A planetary fruit salad

Here is a planetary fruit salad – a scale model of objects in the solar system (click to zoom). The Moon and the smaller planets are on the top left saucer. The lower right saucer represents the rings of Saturn.

On this scale (roughly 1 to 2 billion), the Moon is 19 centimetres from the Earth, the Earth is 73 metres from the Sun, Jupiter is 380 metres from the Sun, and Pluto is around 3 kilometres from the Sun.

Object Diameter Scaled Diameter Model
Sun 1,392,700 km 68 cm Beach ball (not shown)
Mercury 4,879 km 0.24 cm Mustard seed (yellow)
Venus 12,104 km 0.59 cm Chickpea
Earth 12,756 km 0.62 cm Chickpea (coloured blue)
Moon 3,475 km 0.17 cm Mustard seed (black)
Mars 6,792 km 0.33 cm Peppercorn (black)
Jupiter 142,984 km 7 cm Orange
Saturn 120,536 km 5.9 cm Lemon
Saturn’s Rings (up to F) 280,360 km 14 cm Saucer
Uranus 51,118 km 2.5 cm Grape
Neptune 49,528 km 2.4 cm Grape
Pluto 2,377 km 0.12 cm Poppy seed

Laws Guide to Nature Drawing and Journaling: a book review


Laws Guide to Nature Drawing and Journaling by John Muir Laws

Having written before about nature journals, a while ago I purchased the Laws Guide to Nature Drawing and Journaling by John Muir Laws of johnmuirlaws.com. This is a wonderful guide to both the scientific and artistic aspects of keeping a nature journal. There are chapter on how to observe as well as chapters on how to draw flowers, trees, and other things. Laws provides three useful observation cues: “I notice,” “I wonder,” and “it reminds me of” (click page photographs to zoom):

This wonderful book is full of practical tips, both on the scientific side and the artistic side. I particularly liked this little curiosity kit:

I haven’t quite finished with the book, but I really love it so far. Other reviews online are also very positive: “I can’t find a thing lacking in this book” (scratchmadejournal.com); “informative and inspiring” (parkablogs.com); “the best book for nature journaling in your homeschool” (proverbs14verse1.blogspot.com). Goodreads rates the book 4.67.

* * * * *
Laws Guide to Nature Drawing and Journaling by John Muir Laws: 5 stars


The modern Trivium and the teaching of science

The “trivium” approach to education derives from “The Lost Tools of Learning,” a 1947 speech by scholar and detective story author Dorothy L. Sayers. This approach takes the seven liberal arts (illustrated above), drops the all-important quadrivium, and applies the remainder in a largely metaphorical way. It is an interesting approach, although it inevitably under-emphasises mathematics. The door to Plato’s Academy was marked “Let no one ignorant of geometry enter (Ἀγεωμέτρητος μηδεὶς εἰσίτω),” and this referred to the most advanced mathematic of his day. I’m not sure that the “trivium” approach to education delivers that level of mathematical knowledge. Then again, does the standard approach?

ΑΓΕΩΜΕΤΡΗΤΟΣ ΜΗΔΕΙΣ ΕΙΣΙΤΩ

Science, on the other hand, can be fitted quite well into the “trivium” model. The three stages of this model (largely metaphorical, as noted) are “grammar,” “logic,” and “rhetoric.”

The “grammar” stage (intended for ages 6 to 10 or so) covers basic facts. Science at this level logically includes what used to be called natural history – the close observation of the natural world. Maintaining a nature journal is an important part of this, as are simple experiments, the use of a telescope, collections of objects (rocks, shells, etc.), and simple measurements (such as recording measurements from a home weather station).



Mother and child nature journaling examples from Nature Study Australia Instagram and website

Dorothy L. Sayers has nothing to say about science in the “logic” stage (apart from fitting algebra and geometry here), but the “logic” stage would reasonably include taxonomies, empirical laws, and an exploration of how and why things work the way they do – that is, the internal logic connecting scientific observations and measurements. A degree of integration with history education would provide some context regarding where these taxonomies and laws came from, and why they were seen as important when they were formulated.


Exploring Boyle’s law with a simple apparatus

In the “rhetoric” stage, the “how” and “why” of science would be explored in more detail, along with practical applications and project work (such as entering a science competition, or possibly even collaborating with local academics on a scientific conference paper).


A US Army engineer helps judge high school science projects (photo: Michael J. Nevins / US Army)

I suspect that quite a decent science education programme could be worked out on such a basis. If any reader knows of it having been done, please add a comment.


Sundials!

Above is an analemmatic sundial. The idea is to orient the sundial facing south, and then place a vertical pointer on the central figure-8 track, in a position corresponding to the date. The sundial above shows a simulated shadow for 2:15 PM yesterday. It can be seen that the sundial tells the time reasonably well, thanks to the inbuilt adjustment for variation in solar position.

For large-scale analemmatic sundials, like the one below, people can stand on the central figure-8 track and act as a human pointer. A sundial like this is fun to have in the garden.

Here are blank sundials for some Southern Hemisphere cities:

The ShadowsPro software will also generate sundials like these, if anyone is particularly enthusiastic.


Nature journals

Having said something about phenology wheels, I thought that I should mention nature journals too. Some years ago, I blogged about the professional aspects of this, but nature journals are a powerful educational tool, because of the way that they focus observational attention. John Muir Laws has good advice on getting started, including “Do not focus on trying to make pretty pictures. That just leads to journal block. Open your journal with the intention of discovering something new. Use the process to help you slow down and look more carefully.



Mother and child nature journaling examples from Nature Study Australia Instagram and website

The very useful Nature Study Australia website also has good advice and several examples, as well as other nature study resources for Australians. Artist Paula Peeters, aiming more at adults, runs nature journaling workshops around Australia, and offers an introductory book for sale or free download.


Nature journaling example from Paula Peeters, who runs workshops around Australia

Nature journals need not only contain pictures and text: a spiral-bound sketchbook will easily accomodate flat objects such as leaves, pressed flowers, feathers, and sun prints. Drawings are an essential aspect, however.


The CNPS curriculum

The California Native Plant Society offers a superb nature journaling curriculum for free download. It includes the observational prompts “I notice… I wonder… It reminds me of…” It advises parents and teachers not to say things like “that is really pretty” or “what a good drawing,” but instead to say things like “Oh, you found a spider on top of the flower! Great observation.” It also provides excellent practical advice on drawing, poetry, and other activities.

With so many excellent guides to nature journalling, why not get started on your own?


A drawing of mine (from quite some time ago)


Phenology wheels

Recently, somebody pointed me at phenology wheels, which are a popular tool for nature study among teachers and homeschoolers. Nature study is all about careful observation and finding patterns, and phenology wheels help with both. Every month, students draw a picture of what they see in the garden or on a nature walk, and the completed phenology wheel then shows an annual pattern. Other activities are possible – see this University of Wisconsin-Madison Arboretum document.

The picture below shows a pair of partially complete mother/daughter phenology wheels from the very useful Nature Study Australia website (they are using the central circle to show indigenous seasons). It is helpful to outline each month’s section in felt-tip pen:


Mother and daughter phenology wheels from naturestudyaustralia.com.au

I’ve generated blank wheels for the Northern Hemisphere and for the Southern Hemisphere, and produced a partially complete wheel of my own (from a European perspective):

Like nature journals, this is an activity both fun and educational!

Credits: lavender watercolour painting by Karen Arnold, sunflowers by Vincent van Gogh, butterfly from here, font is Jenna Sue, wheel constructed using R (with DescTools::DrawCircle, rasterImage, and the showtext package).


Mathematics in Action: Vehicle Identification Numbers

Motor vehicles have a 17-character Vehicle Identification Number or VIN on a metal plate like the one below, usually on the driver’s side dashboard, or on the driver’s side door jamb, or in front of the engine block:


A Vehicle Identification Number (VIN) plate (Photo: Michiel1972)

VINs offer an interesting example of check digit calculation. The central digit (or an X representing 10) is a check digit (calculated modulo 11) used to detect errors. Any letters in the rest of the VIN are decoded like this:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 1 2 3 4 5 7 9 2 3 4 5 6 7 8 9

The check digit calculation involves decoding the VIN, and multiplying the resulting numbers by the weights shown in blue, giving the products in purple:

VIN L J C P C B L C X 1 1 0 0 0 2 3 7
Decoded 3 1 3 7 3 2 3 3 10 1 1 0 0 0 2 3 7
Weights 8 7 6 5 4 3 2 10 0 9 8 7 6 5 4 3 2
Product 24 7 18 35 12 6 6 30 0 9 8 0 0 0 8 9 14

These products are added up modulo 11 (meaning the sum is divided by 11 and the remainder taken). In this case, the sum is 186 = 10 = X (mod 11), which makes the VIN valid, because it matches the original central X. What about the VIN on your vehicle?