Constructivism: How to Use It to Improve YOUR Teaching and Learning

by Barbara RademacherFor EDUC 8101-3Spring 2011Walden University

IntroductionConstructivism – in its many forms – is an important education theory.

Since the 1990’s, constructivism has dominated mathematics education.

In this workshop, you will: use constructivist methods to learn about constructivism, learn about traditional educational theories, and maintain your

interest by filling in blanks, learn about and discuss the types of constructivism, learn about constructivist teaching methods you can use to

improve YOUR teaching and learning, and brainstorm teaching activities you can use yourselves.

When you see this icon…

Click on it to learn more about the subject covered on the slide.

Building MeaningRefer to your handout for the first activity.

You will spend three minutes writing down every mental image and word that occurs to you when you hear and see the word CONSTRUCT.

Your Theory of ConstructivismWhat do you think the Theory of Constructivism is all about? Write your thoughts.

I think the Theory of Constructivism says that …

Share Your Theory

Now, all the participants in this workshop will share with each other their theories about what CONSTRUCTIVISM is.

Reconsider and RewriteHearing the theories of others may have caused you to alter your thinking. Rewrite your Theory of Constructivism.

I Now think the Theory of Constructivism says that …

CONGRATULATIONS!You Have Just Practiced

ConstructivismFirst, you considered a new word: Constructivism.Second, you associated words you already knew with

the root word that is the source of the word Constructivism.

Next, you guessed what the word constructivism might mean.

You discussed your ideas with others who were also developing guesses about the meaning of the word Constructivism.

Finally, you rewrote your theory based upon the ideas of others.

Constructivist Theory says:People are constantly building knowledge like they build houses from materials they already have on hand, and then creating new knowledge like they might build a new house.

Other people influence how individuals create knowledge just like neighbors influence the styles of house that are built.

What Came Before Constructivism?

Transmission TheoryFrom ancient times to the present, many teachers and theorists have insisted that students – both children and adults – are empty vessels waiting to be filled by a teacher.

COGNITIVISM• Developed by the famous

educational theorist, Jean Piaget.• All people learn by relating new

information and facts to older ones in a process called assimilation.

• When humans learn something so new it cannot be assimilated, they create new mental structures called schemas. This is a process called accommodation.

• Learning takes place in the individual.

Stage Theory• There have been many stage

theorists, but the most famous have probably been Piaget and Erickson.

• Stage theories say that people develop by going from one stage to another sequentially.

• Higher stages are superior to lower stages.

• Education should be offered according to the stage the student is in.

COGNITIVISM CONSTRUCTIVISM

SIMILARITIES

Schemas (aka schemata): People learn relatively new facts by relating them to previously learned facts which make up the way they view the world.

People understand relatively new information by building it onto related facts which are built on a foundation of related information.

COGNITIVISM CONSTRUCTIVISM

SIMILARITIES

When faced with entirely new information that cannot be fit into previous schemas, people create new schemas.

When faced with entirely new information that does not fit on a previous foundation, people have to lay entirely new foundations on which the new sets of facts can become building materials.

Varieties of Constructivism

There are many ways to be a constructivist.

Besides education, constructivists are concerned with questions like:•Who does the learning: The individual or the group?•Is there an objective reality?

Mental Structures

Piaget’s Constructivism

People learn by building mental structures called schemas that interpret external reality.

People learn new information by relating it to already known information.

Schemas are like building blocks.

Emphasis is on Action

Discovery Learning

People discover information through performing activities.

The Mind is An Active Computer Information Processing Theory

The mind is an active processor of information.

Knowing is active (not passive), based on previous knowledge, and takes place in the individual.

There is objective truth that cannot be known perfectly.

Mind is Located in the BrainWeak Constructivism

Similar to Information Processing Theory.

The mind is located in the brain and nervous system.

Truth is objective and “out there”.

Truth can be known imperfectly.Chief proponent: Paul Ernest

Detractors call this “Trivial” Constructivism.

Truth Cannot Be KnownRadical Constructivism

Humans build knowledge on a foundation of previous knowledge.

Truth may exist but humans cannot ever know it.

Learning is using the senses to make successful guesses about objects we encounter.

Learning occurs in the individual.Chief proponent: Ernst von Glasersfeld

Knowledge is Built in GroupsSocial Constructivism

Individual mind, alone, doesn’t exist. Mind is part of society and culture.

Learning cannot occur in isolation.Humans construct reality and change it

constantly so that it fits the true reality better.

Conventional knowledge is socially accepted.

Chief proponent: Lev Vygotsky

Paul Cobb’sEclectic Constructivism

Click on Dr. Cobb’s photo to go to his faculty web page.

Paul Cobb

• Cobb holds Peabody Chair in Teaching and Learning at Vanderbilt University.

• A dominant influence on mathematics education.

• Author of many, many journal articles and books about constructivist teaching methods.

• Currently working on equity and diversity issues in mathematics education.

Cobb’s ConstructivismMost people conduct intricate mathematical calculations in real-life situations.

Where they have problems is in the classroom.

Cobb’s Constructivism

• People learn by linking new knowledge to old.

• Students learn math by being part of groups of people doing math, a process called “enculturation”.

Cobb’s Constructivism

Students and teachers together make up the classroom culture.

Cobb’s Constructivism

When students share their constructions, their understanding improves.

Cobb’s Constructivism

When students reflect together about how they developed their constructions, their concepts often become permanent ideas, and they are able to use those ideas outside the classroom (transference).

Cobb’s Constructivism

Students construct their own concepts regardless of the teacher…

but those concepts may not resemble the teacher’s concepts.

Cobb’s Constructivism

Learning to use mathematical symbols is not a separate skill from learning math-ematical concepts; students develop both skills at the same time.

Suggested Teaching Methods

Cobb video: Improving schools, teaching and teachers.

AttentionTeachers should listen carefully to students and watch their body language in order to try to comprehend how each individual is constructing concepts.

Stand on Giants’ Shoulders

Teachers need to introduce each new topic by relating it to what students have already learned. Students learn by relating new knowledge to old.

Enculturation

Teachers need to use group work so that students can share their understandings with each other.

DiscussionsTeachers need to encourage whole-class discussions of mathematical topics so that students can “negotiate” meanings with their peers and with the teacher. Discussing concepts has been shown in research to increase student engagement.

Video Record

If possible, teachers should video record whole-class discussions, and study the videos after class in order to better understand students’ thinking processes.

Creativity

To promote student engagement, teachers should assign a few harder word problems and encourage students to solve them using any method, even “street math”.

Tolerance

Teachers must be willing to tolerate wrong answers in order to concentrate on the methods students are using to solve problems.

Conclusion

Now that you are experts in constructivist methodology, we will go around the room and discuss a method you might use with your students.

Please, briefly jot down your thoughts and the thoughts of others so that you can engage in group constructions.

On your handout, you have room to take notes and a list of sources.

Videos about Constructivism

von Glasersfeld http://www.youtube.com/watch?v=zTsY3TosVX0 http://www.youtube.com/watch?v=YozoZxblQx8http://www.youtube.com/watch?v=GpWbUWroPuA

Constructivism: http://www.youtube.com/watch?v=YkENpwnlDTI

Abbott talks about Constructivism: http://www.youtube.com/watch?v=F00R3pOXzuk

Constructivism for the Beginning Educator: http://www.youtube.com/user/PatDA1#g/u

Constructivist teaching using blogs and wikis: Dr. Helen Cohen (University of Maryland) http://deimos3.apple.com/WebObjects/Core.woa/Browse/umd-public.4444871239?i=1289520483

Books and journal articles used to prepare this presentation

Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational

Researcher, 23(7), 13.

Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research

in Mathematics Education, 28(3), 258–277.

Cobb, P. (1988). The Tension Between Theories of Learning and Instruction in Mathematics Education. Educational

Psychologist, 23(2), 87.

Cobb, P. (2002). Reasoning With Tools and Inscriptions. Journal of the Learning Sciences, 11(2/3), 187-215.

Ernest, P. (1996). Varieties of constructivism: A framework for comparison. In L. Steffe, P. Nesher, P. Cobb, G. A. Goldin, &

B. Greer (Eds.), Theories of mathematical learning (pp. 335–350). Mahwah N.J.: Lawrence Erlbaum Associates.

von Glasersfeld, E. (1996). Aspects of radical constructivism and its educational recommendations. In L. Steffe, P. Nesher, P.

Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning (pp. 307-314). Mahwah, N. J.: Lawrence

Erlbaum Associates. Retrieved from http://www.questia.com/PM.qst?a=o&d=37042395#

Steffe, L., Nesher, P., Cobb, P., Goldin, G. A., & Greer, B. (Eds.). (1996). Theories of Mathematical Learning. Mahwah, N. J.:

Lawrence Erlbaum Associates. Retrieved from http://www.questia.com/PM.qst?a=o&d=37042395#