Design Experiments

  1. Montessori
  2. Clements and Samara
  3. Hoyles and Noss
  4. Contextual Design
  5. Comparing Design Research Approaches

Research

  1. Design Problem
  2. Literature Review
  3. Work Models
  4. Design Patterns
  5. Design Experiments
  6. Lesson Ideas
  7. Montessori Computes
  8. Thinking About Circles

Related Links

Patterns and Design

Montessori

Hoyles and Noss

I just started reading Learning Mathematics and Logo by Hoyles and Noss (1992).  This page will hold notes on that reading.

In their preface Hoyles and Noss say:

"Research only flourishes if it is informed by the createion of environments that have been developed for and used by children.  On the other hand, it makes no sense to create curricula that ignore the epistemology of mathematics, what is known of children's understandings or the settings in which they are developed." (Hoyles & Noss, 1992, pp. ix-xx).

So far, so good.  Then they go on to say:

"For this reason, if for no other, the reader will not find in any of the subsequent chapters research that aims to investigate the effects of Logo 'treatments,' or 'curriculum development' that consists of examples of hierarchical sequences of Logo tasks." (Hoyles & Noss, 1992, p. xx)

Does that follow?  Why or why not?

Would Montessori agree with idea that we're not looking for the effects of 'treatments'?  I'm not sure.  She relied on observation rather than traditional pretests and posttests to assess the environment, the teacher and the child.  She wasn't primarily worried about getting kids to improve performance on particular tasks.  Part of her work was to help kids acquire their native culture (including math and language), but this was only part of the primary work of nurturing the spirit.  It was also critical, for example, that kids develop deep concentration and learn to interact peacefully with the teacher and other students.  All of these might be considered "effects" of Montessori "treatments", but I don't think these are the kind of effects and treatments the authors are talking about.

Montessori doesn't see education as something that a teacher does to a child.  Rather, her focus is on the work of the child.  Still, she has made comparisons of her didactic apparatus to apparatus used in physical therapy, so there is an idea of treatment, but it is the kind of treatment in which the person being treated is necessarily an active participant.

"Such approaches seem to us to be fundamentally misguided in that they guarantee at their outset the impossibility of real change and effectively marginalize the innovatory potential of the technology they seek to investigate." (Hoyles & Noss, 1992, p. xx)

What about Montessori's webs of activity?  Her approach is related to Bruner's spiral curriculum, but also Rand Spiro's idea of criss-crossing a terrain in order to see it from many perspectives and get a good lay of the land.  Do her webs constitute "hierarchical sequences of... tasks?"

If this is the case, why and what does a good design and investigation process look like?

"both Loethe and Hillel start from an epistemological analysis of geometrical and algebraic concepts, respectively, and only subsequently discuss the implications and possibilities of children's behavior.  Kynigos, Edwards, and Sutherland, on the other hand, base their approach more closely on curricular priorities, and on their knowledge of children's understandings and misunderstandings of the ideas under consideration during their Logo activities." (Hoyles & Noss, 1992, pp. 3-4)

In design, a good idea might originally come from anywhere--when you notice some interesting mathematical property, or when you see kids having trouble with a particular activity, or when you are conducting an interview with a teacher.

A key Montessori-ism in this respect is "follow the child," but Montessori herself had different starting places for designs.  Montessori started with ideas from different sources, e.g. the work of Seguin (geometric insets) and the observation of children (she saw kids hanging on a gate or railing and set up something like that in her classroom for kids' physical development).  So there's not a step-by-step process for coming up with ideas.  There's not really a step-by-step process for refining ideas either.  How do I want to represent the design process?

What are the heuristics to guide the invention, assessment and development processes?  There are design patterns to help when you run into problems in the design and development process.  What are the guides for assessment?