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**

Constructivist

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

Advantages

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.

Disadvantages

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

Disadvantages

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).

Advantages

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

Implementation:

Math Exemplar

Time involved

Problem Solving Based Activities

Number Talks

Safe learning environment

Teacher is facilitator

Implications

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:

**Discussion:**

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

Constructivism

Enthusiast

Tiana Fowler

Constructivism

Enthusiast

vs.

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?