CONSTRUCTIVIST
LEARNING
Concepts
For Understanding Education: This is an online
version of a book on education.
A Constuctivist Bridging Example: This is a more conceptual version of The Bridging Question Strategy
Types of Constructivist Learning Resources: All of the materials in the mathematical sections of this website are constructivist learning resources. However the resources most fully developed while deliberately thinking about types of constructivist learning resources can be found in the Elementary Math section and the Ordinary Algebra section.. A conceptualization of concept construction and constuctivist learning resource types is given in Constuctivist Learning Resources. This paper has two equally important parts, the main text and the appendices. They are related and can be read in either order.
The main text of Constuctivist
Learning Resources is available in both an HTML and MS Word version.
They both have a link to an MS Word version of the appendices.
The main text in this paper makes a distinction between various resource types that apply both to the design and use of constructivist learning resources. We use four parameters for thinking about concepts. We also use the significance and achievement parameters from the Descriptive Psychology behavior description concept. Supplements are included with the main text, in order to develop some off the ideas in more detail. The appendices illustrate three of these resource types in terms of some mathematical activities. These activities are directed towards some favorite problems of mathematical hobbyists, namely finding magic squares. These problems are easy to understand, but many related questions are not easy to answer. The activities will provide ideas for exploring such questions. More significant, these activities may help the learner construct an expanded concept of a mathematical function that will seem manifest rather than remote. Additional materials for a constructivist learning workshop centered on 3´3 magical squares can be downloaded as MS Word files.
A Constuctivist Bridging Example The activity of developing new concepts and competence in using them involves activating the relevant prior understanding of related concepts and knowledge. One constructivist way for activating prior understanding is what we will call bridging. This present paper uses an example to relate bridging to a parameter for understanding concepts. Hopefully will illustrate these concepts sufficiently to suggest other uses. The example focuses on a conceptual understanding the undoing method used in finding a root to an algebraic equation. This method can be related to the everyday experience of a wrapping package, as well as to a number of other ordinary reversal processes. Clearly much more in the way of understanding a variety of mathematical concepts is involved in this method, but at least some perspective can be added by this comparison.
Explorable Clusters: The focus of this paper is on formulating a concept called an explorable cluster. I want to emphasize that an explorable cluster is merely one type of resource that can be designed for constructivist learning. It is a type that can be used in an extremely flexible an open-ended manner to both assist students in immediate concept construction and provides a basis for the construction of more remote concepts at a later time. It is also a resource type that easily lends itself to being redesigned. A paradigm case formulation is used to present this concept.
Rock Paper Scissors Explorable Cluster for Probability This paper is an example of an explorable cluster that is taken from the paper above. Email me if you want an MS Word version.
Coin Flipping & Voting Probabilities This resource is an extension of one of the realms from the Rock Paper Scissors explorable cluster, it could be taken as an alternative initial realm. Sections 1 and 2 are both group-plan constructivist-learning resources followed by a dialog type resource in which imaginary students use the plan. The group-plan is for any group of four or more students who are learning about probability concepts. The dialog is primarily for their teacher, altho it could also be used by the students. Section 1 is intended both to help students appreciate some of the mathematical concepts involved in probability and to obtain a feeling for how mathematical probabilities relate to what actually happens in coins flipping trials. Section 2 presupposes basic probability concepts and applies them to simple voting situations and on how voting probabilities might relate to reasons for voting.
I welcome email from anyone
interested in constructivist learning,
Links for Constuctivist Learning: More links will be added later. Please email me if you have any suggestion, indicating something about any that you suggest.
http://www.odu.edu/Educ/act/ This is the official website for ACT, Association for Constructivist Teaching.
http://www.odu.edu/educ/act/journal/vol15no1/index.html This is the first issue of the ACT on line journal.
http://www.cdli.ca/~elmurphy/emurphy/cle.html This website created by Elizabeth Murphy contains an essay entitled Constructivism: from Philosophy to Practice.
http://faculty.washington.edu/krumme/guides/bloom.html and http://www.humboldt.edu/~tha1/bloomtax.html These website contain Bloom’s Taxonomy of Education Objective. This taxonomy can be useful reference when designing constructivist learning resources or when teaching from a constuctivist perspective.