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Friday, July 23, 2021

A Timeline of Mathematics and Gödel’s Incompleteness Theorem

This week TED-Ed published a new video about Gödel's Incompleteness Theorem. This is the latest in a long list of mathematics video lessons produced by TED-Ed. The timing of the video was perfect for me as I had planned on writing about Mathigon's Timeline of Mathematics this week. That timeline includes an entry about Gödel's incompleteness theorems.  

Mathigon's Timeline of Mathematics is an interactive timeline of developments in mathematics throughout history. The timeline begins with the development of the first counting systems and progresses through today. Throughout the timeline there are images and names to click on to learn more about each development. For example, at the beginning of the timeline you can click on an image of the Ishango Bone to learn that this artifact is the oldest representation of early counting systems. Much later in the timeline you can click on the image of Kurt Gödel to learn about his contributions to mathematics and click on examples of his theorems in practice. 




Applications for Education
The Timeline of Mathematics provides a good opportunity to combine mathematics and history into the same lesson. The early artifacts in the timeline are appropriate for use as an introduction to the development of counting and basic arthimetic. Items later in the timeline are more appropriate for conversations in middle school and high school settings.

Primary vs. Secondary Sources

A couple of times this week I have written about using primary sources in history lessons and or research lessons. That has reminded me of a couple of good videos that can help students understand the differences between primary and secondary sources. 

The Minnesota Historical Society offers a fantastic video on the topic of primary v. secondary sources. By watching the short video students can learn what a makes a resource a primary or secondary source. The video provides a handful of examples of each along with a description of what makes the example a primary or secondary source. This is probably the best video that I have seen explain the differences between primary and secondary sources.



Using Primary & Secondary Sources is a video that was produced by the Oregon School Library Information System. The video is intended to help elementary school students understand the difference between primary and secondary sources. The video uses some clear examples of each type of source and how those sources can be used in the research and writing process. The best part is that there are examples aligned to multiple subject areas including art and science.

World History Commons - Annotated Primary Sources for Students

World History Commons offers a free collection of more than 1700 primary sources covering a wide array of themes and events in world history. The best part is that all of the primary sources in the collection are annotated with helpful notes for students. World History Commons also offers a collection of free teaching guides that incorporate the use of primary sources. 

The search function on World History Commons searches the entire site instead of just the primary source collection. The primary source collection itself does have some filters that you can apply as you browse through the collection. You can filter according to region of the world, time period, subject, and source type (audio, image, text, video, or object). The world, time period, and source type filters do exactly what you'd expect. The subject filter is a little trickier because some events could be classified into multiple subjects but might only appear under one of the filters. 

The teaching guides section of the World History Commons offers some lesson plans and advice on strategies for teaching with primary sources. The guides are aligned to specific primary sources within the World History Commons collection of primary sources. Your search for teaching guides can be refined according to time period, region, and subject. 

Applications for Education
The World History Commons is a resource that everyone who teaches world history lessons should have bookmarked. While the primary sources on their own are useful, the annotations can help students understand the significance of what they're seeing and reading. The teaching guides are also helpful in providing some inspiration for how to use primary sources in a variety of settings. I particularly enjoyed reading through this guide to teaching about Chinese propaganda posters