Defining Topics for Authentic Learning Experiences in a Mathematics Classroom



Introduction

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

Update

Following 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      
 HOM x x
 MMV x x  x
 DAM x  x 
 TAI  x  x
 EHM  x x x
 SAT   x x
 SUE   x x
 PGT  x  x
 SAE x  x x
  4 5 6 8

What do you think of my mapping of topics to dominant mathematical areas?

11 - 13 Year Old
13 - 15 Year Old 
  HOM   
 MMVCost Of Living Index    
 DAM Geometric Constructions Building Construction Math ToolBox
TAI   
 EHM   
 SATRatios with Bike Gears    
 SUE   
  PGTCard Tricks 1   
 SAE Rankings System for Tennis   

16 - 18 Year Old 
 HOM   
 MMVThe Mathematics of Money   
 DAM   
 TAI Number Systems from Symbols   
 EHM   
 SAT Satellite Dish Project    
 SUE   
  PGT Card Tricks 2   
 SAE   

Higher Level Extension 
   Guiding Question
 HOM                                                   
 MMV  
 DAM  
 TAICircuit Design for Calculators  How does Electrical Current carry out Calculations ?  
 EHM  
 SAT  
 SUE  
  PGT  
 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. 

Further Update

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
 HOMHistory of Maths SitesSt Andrews University
Oregon University
Witchita State University 
 MMV
Time Value of Money
Investopedia 

Maths of Work & Everyday Life 

http://www.tvmcalcs.com/
https://www.investopedia.com/

MWAEDL
 DAM
.   
         
       Artful Maths             



 https://www.artfulmaths.com/  


 TAI
PoluUp

 Automate the Boring Stuff 
https://www.polyup.com/

 https://automatetheboringstuff.com/ 
 EHM

Maths & Our Healthhttps://nrich.maths.org/13085 
 SAT

 Adventure in Space Science Mathematics NASA - Mathematics in Space  
 SUE

 GapMinder  https://www.gapminder.org/
  PGT
      
 Arthur Benjamin https://www.arthurbenjamin.info/  
 SAE
 
Mathematics in the Movies & SportsMathematics 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.

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