# Design

## 3D multiplication table

The 3D multiplication table is a three-dimensional embodiment of the one hundred products in the familiar 10-by-10 multiplication chart. The result is an intriguing object-to-think-with that supports mathematical inquiry by making salient logical and quantitative properties that are embedded in the regular multiplication table yet are difficult to see therein. The object thus affords new ...

## 4-Block Stalagmite

Sample Stalagmite is an interactive computer-based model. The model is a part of the ProLab curriculum designed by Dor Abrahamson initially at Uri Wilensky’s Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern University and later at UC Berkeley. The EDRL website features some of these latter models as relevant to our publications. We are grateful to ...

## 4-Blocks NetLogo model

The 4-Blocks NetLogo model, too, is an interactive computer-based embodiment of the 4-Block mathematical object, simulating an empirical probability experiment in which the randomness generator is a compound of 4 squares that each can independently be either green or blue. The model helps conceptualize relations among theoretical and empirical aspects of the binomial function: combinatorial analysis (what ...

## Body-Scale Geometrical Solids: Icosahedron

Goals: Learners will construct icosahedra of varying scales and of various materials. They will then use these various models to think through questions about the geometric properties of icosahedra (number of edges and vertices, cross-sectional shapes, etc.). Learners will reflect on how properties of scale and materiality shape ...

## Combinations Tower

The combinations tower, a theoretical-probability artifact, is the distributed binomial sample space of a stochastic device from the X-Block family, such as a 4-Block, a 2-by-2 grid in which each square can be either of two colors. The 16 unique configurations of the 4-Block are arranged in the tower according to the number of white (green) ...

## Dice Stalagmite

Dice Stalagmite is an interactive computer-based model. The model is part of the ProLab curriculum designed by Dor Abrahamson initially at Uri Wilensky’s Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern University and later at UC Berkeley. The EDRL website features some of these latter models as relevant to our publications. We are grateful to ...

## Histo-Blocks

Histo-Blocks is an interactive computer-based model. The model is a part of the ProLab curriculum designed by Dor Abrahamson initially at Uri Wilensky’s Center for Connected Learning and Computer-Based Modeling (CCL) at Northwestern University and later at UC Berkeley. The EDRL website features some of these latter models as relevant to our publications. We are grateful to ...

## Mathematics Imagery Trainer

The Mathematics Imagery Trainer (MIT) is an interactive technological system designed to create opportunities for students to develop new sensorimotor schemes from which emerge mathematical concepts. In particular, the MIT for proportion (MIT-P) is geared to support the construction of proportional equivalence. We have done extensive research on this design and using variety of media. Here we ...

## The Eye Trick

Overview The Eye Trick is an activity for grounding the concept of proportion in perceptual judgments of geometrical similitude. The “trick” is that students judge similarity by creating an optical illusion of identity. Later, they use a stretchy ruler to determine measures, and they tabulate these measures in what becomes a ratio table. The Eye Trick: same ...

## The Marbles Scooper

The marble scooper is a device for sampling a fixed number of marbles out of a vessel containing many marbles, such as a box with equal numbers of green and blue marbles. We have built scoopers that sample exact numbers of marbles—a 4-Block marble scooper and a 9-Block marble scooper. Here we willl feature the 4-Block marble scooper that takes samples ...