Hypotheses Testing in Project and Inquiry Based Instruction

The Constructivist theory believes that knowledge is constructed in the mind of the learner. A natural extension of this theory is the Constructionist theory which believes learning occurs in the mind as a student builds an artifact. Both of these theories share qualities. In the learning environment, the teacher is a facilitator while the learner is expected to investigate, create, collaborate and use multiple strategies to arrive at a conclusion. The project/artifact should be a genuine, authentic task which will be shared and which will be graded on a rubric. In the student project, there are three phases: the planning stage, the implementing stage and the processing stage. (Orey, 2001)

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

Concept Maps

This concept map was designed at www.bubbl.us to be used with a Virtual Field trip at
http://www.thetech.org/exhibits/online/robotics/



Great new video at The Futures' Channel

Cognitivism In Practice with Technology

The cognitive learning theory states that learning is the ability to store facts, processes and episodes in long term memory and to be able to retrieve them through a complex network based on connections to other ideas. Michael Orey describes a three stage processing model for information processing: Sensory Input, Short Term Memory and Elaboration or Rehearsal for Long Term Memory (Orey, 2009).

Teachers should utilize technology as an instructional strategy to complement all stages of the learning process. Four of the eight multiple intelligences described by Howard Gardner (Orey, 2001) identify a sense as a way human beings process information: verbal/linguistic, visual/spatial, bodily/kinesthetic and musically. The cognitive theory works best when two of the senses are used together a process called the dual-coding hypothesis. This way, the brain will code the information through two pathways in the brain. The use of informational images with a fact in a Powerpoint presentation can create an associative connection. For example showing a skier on a steep mountain will help students understand the concept of slope on the Cartesian graph. Computer simulations are also a powerful tool to visually see how changes is the numerical value of the slope could change a steep black diamond run to a flat cross country ski experience.

A learner can only process 5 to 9 pieces of information at a time in short term memory. To organize these facts or processes, the data needs to be arranged to make connections between them. A word processor, such as Microsoft Word can be used in note taking by using bulleted lists, tables or the AutoSummarize feature. If a student needs to revise their work, there is also the Tool – Track Changes feature. The use of two column notes or templates will also tie in the dual-processing hypothesis. New research by Novak’s research program at Cornell has discovered that a concept map imitates the storage process of our own human brain (Novak & Cañas, 2008). Teachers can use concept maps to plan their units or students can construct their own at places such as My Webspiration or Spinscape. There are also many types of advanced and/or graphic organizers which serve to enhance a “students' ability to retrieve, use, and organize information about a topic.” (Hansen, 2009). Templates are available on the internet.

Technology is also a valuable tool in the elaboration process of transferring information to long term memory. The learner can create episodes through Virtual Field trips, podcasts, teleconferences or experiential learning activities such as internships, co-ops, service learning or role playing scenarios. (Orey, 2001).

For teachers to effectively incorporate technology in their instruction, they should plan activities so students are learning WITH multimedia, not from it!


Hansen, Kevin. (2009). Technology that Works. Retrieved November 15,2009 from
http://technologythatworks.wikispaces.com/Cues%2C+Questions+%26+Advance+Organizers

Novak, J. D. & Cañas, A. J. (2008). The theory underlying concept maps and how to construct and use them, Technical Report IHMC CmapTools 2006-01 Rev 01-2008. Retrieved November 15, 2009 from the Institute for Human and Machine Cognition Web site: http://cmap.ihmc.us/Publications/ResearchPapers/TheoryUnderlyingConceptMaps.pdf

Orey, Michael. (2009, March). Cognitive Learning Theories. Bridging Learning Theory, Instruction, and Technology. Laureate Education Inc. Baltimore, MD.

Orey, M.(Ed.). (2001). Experientaial Learning. Retrieved November 15, 2009, from http://projects.coe.uga.edu/epltt/
Orey, M.(Ed.). (2001). Multiple Intelligences and Learning Styles. Retrieved November 11, 2009, from http://projects.coe.uga.edu/epltt/

Using Behaviorism for Improving Effort

I teach freshman in an Introduction to Algebra course. In the transition from middle school to high school the expectations increase. Students are expected to take more responsibility for their learning and behaviors. The book Using Technology with Classroom Instruction that Works highlights two of McREL’s classroom recommendations for teachers:

1) “Explicitly teach students about the importance of effort”
2) “Have students keep track of their efforts and achievements”. (Pitler et at..,2007)

To put this into practice with the Behaviorist Theory, the teacher must define for the student the behaviors expected. By starting with an Effort Rubric, students can self-assess where their behaviors fall in terms of Class Notes, Attention, Participation, Homework and Studying. To continue to reinforce the importance of these behaviors, student could track their progress in a spreadsheet, easily converted to a visual graph.

If the desired behaviors are seen, the teacher can offer a positive reinforcement. While developing these skills, positive reinforcement will also be reward by increased grades. They will also see their peers modeling positive behaviors. Students will then begin to internalize the correlation between effort and achievement, and mature into productive, successful high school students.

Hansen, Kevin. (2009). Technology that Works. Retrieved November 11, 2009 from
http://technologythatworks.wikispaces.com/Reinforcing+Effort .

Pitler et at..(2007). Using Technology with Classroom Instruction that Works. Mid-continent Research for Education and Learning (McREL).

Forms of Data Represenations

NCTM Data Representation:
Last spring, I attended a lecture in Washington DC given by Jim Rubillo; a former President of the National Council Teachers of Mathematics. One of his topics was multiple representations of data:

Bridging Learning Theory, Instruction, and Technology

This week I will begin a new course at Walden University called Bridging Learning Theory, Instruction, and Technology. I learned so much in my last technology based class and feel I have successfully transferred that knowledge directly into the classroom. Over the summer, I taught members of my department about wikis and convinced them to start a department wiki at

www.hurricanemath.wikispaces.com

The students are able to support each other and collaborate using a technology they love. It has been a huge success - even the local paper wrote an article about it!