Task Summary By Goals


These are grids analyzing course tasks by various Quality Matters metrics.

Course Learning Objectives and Unit Learning Objectives


Stars * indicate correspondences between course and unit objectives.

Course Learning Objectives: By the end of the course, each student will be able to...
...Use multiple representations in teaching mathematics
...Evaluate and design tasks involving problem posing and problem solving
...Identify tasks by levels of Bloom's taxonomy and design balanced units with tasks at multiple levels
...Design and re-design learning units in algebra, calculus, geometry and statistics
...Actively use educational technology leadership skills: blogging, wikis, forums, simulation software, web conferencing, etc.
...Actively participate in multiple educator online communities
The objectives of Week 1 are:
  • To get to know one another
  • To start using some of the course's tools and technologies in the context of multiple representations.
  • To name major representations used in secondary mathematics, to create several comments and posts about the topic
  • To participate in online communities where the topic can be discussed.
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The objectives of Week 2 are:
  • To define main entities constituting mathematics
  • To plan for student problem-posing
  • To understand and describe the differences between problems and other entities
  • To list criteria of problem solving
  • To evaluate given material's potential to promote problem solving, and to find problem-solving resources by topic.
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*


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The objectives of Week 3 are:
  • First introduction to Bloom's taxonomy: to define the six levels of thinking
  • To apply knowledge of multiple representations and problem solving to algebra and calculus
  • To define the idea of linearity, to use it in algebra or calculus task design, and to critique lessons about linearity
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*
*
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The objectives of Week 4 are:
  • To define levels of geometric reasoning within the Van Hiele model
  • To discuss whether levels apply to groups, persons, or particular activities of a person
  • To design activities connecting algebraic and geometric reasoning
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*
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The objectives of Week 5 are:
  • To collect a library of visualization tools
  • To design and to critique statistics lessons
  • To trace the implications of ubiquitous data-collection devices
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*
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The objectives of Week 6 are:
  • To analyze tasks for balance among different activity types
  • To focus on student-generated math content

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*
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The objectives of Week 7 are:
  • To apply measures for reducing math anxiety to your activity design
  • To reflect on values comprising "math sophistication"
  • To summarize community activities to take to students
  • To celebrate the successful completion of the course!



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Unit Learning Objectives, Learner Engagement and Course Technology


Since all technological tools support collaboration and sharing, Engagement and Technology go together.

Unit Learning Objectives
Learner Engagement and Course Technology
The objectives of Week 1 are:
  • To get to know one another
  • To start using some of the course's tools and technologies in the context of multiple representations.
  • To name major representations used in secondary mathematics, to create several comments and posts about the topic
  • To participate in online communities where the topic can be discussed.
The main technology tools this week are blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 2 are:
  • To define main entities constituting mathematics
  • To plan for student problem-posing
  • To understand and describe the differences between problems and other entities
  • To list criteria of problem solving
  • To evaluate given material's potential to promote problem solving, and to find problem-solving resources by topic.
The main technology tools this week are Diigo, screencasts, forums, blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 3 are:
  • First introduction to Bloom's taxonomy: to define the six levels of thinking
  • To apply knowledge of multiple representations and problem solving to algebra and calculus
  • To define the idea of linearity, to use it in algebra or calculus task design, and to critique lessons about linearity
The main technology tools this week are Wolfram|Alpha, Diigo, screencasts, forums, blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 4 are:
  • To define levels of geometric reasoning within the Van Hiele model
  • To discuss whether levels apply to groups, persons, or particular activities of a person
  • To design activities connecting algebraic and geometric reasoning
The main technology tools this week are GeoGebra, Diigo, screencasts, blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 5 are:
  • To collect a library of visualization tools
  • To design and to critique statistics lessons
  • To trace the implications of ubiquitous data-collection devices
The main technology tools this week are Diigo, screencasts, blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 6 are:
  • To analyze tasks for balance among different activity types
  • To focus on student-generated math content
The main technology tools this week are Diigo, screencasts, blogs, email groups, live webinars, online videos and wikis.
The objectives of Week 7 are:
  • To apply measures for reducing math anxiety to your activity design
  • To reflect on values comprising "math sophistication"
  • To summarize community activities to take to students
  • To celebrate the successful completion of the course!
The main technology tools this week are screencasts, blogs, email groups, live webinars, online videos and wikis.

Unit Learning Objectives and Bloom's Levels by Task


Revised Bloom's Taxonomy:
6 - Creating
5 - Evaluating
4 - Analyzing
3 - Applying
2 - Understanding
1 - Remembering

Tech level 2 requires Understanding of some new technology. This is typically time-consuming.

Because the course takes place online, where you can always look information up, there are no tasks absolutely requiring Remembering (tech or ed level 1). However, memory is an assumed part of all other levels of tasks.

Because this class focuses on educational topics, technology use stays at low levels of Understanding and Applying. One can argue that blogging is tech level 6, since people create blogs, but I would consider creating a platform for blogging tech level 6, and blogging itself ed level 6. The tables below are filled in accordingly to this somewhat arbitrary distinction between technology and education.
The objectives of Week 1 are:
  • To get to know one another
  • To start using some of the course's tools and technologies in the context of multiple representations.
  • To name major representations used in secondary mathematics, to create several comments and posts about the topic
  • To participate in online communities where the topic can be discussed.
Task
Bloom's levels - tech
Bloom's levels - math ed
1-1 Join ed526b wiki, edit Week 1 page
2, 3
-
1-2 Join ed526b email group
2, 3
-
1-3 Write an intro email
2, 3
6
1-4 Make a blog
2, 3
-
1-5 Blog post: goals of math ed
2, 3
4, 6
1-6 Find and review an online source on multiple representations
3
2, 4, 5, 6
1-7 Find and comment at an online source on multiple representations
2, 3
2-6
1-8 Class meeting
2, 3
2, 4, 6
1-9 Live online event
2, 3
2, 4, 6
.
The objectives of Week 2 are:
  • To define main entities constituting mathematics
  • To plan for student problem-posing
  • To understand and describe the differences between problems and other entities
  • To list criteria of problem solving
  • To evaluate given material's potential to promote problem solving, and to find problem-solving resources by topic
Task
Bloom's levels - tech
Bloom's levels - math ed
2-1 Make a screencast
2, 3
2, 4, 5, 6
2-2 Describe 7 math entities belonging to a topic, in detail
3
2-6
2-3 Discuss differences between exercises and problems
3
2-6
2-4 Reply to a WCYDWT thread
3
2-6
2-5 Write an article or a book review in the blog
3
2, 4, 5, 6
2-6 Blog about Art of Problem Solving
3
2, 4, 5, 6
2-7 Make a Diigo account and add useful links
2, 3
2, 5
2-8 Class meeting
3
2, 4, 6
2-9 Live online event
3
2, 4, 6
2-10 Edit the Wikipedia article created on the basis of last week's contributions
2, 3
2-6
.
The objectives of Week 3 are:
  • First introduction to Bloom's taxonomy: to define the six levels of thinking
  • To apply knowledge of multiple representations and problem solving to algebra and calculus
  • To define the idea of linearity, to use it in algebra or calculus task design, and to critique lessons about linearity
Task
Bloom's levels - tech
Bloom's levels - math ed
3-1 Compare "pro" and "con" reviews of Bloom's
3
2-6
3-2 Design an algebra or calculus unit on linearity
3
2-6
3-3 Critique an algebra or calculus unit on linearity
3
2, 4, 5, 6
3-4 Join MathForum and participate in a discussion
2, 3
2-6
3-5 Use Wolfram|Alpha to solve a system of linear equations, and reflect.
2, 3
2-6
3-6 Make a blogroll
2, 3
4, 5, 6
3-7 (optional) Review an article
3
2, 4, 5, 6
3-8 Class meeting
3
2, 4, 6
3-9 Live online event
3
2, 4, 6
.
The objectives of Week 4 are:
  • To define levels of geometric reasoning within the Van Hiele model
  • To discuss whether levels apply to groups, persons, or particular activities of a person
  • To design activities connecting algebraic and geometric reasoning
Task
Bloom's levels - tech
Bloom's levels - math ed
4-1 Critique Van Hiele model (and a media piece describing it) and answer questions
3
2-6
4-2 Design a geometry unit on symmetry
3
2-6
4-3 Critique a geometry unit on symmetry
3
2, 4, 5, 6
4-4 Build a GeoGebra applet and describe its use in ed
3
2-6
4-5 Help a partner build on last week's student unit
3
2-6
4-6 Class meeting
3
2, 4, 6
4-7 Live online event
3
2, 4, 6
4-8 (optional) Join The Educator PLN ning and reflect on PLN
2, 3
2, 4, 5, 6
.
The objectives of Week 5 are:
  • To collect a library of visualization tools
  • To design and to critique statistics lessons
  • To trace the implications of ubiquitous data-collection devices
Task
Bloom's levels - tech
Bloom's levels - math ed
5-1 Describe five less common data visualization techniques and their educational use
3
2-6
5-2 Design a probability or statistics unit
3
2-6
5-3 Critique a probability or statistics unit
3
2-6
5-4 Find and add items to the Diigo group Math Links
2, 3
2, 5
5-5 Help a partner build on last week's student unit
3
2-6
5-6 Class meeting
3
2, 4, 6
5-7 Live online event
3
2, 4, 6
5-8 Read and critique an article
3
2, 4, 5, 6
.
The objectives of Week 6 are:
  • To analyze tasks for balance among different activity types
  • To focus on student-generated math content
Task
Bloom's levels - tech
Bloom's levels - math ed
6-1 Analyze a math textbook chapter by Bloom's taxonomy levels and make a review
3
2-6
6-2 Design Creating level student activities
3
2-6
6-3 Design assessments for tasks of different levels
3
2-6
6-4 Reply to a discussion of a MAA column
3
2, 4, 5, 6
6-5 Help a partner build on last week's student unit
3
2-6
6-6 Class meeting
3
2, 4, 6
6-7 Live online event
3
2, 4, 6
.
The objectives of Week 7 are:
  • To apply measures for reducing math anxiety to your activity design
  • To reflect on values comprising "math sophistication"
  • To summarize community activities to take to students
  • To celebrate the successful completion of the course!
Task
Bloom's levels - tech
Bloom's levels - math ed
7-1 Improve other people's student units from weeks three to five, addressing the issue of math anxiety
3
2-6
7-2 Improve other people's student units from weeks three to five, addressing values comprising "mathematical sophistication"
3
2-6
7-3 Write a reflection about the course, answering questions
3
2-6
7-4 Class meeting
3
2, 4, 6
7-5 Live online event
3
2, 4, 6
3 optional tasks: Define and do three tasks typical of this class, to make up for those missed in the past.
3
2-6
I marked technology we use in the class by either level 2 - Understanding, or level 3 - Applying. Tasks marked with 2 require learning a new tech tool. These tasks can be cognitively demanding, emotionally intense and time consuming.

In Week 1, we had 8 out 9 tasks marked with Understanding Technology
In Weeks 2 and 3 each, there are 3 tasks requiring new tech actions, though I realize that tech introduced during Week 1 is still new.
In Weeks 4 and 5 each, there is 1 such task
In Weeks 6 and 7, we use tech introduced before

The design goal here is for technology to fade into the background, and to become ubiquitous in our work with math ed content. I think this would not happen if we kept learning 2-3 new tools every week.

Quality Matters full list


These are the metrics used for QM.
Course Learning Objective
By the end of the course, each student will be able to...

Unit Learning Objective
Bloom's Level
Resources and Materials
Learner Engagement
Course Technology
Assessment Course/Unit