# Talk:Using Visualizations to Teach Mathematics with Understanding (Spring 2015 Mini-Course)

## Contents

- 1 -- Bobbi Scirbona (talk) 23:03, 30 April 2015 (EDT)
- 2 -- Melissa Connor (talk) 00:39, 1 May 2015 (EDT)
- 3
**Unit 1: What do we mean by “Learning with Understanding”?** - 4
**Unit 2: What are visualizations? And why are they important?** - 5
**Unit 3: Creating Meaningful Visualizations for Teaching Mathematics** - 6
**Unit 4: Putting Ideas into Practice** - 7 -- Kimberly 00:46, 4 May 2015 (EDT)
- 8 Instructor comments on your mini-course -- Jz833665 (talk) 12:07, 4 May 2015 (EDT)

## -- Bobbi Scirbona (talk) 23:03, 30 April 2015 (EDT)

Melissa,

I think you are off to an excellent start with your mini-course. One thing that I particularly liked was that you broke each unit into lessons, and those lessons each have their own page. This really helps to keep your pages uncluttered and easy to read and follow.

1. Learning Outcomes (9/10) - The learning outcomes on your mini-course homepage clearly align with the overarching goals for participants to use visualizations to teach for deeper student understanding of mathematics. Unit level objectives are also clearly expressed and include an appropriate performance component. One thing that is unclear to me is where these objectives fit into your curriculum map. Do these objectives correspond with the numbering on your portfolio page?

2. Content-Goal Consistency (10/10) - I think the resources that you have included are excellent. They are both informative and engaging. The resources provide the information necessary for participants to fully complete the assignments and meet the learning objectives.

3. Instructional Sequencing (20/20) - I like that you start your course with a lesson that is devoted to learning for understanding before you move on to how visualizations can be used to increase student understanding. In addition, you have the participants look at what it means to learn for understanding followed by why learning for understanding is important in the 21st century. This really sets the stage and lays a good foundation for the rest of the course.

4. Engagement/Interaction - (20/20) - The variety in resources and number of videos presents the information in an engaging manner. Your use of questions and statements in the reflection portion of each lesson provides the participants with guidance and a focus when viewing resources. The culminating discussion also helps participants to reflect on their learning and interact with other participants to build knowledge collectively by sharing experiences.

5. Technical Quality - (9.5/10) - The pages are clearly labeled, and links make it easy to navigate throughout the course. The images are crisp and colorful and make the course pages visually attractive. I like the way you cited the images by creating a caption under the picture rather than cluttering the reference section at the bottom of the page. The only thing that I noticed were a few spelling errors - 1. Course intro page, Introduction , "What does __in__ mean to teach/learn..." (it?) 2. Lesson 1 Intro , "Before we __more__" (move?), 3. Lesson 2 Intro, "What the __difference__ are" (differences?)

6. Extended Resources - (9/10) - All resources are linked and acknowledged. One thing I would suggest (which I will be adding to my course) is to include a list of optional readings/resources for additional information. These might be helpful when making assignments that require participants to include an outside source.

I think your mini-course is developing nicely and look forward to seeing the final product.

## -- Melissa Connor (talk) 00:39, 1 May 2015 (EDT)

Thanks, Bobbi!!! I know I have to proof read this and I think the extended resources are a good idea.

Good point about the learning outcomes. So for my curriculum map,I started with the prerequisites, matched that to a performance objective, and then I designed sub-performance objectives to reach performance objectives #1-8 on my portfolio page.

Perhaps I have to combine these sub-performance objectives....

From the performance objectives I matched #1-8 to a unit. From there I summarized my learning outcomes in one sentence. So this is what I am thinking....

Summary of over-reaching target objective of whole class:

- Participants will develop their skills to recognize and create quality visualizations to teach mathematics with understanding.

Then I have my over-reaching target objectives (aka learning outcomes):

- Conceptualize the idea of teaching and learning with understanding.
- Identify what visualizations are.
- Identify characteristics of meaningful and effective visualizations.
- Develop skills to create visualizations.
- Explore tools and strategies for using visualizations in the classroom and how to transfer these skills to students for his/her own use.

Then, my performance objectives:
1. Participants will **compare and contrast** reform teaching methods, methods that encourage teaching for understanding, and traditional teaching methods .

2. Participants will **identify** advantages of visualizations for teaching with understanding.

3. Participants will **apply** what they have learned to critique both good and bad examples of visualizations for mathematics using the internet.

4. Participants will **identify** characteristics of meaningful visualizations effective for supplementing instruction for mathematical understanding.

5. Participants will be able to **create** plans to integrate visualizations in mathematics lessons.

6. Participants will **analyze** a series of visualizations created with Geometers' Sketchpad to model strategies for designing classroom lessons and/or materials.

7. Participants will be able to **construct** a visualization for a given mathematical concept.

8. Participants with **reflect** on ways to transfer skills for using visualizations in mathematics to students by collaborating in a peer discussion.

sooooo.....

**Unit 1: What do we mean by “Learning with Understanding”?**

- 1. Participants will
**compare and contrast**reform teaching methods, methods that encourage teaching for understanding, and traditional teaching methods .

Activities to meet this objective: (???)

- Participants will explain the advantages of learning with understanding by completing a two paragraph refection.
- Participants will compare reform teaching methods and traditional teaching methods by analyzing research.
- Participants will clarify any misconceptions about learning with understanding in a class discussion.

**Unit 2: What are visualizations? And why are they important?**

2. Participants will **identify** advantages of visualizations for teaching with understanding.

3. Participants will **apply** what they have learned to critique both good and bad examples of visualizations for mathematics using the internet.

4. Participants will **identify** characteristics of meaningful visualizations effective for supplementing instruction for mathematical understanding.

Activities to meet this objective: (???)

- Participants will describe what visualizations are and will explain why visualizations are important in mathematics using a class discussion.
- Participants will identify how students learn and how visualizations supplement learning with understanding by collecting and analyzing research.
- Participants will explain if visualizations are useful tools for students by reviewing a case study by Edens and Potter and discussing results in a class discussion.

**Unit 3: Creating Meaningful Visualizations for Teaching Mathematics**

5. Participants will be able to **create** plans to integrate visualizations in mathematics lessons.

Activities to meet this objective: (???)

- Participants will be able to discuss plans to integrate visualizations in mathematics lessons.
- Participants will construct a visualization for a given mathematics concept.
- Participants will identify both good and bad examples of visualizations for teaching mathematics using the internet.

**Unit 4: Putting Ideas into Practice**

6. Participants will **analyze** a series of visualizations created with Geometers' Sketchpad to model strategies for designing classroom lessons and/or materials.

7. Participants will be able to **construct** a visualization for a given mathematical concept.

8. Participants with **reflect** on ways to transfer skills for using visualizations in mathematics to students by collaborating in a peer discussion.

Activities to meet this objective: (???)

- Participants will analyze a series of visualizations created with Geometers' Sketchpad to model strategies for designing classroom lessons and/or materials for using visualizations to teach mathematics with understanding.
- Participants will create a lesson with visualizations.
- Participants will reflect on ways to transfer skills for creating visualizations to learn with understanding to students using a class discussion.

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## -- Kimberly 00:46, 4 May 2015 (EDT)

Melissa,

Great start to your mini-course, your portfolio, course, and lesson pages look really good so far!

1. Learning Outcomes (9/10) - I think that your outcomes for the course are clearly listed and flow well together. I also, really like that you have dedicated one lesson to each objective in unit one.

2. Content-Goal Consistency (10/10) - The content that you are providing the learners with seems to give the perfect amount of information to allow the participants to complete the tasks at hand. additionally as I said above I think that it is great that you have one lesson per objective, this will allow the learners to stay focused and fully accomplish each objective or goal since they are focusing on one at a time.

3. Instructional Sequencing (20/20) -I love your instructional layout. You first give a bit of background on the material then dive into what exactly it means to teach using visualizations, then apply that to teaching math, and then eventually put it to practice. This will provide the learners with plenty of support and a natural flow and relation of the material.

4. Engagement/Interaction - (20/20) - The videos and discussions that you have provided for the participants are all very interesting and informative and should lead to some great conversations.

5. Technical Quality - (9/10) - Overall your mini-course has a very clean and uncluttered look. It is easy to navigate. The one thing I would be sure to do is proof read before you submit it as complete!

6. Extended Resources - (10/10) - All of your resources relate to the content and enhance the experience of your mini course.

## Instructor comments on your mini-course -- Jz833665 (talk) 12:07, 4 May 2015 (EDT)

Melissa,

I'm very pleased to see your mini-course coming into this whole structure through the ID process that you've gone through! Each ID component is strong in your design. Your Unit 1 is well organized, informative, and interactive.

Each of your lessons follows the storyline of overview-read/watch-reflect on questions. A possible change you may consider is to bring the questions currently listed under reflection earlier, maybe to the end of your lesson intro/overview part. The questions will first serve as a guide, and then as the focus of the reflection section, (where you do not fully repeat the questions, but will refer to the questions listed in the beginning of the lesson).