Making it countMaking it count

Mathematics and Mathematics and the Heritagethe Heritage

Why use mathematics Why use mathematics and heritage?and heritage?

The historic environment can offer a The historic environment can offer a context for mathematical problem context for mathematical problem solving;solving;

Mathematics can be used as a tool Mathematics can be used as a tool for historical problem solving;for historical problem solving;

Both types of problem solving are Both types of problem solving are real problem solving and not just real problem solving and not just simulations or detached exercises. simulations or detached exercises.

Mathematics

Historic Environment

Aids enquiry into

Gives a context for enquiry using

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next)

The golden section numbers are ±0·61803 39887... and ±1·61803 39887...

The Golden SectionOr Golden Rectangle

Golden Rectangle?

Golden Rectangle?

Golden Rectangle?

How many angles?

What sort of Angles?

Why?

What shapes were used in this place and why were they used? Collecting shapes and explaining them.

ShapeShape WhereWhere??

DecoratiDecorationon

DefenceDefence Taking Taking weightweight

Why use particular shapes?

What sorts of symmetry?Rotational or line?

Why? Decoration, equal space, equal light, equal weight?

What sorts ofsymmetry?Rotational or line?

Why? To take equal weight? Give equal light? To give equal space?

What sorts ofsymmetry?Rotational or line?

ShapeShape WhereWhere??

DecoratiDecorationon

DefenceDefence Taking Taking weightweight

What sorts ofsymmetry?Rotational or line?

What sorts ofsymmetry?Rotational or line?

What repeating patterns can you see here?Can you make a formula for predicting what would be next in the sequence?

What was important in the design of this space?Looking for symmetry, number patterns, and proportion.

Proportions

Suggest a method of gauging the proportions of this building?Why did they use these proportions?

Which was the most important room in the Théâtre Royal de la Monnaie - Muntschouwburg?

Use the matrix to find the most important room.

Choose a room and score each out of 10, with 10 being most

of the thing.ROOM Heat Light Space Floor

coveringdecoration walls'

decorationFurniture Total

What maths was used in this room?

Squares

Line Symmetry

Repeating patterns

Mathematics, artefacts and Mathematics, artefacts and chronologychronology

How long did it take to How long did it take to make this make this object?object?

Could we make the same Could we make the same thing thing faster or slower in the faster or slower in the present?present?

Do we know when it was Do we know when it was made?made?

Maths, artefacts and Maths, artefacts and symmetrysymmetry

Do the artefacts have Do the artefacts have repeating patterns of shapes repeating patterns of shapes that are symmetrical?that are symmetrical?

Are there any artefacts that Are there any artefacts that have patterns that are not have patterns that are not symmetrical?symmetrical?

Maths, artefacts and Maths, artefacts and anglesangles

Can you find any Can you find any right angles in the right angles in the object?object?

Are there any other Are there any other angles? What sorts are angles? What sorts are they?they?

Maths, artefacts and Maths, artefacts and symmetrysymmetry

• Which artefacts are Which artefacts are symmetrical? Why is this? symmetrical? Why is this? Could it be for taking Could it be for taking equal weight on all sides, equal weight on all sides, for decoration, giving for decoration, giving equal room on all sides or equal room on all sides or being able to be held on being able to be held on all sides?all sides?

Maths, shapes and Maths, shapes and artefactsartefacts

• Give a friend a list of Give a friend a list of mathematical clues to a mathematical clues to a mystery object and let mystery object and let them find it. Make them find it. Make collections of artefacts collections of artefacts with the same with the same mathematical properties mathematical properties

Maths and artefactsMaths and artefacts

If the artefact is If the artefact is broken can you broken can you suggest what it would suggest what it would have looked like? have looked like? How have you arrived How have you arrived at your solution?at your solution?

PurposePurpose Formats to Formats to emphasis this emphasis this purposepurpose

Describing Describing Nominal scalesNominal scales

ClassifyingClassifying

(sorting into (sorting into groups)groups)

Topic web, Venn Topic web, Venn diagram, tree diagram, tree diagram, attributes diagram, attributes matrixmatrix

Comparing Comparing (showing (showing similarities and similarities and differences)differences)

Bar-chart, rating, Bar-chart, rating, attributes matrix, attributes matrix, preference matrixpreference matrix

Ordering Ordering (arranging in (arranging in sequence)sequence)

Time chart, ordered Time chart, ordered list, network, flow list, network, flow chartchart

PositioningPositioning

(locating in (locating in space)space)

Scale model, map, Scale model, map, scale drawing, planscale drawing, plan

InterrelatingInterrelating

(co-ordinating (co-ordinating similarities)similarities)

Table, histogram, Table, histogram, scatter graph, graph, scatter graph, graph, algebraic formulaealgebraic formulae

Historical and archaeological

evidence

Organise and communicate the solution

Chronology, knowledge and understanding,

interpretation

Solve the historical problem

HISTORICAL CONTEXT

Key questions

Historical enquiry

skills

strategic skills

mathematical skills

REAL LIFE CONTEXT

Problem Solving in History

PROBLEM SOLVING WITH HERITAGE