Schottenbauer Publishing

Schottenbauer Publishing
Showing posts with label education. Show all posts
Showing posts with label education. Show all posts

Saturday, April 30, 2016

Comparing Harmonic Oscillation and Rotation

Graphs of harmonic oscillation and rotation appear very similar when charted on graphs. Harmonic oscillation consists of a mass which moves back and forth in repetitive motion on one axis. Rotation consists of a mass in circular motion around a central point. On a graph, the mass appears to be moving back and forth in repetitive motion on each of two axes.

 Consider the following graphs, excerpted from books by Schottenbauer Publishing.





Discussion Questions
  1. Which graphs show harmonic oscillation? 
  2. Which graphs show circular motion?
  3. Describe the relationship between x and y components in circular motion.
  4. Using these graphs, describe at least one similarity between harmonic oscillation and rotation.
  5. Using these graphs, describe at least one difference between harmonic oscillation and rotation.

Over 8,000 graphs from Schottenbauer Publishing provide real-life topics for student learning, including sports, transportation, construction, environment, music, entertainment/toys, and general physics. 
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Friday, March 11, 2016

Graphs Memorabilia

Celebrate graphs with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. A direct link is included below:

A variety of other STEM education collections are also available from Schottenbauer Publishing on Zazzle, which features regular sales on most items.  
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Monday, October 5, 2015

The Origin of Graphs

What is the meaning of the term "origin"? 

 According to Dictionary.Reference.com, there are up to eight meanings, two of which are mathematical. The first of these is commonly found in elementary and post-secondary graph-reading skills, while the second (not included here) pertains to more advanced math. 

 To answer the above question using the common math definition: Every graph in a Cartesian coordinate system has an origin, which is defined as the intersection of the axes. 

 Placement of the origin can dramatically affect the presentation of the graph. Consider the following two graphs, which present the same data, but with different origins.


Discussion Questions
  1. For each graph, identify the following coordinates: (a) Initial Position, (b) Final Position, (c) Minimum Position, and (d) Maximum Position. 
  2. What is the relevance of the origin in each graph (if any)?
  3. Which graph is more useful for visual analysis?
  4. Do any additional differences exist between the graphs? If so, what difference(s) exist?
  5. Do the graphs contain any distortion of data, due to method of collection? If so, what is the distortion? How might the distortion be corrected?

Now, consider a different meaning of "origin." This definition is not mathematical; rather, it refers to "the first stage of existence," or the creation of an entity.

Using this definition, what are the origins of the over 8,000 graphs of sports, transportation, construction, environment, music, entertainment/toys, and general physics from Schottenbauer Publishing? 

Created by M. Schottenbauer, Ph.D. in laboratory settings, these graphs represent several years of intermittent data collection and graphing activity. The objects studied in the graphs consist of the properties and motion of toys, hobby equipment, household objects, musical instruments, and sports equipment, measured and manipulated by the author. All music and sports activities were conducted by the author, including performance samples on 33 musical instruments and exercises from over 30 sports. Videos of some of these activities are available on YouTube.
Blogs with Free Graphs
  • Sport Science


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          Wednesday, September 9, 2015

          The World in a Graph

          What is more entertaining than learning science and math from the real world? Combining STEM education with fun, The World in a Graph by M. Schottenbauer, Ph.D., is a curiosity piece for educators and students alike. This concise anthology of 28 graphs presents a spectrum of interesting topics from sports, transportation, construction, environment, music, and entertainment. Graph topics, in the same order presented in the book, include:

          • Sports
            • Baseball 
            • Tennis
            • Ice Hockey
            • Snow Skiing
            • Running
            • Walking
            • Biking
            • Weightlifting
            • Gymnastics
            • Track & Field
            • Figure Skating
            • Ballet
          • Transportation
            • Wheels
            • Cars
            • Planes
            • Trains
            • Boats
          • Construction
            • Material Strength Testing
            • Electricity
            • Indoor Lighting
          • Environment
            • Natural Light
            • Natural Water
            • Wind
          • Music
            • Vibration
            • Sound Waves
          • Entertainment
            • A Moving Block
            • A Falling Domino
            • A Rolling Marble

          These topics provide a rich selection of concepts from physical science and physics education, including:


          • General Mechanics 
            • Force 
            • Friction 
            • Material Strength 
            • Collisions 
            • Energy 
            • Momentum 
            • Free-Fall 
            • Projectile Motion 
            • Motion on a Plane 
            • Motion on an Inclined Plane 
            • Rotational Motion 
            • Harmonic Oscillation 
          • Electromagnetism 
            • Electric Potential 
            • Current 
            • Power 
            • Light 
          • Acoustics 
            • Vibration 
            • Sound Waves 
          • Biophysics 
            • Electromyogram (EMG) 
            • Range of Motion or Joint Angles (Goniometer)


           These topics provide a variety of important concepts from math, including the following types of mathematical functions:

          • Math Topics
            • Straight Line
            • Curve
            • Parabola
            • Exponential Function
            • Sinusoidal Function
            • Integral
            • Derivative
            • Damping Function
            • Random Error

           The World in a Graph by M. Schottenbauer, Ph.D. is available from multiple internet retailers, in paperback and Kindle digital editions, as well as wholesale.
          Schottenbauer Publishing offers a wide selection of books, featuring over 8.000 graphs from sports, transportation, construction, environment, music, entertainment, and general physics. Additional information is available on the blog Science and Math Education.
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          Thursday, July 30, 2015

          Graph Lines Up & Down: The Meaning of Change

          Line graphs go up and down. What is the meaning of change? Consider the following three graphs, excerpted from Volumes 1 & 2 of The Science of Home Construction from Schottenbauer Publsihing:




          Discussion Questions
          1. What does the horizontal straight line represent?
          2. Why does the force line go down, and not up?
          3. What does the gradual, curved slope represent?
          4. What does the vertical straight line represent?
          5. What is the maximum force leading to breakage?
          6. Over what time is the force applied?



          Discussion Questions
          1. What does the horizontal straight line represent?
          2. Why do the power and current increase?
          3. What does the first bump represent?
          4. What do the final 2 bumps represent?
          5. Does it take more or less power to remove the screw? Why?
          6. Why is the power to remove the screw not negative?
          7. What is the maximum real power? 
          8. What is the maximum apparent power? 
          9. What is the maximum current?





          Discussion Questions
          1. What physical action is required to make this particular graph? 
          2. What do the three lines represent? 
          3. Why does the angle increase during each rotation event? 
          4. Why does the velocity go down and up during each rotation event? 
          5. Why does the acceleration go down, up, and then down during each rotation event?
          6. How many times is the screwdriver turned?
          7. How many angles is the screwdriver turned each time? Make a list containing the value for each event.
          8. What is the average angle turned by the screwdriver?
          9. What is the total angle turned by the screwdriver?
          10. Over what period of time is the screwdriver turned during each rotation event? Make a list containing the value for each event.
          11. What is the average length of time for a turn of the screwdriver?
          12. What are the minimum and maximum angular velocity values?
          13. What are the minimum and maximum angular acceleration values?

          Over 8,000 graphs from Schottenbauer Publishing provide real-life topics for student learning, including sports, transportation, construction, environment, music, entertainment/toys, and general physics. 


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          Monday, July 27, 2015

          Physics Theory vs. Physical Reality

          The theories of physics consist of neat, clean, mathematical formulas, derived from laboratory conditions. Although these formulas apply to all real life, the data collected from the real world demonstrates much more complexity, resulting in messy graphs.

           Consider the following two neat, simple graphs, taken from simple laboratory experiments:


          Discussion Questions for Each Graph
          1. Describe the graph in words. 
          2. What phenomena is demonstrated? 
          3. What physics theory or theories apply? 
          4. Is the graph consistent with theory?

           Now, consider the two graphs below. These graphs show real-life conditions which are mathematically messy.



           Discussion Questions for Each Graph
          1. Describe the graph in words. 
          2. What phenomena is demonstrated? 
          3. Why is the graph messy? 
          4. How can the graph be analyzed with theories from physics and/or math?

          In elementary and high school classes, emphasis is often on the clean, neat graphs which perfectly illustrate theory. Including messy graphs from real-life conditions can provide a segue into the advanced physics and mathematics topics which are required for working in Science, Technology, Engineering, and Mathematics (STEM) fields as a career scientist.

           Over 8,000 graphs from Schottenbauer Publishing provide real-life topics for student learning, including sports, transportation, construction, environment, music, entertainment/toys, and general physics. 


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          Saturday, July 18, 2015

          Considering Sources of Error in Graphs

          The topic of error is essential when teaching graphs. Error describes inaccurate data, resulting in a graph which does not match the real-life phenomena it intends to measure. Error may occur at one or more points on the graph, which may be found in one or more segments of the graph.

          Graphing errors may occur when the measurement device is not accurate, or when data is not properly recorded. Not all errors may be what they seem, however. Sometimes graphs accurately portray an inaccurate performance. Is it possible to determine the source(s) of error from a graph alone? 

          Consider the following two graphs, excerpted from the book series The Science of Home Construction from Schottenbauer Publishing:






          Discussion Questions
          1. Does either graph contain error? Why or why not?
          2. Does either graph show error due to the measurement device? Why or why not?
          3. In either graph, does the real phenomena provide an unexpected contour? Why or why not?
          4. For either graph, would changing the perspective increase/decrease the apparent error? Why or why not?
          5. Redraw these two graphs, eliminating the likely error(s).

          Schottenbauer Publishing offers over 100 books with graphs of popular topics, including sports, transportation, construction, environment, music, entertainment/toys, and physics. Free samples from these books are featured in the following free blogs, which contain graphs, videos, and discussion questions:


          Blogs with Free Graphs
          • Sport Science


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                  Wednesday, April 8, 2015

                  Application of Graphs in Education

                  Graphs are useful tools for education. Relevant in almost any class in elementary or secondary school, graphs can be incorporated into math, science, language arts, physical education, art, and music. How can graphs be used to enhance traditional education, through examples and projects? This blog is dedicated to the use of graphs in class, as a stimulus for interdisciplinary learning in both mathematical/scientific and language arts.



                  Where Can I Find Graphs for Education?

                  Over 8,000 graphs are available from Schottenbauer Publishing, collected into exciting topics in sports, transportation, construction, environment, music, entertainment, and general physics. Multi-volume series within these areas contain graphs centered on various themes, while anthologies of 28 graphs provide a variety of mathematical functions related to specific topics. Educators in schools and homeschool, who lack time and/or budget for making extensive graphs, may find these useful reference tools for multiple projects across different classes. 

                   Books are available from CreateSpace wholesale, as well as Amazon, Barnes & Noble, Books-a-Million, and other internet retailers!

                  Schottenbauer Publishing also offers free blogs on specific topics, featuring graphs, discussion questions, and videos. Topics include:
                  Blogs with Free Graphs
                  • Sport Science


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