The purpose of Information visualization tools or Info-Vis is to create TELE’s where students can explore more abstract concepts to help build conceptual understanding. First I found it helpful how Clements (2014) uses Zimmermann and Cunningham (1991) definition of visualization in Math as “to describe the process of producing or using geometrical or graphical representations of mathematical concepts, principles or problems, whether hand drawn or computer generated. ” In this week’s readings I explored NetLogo and how it could be used to help students build understanding around decimals. Often as we begin the exploration of decimals students apply the knowledge of numbers help previously. For example 100 is bigger than 50 they can draw 100 things and then 50 and show that their thinking is correct. When you change that to 0.101 and 0.0101 you often find they say they are the same, there is 101 in each and struggle to imagine/conceptualize what 1/10^{th} and 1/100^{th} of something looks like. Finkelstein et al. (2005) looked at the effects of learning in a science classroom with students learning circuits and found that overall the long term understanding was greater for those students who used computer generated simulations versus those that used real circuits. It is encouraging to hope that the same would apply in this scenario allowing for deeper and greater understanding of decimals.

**Comparing Decimals**

**Goal:** Students will be able to compare and order decimals from largest to smallest.

__Materials Required:__

Chrome Book

App – NetLogo – Colour Fractions

__Lesson (using LfU model)__

**Motivation:**

– students are presented with two decimal numbers on the board, they can choose how much additional recess time they will receive. Their goal is to determine which will give them more recess time.

**Knowledge Construction:**

– students working on own write down the two numbers and what they know so far.

– Students working in partners compare what they know and complete the following statement that “I believe ________ will allow us more recess because (provide reasoning – using words, pictures.

– Students access Color Fractions Model on NetLogo site and start by using it to represent known decimals, such as 0.1 and 0.5 to build familiarity with program.

– Students create Color Fractions Model for two represented decimals

– Students use models to determine which decimal in indeed larger.

**Knowledge Refinement:**

– Students return to initial statement and refine as needed with a focus on expanding and using new knowledge of why one number is larger.

**References:**

Clements, M. K. A. (2014). Fifty years of thinking about visualization and visualizing in mathematics education: A historical overview. In *Mathematics & Mathematics Education: Searching for Common Ground* (pp. 177-192). Springer Netherlands. Available from UBC. https://lib-phds1.weizmann.ac.il/Dissertations/Mathematics_and_Mathematics_Education.pdf#page=175

Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physics Education Research,1(1), 1-8. Retrieved from https://journals-aps-org.ezproxy.library.ubc.ca/prper/abstract/10.1103/PhysRevSTPER.1.010103

Wilensky, U. (2005) NetLogo Color Fractions model. http://ccl,northestern.edu/netlogo/models/ColorFractions. Center for Connected Learning and Comptuer-Based Modeling, Northwestern University, Evanston, IL.

Wilensky, U. (1999) NetLogo. http://ccl,northestern.edu/netlogo/ . Center for Connected Learning and Comptuer-Based Modeling, Northwestern University, Evanston, IL.

Xiang, L., & Passmore, C. (2014). A framework for model-based inquiry through agent-based programming. Journal of Science Education and Technology, doi:10.1007/s10956-014-9534-4

I really like what you chose for this activity with decimals! I like that they are motivated by recess time, something so relevant to their daily lives. I agree that the Color Fractions model on Netlogo could be a valuable tool, particularly in showing decimal values for students who struggle understanding the concept of being smaller than one but more than zero. I also really liked Illuminations as a way to explore fractions. This could be used together so students can really understand the relationships between fractions and decimals. Thanks for the post!

Jocelynn

Thanks for the great idea Jocelyn and connecting to Illuminations as well. I will go check it out as while i liked NetLogo it required a download and getting programs downloaded on district devices is often not as quick as I would like. Sarah

Hi Sarah

I like the fact that you brought up ways to be more abstract in students learning. I know in my senior physics class…many students have a difficult time explaining how convert cm to m etc. They know the answer, but they do not know how to explain how they solved it…you just move the decimal 2 to the left. I remember recess in elementary school — favorite part of the morning…and then we had a little snooze in the pm 🙂

I wonder if you could share some screen-shots or videos of the “App – NetLogo – Colour Fractions” in action.

A good next step might be to share some of your student’s work…or how they felt about the lesson.

To keep the conversation going — make sure to respond to at least two other learners as well respond to all learners that respond to your own post. When responding to other learners, expand the discussion and please use references to support your ideas/thesis/concepts etc.

Christopher

Hi Sarah,

Thanks for your lesson outline! It looks great. I was reading your comment about Finklestein and found it interesting as it contrasts with what I read from Srinivasan et al (2006). This group was looking at the difference between computer software simulation and hardware based simulation in an electrical telecommunications course and found that there was no difference in learning outcome. What they did find was that the students strongly preferred “real” experiences over those obtained with software simulations. It would be interesting to look for a systematic review of software based simulation to see the overall effect on learning outcome. It is hard to tell what the true effect is when only looking at one paper vs. another.

Mo

Srinivasan, S., Pérez, L. C., Palmer, R. D., Brooks, D. W., Wilson, K., & Fowler, D. (2006). Reality versus Simulation. J Sci Educ Technol, 15(2), 137–141. http://doi.org/10.1007/s10956-006-9007-5