# Teaching statistics with Fruit Gums

Fruit Gums can be used to demonstrate the concept of standard deviation.

Calculating standard deviation is easy, it’s simply:

Which, with the right teaching, and enough practice, anyone can learn to do. Understanding what standard deviation means is far more difficult.

I bought three boxes of Fruit Gums …

… and sorted them by flavour.

I collected the data in Excel which yielded the following spreadsheet:

The issue of standard deviation is summed up in the question: “What is the largest and smallest number of each flavour that you can expect to find in each box?”

Lime is a special case. The were seven lime fruit gums in each box, meaning the standard deviation was zero. You could therefore – based on this sample alone – expect to find seven lime fruit gums in each box.

The standard deviation of a sample is a measurement of its spread, it tells you the mean distance from the mean.

For lemon fruit gums the mean is 19.0 plus or minus a standard deviation of 2.2. You could therefore expect to find – on average, based on this sample alone – between 16.8 and 21.2 lemon gums in each box. A box containing 25 lemon gums would be way outside the expected average contents.

The only outlier in this dataset is the first box’s orange gum count; based on the data collected we would expect a maximum of 21.2 orange gums. Clearly more fruit gums research is required.

# Learning Styles are nonsense

As a teacher I was trained that pupils fall into one of three groups:

• Visual learners learn best by reading and writing notes and watching demonstrations and videos.
• Auditory learners learn best by listening to their teacher and by talking about and discussing the material being studied.
• Kinaesthetic (or “active”) learners learn best by doing; by carrying out experiments and directly experiencing the material in a hands-on way.

and that pupils should be taught according to their preferred learning styles.

A report by the Learning and Skills Research Centre (Coffield et al, 2004) found that:

“A thriving commercial industry has also been built to offer advice to teachers, tutors and managers on learning styles, and much of it consists of inflated claims and sweeping conclusions which go beyond the current knowledge base and the specific recommendations of particular theorists.”

and that:

“[F]or [some teachers], learning styles are the central doctrine in a quasi-evangelical crusade to transform all levels of education.”

As a result names like Myers-Briggs and Honey & Mumford have become all too familiar to teachers.

A paper by Krätzig and Arbuthnott (2006) investigated the learning styles hypothesis. Their results were damning, to say the least.

They found that:

“[T]here were no significant correlations between learning style and objective memory performance … [our] results cast doubt on the central assumptions of the learning style model as it is used in education.

“An assessment of learning style does not provide information about an individual’s best learning environment.”

and concluded that:

“[F]ocusing on learning styles as defined by sensory modalities [learning styles] may be a wasted effort … [M]ost people are likely multimodal and multisituational learners, changing learning strategies depending on the context of the to-be-learned material.

“[P]resenting material to students in multiple sensory modalities is undoubtedly beneficial to learning and interest.”

Harrison et al (2003) investigated the tests used to assess pupils’ learning styles and found that:

“There are a myriad of instruments available commercially, from standardized formal tests of learning styles to informal learning styles questionnaires that claim to provide educators with information on students’ unique approaches to learning. Unfortunately, most of these instruments lack a sound theoretical basis. Indeed, many have never been validated, and it is uncertain what exactly is being measured.”

This agrees with initial findings by Krätzig and Arbuthnott  in which the two different methods they used to assess pupils’ learning styles agreed only 45% of the time.

Harrison et al concluded that:

“[T]he ability to draw on multiple strategies for different tasks distinguishes good and poor learners.”

Now don’t even get me started on Gardner’s Theory of Multiple Intelligences.