BP8_RILS Publication

The outcome of my Relevant and Innovative Learning Scenario.

First, the details:
Relevant and Innovative Learning Scenario
Jessica Wunder


Brief Overview:

In this RILS, students will work in groups to use a virtual, interactive program (manipulative) to find solutions to mathematical problems, and explore algebraic concepts in a game like setting. Students must use reasoning, logic and application of previously learned material to solve problems, in a manner that encourages exploration and problem solving through trial and error.

1. Target Audience- College students in a College Algebra course. Students range in age from 18 to 40+, with most students in the mid-20s. Students have a variety of mathematical knowledge and comfort level, but most students have little algebra skills or knowledge beforehand and need remedial work in pre-algebra topics.

2. Materials–
a) Internet capable laptop with working internet connection. (All students should have this, as students have school supplied laptops)
b) Link to website for virtual activity (provided by instructor)
c) Activity worksheet with exploratory questions and prompts
d) Pencil and additional paper as needed to answer the questions and provide answers


3. Objectives– At the end of this scenario, the learner will be able to:
a) Recall previous lessons on the topic used
b) Analyze a scenario and identify mathematical concepts and ideas that are being used or needed
c) Apply laws, rules and ideas of the specific topic (e.g. fractions) to solve given problem
d) Explain processes used to solve either processes they used that worked, or proposed processes based on their exploration
e) Relate specific mathematical concepts used in the activity to real world scenarios


4. Procedure–
a) Instructor will give brief introduction to what the virtual activity is, and guided through a brief tutorial on its purpose and use. This may vary depending on the specific manipulative used, but shouldn’t take more than 5-10 minutes
b) Instructor will give student 10 minutes to explore the manipulative themselves and “play” with features
c) Students will then be put in groups of 2-3 students
d) Each group will be given an activity sheet
e) Students with then be instructed to work in groups to answer the questions on the activity sheet. Students will be given 20 minutes to work together. At this time the instructor will clearly outline what is expected of students: students are to work to find solutions, record those solutions, and eventually present their findings. The instructor should place an emphasis on process, encouraging to students to explain their processes and remind students that will not be penalized for “wrong” answers, so long as they can explain what they did, and if the answer was wrong, what they might do differently next time.
f) The activity sheet will ask students to find solutions to 3 different problems, by working together to accomplish 3 goals (one goal per problem). E.g. using different ratios, get the bike from point A to point B in 5 steps.
g) Students will record their answers, and their process (e.g. how many steps did it take you to get to point B? What ratios did you use? ) on the activity sheet
h) Instructor should be moving through the groups, stopping to see how each group is doing, ask if they have questions, and/or to listen to group dynamics and interaction.
i) Students will submit the activity sheets, one per group, when finished.
j) When complete, students will be asked to submit a paragraph, individually, reflecting on the experience. The format will be free answer, but students must write about the experience, what they learned, and if they felt it helped them.
k) If time allows, groups will be asked to share their results with the class, with an emphasis on process. Students are not expected to get all three answers/questions correct, but encouraged, through instructors instructions and introduction, to explore and share the processes they used to find answers. Each group will present their results for the three questions, with each student presenting a different question.


5. Web 2.0 Tool– Virtual Manipulatives are used for this learning scenario. Virtual manipulatives are interactive, computer based (often web based but not always) manipulatives, often with a focus on math. Virtual Manipulatives encompass a variety of individual websites and tools. There is a National Library of Virtual Manipulatives which can be found at this site: http://nlvm.usu.edu/en/nav/vlibrary.html


6. Social Participation/Social Learning– One of the integral processes of the activity is for the students to work in groups, of at least two students. Learners must work together to figure out the processes of the program, and how to solve the problems. In working in groups, students must collaborate and communicate with each other to figure out solutions. Communication and group learning are key processes to the activity. All members of the group must participate, with group participation being part of the assessment. Students are also asked to share their results with the class, which encourages social communication (presentation) skills. Each student must present a question, so that ALL students are participating (see assessment section).

7. Making Connections– Students will use previously learned concepts as a foundation for their understanding of the topic the activity uses. I.e. if the manipulative is based on ratios, students must have and use understanding of fractions to work on the activity for ratios. Students also must engage critical thinking and logic skills. The exploratory nature of the activity provides an opportunity to further refine and “exercise” their current level of critical thinking, deduction, and pattern recognition skills. Further, the virtual manipulatives often use real world scenarios and examples, which help to connect the material and it’s importance to every day situations and thinking.

8. Create/Produce – Students will have an end product of their completed group activity sheet, along with their individual reflection. Students will also present findings to the class, and are therefore creating (and must plan for) a group presentation.


9. Assessment – Students will not be graded on accuracy of answers but participation and content. The following rubric will be used to assess collaboration, effort, content, and participation.

Out of a scale of 10	Exceeds Expectations 8 – 10	Satisfactory 5-7	Not Satisfactory 0
Collaboration/Communication	Engaged with other group members and actively encouraged other members ideas and opinions. Made significant contributions to discussion and ideas.	Engaged with other group members. Contributed to discussion.	Did not engage or interact with other group members. Made no contributions to ideas or discussion of activity.
Content (Reflection)	Produced response with excellent grammar and clear communication of ideas. Reflection was relevant and provided clear insight into students experience, thoughts, and process.	Produced response, in full sentence form for personal reflection. Reflection was relevant and insightful to students experience.	Made little to no response for personal reflection. Personal reflection was not relevant to the activity, class, or topic.
Participation (Group presentation)	Student made presentation on one of the three question.  Presentation was clear and listener could easily follow train of thought and understand the process used.	Student made presentation on one of the three questions.	Student did not present or contribute to group presentation.

10. Reflection –
a) Students are asked to reflect on the process they used to answer the questions and solve the problem, as part of the activity sheet and personal reflection. Through this process they are forced to examine their methods and determine what they might have done differently. Students also share this reflection in their group presentation and personal reflection paragraph

b) Part of the purpose of the student reflection paragraph to help give the instructor insight on the students thought processes during and after the activity. This helps the instructor determine if this activity is perceived as helpful to the students. Instructor also receives indirect feedback and opportunity for reflection as they watch and interaction with students in the group work stage as well as the group presentation.

How did it go?

Reflection and Comments:

As I said in my video, I found the overall project to be successful. I got some great feedback for the activity and am ready to make some revisions to the activity and worksheet.  From here, I know I need to adjust the questions on the worksheet, and make some changes for clarity when I introduce the activity. I'm probably going to run the students through one of the trials with me, having them watch and follow along as I show them on the big screen. I'm also going to remove the group presentation aspect, due to time. I REALLY wanted to keep it, but based on time constraints, we felt the time was better spent allowing them to fully understand and use the manipulative. The feedback and positive response from my coworkers made this an enjoyable experience. We had a great discussion about student engagement and what aspects of the activity would help that, and what aspects needed to be changed. The conversation wound up being an hour long!

 I admit I was worried and nervous about the idea before presenting it to them, but they responded well to it and again, I got some fantastic feedback. I didn't mention it in the video, but this activity was actually a trial run for one of the activities I will be having my students engage in as part of my CBR project. My CBR project revolves around students using virtual manipulatives to reinforce different lecture topics. I already had one activity that had been tested earlier, and was struggling to find another manipulative that i really liked. Through the RILS I was able to find another manipulative and refine the associated activity. So this RILS was successful in more than one aspect! 

To be honest, I've been stressed and a little scared about my CBR. But as a result of the feedback and encouragement I've received from this test trial, I'm a lot more confident about how doing the full project in November. 

I still have a lot of work to do, but I think the final result will be well received by my students. I think they'll learn and have fun while doing it, and isn't that what we're all trying to do?

I do wish I was able to get footage of my coworkers engaging in the activity, but that just wasn't happening, so I had to use stills and stock footage for the video. I hope it isn't too dry, and I really look forward to your comments and insights!

PE4_Virtual Manipulatives

For the next few posts, I'll be exploring some virtual manipulative websites for my RILS project.

Virtual manipulatives are, basically, interactive, web or computer based applications that allow for exploration of mathematical concepts. Virtual manipulatives were originally created to model "concrete" math manipulatives such as base ten blocks, algebra tiles, blocks and so on.
As the use progressed, these virtual manipulatives got more detailed and have since expanded beyond their initial repertoire. Now, they are not just used instead of concrete manipulatives but offer ability to allow students to explore spatial aspects, and multiple representations of concepts in a way that is more difficult for concrete manipulatives.


There's a pretty big collection of virtual manipulatives on the internet, ranging in content from basic mathematics (fractions, counting, etc) to algebra, geometry and calculus. Many of them are aimed at students in elementary and middle schools, although there are some for high school and college level students.

439,000 results!

For me, I'm hoping to use a virtual manipulative to get my students, who are learning pre-algebra concepts, to engage in an activity that will help them to think about math differently. Many of them dis like math and find it boring. I'm hoping that by using the virtual manipulative they can explore the concepts they're learning in lecture, in a fun manner. Many of the manipulatives use game or game features to demonstrate ideas and enhance understanding. I think the manipulatives are also useful because they don't require just one specific piece of knowledge. A student or learner has to use and incorporate various types of knowledge when working. There's the spatial aspect, logic, reasoning, problem solving, and of course the specific topic they're working on.


Ok, so I've described my tool and how I'm going to use it. There's only one problem:
Which one??

Virtual manipulatives encompass a broad spectrum of different specific tools. They all use the same basic ideas and methods, but differ in how they present the idea and how they ask the student to explore and demonstrate knowledge. There are some that are very much geared to younger children, some that are more sophisticated.

As simple as fraction circles

or as complicated as probability and chaos analysis

I've spent quite a bit of time combing many sites and educational search engines, finding, looking at, examining and playing with different ones.
As I've said before, they run the gamut from basic counting to calculus. There isn't just one, but _many_.

Seriously, it was kind of exhausting. I would find something that had a good idea, or a good delivery system… but was too childlike for my students.


I'm a fan of using games to teach, so I admit I was often tempted or drawn towards the more game like activities. However, many of those were also geared towards younger students.

Part of the challenge, for me at least, was to find something that age appropriate, but content appropriate.

See, my students are older, college aged. But they're also largely artists and musicians and "Creative" types. Many of them have had negative experiences with math in school before and have a made a point to avoid it at all costs. So, many of them have weak skills in some of the "core" content and foundation materials. Fractions, percentages, decimals, ratios… are areas that a lot of my students struggle with.

SO I want to find material that would help them in these areas, that i thought they needed the most help in. But, again, much of the material is grouped by content in terms of primary school groupings. So because fractions, and decimal work is taught in earlier years, most of the manipulatives I found were geared towards younger students.

BUT! I persevered… and eventually, my late night searching led to me three sites that i thought would help me the most:




First, the National Library of Virtual Manipulatives.

This was the very first site I encountered when doing searches for and researching virtual manipulatives. It's been on my list and radar ever since. In narrowing down my choices, it was an obvious contender. It has content spanning from "basic" number and operations to data analysis and probability, while also spanning the age range from Pre K to high school. There are a lot of good looking tools and ideas here. I've already explored the site extensively, but I've chose a few specific manipulative examples that I want to play with further.

I like the way it shows functions as input and output

Second: Interactivate website
The site contains many activities but there was a few in particular that I thought might be useful. The equivalent fractions activities seem like something that might help my students to better understand the relationship between fractions, in a visual/spatial manner.

Equivalent fractions finder

I'm looking at the equivalent fractions finder and some of the other fraction functions.


Finally, I've also been looking at the Illuminations site. The manipulatives on this one are similar to the Interactivate manipulatives, although there seem to more that are suited for older learners.
I've looked at several, but keep coming back to this one with ratios:

I show cased this on in my OMM post, and so I have a bit more experience with it. It involves a good amount of problem solving and analysis, but it's also fun and challenging. (or at least I think so)


So which one will I use for my project?

Stay tuned to find out!

BP7 OMM

Ok, here's my one minute movie. I actually choose a tool that I hadn't reviewed in my previous web2.0 posts, but was a tool I had been researching, reviewing and looking into for my CBR project.

The tool I chose to review is actually part of a larger category of web2.0 tools called virtual manipulatives. Theyre interactive programs/software used for teaching and reinforcing mathematical lessons.

For this project, and for my CBR I've been looking into the Illuminations website of virtual manipulative tools. You can see the site here: Illuminations

My "commercial" is as much of a commercial for the idea of using virtual manipulatives as it is for the site/tool itself. I created with the idea of using this to pitch my project to administration.

I look forward to your feedback!




Note: The image of the boy with the chalkboard is courtesy of Microsoft Clip Art. The image is royalty free and was retrieved from here:
Microsoft Clip Art Chalkboard Image