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Full Description

ED218 - Developing mathematics: The early years
Arcadia University
Spring 2012

Dr. Maria Droujkova

Phone: 919-388-1721
Email and chat:
Skype: maria_droujkova


The goal of the course is to assemble a toolkit for helping young children develop mathematically. In particular, the course will have the following overarching themes:
  • Personally meaningful and relevant mathematics achieved through projects, games, problem-posing and problem-solving
  • Computer-based mathematics, including interactive simulations, modeling tools, solvers, and children programming platforms
  • Lifelong learning for teachers, with the focus of online communities and networks for teacher support, and building your personal learning networks
Each week, we focus on a theme. The assignments are relatively open, and I will help you modify them to fit your goals and needs. There are weekly online meetings, as well as communication by email.
The course is open: we may have students from outside Arcadia joining some activities, as well as joining activities in other online communities. For more information on how it works, see this Wikipedia article: MOOC

Musical Interlude


Required materials

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 during 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 - it's not supposed to. 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 7-8 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.

Weekly themes

There are 15 weeks and 13 content goals, with the first week for introductory work, and the last week for summaries. You will select half of the themes.
  1. Introduction, setup, review of your goals and needs
    • Tech we use
    • Selecting your content goals
    • Meeting one another
    • Selecting personal course projects
  2. What about algebra in Kindergarten? The scope of modern elementary math.
    • What you think should be taught
    • State and federal standards
    • Math content vs. math practices vs. math values
  3. Teachers as designers: planning what students will do
    • From student actions to learning goals
    • What is a good task?
    • OERs (open educational resources) you can make and use
    • Tutoring and solitary work, small groups, large groups, and networks of learners
  4. Helpful math ed people you may want to meet
    • Designers and authors
    • Bloggers
    • Communities and their leaders
  5. Computer-based vs. computer-delivered mathematics
    • What math can young children do with computers that they won't do without?
    • Aspects of math learned from modeling, programming, and intrinsic gaming
    • "A computer will never replace a human" - a cannibal proverb
  6. Put M in STEAM: science, technology, engineering, arts and mathematics
    • Growing math eyes and seeing math everywhere
    • Math as a source of power in the society
    • Projects, holidays, field trips
    • Humanistic mathematics
    • Global issues and mathematics
  7. Assessment
    • Summative vs. formative assessment
    • Human and computer assessment
    • Punished by rewards: assessment, intrinsic motivation and student-teacher conflicts of interest
    • Teacher, peer and community assessment
  8. Intellectual, developmental, social, cultural and motivational diversity
    • Individual student goals within group tasks
    • The mind and the body, or what to do with a hungry, tired student
    • Stages of development vs. student age
    • Students care about different things
    • Ethnomathematics
    • School math and situated math
  9. <your theme here>
  10. <your theme here>
  11. <your theme here>
  12. <your theme here>
  13. <your theme here>
  14. <your theme here>
  15. Summary and your project reports <you select the format>



Each 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, such as blog posts, 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.
Arcadia students will be awarded grades through the university system. Other participants will receive a certificate from P2PU School of Math Future. 



Photo: Statue of Arete in Celsus' Library in Ephesus. 

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).



Kung Fu Flame Warrior

Picture: Kung Fu Master, from Flame Warriors by Mike Reed 

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.


Task Discussion