Why Bother Taking the Time to Go Hands-On?
Dr. Ben Mardell, Phd with the Project Zero at Harvard University has said, "kids learn through all their senses and they like to touch and manipulate things." Basically, hands-on activities activate more regions of students' brains.
It’s actually pretty simple. As Judy Dodge author of 25 Quick Formative Assessments for a Differentiated Classroom states "The more parts of your brain you use, the more likely you are to retain information, if you're only listening, you're only activating one part of the brain," she says, "but if you're drawing and explaining to a peer, then you're making connections in the brain." That’s why things like doodle notes and hands on activities are so important. Activities like these are easy to implement and immensely beneficial to the students. 1. Cut & Paste
It can sometimes sound rudimentary, but a simple cut and paste activity is a tried and true method of learning. Kinesthetic learning is a great way to engage your students. Have your students cut up diagrams or models from worksheets or even a photocopy of textbook samples.
Then have your students arrange them on paper and scotch tape them down to create the original, then re-number and write/tweak the actual question (save time drawing the diagram or model yourself). Here is a great example of a hands-on pythagorean classroom activity from Kyle Krafka. 2. Folding
Another great illustration of the Pythagorean theorem is through paper folding. By folding a plain sheet of paper your students get a first hand look on exactly how this theorem is applied. This one moves fast, but is really spiffy!
This origami-style activity will help your students see and remember how the theorem actually applies. The great part is that it is a general proof that works for different right triangles, and you can actually fold further to get different versions. 3. Project: Create a 3-d Model
Have your students team up in pairs and create and actual 3D model of the theorem. They can use small balls, blocks, jelly beans, water, or even wadded up balls of paper to show how the side lengths work out. Here is an example that a few students came up with in their own math project.
4. Concept-Based Doodle Notes
This set of doodle notes is a great way for students to record and reference the basics of the Pythagorean Theorem. Visual note-taking is a strategy that is as hands-on as notes can get, and has been proven to boost focus, learning, and long-term retention.
Teaching fundamentals is extremely important. However, what you really your students to retain is the real meaning of it all.
Taking concepts such as the Pythagorean Theorem out of the text (beyond just memorizing a formula) and into our hands is a wonderful way learn. Do you have any tips or tricks you use in your classroom? Let us know what you do in the comments below! Enter your email address to get future articles, free lessons, updates, and more math education ideas: To Read Next:
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2/23/2017 3 Comments KEY SKILL: Teaching Students to Test Cases And Use Examples & Counterexamples in Math Class
The easiest and most concrete way I've found to do this is through "always, sometimes, never" questioning.
Kids cannot think through these types of questions without mentally testing cases. And if you go a step beyond to have them support their answers, they will be forced to justify by using both examples and counterexamples. BONUS: This type of question almost ALWAYS inspires some solid "math talk," so make sure to let your classes work in pairs or showcase their reasoning at the board to get that conversation going. Here are some examples to try to incorporate: Testing Cases in Algebra:
Often, students may think they know the answer and then in testing, they'll come across a different situation that violates the "rules" they were imagining originally.
Make sure to have them try every case they can think of that fits the "premise" criteria and then see if they can reach a conclusion about whether each statement is always true, sometimes true, or never true.
Samples with Quadratics: Always true, sometimes true, or never true??
Pre-Algebra Examples:
Have kids try these samples, and be sure that they support their claims by providing both examples and counterexamples.
See if they can develop some systems to organize their work and be sure that they have tested every possible case.
Samples with Integers: Always, sometimes, or never true??
Students will need to test in different orders and justify their answers by showing each case and whether it turned out to be a true or false statement.
Geometry Challenges:
These ones work well at the board, because students can watch one another draw the figures and see which cases work out.
If you have access to geometry software like GeoGebra, you can use that as well. Have students draw each triangle and see if they can drag a vertex to meet the criteria.
Samples with Triangles: Always, sometimes, or never true??
Best Ways to Try It:
All the sets I develop with this type of questioning include 36 statements to classify.
My favorite 2 ways for students to work through these types of questions are in partners in a worksheet, or as teams with a sorting activity with a notebook on the side. PARTNER WORKSHEET: I lay the statements out in a grid so that when they color each statement that is NEVER true RED, each statement that is ALWAYS true BLUE, and each statement that is SOMETIMES true PURPLE, it creates a pattern that I can check really easily in just 2 seconds. This makes it really easy to check it over as I walk around and just point to ones that I can see are incorrect. They go back to the drawing board on those statements and continue their (sometimes heated) discussions!
SORTING ACTIVITY:
I cut the statements (larger print version) into cards and have small teams or pairs of students sort them into categories based on whether they are always, sometimes, or never true. Be sure that they have notebooks available, because at any moment they may be required to provide examples to support their answers. You can also hand out the cards and have students come up to the front in a whole-class setting to tackle challenging ones. These are pretty versatile. It's nice to hear a student model an explanation and show the class how they tested different cases to reach a conclusion. Get Pre-Made Sets
Each time I develop a set, I pull together my worksheet version and my sorting version so both are included.
Browse the sets that will work well for your classroom and get your kids thinking critically! Pre-Algebra: Algebra: Geometry: Get Inspired:To Read Next:
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: |
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