General Tech Tool: Geometer's SketchPad & SketchPad Explorer for iPad

Geometer's SketchPad is a tool I was first introduced to a few years ago, but shied away from because I had no prior knowledge and limited technology available to me at the time. While I still have yet to implement this in the classroom, it is one of the tools I am looking at using for next year as we build a more blended-PBL classroom style of teaching at our school. Since I am not as familiar with this tool, I will leave it to a classmate of mine, Terry C. to explain and evaluate. I'll cover the iPad version after!

Original CEP Post

Specific Math Activities using Geometer's Sketchpad (GSP)

Overview

Curator: Terry C

Name of Tech Tool: The Geometer's Sketchpad (GSP)

Brief Description of Tech Tool: The Geometer's Sketchpad is a dynamic, interactive software that supports the teaching of mathematics through the creation, visualization, and manipulation of geometric shapes, mathematical models and graphical representations relevant to geometry, algebra, and calculus. The software is developed and sold by McGraw-Hill Education.

Additional Information

A multitude of resources, ranging from lesson plans and activity guides to tutorials and professional development/training sessions are available for Geometer's Sketchpad.

McGraw-Hill Education maintains several sites that offer tutorials on how to use the software, free classroom activities, and an online community to share new ideas on how to use Geometer's Sketchpad in the classroom:

• Geometer's Sketchpad Resources
• Geometer's Sketchpad Resources Center
• Sketch Exchange - Online Community

A community of Geometer's Sketchpad users have also posted their own lessons and activities for the software on the web:

• The Math Forum @Drexel: Sketchpad Resources at the Math Forum
• Kutztown Unversity: Geometer's Sketchpad Lessons
• Math Bits: Working with Geometer's Sketchpad
• The University of Georgia: GSP Lessons
• Technological Education Consulting: Sketchpad Sketches
• Nate Burchell's Dynamic Geometry Site
• University of Virginia Center for Technology and Teacher Education

Numerous videos and video tutorials for Geometer's Sketchpad are also available on YouTube:

• Geometer's Sketchpad YouTube Videos

System Requirements

Geometer's Sketchpad Installation Guide and Licensing Agreement

For Version 5:

Windows system requirements:

Pentium-based system or equivalent

Windows XP or later

300 MB free disk space

Optional: Internet connection*, Adobe® Reader or Adobe Acrobat®

Macintosh system requirements:

Intel-based system (Note: PowerPC users may use Sketchpad Version 5.04 or earlier, available on the download page.)

Mac OS 10.4 or later

300 MB free disk space

Optional: Internet connection*, Adobe® Reader or Adobe Acrobat®

• An internet connection is required for downloading Sketchpad 5, deregistering Sketchpad 5, and watching Sketchpad Movies.

Geometer's Sketchpad currently is not compatible with iPads and Android devices. Sketchpad Explorer is available as a free iPad app in the iTunes store.

SketchPad Explorer

Curator: Kristen (Me)

Overview: SketchPad explorer is the iPad version of Geometer's Sketchpad. While it does not have all of the same capabilities, it does provide a good amount of activities to explore using this dynamic modeling software. 

Technical Costs & Considerations: Aside from owning or having access to an iPad, there is no cost to download this app. 

Additional Information: I have downloaded the SketchPad Express app and find that I am very much enjoying it and the flexibility it gives me to model mathematics and to play with the modelings they provide. This is a great resource to take advantage of the Representing and the Automating affordances of technology. The app is easy to use and a free resource for you to use in your classroom. After following a brief tutorial and exploring some of the cooler features of mathematics that SketchPad can demonstrate, you get the opportunity to browse through the library and find various activities already created just for this app. Topics include:

• Elementary Mathematics
• Geometry: Constructions
• Geometry; Ellipse Constructions
• Algebra: Dynagraphs
• Algebra: Slope
• Sketch Exchange Community Site
• The Sketch Exchange Community site allows you to browse lessons created by other SketchPad users that are specifically geared toward use with the iPad app. Simply browse with the appropriate search, and you'll find a vast treasury of activities to use.

How this Supports & Supplements PBL/PrBL:

Geometer's SketchPad and it's iPad counterpart SketchPad Express both provide a dynamic workspace that allows students to get visual and study geometry synthetically (without coordinates), while manipulating their ideas to round out their reasoning. With Geometer's SketchPad, you have more freedom to create your own models than with the Express version, but the Express version has some very interesting lessons that require critical thinking and analysis to truly gain an understanding. In my opinion, I like Geometer's Sketchpad best for PBL because it allows for the user to create more independently and to model and play with their own thinking to draw conclusions. However, I like SketchPad Express a lot for PrBL as it provides solid lessons that are truly inquiry based placed into a dynamic environment where students can manipulate the tools and build their thinking.

Problem-Based Learning: NRICH

The goal in Project-Based Learning and Problem-Based Learning is to give your students a deeper and more meaningful experience with the content. At NRICH Mathematics, enriching activities is the name of their game. This website is accessible to students and teachers alike and offers both a rewarding experience to engage in deeper learning through interaction with their various mathematical tasks and lessons. On the student side, students can explore "live" problems designed for their desired grade level as well as weekly problems, videos and articles on mathematical thinking and strategies. On the Teacher Side you will find an amazing array of resources available to help you get your students thinking like mathematicians!

Why I LOVE NRICH:

• Weekly Challenge problems, complete with warm-ups
• The Trending Section to let you know what is hot right now
• Exploration activities to use with your students in the Current Section
• Right now is Dotty Paper, which is exactly what I'm using in a project for my classes this marking period!
• Curriculum links for "rich tasks" at various levels.
• Teacher Resource links as well
• STEM resources and STEM Mapping
• Cross-curricular works best with PBL

Problem-Based Learning: Mathematics Assessment Project

The Mathematics Assessment Project has been developed to help bring life to the middle and high school CCSSM through both formative and summative means. Available at the website are tasks, assessments, and lessons designed to facilitate 21st Century skills like problem-solving and critical thinking and foster creativity in the math classroom. The resources are free to visitors and can be downloaded at your convenience.

Reasons I LOVE Mathematics Assessment Project:

• Search by grade, type of activity, or best of all STANDARDS & PRACTICES
• Search, Click and be lead to an activity that suits your needs!
• Lessons are broken down into 2 categories: problem solving and concept development. Two critical areas to develop in Project-Based and Problem-Based learning!
• Activities are available for grades 6-12, but don't feel limited by the designed grade level, I've used 7th grade activities quite successfully in my high school classroom.
• Think of the differentiation possibilities! 
• Lessons I've used successfully in the classroom: 
• Applying Angle Theorems-7th Grade Conceptual Lesson
• 2D Representations of 3D objects- High School Conceptual Lesson
• Tasks are ranked from novice through expert for both middle and high school grades!
• MAP is supporting YOU with Professional Development Modules to learn how to use their materials and foster the kind of classroom atmosphere you want!
• Ready Made assessments that you can take in part or in whole, with answer keys

Problem-Based Learning: Math Pickle

We all know what it's like to be "in a pickle", and that is kind of what it is like to be participating in Problem-Based Learning... one giant Math Pickle. Over at Math Pickle, they are trying to make mathematics engaging and "hard" fun. Math Pickle in and of itself is a wonderful site to explore, filled with videos of lessons, activities, and ramblings sure to engage you and get your creative juices flowing.

Why I LOVE MathPickle:

• If I didn't make it clear earlier, I love their videos! 
• You can even get video support by grade level or topic, making finding what you need a breeze.
• Their emphasis on continually developing problem-solving skills and Higher Order Thinking through games. 
• The $1,000,000 Problems, truly what you are here to search out if you are interested in Problem-Based Learning. This link provides you with access to various math challenges for all grade levels and the teaching tools to accompany them. You also get to see a video of the $1,000,000 problem in action!
• Don't feel limited by the grade level, if your students are new to think kind of problem-solving a vast array of these problems are likely to be challenging for your students. Think of the differentiation possibilities!

Problem-Based Learning: Emergent Math PrBL Curriculum Maps

If you believe in a higher being than this is where the Hallelujah chorus would begin. Let me welcome you to the CCSS PrBL Curriculum maps for grades 4-12 with both Integrated and Traditional high school pathways brought to you by Emergent Math. Over at Emergent Math, they've compiled resources from bloggers and teachers all over  and aligned them with the various curriculum mappings provided by CCSS. If you are someone who wants to try out Problem-Based Learning in your classroom, and you already have a district- or school-provided curriculum to follow that is aligned with the CCSS, this is the resource for you!

Reasons why I LOVE the Curriculum Mappings:

• Mappings are available at all different grade levels, and standards are available at all different grade levels (in some cases at least), having all of these mappings allows for me to level-up or level-down the PrBL for my students on a more individualized basis: Hello Differentiation!
• Resources come from a variety of sources and have a wide-range of activities. Search out the ones you love and the ones you'll leave. 
• Also, with the plethora of resources, you're bound to find something that works for your given situation in your classroom, be it monetary or technology constraints, there is something for everyone. 
• The Mappings are constantly being updated with new resources, you can even submit your own!

Problem-Based Learning: Powerful Problem Solving from the Math Forum @ Drexel

The Math Forum @ Drexel sure know what they are talking about when it comes to teaching students Higher Order Thinking skills through engaging mathematics like Problem-Based Learning. Their book, written by Max Ray, Powerful Problem Solving, has been an interest of mine for the last few months as we are studying it in a graduate class I am taking. I am thankful to have had the opportunity to close-read the text and explore their online resources, which I am happy to share with you!

This book provides a novice Problem-Based Learning teacher with many tools to create a successful implementation of the strategy in their classroom. There are over-arching themes interwoven throughout the book focusing on areas of problem-solving strategies that have activities to accompany them. While these are great in and of themselves, you truly need some good rich tasks to use these practices with. Enter their companion website and my currently most frequently accessed link: Powerful Problem Solving.

Reasons that I love the PPS Online Resource Website:

• They have a multitude of videos linked to their strategies and Problems of the Week so that you can see what they look like in action. 
• You can also hunt them down on YouTube, but I like the layout of this version.
• The Chapter-By-Chapter resources, giving you access to activities and tasks relayed in the book, additional problems, supporting applets, student-hand outs, etc... 
• Links to their free Problems of the Week (though signing up for your class and receiving access to all of them may not be a bad idea!)
• Remember, the resources from the PPS website also give examples of the activities to use with these tasks!
• These are pre-designed Problem-Based problems for you to use in your classroom, which you can use whole-sale or use as models for designing your own Problem-Based problems!

For more information specifically about the Math Forum @ Drexel, check out a page by Terry, a classmate of mine, with links to other specific resources available from the Math Forum @ Drexel.