Evonne Tutkaluk

MC-Intro: Resource Share

Visualization Questions:

Why is visualization necessary (or not) for student understanding of math or science?

I truly believe visualization in math is essential in helping students make connections with abstract concepts. In my experience, visualization engages students in a very unique way that helps them generate a more accurate understanding of concepts. In this way, students are able to solidify new learning through authentic (many inquiry-based) learning situations they experience in front of them on the computer screen.

What are the multiple ways that students’ understanding could be represented with this dynamic visualization software and what are the implications for teaching practice?

Students can formatively assess themselves by doing multiple practice questions on the math help websites, applets, simulations, interactivities, etc. Also, teachers can give student assessment questions either via a written paper quiz or an online quiz on a website or class wiki. Teachers can group students to ensure collaboration in examining of the learning the new concept. In particular, teachers can use government education websites that have curricular-based test banks and practice questions. Sites like Quest A+, Learn Alberta, Testbank.com are popular for Alberta teachers.

What are some ways that a students’ understanding could be challenged with dynamic visualization software?

The great thing about visualization software is that students are able to see concepts in a very meaningful way; however, this may also challenge students’ prior learning and understanding. Students often have to reconcile prior learning and misconceptions with new learning and understanding to ensure refinement of the new learning. As most are web-based programs or websites that house interactivities that engage students in a highly visual and tactile way where what they see is able to add a new dimension of understanding of the concept. This is helpful in students’ skill development as at times they may work collaboratively in the future.

I agree with the research, CoSN (2009), which indicates current and future employers are looking for new hires that can problem solve and work together in a collaborative team atmosphere. I know Janet mentioned Youtube videos already but I had to add a number of my favourites here for you (see below at the bottom of my post. The first five videos are my ultimate favourites that also support the point of preparing students for their futures as we are now 21^st century teachers teaching 21^st century learners and there are numerous more videos on the topic. I think these videos are excellent to show at staff meetings or professional development days. Learning and teaching is evolving, time to evolve with it!

What are the social opportunities and potential cognitive opportunities that may emerge from interaction with this software? How are the specific features of the software connected to these opportunities?

Many of the simulations could be stand-alone activities. However, many could definitely support social affordances of learning as students collaborate in groups engaging with the visualization / simulation / web-based applet activity. As I mentioned before the immediate formative feedback that students gain via making predictions, testing their predictions, evaluating their data and learning by manipulating the data and simulations is instrumental in students formulating an understanding of the concept being studied. Cognitive and constructivist active learning is embedded in the activities and simulations of this site and the design model of the applets, activities and simulations align well with the learning theories and frameworks we studied in Module B (Anchored Instruction, SKI, LfU & T-GEM). I encourage every interested math teacher to bookmark this site into favourites.

How would you use this technology in a classroom?

I could select specific activities or applets from the site for the students to explore or I could give them 20 minutes to explore the site alone and then collaboratively for about 20 minutes in pairs or small groups where they could each share the activity(ies) that they personally selected and would find useful to their learning. This could also be a carrot-type activity to engage them with the site initially to begin with before I (the teacher) provide them with an assignment to complete including an applet or activity from the site. The carrot-activity could satisfy Edelson’s (2001) LfU model of students’ desire to learn as this activity could motivate and inspire students to learn or participate in the activities. It’s hard to narrow down because really, this site and a few others I found are excellent places to start for math teachers to engage their students in meaningful (and often authentic) math-related learning activities.

References

CoSN – Consortium for School Networking (2009). Learning to change, changing to learn. Pearson Foundation International Conference on Education. Retrieved October 6, 2009, from http://www.pearsonfoundation.org/pg5.6.html

Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385.
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Resources to Share:

1. Math Applets from Analyze Math http://www.analyzemath.com/
& Mr. Walker’s Technology Blog – Developing 21^st Century Skills One BYTE at a Time

Mr. Walker’s Technology Blog houses links to Interactive Math & Science Applets, Simulations and activities & the National Library of Virtual Manipulatives for Math and more!

http://blogs.jefftwp.org/wordpress/walker/2010/03/01/interactive-applets-for-high-school-math/

Some of my favourite applets are from http://www.analyzemath.com/math_software.html and the links I found initially on Mr. Walker’s Technology Blog. I really like the videos the site provides as well. The great part is that these are web-based and anyone, in particular, our students, can access them anytime to help practice and help solidify their understanding of the concepts. The visualizations do help their understanding as they see and immediately experience what happens to the graphs when they manipulate the various variable parameters. Powerful visualizations indeed! It’s so hard to pick just one but the following below are quickly becoming favourites for each of my classes:

My ultimate favourite one for my grade 12’s (Understanding and Analyzing Graphs of Periodic Functions) explores all the parameters a, b, c and d and how specific manipulations to these parameters change the graph in different ways. The best part about it that I like is the simplicity and the time it saves. These visualizations and graph changes would take lots of time and screen switching and entering equations to create these graph simulations on graphing calculators.

http://www.analyzemath.com/function/periodic.html

My grade 11 math classes are currently exploring quadratic, absolute value and rational function graphs.

Math 20-2 Quadratics:

http://www.analyzemath.com/Graphing/GraphingQuadraticFunction.html

http://www.analyzemath.com/quadraticg/quadraticg.htm

http://www.analyzemath.com/math_videos/functions/quadratic_graph.html

http://www.analyzemath.com/quadratics/quadratics.htm

http://www.analyzemath.com/XaxisReflect/XaxisReflect.html

Math 20-1 Absolute Value & Rational Functions:

http://www.analyzemath.com/Absolute_Value_Function/Absolute_Value_Function.html

http://www.analyzemath.com/math_videos/functions/rational_graph.html

2. Mathletics

http://www.mathletics.ca/

3. Maple Leaf Math Challenge

http://www.mathletics.ca/canadianmathchallenge/

4. Educational Simulations

http://www.techtrekers.com/sim.htm

5. PhET Interactive Simulations – University of Colorado at Boulder

This is probably one of my favourite sites that I’ve come across that expands to each subject area.

http://phet.colorado.edu/en/simulations/category/math

6. Spartacus Educational – Maths Websites

http://www.spartacus.schoolnet.co.uk/REVmaths.htm

7. IXL Math Practice

http://ca.ixl.com/math/grade-9/find-the-number-of-solutions-to-a-system-of-equations-by-graphing

8. Resource Room – Free-spirited Structured Multisensory Learning

http://www.resourceroom.net/Math/eightetal.htm

9. Interactive Math & Science Websites

I’m impressed with is the one; it’s another favourite. It’s presented in a ‘slideshare’ format with live links. Unfortunately there’s advertising at the top but it’s worth the time to explore all the various resources this site provides.

http://www.slideshare.net/kbrooks/interactive-math-and-science-websites

10. Videos

Dalton Sherman’s Keynote Ppeech at a Welcome Back Teacher PD Day 8:56 min
My Favourite by far – this video was shown at one of my school divisions professional development days – very inspiring indeed: 10 year old intellect Dalton Sherman

https://www.youtube.com/watch?v=yZm0BfXYvFg

Skills for our students future 42 seconds

https://www.youtube.com/watch?v=NhSpdeHE9HI

Learning to Change – Changing to learn 5:37 min

https://www.youtube.com/watch?v=tahTKdEUAPk

A Vision of K-12 Students Today 4:08 min

https://www.youtube.com/watch?v=_A-ZVCjfWf8

A vision of Students Today (this one is different) 4:45 min
https://www.youtube.com/watch?v=dGCJ46vyR9o

Did you know 3.0? 4:45 min

https://www.youtube.com/watch?v=jp_oyHY5bug&feature=related

Seven skills students need for their future 29:12 min

https://www.youtube.com/watch?v=NS2PqTTxFFc