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📺 Scottish Maths Conference 2022 Presentation - Fun Functions Investigations 2022.03.05

Modelling Instruction

Pre-prepare interactive graphs, that simulate data, and apply controlable noise to make it messy. Then students graph that data and fit various functions to it. You can use use and fit any function you want, differentiating across levels appropriately.

“There’s always lots of discussion (and concern) about how to teach traditional mathematical thinking to kids. But looking to the future, this pales in comparison to the importance of teaching computational thinking. Yes, there’s a certain amount of traditional mathematical thinking that’s needed in everyday life, and in many careers. But computational thinking is going to be needed everywhere. And doing it well is going to be a key to success in almost all future careers.”

- Stephen Wolfram, 2016

Students should spend less time listening and imagining, more time experimenting and seeing.

If things break you can always reset.

Tinkering with something which already works should automatically reinforce the logic of WHY it works

Giving immediate visual feedback is much more informative than mere ‘right/wrong’ ‘correct/incorrect’ feedback.

Today’s Goals

Speed up the onboarding process, so that more teachers are confident enough with using the technology, that they will try this method of instruction

A. Share a collaborative spreadsheet with worked examples (data & fit graphs) for all sorts of functions

You can download the Excel Spreadhseet file I am using here

Simulate data can be as simple or complex as you want. It makes it clear that we are imposing an idealised MODEL, but reality looks NOISY.

Every time you teach this topic, make and share a new collaborative version, then students do the work of creating new material, and the teacher can sample the best examples for next time

B. Show how to add random noise to make data more messy and realistic, in Excel

Use control parameter to be able to tune how intense the noise is. This quickly gives many different examples of one general model.

C. Show how to transfer that data, fit it, and export nice graphs with Desmos.

If your software uses ‘,’ instead of ‘.’ as the decimal delimiter, open a word document and use find-and-replace to save the tedium of manually changing individual symbols

Use ‘~’ in Desmos to tell it to fit a regression.

In Desmos each variable must be UNIQUELY defined, be sure you don’t have two different expressions both trying to give competing definitions for the value of a variable.

Bonus 1: Discussion on Using Graphic Calculators to Introduce Functions

What has worked, what hasn’t worked, in your experience of using data (real-world or simulated) when introducing new Function Graphs?

What skills will Graphic Calculators make obsolete? Will “how to manually find the equation of a straight line between two points” become as out-dated as “how to use a slide-rule to calculate logarithms”?

If we could fully automate the tedium, what are the underlying skills/concepts we aim for students to learn when we teach Functions?

Bonus 2: How to explore and gather Real-World Data from GapMinder

Use Gap-Minder!

Graph of CO₂ Emissons for Kazakhstan, Brazil, and the Netherlands (this is also available in the last tab of the downloadable spreadsheet.)

Bonus 3: How to use MathPix Snip to quickly import text and data from image screenshots

Using Desmos has few disadvantages, but one is that it can’t directly EXPORT the raw data it generates. Using MathPix Snip you can take screenshots and automatically extract text, data, and even mathematical equations.


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