2/6/2017 9 Comments Discovery – Based Interactive Math Apps for Visualization & Inquiry (Grades 6-12)
Tech as a Tool for Exploration & Visualization
Although I just posted recently that I strongly believe that the classroom needs to be rooted in pen and paper, that does not mean that our students need to be stuck in an era before technology. There is nothing wrong with allowing eager learners the ability to take advantage of living in the 21st century. In fact, that is part of what education is all about. Improving ways to teach, learn, and grow is how we make the world a better place.
I think the most effective way to integrate technology in a math classroom in the 21st century is to use interactive apps that allow students to explore, investigate, manipulate, and visualize properties. Allowing children and young adults to explore math through virtual tools is amazing. They can discover new connections by engaging on new levels which will increase their academic success. Most of us grew up in classrooms with limited technology. Just a few decades ago there was typically only one computer lab for the whole school and we all took turns getting to experience the cutting edge technology of DOS, Windows and Macintosh. This was the birth of technology in the classroom; integrating virtual lessons to enhance our comprehension while having fun. And those were the days that were the best. When it was your classroom’s turn to play Number Munchers, you were having a great day at school. You could sharpen your basic math skills while playing video games, which was living and learning in the future to our parents. Not to mention a ton of fun for us kids. Tech for Hands-On Student Engagement
Adding excitement helps improve the ability to learn through increased engagement.
Our kids get the same thrill and benefit of having technology in their classrooms as well. Even though the technology has grown leaps and bounds since we were in grade school, the feeling is the same. We are instantly more enthusiastic when we are able to explore concepts through other platforms.
Top 7 Interactive Apps & Virtual Tools for an Inquiry Approach
1. GeoGebra - It’s no secret that I love GeoGebra. Their application of dynamic mathematics software is great for all levels of education. It brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package.
2. Ooops App - This “Order of Operations” activity is a fun way to practice the order of math equations and problem solving. This addictive game app sharpens math skills as well as cognitive development and critical thinking for any algebra students. 3. Hands-On Equations - Just like it sounds, this Hands-On app allows you to interact with algebra with games and lessons. Students will have fun with the experience of having success with sophisticated algebraic equations. 4. Attributes by Math Doodles - Discover the joy, wonder, and fun of mathematics through patterns and interactive puzzles while using different parts of your brain. The key to understanding math is understanding patterns. That’s why this app is perfect for exploring math. In a brain-based approach like my own favorite Math Doodle Notes, students get to creatively use both hemispheres of their brain while learning basic and complex concepts. 5. Algebra Touch - Students really get a hands on feel with this app. Using the touchscreen technology you can manipulate algebraic equations, such as isolating variable by dragging X’s and Y’s to either side of the equation. It’s a perfect all levels of algebra, from beginners to advanced. 6. Geometry Pad - For a more advanced geometry student, this app packs tons of benefits. Students and teachers can use it in class for a deeper understanding of geometric concepts. Easily create complex geometric sketches, measure everything you have in a document, and experiment with shapes and transformations. 7. PhET Interactive Simulations: Math - “Beautiful and responsive tools bring light to tricky math concepts.” This free app is great for students and teachers in beginner or advanced math subjects. It includes a draggable “Trig Tour,” an interactive “Function Builder,” curve fitting and graphing apps, and more!
Technology will never fully replace performing math by hand, yet it is a fantastic way to explore mathematical concepts. I hope some of these help build your students understanding of higher-level math concepts! Share your own favorites in the comments area below to help us discover more great apps!
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9 Comments
Pros & Cons
With everything in life, there should be balance and moderation. Long gone are the days of projectors and vis-a-vis pens. Students in this day and age relate to technology. It does play an important part in getting students excited about learning.
Yet, it has to have its place. It can’t be the central means of learning. I believe that we cannot just follow the one to one and iPad device trend we’ve been seeing in math. Overall, Google classrooms & digital practices are not better for math students. In fact, they can actually be seen as drawbacks in a math-specific classroom. Don’t get me wrong, technology is great, especially when it comes to applets that show mathematical concepts. I love to use hands-on software like GeoGebra, where students can drag vertices, see relationships, and make discoveries. Technology can be great for introducing or exploring big-picture concepts. Online models can also be helpful. They are far more convenient than distributing fraction pieces or algebra tiles, and can sometimes show ideas more clearly than the tangible models can. These apps can be extremely helpful for students but we need to be careful that we don't let them take over the classroom. They are not always beneficial, and can even be a hinderance in situations when we need students to get pencil-and paper notes, practice algebra work line by line, or work with diagrams. Blending the Two
The best model is to “blend” learning - combine tech with hands on or paper-based teaching.
Students will get the most out of a lesson if tech is used only when it enhances the lesson, not dominates it. Practicing concepts by hand on paper is irreplaceable in the math classroom. It’s not only a more effective means of showing the work, it is also more effective for student retention. The connections the brain makes when the hands are writing is stronger than it is with technology. Resisting the "Paperless" Trend
This can be seen in a study published in Psychological Science by Pam Mueller & Daniel Oppenheimer of Princeton University and UCLA. Several students wrote out their notes either by hand or on a laptop. The study found that the students that wrote their notes by hand actually learned more. Their memory was tested for factual detail, conceptual comprehension, and synthesizing capabilities.
While the students who used laptops ended up with more words from the lecture in their notes, their understanding of the concepts were weaker than the students that hand wrote their notes (source). And this study is actually a great illustration of Robert A. Bjork’s 20 year old concept, “desirable difficulty.” It simply states that sometimes, doing things the easy way actually hinders our ability to learn. Obstacles that frustrate us help us learn. While technology can make note taking and learning seem easier and more fun, it takes away the challenge and creativity. One of the main challenges in handwriting notes is discerning what information to take down. A method like visual note taking is another way to help students retain information. Students can feel empowered when taking down notes by hand, in charge of the information they are learning as well as how it is presented on their notes, taking them to another level of engagement in the lesson. Tech Devices Have Their Place...
It would be a disservice to our students to eliminate all technology from the classroom. After all, this is the 21st century. Having tech savvy skills is a necessity for success in the workforce. That’s why we do need to incorporate iPads, laptops, and apps. It is important that students understand the place technology has in the world.
And it is truly that simple, the technology in the classroom has its place. We cannot simply turn all classrooms into a high tech, digital world. Math assignments and notes have to continue to take place on paper. The convenience of Google Drive, typing and tablets are not meant to replace the traditional classroom, only enhance it. ...But Don't Ignore the Concerns
Remember that these “conveniences” are not always a benefit. They can actually become pretty inconvenient challenges. It takes forever for teens to type into a computerized equation editor. To try to work with exponents, fractions, and radicals on a computer screen wastes so much valuable class time or homework time. It takes away from the flow of the learning experience.
I also feel really sorry for students who are not even given textbooks anymore. Some schools expect them to only access their text online. This is a big challenge in math, where we use problems from the book. Kids are now restricted to places with internet access and can no longer do homework on the bus or while waiting for sports games. It's important to keep the focus on tech as an enhancement to a lesson, and not lose the benefits of hands-on activities and paper / pencil learning in math class. What are your feelings on technology in the classroom? Do you feel your students’ learning experience is being hindered or heightened by the increasing role the digital age plays in education? Share how you feel in the comments below, or give any tips you have to share if you have found that balance that blends digital and paper just right! To Read Next:
This in itself is enough to convince me to stick with the visual note-taking, but as I have been digging deeper into more and more research to explain the incredible boost in student learning after using the doodle note strategy, I've come across more and more reasons that are probably behind this success for the kids.
The psychological research I have been exploring lately is called "Dual Coding Theory." It originated with Paivio in the 70s, and explains how visual and linguistic information is processed in two different areas of the brain. In essence, as new input enters the brain, it's stored in short term memory in two distinct categories. Graphic information, images, and other sensory input are processed in the VISUAL center while auditory input, words, and text are processed in the LINGUISTIC center of the brain. This is a great way for our brain to take in both types of information, and the system works very well. However, in order to convert the new information into true learning, we need it to be saved and stored in long term memory. To do this, we need referential connections between the two zones. We have to CONNECT the information in the visual area with the information in the linguistic area.
When we are able to blend the text/auditory input together with the images, we boost the potential for retaining the information!
This means that not only are the individual words and ideas committed to long term memory more effectively, but the associations between them are retained as well. Our students can understand the big ideas and concepts AND remember the vocabulary and details more consistently. It's another huge reason that the student brain responds so well to a visual note-taking strategy!
A related theory, the "Picture Superiority Effect" is supported by studies that show that blending images with text offers a stronger learning experience than using text alone. It turns out that this boosts both the memory of the individual terms and ideas as well as the associations and connections between the concepts.
This is why we use certain visual brain triggers in addition to using text. For example, a stop sign has to instantly register an idea in our brains: STOP. So, in combination with the word (text input), we also always see the same shape (graphic input) as well as the color red (additional visual input). These blend together to send the right signal to our brains more effectively.
A good visual note-taking strategy incorporates what I like to call "visual memory triggers." These can be images that contain or represent an analogy that helps the student understand. They can also be graphics that blend text and pictures to stick in the students' brains.
These are the types of input that really last in a student's long-term memory. For example, students remember the term "surface area" being written in the handle and bristles of a paintbrush and remember that it represents covering the outside of a sharpe (like painting). Check out more samples of visual triggers that can be incorporated into doodle notes here. Doodle Note Basics: These are all incredible reasons to start incorporating doodle notes into your lessons! Here are the basics behind doodle notes:
More about the doodle note strategy: http://www.doodlenotes.org/ My video explaining Dual Coding Theory: http://www.tools4teachingteens.com/video-blog/dual-coding-theory-visual-note-taking Dual Coding Theory vs. "Learning Styles": (Guess which is valid and which may be a myth!) http://www.mathgiraffe.com/blog/the-surprising-truth-about-learning-styles Be sure to sign up for my email list for additional ideas, updates, and resources:
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