1
Reasoning w/o Arithmetic 2 Function
Studies
3 PolyDials4
Animated Triangles5
Linear Algebra6.
Calculus7.
Infinite Sums8. Pebble Arithmetic9. Ratios & Scaling10. Three Pts Determine ...11. Carpet Theorem ...12. Algebraic Generalisations13. Exchange

My
personal preferred way of working with animations and applets is in plenary. With animations, I like to
show the annimation once and then invite personal and paired
reconstruction of the incidents. This usually leads to differences or
to gaps which inform a second viewing. Once there is an agreed narrative, attention turns to accounting-for
what happens mathematically.

With other applets, I try to provoke mathematucal thinking and then show how the applet can be used to explore more deeply.

With other applets, I try to provoke mathematucal thinking and then show how the applet can be used to explore more deeply.

Secret Places (homage to Tom O'Brien): Secret Places; notes; online applet

there is a 2D version inside the zipped folder using surfaces such as a cylinder, mobius band, torus, and Klein bottle

Magic Square Reasoning: Reasoning based on the properties of magic squares but wihtou ever referrin to a particular magic square. PPT

Revealing Shapes: The applet provides Opportunities for reasoning, following consequences of possibilities and so bringing to awareness that choices have consequences. (This applies in the social realm as well as in mathematics.) Experience suggests that quite young children can manage this. (RevealingTheShapes) If you generate an interesting example and you want it included in the applet, send me a picture and I will build it in (j.h.mason @ open.ac.uk). The current examples are visible here

The applet is designed to be downloadable (unzip the folder and then open the html file in a web browser)

More-or-Less is a task structure originated by Dina Tirosh and Pessia Tsamir. The idea is to present a grid and ask students to construct vraiations on the object in the central cell which vary one or both of two possible attributes. A related structure exploited by Colin Foster is to provide a grid with attributes as row and column entries and then invite students to construct one or more objects in each cell.

More-or-Less perimeters and areas

ZIGZAGs: initial stimulus to exploring absolute value function through first generating and then characterising zigzag functions of the form |||x-1|-2|-3|. Animation1; Animation2

Cobwebs provides a stimulus to learn to read graphs by tracking coordinates to discover a locus and that composition is not commutative. Download Zipped Folder

The applet makes it easier to check (by eye) that various alignments seem to be inevitable. There is the challenging task of relating two polynomials so that both their composites display the appropriate degree!

See Notes for questions, prompts and explanation of buttons.

CHORD STUDIES: stimuli to think about the relationships between the chord-slope function where one end of the chord is kept fixed, and the slope-chord function where the interval width of the chord is kept fixed, and then allowed to approach 0.

Animation;
Cabri
page1; Cabri
page2

COBWEBS: Application of compound maps to iterations, including a cyclic iteration. Iter1; Iter 2; Iter3 ;

PHASE DIAGRAMS & PARAMETER PLOTS:

Phased by Distance: given two points in the plane, measure the distance from P to each and then use these as coordinates to graph the position of P.

CEILING - FLOOR (Nov 5 2010)

Explaining why the graphof ceiling(x-a) - floor(x-b) looks the way it does, and how to force the segments to be equal in length. Ceiling - floor download; Ceiling - floor web ;

INTERESTING FLOOR FUNCTIONS (Nov 2011)

Functions with interesting
properties concerning differentiability at x = 0. Floor-Function Download; Floor-Fn web;

DownLoad PolyDials folders (need unzipping)

The applet is rough as yet: files have to be opened directly or you can construct your own. For further information contact me.

iInscribed Squares

This applet is about inscribing squares in a triangle. It is in early draft form and will have more extensions. Web version; Download

(zipped folder: open html file; keep all three files together)

I use these after showing people how an elastic can be stretched. In particular, mark the midpoint and the one-third point along an elastic. Now stretch (hold one end fixed and pull the other) until the one-third-point is where the midpoint was originally. By what factor has the elastic been stretched? Generalise!

Through exercising
mental imagery and drawing upon the mathematical theme of freedom and
constraint, it is not difficult to build up to the theorem that three
points determine a circle (measure the freedom under constraints such
as 'circle passes through 1 pt', then '2 pts' then '3 pts' of the
centre of the circle). The applet then provides supportive imagery. The
applet can also be used to explore the questions of 'how many points
determine a square' (and what constraints might be needed) and 'how
many points determine a rectangle. 3 Points Determine
applet

This observation can be applied in many situations. For example,

Circles in Circles: download; notes; online applet

Areal Relation: download; notes; online applet 1; online applet 2

Archimedes Salinon: download; notes; online applet 1; online applet 2