Part 1. Mathematics is everywhere! In this assignment, you will learn about the

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Part 1. Mathematics is everywhere! In this assignment, you will learn about the idea of “mathematizing” your world. That is, learning to look at the world around you through a mathematical lens. You will also do a peer review of 3 classmates to see what they came up with.
First we would like you to take a look at some examples of how people have mathematized their world. You will see children asking mathematical questions as they interact with everyday items through descriptions from blog posts. I’ve also shared examples of counting tasks, a task called “which one doesn’t belong,” and “same-different.”
Hopefully, one of these examples will inspire you to mathematize something in your own world. Here are some choices for how you can complete this task. Have fun with it! 1. You can find an object or an activity and ask some mathematical questions about it on video or on a word document. 2. You could make up your own Same-Different (see below) through found objects or photos you already have.
3. You could make up your own Which One Doesn’t Belong (see below) through found objects or photos you already have.
Task 1: Look at examples
Example 1: Blog Posts to read for inspiration (Read at least ONE)
“PistachiosLinks to an external site.” from Talking Math with Your Kids
“Mathematical Art: KolamLinks to an external site.” from Thinking with Children
“PeepsLinks to an external site.” from Talking Math with Your Kids
Example 2: What’s the Same? What’s Different? Check out this websiteLinks to an external site. for more examples.
Inspired by my most recent trip to visit my family in Malaysia. What’s the same, what’s different about my two hands in this image? Example 3: Counting Collections
Inspired by a tweet I saw about children and families working on interesting counting tasks at home. How many tangerines did abuelita peel that are on the plate?
Example 4: Mathematizing an activity Inspired by my nephew Azriel teaching me a Fortnight Dance.
How long does it take Azriel to do one complete round of dance? How long does it him to do 10 rounds? 100 rounds? 1,000 rounds? n rounds? How many rounds of dance can he do in 3 minutes? 20 minutes? n minutes?
Example 5: Which One Doesn’t Belong? Check out this websiteLinks to an external site. for more examples.
Inspired by my friend’s garden last year. What reason can you give for why each one doesn’t belong? Task 2: Make a video or take pictures and make a word doc to mathematize your world
Once you have read these posts, use video or images of something that matters to you or that you are doing in your everyday life. Upload a short video or very brief document.
1) Remind classmates of your name.
2) Your image/object/video and what inspired you or why it matters to you
3) A couple mathematical questions that you can ask.
Part 2
To launch us into our mathematical work together, we’re going to explore a famous game called Nim. Variants of Nim have been played since ancient times, all around the world. It is thought to have originated in China and is related to a Chinese game called “picking stones.” One of the earliest computers , the “Nimatron” from the 1940 World’s Fair, was designed to play Nim.
NimPicking Stones”Nimatron” Computer
We love Nim because it’s simple enough that elementary school students can play it, but it’s also deeply mathematical! There are even published mathematical papers about winning strategies.
We’re going to explore Nim in two stages:
Here, in this Initial Exploration, you’ll learn to play the game and start thinking about how to win it. You’ll upload to Canvas your initial ideas about how to win the game.
During our first synchronous class session, we’ll discuss winning strategies to deepen our understanding of the game.
It’s important to understand why we’re spending this time playing and analyzing Nim. It’s not because every elementary school teacher needs to know this game; they don’t! It’s because Nim gives us a chance to reflect upon what it means to learn and do math and about the kinds of mathematical experiences we want to provide elementary school students. As we mentioned in this introductory video, you’re wearing two “hats” in this course. With your “student of math” hat on, think about the structure of the Nim and how and why winning strategies work. With your “student of teaching and learning” hat on, reflect upon what your experiences with the game teach you about learning and teaching mathematics.
Task 1: Learn the rules of “1-2-3 Nim on the 20-Frame”
Read the directions: Initial Task_123 Nim on 20 Frame.docx
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You can watch one round of Nim. The person who takes the last object of 20 wins.
How_to_Play_123_Nim.movDownload How_to_Play_123_Nim.movPlay media comment.
Task 2: Play“1-2-3 Nim on the 20-Frame” with someone.
As you play, try to come up with a “winning strategy.” That is, try to come up with a strategy you could use to win every game. In addition, think about when you know you’re going to win or lose. Can you tell you’re going to win or lose before the end of the game? You might have to play the game a lot before you can figure out a winning strategy!
You can print out this 20-frame and use small household objects (eg. coins) : 20 frame.docxActions
Or, you can use this online version: NIM21_p.htmlActions
Task 3 – Submit your initial ideas to Canvas.
Share your learning by describing your winning strategy for “1-2-3 Nim on a 20-frame.”(Up to 1 page.) Try to explain why the strategy works and how you know it will help you win every time. Include a diagram to make your thinking clear. It’s okay if you haven’t found a complete winning strategy yet! Just share what you’ve figured out so far. Tentative ideas and questions are welcome. If it helps for you to scan your diagram, you can use your phone, or an app to make a scan such as Genius Scan or Office Lens. iPhones can also scan documents through the notes app (just click the camera icon on a new icon and choose “Scan Document”). It’s okay if all of your work is handwritten or if you want to type some of it. But do try to use a dark pen so that others can easily read your handwriting. You can also use color pens for annotations.
PART 3 Each reading/ set of readings in this course has a reading response or discussion board. For reading responses, roughly, we expect your reading responses to be ½-¾ page, 1.5 spacing, normal margins. Feel free to exceed that length if necessary to explain your thinking. It’s also fine to write your response as bulleted paragraphs.
1) Watch Dan Finkel’s TEDx talk “5 Principles of Extraordinary Math Teaching” (approx. 14 minutes). Dan is one of the co-founders (with Katherine Cook) of a Seattle organization called Math for Love (mathforlove.com) that aims to engage children in authentic mathematical work.
Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainierLinks to an external site.
2) Watch this video of Danny Martin (he/him), a professor of mathematics education at University of Illinois, Chicago on the brilliance of Black children (approx. 32 min).
Martin, Math Education for African American ChildrenLinks to an external site.
3) After you have read, respond in writing to the following prompts. (Approx. ½ page in total; 1.5 spacing)
In his video, Dan Finkel describes 5 big ideas about doing and learning math. Choose the one that feels most meaningful to you, for whatever reason – it feels important, challenging, surprising, etc. State the principle, explain what it means in your own words, and then explain why you chose it.
Make connections between Finkel & Martin’s video. What does it mean to recognize Black children’s brilliance? What do teachers need to do in order to better serve historically marginalized student .
PART 4 Now that you’ve explored and counted in Base Six (which we called Base “Splat”), it’s time to try adding and subtracting! As you do the tasks below, keep in mind our purpose for exploring alternate bases like base six. We’re not suggesting that elementary school students should learn to work in alternate bases; it’s sufficiently challenging for them to learn base ten! It’s useful for us to work in alternate bases for two reasons:We’re so fluent in base-ten that it can be hard for us to see all of the concepts and skills involved in learning it. Re-learning to count, add, and subtract in alternate bases can help us unpack what we learned in elementary school, which should make us better teachers.
When we work alternate bases, we face some of the same struggles and challenges that children experience when learning base 10. It can remind us what it’s like to learn this content and make us more empathetic to children who struggle with it.
Task 1: Try Adding & Subtracting in Base SplatDownload this “Operating in Base Splat” handoutActions and solve the problems. You can also just copy the problems on a blank sheet of paper. Note that in every problem, the numerals are already in Base Splat. For example, here’s a picture of the first problem.If you get stuck on any of the problems, try drawing a picture or using objects like counters!Note that you only need to complete the first page of problems (#1 – 6); the second page is optional. Task 2: Check Your Understanding on Problems 1 – 4Check this answer keyActions for problems 1 – 4.Task 2: Submit Your Answers to Problems 5 & 6Upload to Canvas a picture of your solutions to problems 5 & 6 on the handout. We will discuss your strategies for those problems next class.

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