20 December 2025

Introduction to Artificial Intelligence – Training a Simple Model

Artificial Intelligence can sound mysterious, but at its heart it’s built on ideas students already know: patterns, data, graphs, and feedback. In this introduction, we strip AI back to first principles by training a very simple model—no coding background required.

What do we mean by “training” an AI model?

Training is simply the process of showing a computer examples, letting it make predictions, and then correcting it when it gets things wrong. Over time, those corrections improve its accuracy.

Think of it like teaching a student to estimate the height of a tree from its shadow:

You give several examples (shadow length → tree height)
The student guesses
You say how far off they were
They adjust their method next time

That loop—predict → check → adjust—is the core of machine learning.

A simple example: predicting exam scores

Imagine we want to predict a student’s exam score based on hours of revision.

Hours of revision	Exam score (%)
1	40
2	50
3	60
4	68
5	75

We might start with a simple rule:

Score = (hours × 10) + 30

This is our model. It won’t be perfect, but it gives us a starting point.

How the model learns

Make a prediction
For 3 hours:
Predicted score = (3 × 10) + 30 = 60%
Compare with the real result
Actual score = 60%
Error = 0 (perfect!)
Adjust if needed
If predictions are consistently too high or too low, we tweak the numbers.

After many examples, the model settles on values that minimise the overall error. That process—reducing error step by step—is called training.

Key ideas students should remember

Data: The examples we train the model on
Model: A rule or equation that makes predictions
Prediction: The model’s output
Error (loss): How wrong the prediction is
Training: Repeating predictions and corrections to reduce error

At GCSE and A-Level, this links directly to:

Graphs and lines of best fit
Averages and spread
Iterative improvement
Cause-and-effect reasoning

AI is not magic—it’s applied maths and logic at scale.

Why this matters in school science and maths

Understanding how a simple model learns helps students:

Demystify headlines about “AI taking over”
See real-world applications of algebra and graphs
Develop critical thinking about data quality and bias
Build confidence with modern technology

At Hemel Private Tuition, we often teach AI ideas using familiar experiments and datasets, so students focus on understanding—not buzzwords.

The Next Step: Training a Model to Classify Images (Cats vs Dogs)

Once students understand training a simple numerical model, the natural progression is to ask:

Can a computer learn from pictures instead of numbers?

Yes—and this is where image classification comes in.

What does “classifying images” mean?

Image classification means teaching a computer to look at an image and decide which category it belongs to.

In our example, there are just two classes:

🐱 Cat
🐶 Dog

The model’s job is simple:

Given a new image, decide whether it is more likely to be a cat or a dog.

Step 1: Images must become numbers

Computers don’t “see” images the way we do.
An image is actually a grid of pixels, and each pixel has numbers attached to it.

For a colour image:

Each pixel has Red, Green, and Blue (RGB) values
Each value is usually between 0 and 255

So an image becomes a very large table of numbers.

This links nicely to:

Matrices in maths
Grids and coordinates
Data representation in computer science

Step 2: The model looks for patterns, not animals

The model is not told what a cat or dog is.

Instead, during training it starts to notice patterns such as:

Fur texture
Edges and shapes
Ear positions
Contrast between background and subject

Early layers might detect:

Straight and curved lines
Light vs dark regions

Later layers combine these into more complex features.

At school level, you can explain this as:

The computer learns which patterns usually appear in cat photos and which appear in dog photos.

Step 3: Training works just like before (predict → check → adjust)

The training loop is exactly the same idea as before:

Show the model an image
Model predicts: “cat” or “dog”
Check the label (we already know the correct answer)
Calculate the error
Adjust the model slightly

This is repeated thousands of times using many images.

The only difference from the simple maths model:

The model has many more adjustable values
The maths happens automatically behind the scenes

Step 4: Testing with new images

Once trained, the model is tested using images it has never seen before.

This is crucial:

A model that memorises training images is useless
We want generalisation, not memory

Example output:

Cat: 92%
Dog: 8%

The model chooses the highest probability.

Key concepts students should remember

Term	Meaning
Training data	Images the model learns from
Labels	The correct answers (cat / dog)
Features	Patterns the model detects
Model	The system making predictions
Accuracy	% of correct classifications
Overfitting	When a model memorises instead of learning

Why cats vs dogs is such a good teaching example

Clear, familiar categories
Easy to understand success and failure
Shows limits of AI (misclassified images are often interesting)
Links maths, computing, biology (vision), and ethics

Students quickly realise:

AI doesn’t understand animals — it recognises patterns in data.

Classroom-friendly ways to explore this (no coding required)

Sort printed images by hand → discuss “features”
Use an online image classifier demo
Compare correct vs incorrect classifications
Change the dataset and see accuracy change
Discuss bias (e.g. only fluffy cats, only small dogs)

This fits beautifully into:

GCSE Computer Science
A-Level Computer Science
STEM enrichment sessions
Cross-curricular maths & science lessons

The big idea

Training an image classifier is just a scaled-up version of what students already know:

Patterns → predictions → feedback → improvement

Once that clicks, AI stops being intimidating—and starts being understandable.

19 December 2025

Investigating Catalysts Using Manganese Dioxide and Hydrogen Peroxide

A classic chemistry experiment that actually works – every time.

Catalysts can feel like one of those abstract chemistry ideas that students memorise but don’t really see. This experiment changes that instantly.

By adding manganese dioxide (MnO₂) to hydrogen peroxide (H₂O₂), students observe a rapid, dramatic reaction that clearly demonstrates what a catalyst does: speeding up a reaction without being used up.

It’s reliable, visual, safe when done properly, and perfect for GCSE and A-level chemistry.

The Chemistry Behind It

Hydrogen peroxide naturally decomposes very slowly:

2H₂O₂ (aq) → 2H₂O (l) + O₂ (g)

Manganese dioxide acts as a heterogeneous catalyst, providing a surface that lowers the activation energy of the reaction. The result is an immediate release of oxygen gas, visible as vigorous bubbling and foam.

Crucially:

The MnO₂ is unchanged at the end
The reaction is faster, not different
Energy is released as heat (the tube warms noticeably - often enough to produce steam)

Method (Student-Friendly)

Add hydrogen peroxide to a test tube or conical flask
Carefully add a small spatula of manganese dioxide
Observe the rapid effervescence
Test the gas produced with a glowing splint (it relights → oxygen)

This works beautifully for live demonstrations, filmed lessons, or practical assessments.

What Students Can Investigate

This simple setup supports deeper scientific thinking:

Comparing catalysed vs uncatalysed reactions
Measuring rate of reaction (volume of gas or foam height vs time)
Discussing activation energy using energy profile diagrams
Reinforcing the definition of a catalyst for exam answers

It’s also a great opportunity to talk about industrial catalysts, linking the experiment to the Haber process, catalytic converters, and real-world chemistry.

Why I Use This Experiment

In my lab and online TV-studio lessons at Hemel Private Tuition, this experiment consistently:

Engages even reluctant students
Produces clear, repeatable results
Makes “catalyst” more than just a definition
Translates directly into stronger exam responses

It’s one of those experiments where students say:
“Oh… now I get it.”

18 December 2025

Making Young’s Modulus Actually Teachable

Hemel Private Tuition – Practical Physics that Works

Young’s modulus is one of those A-level Physics experiments that ought to be conceptually beautiful but, in practice, often turns into a frustrating exercise in squinting at a vernier scale and arguing about micrometres.

Traditionally, students measure the extension of a long metal wire under load, often using a vernier scale or travelling microscope. It is technically correct — but also:

fiddly
time-consuming
prone to large percentage uncertainties
difficult for weaker practical students
and not especially engaging

A Better Approach: Lascells Strip & Wire Testing Clamps

Using Lascells Strip & Wire Testing Clamps, we can transform the experiment into something that is:

clear
visual
safe
cheap
and far more effective for teaching the physics rather than the micrometry

Instead of metal wires, students test plastic strips cut from carrier bags from different manufacturers. The behaviour is immediately visible, repeatable, and ideal for identifying key material properties.

The Physics You Can Actually See

With increasing load, students can clearly observe:

Elastic behaviour – the strip returns to its original length
Limit of proportionality – extension no longer proportional to force
Elastic limit – permanent deformation begins
Ultimate tensile strength – the maximum force before failure

These concepts are often abstract when using metal wires. With plastic strips, they are obvious.

Full Experimental Method

Apparatus

Lascells Strip & Wire Testing Clamps
Plastic carrier bags (cut into uniform strips)
Metre ruler or fixed scale
Mass hanger and slotted masses
Clamp stand
Safety tray (to catch masses if the strip fails)

Method

Prepare the sample
- Cut strips of equal width (e.g. 10 mm) from different plastic bags
- Measure the original length $L_0$
Set up the clamps
- Secure the plastic strip vertically between the Lascells clamps
- Attach the lower clamp to a mass hanger
Apply load gradually
- Add masses in equal increments (e.g. 50 g or 100 g)
- After each addition, measure the extension
Record data
- Force (N)
- Extension (m)
- Note any permanent deformation on unloading
Continue loading
- Until the strip clearly leaves linear behaviour
- Stop just before failure (or allow failure with eye protection and clear space)

Results and Analysis

Typical Results Table

Load (N)	Extension (mm)
0.5	2
1.0	4
1.5	6
2.0	8
2.5	11
3.0	15

Graph

Plot Force vs Extension
The straight-line region shows Hooke’s Law
The point where the graph curves marks the limit of proportionality

Discussion Points

Why different plastics behave differently
Why metals show a much smaller elastic region
Why this experiment has larger extensions but smaller uncertainties
Why real engineers test polymers differently from metals

Why This Works Better Than the Traditional Wire Method

✔ No microscopes
✔ No long wires under tension across the lab
✔ No students struggling to read verniers
✔ No huge uncertainty in extension measurements
✔ Far safer — especially for mixed-ability groups
✔ Much cheaper equipment
✔ Much quicker
✔ Much clearer physics

For teaching Young’s modulus as a concept, this approach is outstanding.

How We Use This at Hemel Private Tuition

In our laboratory and online TV-studio lessons, this experiment:

reinforces material properties visually
builds confidence in graph interpretation
supports exam-quality evaluation answers
works brilliantly for OCR, AQA, and Edexcel specifications

Students leave understanding why materials behave as they do — not just how to fill in a table.

17 December 2025

Complex Numbers – From Argand Diagrams to Real Problems

Complex numbers often feel like a strange detour in A Level Maths. Students meet the imaginary unit $i$ , are told that $i^2 = -1$ , and may reasonably ask: why do we need this?

The answer is that complex numbers are not just mathematical curiosities. They are essential tools in engineering, physics, electronics, signal processing, and control systems. Understanding them opens the door to solving problems that cannot be handled using real numbers alone.

What Is a Complex Number?

A complex number has the form:

z = a + bi

where:

$a$ is the real part
$b$ is the imaginary part
$i = \sqrt{-1}$

Every complex number can be represented as a point on a plane, rather than a point on a line.

Argand Diagrams – Seeing Complex Numbers

An Argand diagram plots:

the real part on the horizontal axis
the imaginary part on the vertical axis

For example, the complex number $3 + 4i$ is plotted at the point (3, 4).

This visual representation helps students understand:

addition and subtraction of complex numbers
magnitude (modulus)
direction (argument)

Modulus and Argument

Modulus

The modulus of $z = a + bi$ is the distance from the origin:

|z| = \sqrt{a^2 + b^2}

This links complex numbers directly to Pythagoras’ theorem.

Argument

The argument is the angle the line makes with the positive real axis:

\arg(z) = \tan^{-1}\left(\frac{b}{a}\right)

Together, modulus and argument allow complex numbers to be written in polar form.

Polar Form and Multiplication

A complex number can be written as:

z = r(\cos \theta + i \sin \theta)

In this form:

multiplying complex numbers multiplies their moduli
adds their arguments

This makes problems involving powers and roots far simpler than using algebraic form.

Real Problems Where Complex Numbers Matter

1. Alternating Current (AC) Circuits

In physics and engineering, complex numbers represent:

voltage
current
impedance

They allow phase differences between voltage and current to be handled cleanly.

2. Waves and Oscillations

Complex exponentials model:

sound waves
light waves
oscillations

What looks abstract in maths becomes practical in physics.

3. Rotations and Transformations

Multiplying by a complex number can represent a rotation and scaling in the plane — a powerful idea used in graphics and robotics.

4. Solving Polynomial Equations

Some equations have no real solutions.
For example:

x^2 + 1 = 0

Complex numbers ensure that every polynomial has a solution, a result known as the Fundamental Theorem of Algebra.

Why Students Struggle – and How to Fix It

Students often struggle because:

the imaginary unit feels artificial
links to real applications are not always shown
diagrams are not used enough

Using Argand diagrams, geometric interpretations, and applied examples transforms complex numbers from abstract symbols into useful mathematical tools.

Skills Highlight

Plotting complex numbers on Argand diagrams
Calculating modulus and argument
Converting between algebraic and polar form
Using De Moivre’s theorem
Applying complex numbers to real-world contexts

Why It Works in Teaching

Complex numbers reward visual thinking and pattern recognition. Once students see that multiplication corresponds to rotation and scaling, many problems become simpler — not harder.

They also prepare students for further study in mathematics, physics, engineering, and computing.

16 December 2025

Measuring Half-Life with a Simulated Radioactive Decay Model

A safer (and still fascinating) way to explore nuclear physics in the classroom.

☢️ What Is Half-Life?

The half-life of a radioactive substance is the time it takes for half the atoms in a sample to decay.
It’s a key concept in understanding radioactivity, nuclear medicine, archaeology (hello, carbon dating), and more.

But since bringing a pot of uranium into a school lab tends to cause… concern… we use simulations.

🎲 The Classic Classroom Simulation

A tried-and-tested method to model radioactive decay is using dice, coins, or counters to represent unstable atoms.

Here’s how it works:

Give each student/group 300 coins (or paper squares, Lego bricks, etc).
Each coin is an atom.
Toss them all — every coin that lands “heads” has decayed.
Remove decayed coins. Count the undecayed ones.
Repeat the process for several “time intervals” (throws).
Plot number of undecayed atoms vs. timE
Compare one set of results with the rest of the class - they will be remarkably similar.
Compare this to playing with 4 stud LEGO bricks, where the decayed particle is a LEGO brick the correct way up, a different rate but the same result.

📉 What You’ll See

You’ll get a lovely exponential decay curve.

It won’t be perfect (radioactive decay is random), but it illustrates the statistical nature of half-life beautifully.

You can even:

Calculate an experimental half-life
Compare different simulations with different starting numbers
Discuss sources of error and real-life limitations

💡 Why It Works

This model helps students grasp:

That decay is random for each nucleus
That half-life is about probability, not a countdown
That decay rates are measurable over time, even if individual events are unpredictable

🧠 Extension Ideas

Use multisided dice instead of coins (e.g., only 1s decay = longer half-life)
Graph multiple runs and compare mean curves
Link the activity to real-life isotopes like carbon-14 or iodine-131
Use spreadsheets or PASCO sensors to enhance digital analysis

🔬 Final Thought

Understanding half-life doesn’t require radiation – just curiosity and some coins.

15 December 2025

Natural Selection in Action – Modelling Evolution with Peppered Moths

Natural selection can feel abstract when students first encounter it in GCSE and A Level Biology. Terms like selective pressure, variation, and allele frequency are easy to memorise but harder to visualise.

The classic peppered moth example brings evolution to life. It shows natural selection happening over a short timescale, driven by environmental change and differential survival — exactly what Darwin described.

The Peppered Moth Story

The peppered moth exists in two main forms:

light-coloured (typica)
dark-coloured (carbonaria)

Before the Industrial Revolution, most tree trunks were pale and covered in lichens. Light moths were well camouflaged, while dark moths were easily spotted and eaten by birds.

As industrial pollution increased, soot darkened tree bark and killed lichens. Suddenly, the dark moths were better camouflaged. Birds ate more light moths, and the frequency of the dark form increased dramatically.

When air quality improved later in the 20th century, the trend reversed.

This is evolution by natural selection in action.

Modelling Natural Selection in the Classroom

Students can model this process using a simple practical or simulation.

Equipment:

Paper moth cut-outs in two colours (light and dark)
Two backgrounds (light paper and dark paper)
Timer
Data recording sheet

Method:

Scatter equal numbers of light and dark moths onto the background.
Act as the “predator” and remove moths you can see easily within a fixed time.
Count the remaining moths of each colour.
Repeat the process over several “generations”.
Change the background to represent environmental change.

Students quickly see one colour becoming more common than the other.

Typical Results

Light background (pre-industrial):

Light moths survive in greater numbers
Dark moths are removed more quickly

Dark background (industrial):

Dark moths survive better
Light moths decline rapidly

Over repeated generations, the proportion of moths changes — not because individuals change, but because survival and reproduction are unequal.

Key Biological Concepts Reinforced

Variation: moths exist in different forms
Selective pressure: predation
Differential survival: better-camouflaged moths survive
Inheritance: colour is genetically determined
Change in allele frequency: populations evolve over time

This helps students avoid the misconception that organisms “adapt because they need to”.

Evaluation and Limitations

Students can critically evaluate the model:

paper moths do not move
predators are human, not birds
time scale is compressed

Despite this, the model clearly demonstrates the principle of natural selection and is highly effective for learning.

Why This Works in Teaching

The peppered moth example:

links biology to history and environmental change
is backed by real scientific evidence
allows data collection and graphical analysis
supports exam questions on evolution and selection

It shows evolution as an ongoing process, not just something that happened millions of years ago.

Skills Highlight

Modelling biological processes
Recording and analysing population data
Interpreting trends over generations
Applying theory to real-world examples
Evaluating experimental models