General Tech Tool: GeoGebra & GeoGebra Tube

I was first introduced to GeoGebra in one of my 400-level college mathematics courses while majoring in Mathematics in my undergrad years at Michigan State University (Go Green!). I will admit that when I first started using the program, I was not a fan. However, since graduating from that program and moving on to teaching in a classroom of my own, I have grown to know and love GeoGebra and all that is has to offer as a dynamic modeling software.

Overview

Name of Tech Tool: GeoGebra

Brief Description of Tech Tool: From their website: GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. It has received several educational software awards in Europe and the USA. Quick Facts: 

• Graphics, algebra and tables are connected and fully dynamic
• Easy-to-use interface, yet many powerful features
• Authoring tool to create interactive learning materials as web pages
• Available in many languages for our millions of users around the world
• Open source software freely available for non-commercial users

Technical Costs & Considerations: GeoGebra is a free dynamic geometry software tech tool that is available across a variety of platforms. GeoGebra is compatible with Macs and PC and is available as an app on iPads, Android devices, Windows tablets, and the Chrome Store. 


Additional Information

A snippet of information I've written up about GeoGebra before: GeoGebra is a very interesting tool that provides multiple affordances in the classroom. Two that stick out are Automating Tasks and Representing Knowledge and Thinking. The tool has the ability to do calculations for you for many tasks that can help the student to focus more on the conceptual idea and less on the procedural. At the same time, GeoGebra has intricate graphic features, which allow users to create and manipulate multiple representations for whatever their problem is. The Tangram Cat problem from GeoGebraTube is a good example of the representation in seeing how transformations are applied to various figures. You could also have students use GeoGebra without specifying any particular applet and allowing them to model their own thinking on a situation in a space that makes it easy to manipulate and tweak to create exactly what they want as their thinking evolves through the reasoning and sense making process.-

Helpful Links from GeoGebra

• GeoGebra Chrome App
• GeoGebraTube
• User Forum

How GeoGebra Supports and Supplements PBL/PrBL

GeoGebra is to analytic Geometry what Geometer's Sketchpad seems to be to synthetic Geometry. GeoGebra focuses on the analytical approach, meaning that it uses coordinates to define geometric figures, and the Automating affordance it allows in the classroom is bar-none, in my opinion. Students using GeoGebra independently or applets from GeoGebraTube are able to manipulate geometric figures and can watch as their manipulations alter the numerical mathematics involved in each figures. This freeing-up of calculations enables the students to more critically analyze the mathematics at work behind the scenes to develop a deeper conceptual understanding of the mathematics. GeoGebra and GeoGebraTube are particularly useful in this way to support PrBL as they provide students a means to create and analyze geometric figures from an analytical perspective. 

General Tech Tool: ALEKS

Assessment and LEarning in Knowledge Spaces, better known as ALEKS, is a tool I am quite familiar with using, as we have been using it to support our math curriculum for the last three years. ALEKS has been used by our teachers and students as an independent curriculum and as a supplement to blended classrooms.

Overview

Name of Tech Tool: ALEKS

Brief Description of Tech Tool: From their website: Assessment and LEarning in Knowledge Spaces is a Web-based, artificially intelligent assessment and learning system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't know in a course. ALEKS then instructs the student on the topics she is most ready to learn. As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained. ALEKS courses are very complete in their topic coverage and ALEKS avoids multiple-choice questions. A student who shows a high level of mastery of an ALEKS course will be successful in the actual course she is taking.

ALEKS also provides the advantages of one-on-one instruction, 24/7, from virtually any Web-based computer for a fraction of the cost of a human tutor.

Technical Costs & Considerations: ALEKS is a subscription based service with a variety of subscription options, each with their own price point: Ordering and Subscriptions. Some courses require Java, while others are accessible to a wide range of operating systems including iPads

Additional Information

ALEKS can be used as a standalone curriculum or in conjunction with your own curriculum. ALEKS has been successful in K-12 and in Higher Ed scenarios, as well as homeschool use. Teachers can align ALEKS use to their current textbooks and curriculum along with the CCSSM and set specific learning goals for the student. Teachers can also create their own quizzes with specific topics, or select assessments that cover recently completed material or the whole course.

Students do well working around their pie like a clock and working from top-to-bottom within each pie slice. As we all know, mathematics tends to build on itself and while students may be successful jumping from one slice to the next, they will likely reach a point where they can no longer access certain pie pieces because they do not have the prerequisite knowledge to continue on.

ALEKS provides open ended questions that require students to work on developing their skills, instead of simply guessing and checking with multiple choice questions. Students can use the "Explain" feature (which is customizable by teachers) to walk through the steps of each problem.

Helpful Links from ALEKS:

• Course Products
• User Guides
• Teacher Resources
• Standards Alignment
• TextBook Integration

How ALEKS Supports and Supplements PBL/PrBL

ALEKS is another great tool to support a blended-PBL mathematics classroom. I use this tool as my procedural practice for my students, and I supplement that procedural practice with both PrBL and PBL in the classroom. I find that my students are able to easily use the system and enjoy working at their own pace. ALEKS provides the procedural practice and ACT prep that I would otherwise have a difficult time implementing in a PBL classroom. While there are no multiple choice questions, students are getting exposure to story problems and procedural practice problems similar to those that they see on high-stakes testing, which alleviates some of the trepidations teachers have when moving to a PBL/PrBL modeled mathematics classroom.

General Tech Tool: Khan Academy

Khan Academy is something that I couldn't live without as a PBL educator. In a PBL math classroom, we are often torn between digger deeper conceptually with the mathematics in the project and needing to make sure our students have procedural fluency. Khan Academy provides me with just what I need to help my students get the best of both worlds.

Overview

Name of Tech Tool: Khan Academy

Brief Description of Tech Tool: Khan Academy is an online resource that has instructional and educational videos on a wide variety of topics, form micro-economics to astrophysics, cryptology and beyond. Khan Academy is most frequently associated with mathematics learning as it provides not only video instruction assistance, but procedural practice in a wide array of skills from middle elementary through trigonometry and beyond.

Technical Costs & Considerations: Users will need access to technology and the internet to access the site. If using it with students, it is a good idea to have students signed up with their individual emails. This is particularly easy if your school uses Google emails. Students will also need access to YouTube since videos are streamed through that service.

Additional Information

Khan Academy users are able to track their individual progress, "level-up" their mastery and earn badges of accomplishment throughout their learning endeavors. Teachers, parents and coaches can track this progress on the back-end and assign specific topics and videos to their students to master.

You can create your own classes in Khan Academy and track any number of students assigned to various learning plans. You can even customize what your students are working on and set dates for when it should be completed as means of differentiation and extension. Then view their stats to see how many attempts they made and adjust your assignments from there. Statistics show student mastery level in addition to this other information, helping you to see how well your student has mastered the procedures.

Helpful Links from Khan Academy:

• Coach and Classroom Resources
• Planning with Khan Academy
• Data, Grading and Accountability
• Blended Learning
• School Pilots

How Khan Academy Supports and Supplements PBL/PrBL

Khan Academy is an awesome supplement to a blended-PBL classroom of any kind, but I particularly appreciate it for mathematics. When working on projects, I can direct my students to specific videos that will help them to learn and practice the procedures they need in order to best utilize the concepts they are developing throughout the project. I can also create customized playlists for each student that includes just what that individual student needs to cover and nothing they don't. 

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.

Project-Based Learning Math Resource: CurrikiGeometry

Curriki is an online host to free teaching and learning resources for educators everywhere. From lesson plans, to units, to entire curriculums, Curriki has something for everyone. For the Project-Based Learning math teacher, one resource available is a gold-mine: Curriki Geometry. Curriki Geometery is Curriki's own CCSS aligned Project-Based Learning math course designed around the principles of PBL. The site has both student and teacher access to it and contains 6 projects that can be used in any manner you choose.

Things I Love about CurrikiGeometry:

• The Comprehensive package of each project.
• Including lesson plans, pacing and differentiation ideas
• A list of websites and resources to use alongside the projects or as-is
• The materials available to help run a successful Project-Based Learning classroom
• The inclusion of technology tools
• Linking to other websites for engaging activities to support the projects

For those of you who may be just starting out or wanting to get your feet wet, taking an entire project may be beneficial to see how Project-Based Learning can work in your school. I always like to have a autonomy and ownership over my projects, so I don't love taking things wholesale, but if someone has a good idea, I'm always willing to tweak it and make it my own!

Project-Based Math Resource: RealWorldMath

RealWorldMath is a website that can be used by students and teachers alike to find real world math applicable projects and lessons designed to show the usefulness of knowing the material. I typically view this website for teachers and have enjoyed looking at their various lesson resources, from Concept Lessons to help my students develop conceptual understanding about various subjects, to Exploratory Lessons designed to show off some of the more interesting and less frequently discussed topics, there is something there for every teacher.

RealWorldMath

Things I LOVE about RealWorldMath:

• The emphasis on developing concepts with the conceptual lessons. These can be forgotten in a Project-Based environment, but are so essential to a PBL math success.
• The tutorials on how to use the technology associated with their lessons and projects
• The lesson outlines available to teachers
• Make sure you sign up for a password to access! It's free, so no worries!
• The blog that you can follow to stay up to date on interesting math connections going on currently in our real world!

Project-Based Math Resource: High Tech High

As I've mentioned in another post, High Tech High is a big inspiration for me. A few of my colleagues had the opportunity to visit High Tech High earlier this year and came back with nothing but raving reviews. So, we've been busy looking at our curriculum and theirs and seeing the strength and weaknesses of of our program and seeing what components we like best about theirs. One piece that we were really interested in learning about was the way they do mathematics. Many PBL schools have told us that while you can do some math via Project-Based Learning, you can't do all of it, so get an online system. High Tech High's math program seems to agree with this statement, as teachers on an individual basis choose online systems to support their learning. However, HTH has made some amazing math projects for the math that they can include.

Things I LOVE about HTH Math:

• Their planning expertise and willingness to share: Unit Planning Guide &Project Planning 101
• Their range of coverage: 6th-12th grade mathematics!
• The thoroughness of their planning
• Alignment with CCSS Math Practices and Standards (Grade 6 Example)
• Started/Complete Unit Planning ideas for each grade level following their proposed Integrated Sequences
• Their Transparency in their alignment to help you better understand their units
• Standards Alignment 10th grade
• The Projects that are linked in their units: great as is or as a jumping off point for your own project design!

Designing a Blended Classroom

Today has been all about taking a break from trying to plan content and curriculum, and instead focusing on and planning out the other major aspects of my class: my classroom setup, and my class structure.

My Classroom Setup

This year, I will be teaching 2 of my 4 classes (and 2 of my 3 geometry courses) in a computer lab, that is shaped like a W. This location has it's benefits in blended learning, for sure, but it also has it's drawbacks to mathematical learning.

From the blended learning standpoint, I couldn't be happier to have access to high quality performance computers-- 20 inch iMacs. My students will be able to access their ALEKS content with little trouble, use the computers for any Geogebra, or other similar product, activity, and view any of the instructional videos with ease.

From the problem-solving mathematics teacher standpoint, I will miss students having work space to use manipulatives, as well as grouped desks to promote group activity and collaboration. The communication factor between students will be decreased with the students facing the perimeter of the classroom.

My Class Structure

As I have been thinking and planning today, I see my class being structure more of as a blended class environment than a flipped class environment. I'm not entirely sure how I feel about that, as I truly want to give flipped instruction a chance. My thought is that I will get some of the general logistics of my blended class planned out now, re-read some of the books and blogs that inspired me to try Flipping and then rework my thoughts and plans.

For now, I've got my neon Sharpies working over-time as the jumbled thoughts in my head are starting to sort themselves out.

Class is broken down into thematic units, and inside of those units students will be addressing Essential Questions. The structure of my class will help me to assess my students' true mastery of the competencies and Essential Questions.

As part of my class structure, students will be required to:

• Collaborate with others
• Demonstrate understanding through Parallel Tasks & Open questions
• Complete weekly project or problem challenges 
• Complete Super-Item assessments
• Keep a Mathematics Binder
• Notes & Quizzes
• Group Work
• Project Work
• Parallel Tasks & Open Questions
• Super-Items
• Portflio of Best Works
• Students will flag or transfer their best works from the unit to the Portfolio section, which I will assess using the competency grading scales to help determine a student's mastery level.

Now that I've got that figured out, I'm going to let my brain soak up the awesomeness, and then get back to planning out the first unit... Parallel tasks, videos, collaborative work, and super-items in all.

Wish me luck!