Complementing these strategies with Hypothesis testing and technology will greatly enhance student understanding. The web site, Instructional Strategies That Work, Marzano, Pickering and Pollock list six classroom strategies in which to apply hypothesis testing: System Analysis, Problem Solving, Historical Investigation, Invention, Experimental Inquiry and Decision Making.
In system analysis, problem solving and historical investigations, the students can investigate using computer simulations to test their hypothesis. In decision making, the students can track the outcomes of different decisions in a spreadsheet to organize the results. In mathematics, experimental inquiry can be used to model and understand a natural phenomenon, such as gravity and its effect in sports.
Next week my Advanced Algebra 2 class will begin studying quadratic functions and their graphs: parabolas. There are many skills involved: finding the vertex using the formula x=-b/2a, finding x-intercepts by factoring, completing the square and using the quadratic formula. This will require some traditional instruction. To see parabolas come to life, I will incorporate both experimental inquiry based instruction and project based instruction.
We will begin our Balls of Fun study, with a project based activity: Parabolas in Flight. The artifact the students will create will be a video of a ball’s trajectory. In the planning stage, the students learn the trajectory formula and watch a demonstration video I upload to teacher tube (http://www.teachertube.com/viewVideo.php?video_id=146265&title=Parabolas_in_Flight&ref=nancykent) In the implementation stage, they will collaboratively make a video of a football pass, basketball shot, golf shot or soccer ball kick. Then using Windows Movie Maker, will investigate the trajectory formula for that specific event. While in the computer lab, they will use an online simulation of a cannon to investigate any additional factors that may affect their calculations. In the processing stage, they will share their video and if given parent permission upload it to teacher tube and link it to our wiki. They will receive immediate feedback from the class presentation and additional feedback from family and friends if they upload to Teacher tube. I am hoping this will take the formulas out of the textbook and bring them to life!
Our next activity will be inquiry based. In the planning stage, the students will learn quadratic regression on the graphing calculator and fill in a template (available at Instructional Strategies That Work - Experimental Inquiry Hypothesis Framework), with a hypothesis explaining the parabolas involved in a bouncing ball. Is each subsequent bounce related to the one before? Does each ball type have its own bounce back rate?
http://hypertextbook.com/facts/2006/restitution.shtml
Image by MichaelMaggs with a Creative Commons Attribution Sharelinke 3.0 License from http://commons.wikimedia.org/wiki/File:Bouncing_ball_strobe_edit.jpg
In the implementing stage, they will use a graphing calculator motion sensor to capture data on the each parabola bounce and compare vertexes, looking for a pattern. As they share they will verify their results with others.
Both of these activities will allow students to construct knowledge in their mind about parabolas and their qualities. The second will allow them to develop a hypothesis and test it. I want to continually align my practice with technology and help instill as many 21st Century skills as I can in my students.
Marzano, Pickering and Pollock. (2009). Instructional Strategies That Work. Retrieved November 24, 2009 from http://allenswanson.org/marzano/Generating_and_Testing_Hypotheses.htm
Orey, M.(Ed.). (2001). Emerging perspectives on learning, teaching, and technology: Constructionism, Learning by Design, and Project Based Learning. Retreived November 24, 2009 from http://projects.coe.uga.edu/epltt/index.php?title=Constructionism%2C_Learning_by_Design%2C_and_Project_Based_Learning
Posts
Nancy,
ReplyDeleteYou really do a nice job of linking theory to practice in your very clear explanation of what sounds like an enjoyable and effective lesson. The example used to illustrate "Parabolas in Flight" is well chosen to appeal to students' experience and interests and the video at TeacherTube is great. Putting the real-world application first gives the students purpose while they are learning the mathematics.
By the way, your link took me to the TeacherTube log-in, but I went in as a guest at http://www.teachertube.com/viewVideo.php?video_id=146265&title=Parabolas_in_Flight&vpkey= .
I'm sending the link of this post to my friends in the math and science departments. Thanks.
-Dug
Hi Nancy,
ReplyDeleteI am quite impressed with the lessons you are taking time to teach your Advanced Algebra 2 class. Actually, I should say that you are not only teaching these students, but acting as a facilitator and providing them with rich and meaningful experiences as a result of implementing the experimental inquiry-based instruction and project-based instruction with today‘s engaging computer technology. If I had had this type of instruction when I took Algebra 2 or math in general, I might have more of an understanding of it by and large, as well as understand how it can be applied to the real-world. I also might not be so intimidated by it!
Due to the time you are taking to plan, develop and implement constructivist/constructionist learning theories, your students will be able to use the innovative computer technologies available to effectively collaborate with one another in the learning process and be beyond engaged.
Again, I am truly impressed!
~Megan
Nancy,
ReplyDeleteWow! You have developed a well-planned unit for your students to understand quadratic functions. I also will be sending your great ideas to the HS math teachers and other math colleagues I have. Your students are really going to have quadratics "come alive" for them as they create parabolic functions, then model them with the motion detectors. I am transitioning from writing rules for patterns to working with functions in algebra. You have motivated me to do similar activities for my students, especially using the CBR to model a function. Thanks, Nancy!
Jennifer
Thanks for all your kind words, I originally started with a lesson from the Texas Instruments Activity Exchange at
ReplyDeletehttp://education.ti.com/educationportal/activityexchange/BrowseBySubject.do?cid=US&brsOpenNode=bt0.o(20)
specifically the Ball Bounce one at:
http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=7650
I am still struggling with possiblity of error rate in the football throw, a small difference in time can make a big difference in height. I might have the students do a follow up writing assignment on that. Even so, I think it will be a valuable lesson.
Nancy,
ReplyDeleteI absolutely love that you are using real world ideas that the students will care about for them to learn the same thing. The idea of using sports gains the interest of the students who normally would pull the "who cares" attitude on you. Great ideas!
An idea for the error rate in the football throw lesson would be to incorporate the running of a receiver. The question could be posed as who error was it? The thrower or the receiver?
Brittany
BL
Oh, I love that idea - thanks! Someone has also suggested I look into a graphing program called LoggerPro, I am not familiar with it, but would love to add that to my lesson!
ReplyDelete