mpsMOOC13 Observer June 24: Peer learning, video conference, mixed ages
This is news from participants in the open online course Problem Solving for the Young, the Very Young, and the Young at Heart.
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Peer learning: here comes everybody!
As of this newsletter forty-two adventurous families, homeschool groups, and math circles said they will work with us to adapt our ten math problems. This July, we will peek into one another’s park meetings, classes, and conversations around the kitchen table. Here comes everybody: veterans with forty years of teaching experience and twenty-month-old toddlers; lovers of Minecraft and supporters of hands-on learning; people from Canada and Saudi Arabia; families with one kid and families with six kids; widely published researchers and beginner citizen scientists.
From the sign-up page:
I’m a long-time homeschooler, and most of my kids are now grown. I like to read (ideal vacation: an enormous library, complete with a comfy chair by the fireplace), and I like to play around with math ideas — for instance, I think Tanton’s Math Without Words is great! – Denise, letsplaymath.net
I am a special education middle school math teacher. I am a self-proclaimed technology nerd and math geek. I love finding new ways to engage my students with technology. My students that I will be working with are the kids I have for summer school. They are special ed and they are going into 6th grade in the fall. – Caryn Trautz
I am a professor of mathematics education — I design, evaluate, and theorize learning activities. I enjoy thinking about thinking. Here’s my lab page. – Dor Abrahamson
I’m a homeschooler dad whose 3 daughters aren’t as interested in math as their dad is. I like to give my kids random math verbal puzzles. The oldest one is very fast at computation, the middle one is very good with concepts. The third one is excited. – Bilal the dad
I’ve had a lifelong interest in math and math education — ranging from majoring in mathematics at University, to teaching elementary school 39 years ago, to starting a local math camp for middle schoolers as a volunteer, three years ago. I enjoy researching and putting together hands-on lesson plans for the camp. The camp website is http://www.YoungMathWizards.com. – Andy Klee
Images by course participants Rodi Steinig, Denise Gaskins, David Wees, and Andy Klee
Video conference questions
One aspect of the course, the initial live conference, generated a lot of questions by email and at the knowledge hub. Here are some questions and answers.
- How do I prepare for the video conferences? – The general topic of the discussion is your dreams for mathematics and the kids. You can prepare by thinking about that topic.
- Is it going to be a one-to-one conversation, or will it involve other people too? – It will be one-on-one, but recorded for others to view later. I will ask permission to record before we begin. You can invite as many family or math circle members as you want!
- Is the video conference a prerequisite for taking the course? – The conference is a part of our sign-up process. It helps to prepare for the course tasks, and provides data for the citizen science study (namely, what people want for math and kids). It also establishes a chat channel with one of the organizers, so that it is easy for you keep asking questions later. Beyond this course, live communication opens up ways to collaborate and to learn that are not available otherwise.
- What if I don’t have a webcam, or my internet is slow? – In this case, we can talk in voice only.
Here is a video conference with Nikki Lineham, a fellow math geek:
Mixed ages? Any ages?
The description of the course says, “The course participants are families, math clubs, playgroups, and other small circles casually exploring adventurous mathematics with kids of any age.” The first research data is in: one of most frequent questions we get is, “Can my teen/four-year-old/grown-up significant other/toddler participate?” Yes!
Our authors Dr. James Tanton, Dr. Maria Droujkova, and Yelena McManaman will help adapt the ten problems to all ages. Course participants will help adapt the ten problems to all ages. We will invite the kids to help adapt the ten problems to all ages. There will be a lot of adaptations! Then we will sort and organize them.
Here is a related question: can we adapt these materials for families with several kids, and for mixed-age math clubs? Can people of different ages be happy doing math together? Let us try! There are a lot of benefits to mixed-age learning. You can see a number of them in this diagram based on Free to Learn by Peter Gray.
Friends and supporters of the course
We received several letters with similar requests:
- Can I follow the research and development efforts without a math club or kids to run the activities?
- Can I just peek at what you do?
Yes, this is now possible! People can subscribe to receive the mpsMOOC13 Observer by email to follow our adventures. It won’t be the same as participating, but subscribers will receive some highlights from the course.
Posted in Grow
Math+Art photography <== Scientific American <== Moebius Noodles
Seeking shapes, surfaces, and curves in nature is a favorite game for mathematicians – and for young kids! The Seattle lifestyle photographer Alex Nguyen reports on an art project about flowers. It was inspired by the Budding Scientist blog, where we recently made a guest post.
This reminded me of the new Mathematical Imagery gallery from the American Mathematical Society, which we featured a couple of times under the #MathScavengerHunt tag on Facebook.
Posted in Make
Problem Solving for the Young, the Very Young, and the Young at Heart: Newsletter June 15, 2013
I am Moby Snoodles, and this is a special issue of my newsletter. You are invited to participate in our next book-making effort. It is also a course, and a citizen science project. For sign-up information, email me at: moby@moebiusnoodles.com
Problem Solving for the Young, the Very Young, and the Young at Heart
Join a cozy mini-MOOC with Dr. James Tanton, Dr. Maria Droujkova, and Yelena McManaman!
Take the course, make a book, contribute to citizen science
The term “problem solving” sounds scary. Who wants problems? Why do we want to subject ourselves and youngsters to problems?
The word “problem” comes from the word “probe” meaning “inquiry.” Inquiry is a much more interesting and friendlier idea. Rather than “attack a problem that has been given to us” let us “accept an invitation to inquire into and explore an interesting opportunity.” Even very young, preverbal children excel at inquiring and at investigating the world around them.
Will this curiosity extend to math learning? Yes, as long as the inquiries remain playful!
This course will help you to support the joyful intellectual play of youngsters in the context of upper-level mathematics. Over three weeks we will discuss the ten key problem solving techniques and show how they can be of relevance and help to the very young. Each technique comes with an interesting query to think about. As the adult leader, you supply scaffolding where students stand while they construct their solutions. In other words, techniques are not only for you to read, but also for you to then translate for the children!
But wait, there is more! This course is a pilot study for a citizen science project for mathematics education. How can we adapt materials for each learner’s unique needs? How can we pick and choose what math to do when? We are excited to invite you to contribute to original scientific research, and to discover new ways of helping children learn!
Course Syllabus
This course is for parents, leaders of math playgroups, and math clubs – with children of any age. The goal is to adapt the same set of materials to different levels and interests. We will publish the materials as a professionally edited, Creative Commons book, with all course members’ names or aliases as contributors. You can see an example at https://naturalmath.com/TheBook
The sign-up tasks will be available on July 1, 2013. You can expect to spend about two hours a week on the course. Each week, you will plan for the next week, tell brief stories of what you did this week, and start analyzing other people’s stories. We will provide more details and guidance on the sign-up site.
Before July 7: sign-up and preparation
- Sign-up interview (Skype or Google+): What are your math dreams for your kids?
- Prepare micro-plans: problems 1, 2, 3
Week 1, July 8-14
- Do and report: stories about problems 1, 2, 3
- Prepare micro-plans: problems 4, 5, 6
- Sort and analyze the data in reports
Week 2, July 15-21
- Do and report: problems 4, 5, 6
- Prepare micro-plans: problems 7, 8, 9, 10
- Sort and analyze the data in reports
Week 3, July 22-28
- Do and report: problems 7, 8, 9, 10
- Sort and analyze the data in reports
Exit question
- What did you and others do to adapt problems?
Participant pledge
We expect each participant to adapt the ten problems, to try them with kids, to report the results online, and to help analyze the reports. You can share you stories by text, video, or audio.
Frequently Asked Questions
Does my child need to count well, remember times tables, and so on?
Not at all. There are no prerequisites. You can adjust problems for very young kids, but also to the high school level.
What resources will I need for this class?
You need the internet to participate, and usual household objects (paper, markers, toys) to do math. We will provide free, open media to support the course.
Can I get a certificate after completing this course?
Yes, you will receive a digital certificate of participation from the course authors and our mascot Moby Snoodles, the math-loving whale.
What is citizen science?
Citizen science is research conducted by large groups of non-professionals, together with some scientists. In this course, participants will contribute to a pilot study in mathematics education. We will tackle a tough question: How can mathematical topics be adapted to radically different students, mixed-age groups, and everybody’s diverse interests?
What’s a mini-MOOC?
A Massive Open Online Course (MOOC) is an online course with interactive participation and open access. Our course uses all our favorite design principles of MOOCs: openness, aggregating free information, and remixing everybody’s ideas. In addition, we aim for a connected, personal experience for every participant. That’s why we only announce our courses in highly relevant communities, talk to every participant as a part of the sign-up, and provide much personal support along the way. We also keep the course short enough for everybody to be able to participate in all the activities. To summarize, our course is a cozy, personal, short and sweet MOOC.
What is it all about?
- Make your own math: DIY, agency, self-regulation, exploration
- Play and let the kids play freely: spaces for exploration, self-regulation, agency, research of what kids would do
- Not all who wander are lost: connections; sorting, classifying and mapping the big picture of math, big and deep ideas, inquiry, connections
- Be the littlest kid: child leadership, child agency, adults as fellow explorers
- Make and share stories: continuity, adding valor and adventure to kids’ actions, research and reflection on the data in the stories, helping others learn from your experiences
How do I sign up?
Email moby@moebiusnoodles.com
Sharing
You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com
More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA
Talk to you again on June 30th!
Moby Snoodles, aka Dr. Maria Droujkova
Posted in Newsletter
Paper Weaving and Grid Games
Patrick Honner’s Moebius Noodles guest post on mathematical paper weaving was very inspiring to me. Mathematical weaving employs one of my favorite making materials – colored paper! It was actually sort of challenging to get started, but after playing around I landed on some solutions which became a nice little unit of paper weaving and grid games with and for young children.
I am imagining that the weaving and the games can be completed in an enjoyable collaboration between adult and child over the course of a day or two. Here are some ideas for setting up the experience and playing the games.
After experimenting a little, a 3/4″ width for vertical and horizontal strips makes a more pleasing final product to my eyes than 1″. To make the vertical strips fold a piece of paper in half and use a paper cutter to cut 3/4″ strips from folded edge to about 3/4″ away from the open edges. Essentially, you are creating a paper warp that is still essentially one piece of paper.
As you can see, below, the horizontal strips weave in very nicely and don’t need any glue or tape to keep them in place if you focus on pushing them gently, but snugly, downward. For the young ones, at least, a basic over/under/over/under weave is challenging enough. Using two horizontal colors creates visual interest and perhaps even a conversation about the patterns you see: alternating colors both vertically, horizontally and diagonally. You can also make a connection to odd and even numbers. Yellow squares in the design show up 2nd, 4th, 6th… places. Green squares are 1st, 3rd, 5th…
The minute I finished the piece above I thought – A GRID! It’s a grid! Over the last couple years I have received mountains of inspiration from the Moebius Noodles blog especially as source of grid games (my favorite so far is Mr. Potato Head is Good at Math). As a result, grids are always in the back of my head. Here are some of the ideas I came up with using a newly woven paper mat/grid and one of my favorite math manipulatives — pennies!
Adult: Oh look! There are three different colors of squares in our woven grid. I’ve got some pennies — I wonder if we could make a square by putting pennies down on only one of the colors?
Adult: That does look like a square. Let’s count and see if there are the same number of little squares (yellow, blue, yellow, blue…) that make up each side? There are! How many little squares are there on each side?
Adult: But, wait! Look what happens when I push a corner penny in toward the center! Yep, it lands on a green square! Let’s do it with the rest of the corners and see what we get. Oh, lovely. A rhombus.
Adult: The corners on the rhombus are on the yellow squares. I wonder what would happen if we pushed them one square toward the middle? Ooooh, look! We have another square. Is it bigger or smaller than our first square? Each side on our first square was six little squares long. This square has sides that are…three little squares long. Cool.
Another exploration, this time growing patterns and a tale of some square numbers who also wanted to get bigger? What little kid doesn’t want to grow up?
And, here’s my favorite. It’s a ‘let’s make a rule’ kind of game. The first penny goes in the bottom left hand corner, and you start counting from there. The first rule here (pennies) was two over, one up. Each time you repeat the rule, you start counting from the last token on the grid.
You’re probably wondering about the buttons? Well, that’s a different rule: one over, one up. Isn’t it cool how they overlap, but not always? Kids can make up their own rules after a little modeling or you can challenge them to guess a rule you made up and keep it going.
And then, of course, the final thing would be to leave the pennies and the paper grid mat out to explore at leisure. Have fun making math!
p.s. After this first foray into mathematical paper weaving, I explored it a little more. Here are more posts on my blog: Weaving Inverse Operations, Multiples and Frieze Patterns – Weaving Fibonacci – Weaving Geometric African Motifs Part 1 and Part 2.
Posted in Make
