory
Knowledge is external to the learner
Learning is Internalising knowledge
While behaviourist and cognitivist theories have their merits, their major downfall is in the view they share of KNOWLEDGE as EXTERNAL to the learner , and LEARNING as the INTERNALISING of knowledge. And so the learning theory of choice in the teaching and learning of mathematics is …

8. constructivist theory
Assumes that knowledge
is constructed from
experience and
personal interpretation
of the world.
The CONSTRUCTIVIST theory! Constructivist theory assumes that knowledge is constructed from experience and personal interpretation of the world (Mergel, 1998, p.8).
Mergel, 1998, p.8

9. Focuses
on the
Unlike behaviourist theory which is teacher-centred, the Constructivist Approach focuses on the learner. It pays attention to learners’ mathematical ways of thinking. It recognises that there is more than one way of ‘doing maths’ - that a variety of effective strategies may be used to solve the same problem(Booker et al., 2010, p.6).

10. Learning mathematics is an
Active
process
ACTION!
The constructivist approach sees learning mathematics as an active process (Booker et al., 2010, p.6). (pause)

11. Continued in Part 2
The constructivist approach sees learning mathematics as an active process (Booker et al., 2010, p.6). (pause)