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Tiana Fowler

on 24 June 2013

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Born March 10, 1919 in Bristol
Died June 22, 1995 in Coventry
Son of a Professor
Educated as a Foundation Scholar
Married Valerie Watts
One son
Interested in how children learn
Richard R. Skemp, psychologist & mathematician
(expert in teaching both)

Biographical Information

Richard Skemp
Constructivism Theorist

Skemp worked from a constructivist point of view years ahead of the widespread use of the term ‘constructivism’, centering on understanding how new concepts are built from existing concepts and fresh experiences (Gough, 2004, p. 72).

Relational Learning
Skemp believed that relational understanding is consistent with intelligent learning.
It’s knowing what to do and why.
Lecturer in Psychology, Manchester University, 1955-52,
Senior Lecturer 1962-73
Professor of Educational Theory, Warwick University, 1973-86;
Director of the Mathematics Education Research Centre, Warwick 1978-86;
Visiting Professor, University of Calgary 1987-94;
Published 3 books and many papers
Educational Background & Publications

Class Activity
Relational Understanding
Engage me
Let me construct!
MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.12
MCC3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?. × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?.
CCGPS Standard
Most noted for: Relational and Instrumental Understanding

Skemp states “To understand something means to assimilate it into an appropriate schema” (The Psychology of Learning Mathematics, pg. 46).

Relational understanding is consistent with intelligent learning. Knowing what to do and why.

Instrumental understanding means habit-learning or learning 'rules without reasons‘. Learning and using rules.

Relational Understanding versus
Instrumental Understanding

Easier to adapt to new tasks
Easier to remember
Relational knowledge is it’s own reward (with less emphasis on reward/punishment)
Natural quality of understanding; not a skill to be learned

Relational Understanding
Knowing what to do and why.

Teachers have misunderstandings
Difficult to assess: Time to talk to every student in determining relational understanding
More to learn; more actual content
Students want the right answer with being shown the right way to do it

Knowing without understanding why
Less knowledge involved
Needs to be reviewed often
Just suppose…more teachers are teaching this way (Does this reflect our our Process Standards).

Is easier to teach and understand
Results and rewards are more instantaneous
Quicker and easier route to figuring out the correct answer

Instrumental Understanding
Learning and using rules

Math Exemplar
Time involved
Problem Solving Based Activities
Number Talks
Safe learning environment
Teacher is facilitator

Common Core Standards reflect Constructivism.
Math Practice Standards mandate students construct relational understandings.
Problem Solving must be premise of math curriculum.

Implications and Implementation
of teaching mathematics using
relational understandings:

1. How do our Common Core Math Practice Standards reflect Skemp's Theory of Relational Understanding?
2. How can we use technology to enhance relational understanding?
3. If you are familiar with creating Prezis, how does that process better reflect relational understanding than traditional Power Points?

Presented by
Tiana Fowler


Instrumental Understanding
You have an understanding of one way and now it doesn’t work because the situation has changed.

Relational Understanding
You have an understanding that you can take different ways and know an alternate way to get there. So, you are able to get to your destination.

Question to ponder:
What happens if there is an accident and you cannot find your way and you have no phone or GPS?

Full transcript