This fast-paced, highly interactive online course introduces tech ideas of the last decade, concepts for the near future, and tried-and-true classics. Throughout the course, you will only use free and open educational resources, because you can continue using them after the course is over. Course themes include:
- Modeling tools and the role of modeling in learning mathematics
- Social tools and the significance of networks and communities
- Manipulatives, tinkering, making: physical tools and hands-on learning
- The role of technology in the development of mundane skills and problem-solving
- Computer-based vs. computer-delivered mathematics
- Humanistic mathematics and the use of technology in the math arts
- Technology for accessibility
Introduction, setup, review of your goals and needs
- Tech we use for the course
- Meeting one another
- Selecting personal course projects
- Starting the Big Questions list
Mathematical modeling and its pedagogical uses
- Models of math ideas vs. mathematical models of things
- Make and share, or consume? Roles of students in modeling
- Models and multiple representations
- Example of modeling software: GeoGebra
Crowd-learning: networks and communities
- Learners who look things up, and learners who upload
- Mathematical problem-solving with computer and social tools
- The power of huge collections
- Examples of social phenomena: Scratch and Project Euler
- DIY and makers
- Comparing and contrasting virtual and physical worlds
- Examples of physical and virtual tech: Montessori and NLVM
- Solvers, calculators, graphers and sending humans to do robotic jobs
- Problem-solving, problem-posing, conjecturing, proving: creating and evaluating in math
- Computer superpowers and what you can't do without
- Examples of computer-based and computer-delivered math: Wolfram|Alpha and Khan Academy
- Math-rich digital arts
- Computational origami, hyperbolic crocheting: 21st century crafting
- Interpretive dance and underwater basketweaving: issues of intellectual honesty
- Examples: Bridges conference and Gathering for Gardner
Accessibility and diversity
- Learning styles
- Tech for boys and girls
- Disabilities and learning tools in mathematics
- Advanced math without prerequisites (young kids, ESL, troubled learners)
- Example: ethnomathematics community
8-14 Your topics of interest (to be determined in earlier weeks)
15. Summaries and good-byes
There are no textbooks for this course. We will use existing OERs (open educational resources), as well as creating some ourselves and sharing them online, to help others learn.
There will be one or two new software tools per week, possibly more in the first week when we set everything up. I select tools that are open and free, and easy to use as attested by their popularity. Thus, contact me quickly if tech is taking too long. Here are examples of technical activities you may need for course tasks:
Use blog search to find a relevant discussion
- Participate in a webinar
- Install a screen capture program and use it to highlight parts of the interactive web site you visit
- Download and install GeoGebra modeling software
You can expect to spend 6-8 hours a week on the course, depending on the week.
You need reliable, high-speed internet access for most of the course work. For many parts, you will need a headset with a microphone. Cheap headsets ($10-15) should be sufficient.GradesEach week, starting Mondays, will have several small tasks, some of them recurring, and some building on tasks from previous weeks. I will count the online results of the tasks by that week's Sunday at midnight Easter US Time. At the end of the course, the grade will be based on the number of finished tasks:
A: 90-100% B: 80-89% C: 70-79% D: 60-69% F: 0-59%
Each week will have a bonus task suggestion. For the purposes of grading, bonus tasks can count toward any week's task total. The goal for bonus tasks is to be fun and personally meaningful. You are welcome to change their nature to make it so.
The majority of course tasks take place in real online communities of teachers and students. This means other people will use your work in their teaching and learning. I trust you to take good care of them. Also, you and other course members will use results of earlier tasks for later tasks.
You will probably get comments and feedback from other people as you do the work. This will help with the quality. For example, teachers who blog actively often say they learn more from writing and comments than from any textbook they've ever used.
Here are example rubrics for different types of tasks. If you have doubts about what makes a quality contribution for each task, you can start from these. If you want more, you can search the web for "What makes a good ___" (blog, article, game, presentation).
- Blog post standards by Maria Andersen
- Article review rubric by Kristin Hines
- Good practices in Twitter chats by Shelly Terrell and Tara Benwell
- What makes a good screencast by Scott
- Rubric for assessing interactive projects by Karen Randall
Most of your course assignments will be live online, which means students (including children) and other educators will use them. You can use your real name and real photo, or an alias and an avatar, for the course work. Here are some points that may help.
- Use your own judgment about the formality of your English. For example, article comments should probably be formal, with full sentences and the standard grammar. Online chat events can benefit from standard abbreviations, such as "PLN" for "personal learning network" or "u" for "you."
- Within hours, tell me if something in the course does not work for you. If an assignment does not make sense, if you don't know how to start, if you see a link going nowhere, if you can't resolve a group assignment conflict - please get in touch. This means something is broken with the course and needs to be fixed!
- Arcadia University code of conduct in the student handbook.
- Some of the assignments may involve critiquing the work of others, or evaluating materials, communities or programs. This can easily lead to hurt feelings. Here are a few suggestions for constructive discussions:
- Focus on content, not personalities. People are better supported professionally through discussions of their work, not themselves.
- You may experience, first-hand, some skirmishes of ongoing math wars. Help ever, hurt never; ask for moderator support if available, or leave the unfriendly place if not.
- When in doubt about posting something, ask yourself: "When I am running for president, what will media say when they find my posting?"
- Please do reuse other people's work in your assignments! This is what community is all about. When you do, please link and reference the source, respect intellectual property laws, and contribute enough of your own content to maintain the balance of giving and taking.