Relative Age Effect

March 3rd, 2015 No comments

Does your child have a better chance of getting into the top ability set for Mathematics if they were born nearer the beginning of the academic year?

5 years ago I read Outliers by Malcolm Gladwell. The blurb states that “if we want to understand how some people thrive, we should spend more time looking around them – at such things as their family, their birthplace, or even their birth date.” He argues how the Relative Age Effect gives advantage to those born nearer the beginning of the year (academic year or sports season). Since reading the book I have wondered whether this phenomenon is in effect in the ability setting of Mathematics pupils in their lower secondary years, i.e. at the age of 12. And now we have the data to be able to answer this question…

Read more…

GeoGebra: Binomial Distribution with Normal and Poisson Approximation

June 6th, 2011 4 comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

This applet is for visualising the Binomial Distribution, with control over n and p.

It also shows the Normal Approximation curve (and how this approximation breaks down for large or small p)
and it shows the Poisson Approximation curve (and how his approximation breaks down if there’s no positive skew)

You can show critical regions at either end by turning the bars red instead of green. The appropriate cumulative binomial probabilities are shown.

GeoGebra: The Ultimate Projectiles Applet!

January 29th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

User-friendly applet designed with perfection and aesthetics in mind.

Play with the checkboxes and X points. Those with a grounding in projectile mechanics will find it is self-explanatory.

You can select: angle of elevation OR range OR an airborne target, for any speed of projection and strength of gravity.
The applet shows the possible trajectories under the given constraints.
The applet also animates balls projected at the selected angle of elevation.

GeoGebra: Tangent Fields & Isoclines

January 29th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

This applet displays tangent fields and coloured gradient fields for general solutions of explicitly defined 1st order ODE’s (i.e. dy/dx = …..)
It also displays the particular solution curve; you can set the boundary condition by dragging the blue point. [Euler’s numerical method is used with error correction]

The applet also shows isoclines where possible [dy/dx=f(x,y) must be polynomial in x and y]

GeoGebra: Probability Venn Diagram with Proportional Regions

March 19th, 2012 No comments
Click the animation to link to GeoGebraTube
(Opens in a new window/tab).

In the latest version of this dynamic Venn diagram you have full control over the values of P(A), P(B) and P(AnB).

The orange area representing P(AnB) is dependent on the distance between the centres of the circles. But this distance is the solution of an equation that cannot be solved analytically, so the Newton-Raphson numerical method runs in the background with four iterations.

The Swearing Graph!

September 2nd, 2010 1 comment

Quintic swear

This is made from a quintic graph (a polynomial of degree 5).  It’s possible to apply the “treatment” to any function, including reciprocal, hyperbolic and trigonometric functions. Read more…

GeoGebra: Graphical Mortgage Repayment Calculator

November 8th, 2012 No comments
Click the animation to link to GeoGebraTube
(Opens in a new window/tab).

Click here to link to GeoGebraTube

Calculate monthly repayments based on the amount you are borrowing and over how many years you wish to repay it.
Calculate how many years it will take to repay your mortgage based on the amount you are borrowing and your monthly budget.

My trip to Alicante: “X Jornades d’Educació Matemàtica”

November 24th, 2012 No comments

This post tells the story of my trip to Alicante, Spain in October 2012 to deliver the opening lecture at the 10th Conference on Mathematical Education, held at the University of Alicante and organised by the Societat d’Educacio Matematica Comunitat Valenciana (SEMCV) Al Khwarizmi. The talk was entitled, “The Value of Dynamic Geometry in Modern Education and Problem Solving in GeoGebra.”

Read more…

Using the mean to find the mode of a Binomial Distribution

March 20th, 2011 No comments

The original motivation behind this investigation was an attempt to save my Statistics students a few precious seconds in their upcoming S1 module paper.

The mean or expectation of a Binomial Distribution is always very close to mode, (the value of X that has greatest probability). I want to know if you can use the mean to reliably predict the mode.

Read more…

Statistical Outliers Impossible in Small Samples

October 13th, 2013 2 comments

How many pieces of data are needed before it’s possible for one of them to be an Outlier?

Read more…

GeoGebra: The Binomial Expansion

February 11th, 2012 No comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

Fully interactive: A geometric representation of the binomial expansion

Control parameters a,b,n in the function f(x)=(a+bx)n
Also control the number of terms in the binomial expansion.

The applet shows the correct function (black) alongside the binomial expansion of the function (green).
It also clearly shows the bounds (x-values) for which the expansion is valid.

Read more…