Summary: What we love in the syllabus of ED218, an open elementary math ed course

[Maria Droujkova]

This is the last week of the course, when I am posting summaries. One of the most interesting aspects to me was our emergent syllabus. You can see the list of tasks on the left of the page:  http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/ 

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The short story: Participant choices led to 2/3 new content, compared to the 2010 version of the course. About 9/10 of the course themes came from participants and about 1/10 from the professor. We loved it.

The moral of the story: Student power to change content means rapid prototyping in instructional design.

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Where did our syllabus come from? These sources:

1. Themes course participants claimed as personally significant, in their sign-up task. Mind map: http://mind42.com/pub/mindmap?mid=994691af-7ac0-42ac-b297-0279be4568fa List: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-2-crowd-sourced-syllabus-january-23-29/
2. Participant comments about tasks. For example, two comments on the list above suggest we don't have "teachers as designers" as a separate task, but incorporate it into other tasks.
3. Participant responses to the tasks of the previous weeks. For example, the depth of responses and the overall interest in the math anxiety ("The Supreme Ruler or Evil Overlord" task) made me include an anxiety aspect again in the assessment task: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-11-math-anxiety-the-supreme-ruler-march-26-april-1/ and http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/week-14-assessment-april-16-22/

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Did participants make much of a difference in the syllabus plans?

This being a for-credit course for some participants, I submitted a tentative syllabus to Arcadia University before the start. I proposed 7 content topics and left 6 more open: http://p2pu.org/en/groups/ed218-developing-mathematics-the-early-years/content/full-description/ Of the topics I planned, we ended up using just one in its original form. This lonely unmodified topic - "Modern mathematics" - happened in the first content week, during our curriculum planning. Three  more topics resemble what I had in mind somewhat: Arts, Storytelling, and Assessment. But they were modified, compared to my original plans for them. Let's say we count them as 50% peer-suggested. 

This means participants suggested 10.5 out of 13, or 88% of content topics. 

I interpreted the suggestions while I transformed them into tasks. After all, we had 60 theme suggestions, some from multiple people in different forms, in the sign-up task alone, with many more comments and ideas during the course. Here is the end result - the 13 topics we ended up exploring:

1. Modern mathematics (professor-generated)
2. Art, math and many answers (reworked)
3. Patterns (participant suggestions)
4. Blogosphere and multiplication (participant suggestions interpreted: number sense, scale, size)
5. Games and play (participant suggestions)
6. Storytelling and literature (reworked)
7. Open-ended problems (follow-up to topic 2; participant suggestions interpreted: deep thinking and problem-solving)
8. Roleplaying and role models (participant suggestions interpreted: games, play, math well-being)
9. Number sense (participant suggestions)
10. Math anxiety and well-being (participant suggestions)
11. Interactive geometry (participant suggestions interpreted: shapes, size, measurement)
12. Problem-solving (participant suggestions)
13. Assessment (reworked)

How does it feel to have 9/10 of the content topics suggested by students, while still being responsible for designing the course? The work tastes very, very differently from the top-down curriculum design. You have to expect the unexpected and think on your feet. Instead of designing by well-edited articles and books made by experts, you start from what students want - expressed in many voices. Then, you merge this diverse, chaotic mass of ideas, interests and directions with past research and development. This means a lot of planning and design work during the course, compared to only working with professional sources upfront. You need to find a place for student ideas, which may or may not be expressed in standard and traditional forms, among all the old, well-formulated ideas in the established community of practice. I wish I figured out ways to make more of this process directly shared with students - see "What's next?" at the end of this email.

The goal is for students to feel like, and to be, peers among others in their professional field. This is such a vulnerable position for newbies, especially new teachers in these rough times! What if they meet hostility? What if they encounter and learn incorrect content? Housing students within pre-packaged, virtual curricular worlds made for them ahead of time, by an expert like me, would feel more secure. Students said they initially worried, but then felt fine adding their voices to veteran math ed online events and forums, editing Wikipedia, and uploading their creations to public Scratch and Geogebra sites a few hours after they first learned the software. It helps to have power over many aspects of the curriculum, and many choices within each task, such as the choice of the reading material.

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How does this course compare to what Arcadia ran before? Here is the syllabus of the course in 2010, which had an interesting and rich design: http://www.scribd.com/doc/91942198/ED218-Arcadia-Fall2010 By my count, it has 10 content topics. It is difficult to compare different courses, and I may talk to the professor who taught it before to obtain more details. These are my very rough estimates of what 2010 topics the 2012 course overlaps, and how much:

1. Talking about mathematics (little to none)
2. 21st century school mathematics (75%, with Modern mathematics)
3. Literacy and math (75%, with Storytelling and literature)
4. Education reform (indirectly)
5. Social justice (indirectly)
6. Posing problems (75%, Many answers and Open-ended problems)
7. Going beyond data (little to none)
8. Patterns and relationships (100%, Patterns)
9. Math workshop (indirectly)
10. Real teachers and real students (50%, with multiple topics such as Math anxiety)

This makes for (0+.75+.75+0+0+.75+0+1+0+.5)/10=0.375 or 37.5% overlap of the 2010 version by the 2012 version. 

Counting the other way:

1. Modern mathematics (75%)
2. Art, math and many answers (25%)
3. Patterns (100%)
4. Blogosphere and multiplication (little to none)
5. Games and play ( little to none)
6. Storytelling and literature (75%)
7. Open-ended problems (50%)
8. Roleplaying and role models (little to none)
9. Number sense (little to none)
10. Math anxiety and well-being (25%)
11. Interactive geometry (little to none)
12. Problem-solving (25%)
13. Assessment (25%)

Which comes to (.75+.25+1+0+0+.75+.5+0+0+.25+0+.25+.25)/13=0.308 or 30.8% overlap of the 2012 version by the 2010 version.

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Themes only tell a part of the story. The next summary will deal with technology we used for the course, and all the difference in the world it made. In many ways, the technology was the curriculum.

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What next? I want to research these ideas:

1. How can we make content topic selection more direct for participants? Currently, the course is still much more of a republic - where the professor interprets what participants say and makes decisions - rather than a direct participatory process.
2. In particular, how can we turn general themes into particular tasks? How can course participants be task designers? For example, "Math well-being and anxiety" was a hot theme for greatly many participants, according to the mind map. The "Supreme Ruler or Evil Overlord" task for this theme was quite interesting and inspiring to design. The joy and the learning experience of the task design was all mine, though. The resulting task turned out popular, including larger networks beyond class participants. But what wild, wonderful, unexpected activities would appear if many participants co-designed the task?
3. How can we make sure the course stays within the institutional scope and sequence, satisfies the graduation requirements, and still supports direct changes of content by participants?

Cheers,
Maria Droujkova
919-388-1721

Make math your own, to make your own math