Let's face it, when it comes to STEM education, maths nearly always gets a dud deal. Maths becomes this tacked on set of processes that's used *in service of *other, more interesting ideas.

But, what if it wasn't left out? What if, instead, maths were at the centre of STEM?

**I believe that if we choose the rights sorts of problems, we can reframe STEM learning opportunities. **Problems that have maths at the heart, can allow students to deepen their understanding – and appreciation – of mathematics, whilst also benefiting from developing other STEM skills.

## Reimagining STEM with a classic problem

Let me explain further, using a classic problem that you can use with your students.

It's a great example of a STEM task that doesn't involve robots. (You don't have to be an amazing coder to teach STEM!)

Here's the problem:

The block stacking problem or Tower of Lire problem dates back thousands and thousands of years. It's also a fantastic example of a low floor, high ceiling problem.

## What makes this a low floor, high ceiling problem?

The block-stacking problem is low floor, because there's little initial information or knowledge that students need to get started. They need to understand what is meant by ‘overhang' and how to measure that distance.

It's high ceiling, because there's an incredible amount of highly complex mathematics that can be used when tackling it. Depending on your students' mathematical skills and knowledge, there's a huge range of approaches they might draw on.

At a Maths Teacher Circles session, involving primary teachers, mathematicians and everyone in between, participants used concepts like fractions, symmetry and harmonic series.

Additional questions can help students to go deeper and further with this problem as well. For example:

- Trial some different designs. What are helpful strategies?
- Compare your designs with a partners. How are they the same/different? Create a new design based on what you notice.
- Can you place blocks so that one extends out by 1/2 a block?

Serious mathematicians have tackled this problem, coming up with approaches such as the Genie's Lamp and the Kingfisher configuration. There's A LOT to explore!

But how does this problem draw in STEM skills?

## How does the block-stacking problem connect to STEM?

Here's a brief overview of what each STEM field is about:

- Science: processes used for gaining and organising knowledge
- Technology: human-made objects, systems or processes that are used to solve a problem or reach a goal.
- Engineering: the use of mathematics, science and materials to solve problems.
- Maths: involves the study and logic of number, space, structure and change.

(NB: the definition of mathematics is varied and debated often! Here's a good article on the topic.)

The block-stacking problem involves:

- Science because students are testing out and learning about concepts such as weight, balance and overhang
- Technology because students are using everyday objects (blocks) and rulers or measuring tapes to explore and make sense of the problem
- Engineering because it brings the S, T and M together.

I'll go into the engineering part some more, because it's perhaps one of the hardest elements of STEM to appreciate.

## Wait, what's engineering?

Engineering is very much about solving problems in the world around us and considering the feasibility of our solutions. An important part of approaching an engineering problem, is to consider the criteria and constraints.

Here's what the team at Engineering is Elementary have to say:

“Criteria: the requirements by which we measure the success or failure of a solution to a problem ( structure, load to carry, community needs, environmental impacts).

Constraints: limitations or factors that determine the scope of how you solve a problem (availability of materials, cost of materials, time to build).”

So, in the block-stacking problem, the criteria are:

- using 10 blocks,
- creating an overhang, and
- the tower staying up.

The constraints include:

- having a limit of 10 blocks,
- the time available to explore it, and
- the tools and resources students have at their disposal (e.g. rulers, web access).

Once students have created a tower with the greatest overhang, they might also consider what would be needed if it were to be an actual tower in a city or town. What area would need to surround the tower? What materials would be best (environmentally friendly, cost-effective, sturdiest)? Who would be needed to build it?

I saw a tweet today and felt the need to respond.

In 1992, way before the “STEM” acronym was being thrown around, Implemented a unit of work that had all the elements of S.T.E.M. working together to achieve an outcome.

Students got to experience and understand each element of S.T.E.M. as vital for a successful outcome.

It has been the basis of my paedagogy for just over 31 years.

Life does not rely on a single discipline for us to exist.

One of many examples:

Had a group of year 5 primary students (girls) using a “Making Process” in a unit of work.

Using authentic components and materials (no cardboard cutouts or icy pole sticks).

On completion of the unit a single question was asked by one of the students “How do computers work?”

Went through a process where I demonstrated and explained the

“Binary Numbering System’s Relationship” to the electronics of a computer.

They truly understood the “Binary Numbering System” to a point where they converted paragraphs of text to “Binary”.

Have worked with Primary Prep’s through to Year 12 students over the years.

Strongly believe, I could not have the results I have had over the years by using traditional teaching methods.

My intent is not to disparage.

Rather present a different notion on what many believe S.T.E.M. Education should

revolve around their own singular discipline.

Yours Sincerely

George Spiridis

Hi George, thanks for sharing your experience with STEM – stories like this deserve to be more widely heard.

Your example of the Yr 5 girls learning about the electronics of a computer, reminds me of what Seymour Papert has written about: in using tools like computers to support more meaningful learning and to teach students to think (instead of merely teaching them processes). For this meaningful learning to happen, the authentic components and materials you speak of, are essential.

Gгeat article.

Thanks!

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