Defining Topics for Authentic Learning Experiences in a Mathematics Classroom
A couple of years ago I became fascinated by project based learning (PBL). As a result, I conducted my own experiments by designing unique educational engagements, based on literature I had read about PBL - 2015, 2017. I was impressed by the engagement achieved and it made me wonder how could I get a similar level of engagement, but with a content base more directly tied to my maths curriculum? The theory that seemed to offer the most promise was the concept of "Authentic Learning & Authentic Assessment". To me, it seemed to offer a reasonable way of combining the strengths of project based learning, together with a process for acquiring understanding of a universally agreed upon useful mathematical content base. As a first step in the process of designing authentic learning experiences in mathematics, I tried to create a comprehensive list of topics that covered the context in which mathematics most commonly appears. I would love your suggestions or additions in the comments, if you think I have left an area out? I have also included some examples of content related to these topics. Another question is whether or not you would map each of these topics to age levels and dominant mathematical areas.
|Topics||Abbreviations||Eg 1||Eg 2|
|1. History of Maths||HOM||Euclid||Proof|
|2. The Mathematics of Money & Value||MMV||New or Used||Renting ?|
|3. Design, Architecture & Music||DAM||Platonic Solid||Sound|
|4. Technology & the Internet||TAI||Fourier Series||Data Scientist|
|5. Eating, Health & Medicine||EHM||Co-Vid 19||Pop. Growth|
|6. Space & Travel||SAT||NASA Origami||More Origami|
|7. Sustainability & the Environment||SAE||Ocean Garbage Patch||Sustainable Future|
|8. Puzzles, Games, illusions, Magic Tricks||PGT||Math Magic||Last Banana|
|9. Sports & Entertainment||SAE||NBA Data||NBA Transforme|
UpdateFollowing on from the first part of this post, what would it look like if we tried to map these 9 categories to a particular dominant mathematical area and included some example tasks and activities.
|Numeracy||Algebra & Patterns||Geometry||Data & Stats|
What do you think of my mapping of topics to dominant mathematical areas?
11 - 13 Year Old
13 - 15 Year Old
|MMV||Cost Of Living Index|
|DAM||Geometric Constructions||Building Construction Math ToolBox|
|SAT||Ratios with Bike Gears|
|PGT||Card Tricks 1|
|SAE||Rankings System for Tennis|
16 - 18 Year Old
|MMV||The Mathematics of Money|
|TAI||Number Systems from Symbols|
|SAT||Satellite Dish Project|
|PGT||Card Tricks 2|
Higher Level Extension
|TAI||Circuit Design for Calculators||How does Electrical Current carry out Calculations ?|
|SAE||https://www.swimsmooth.com/||What influence does Geometry have on Swimming Efficiency ?|
Do you have any further suggestions for the Table - feel free to add these to the Comments.
In order to make these 9 categories conceptually clearer, I thought it would be a good idea to have a reference website for each and a picture icon. Do you have any suggestions to help me complete my Table?
Websites Suited to Each Topic Area
|TOPIC|| ICONS ||NAME||URL|
|HOM||History of Maths Sites||St Andrews University|
Witchita State University
|MMV||Time Value of Money|
Maths of Work & Everyday Life
Automate the Boring Stuff
|EHM||Maths & Our Health||https://nrich.maths.org/13085|
|SAT||Adventure in Space Science Mathematics||NASA - Mathematics in Space|
|SAE||Mathematics in the Movies & Sports||Mathematics in the Movies |
Mathematics in Sports
Please add your suggestions in the comments below or better websites or activities if you know of them.
Also here is an example of additional resources in the form of an Authentic Assessment Toolbox.