Week 11: Math/ Science Learning Activities
Part One: Simulations
The following observations were made about four different math simulations and interactive applets available online. I discuss my personal reaction, ease of use, appropriateness, educational value and applicability about each simulation.
Solving Right Triangles Online Manipulative
The National Library of Virtual Manipulatives offers numerous educational simulations that provide great insight for students when as teaching tool. This particular application is called the Right Triangle Solver and provides students with immediate feedback on vital practice skills. There is a separate applet for solving triangles with the Laws of Sine and Cosine available as well.
Translating and Scaling the Graph of Sine
This Gizmo would be perfect for teaching trigonometry students about the effects different values in the equation have on the graph of trigometric functions. There is a second activity available that shows additional trig functions and their graphs.
Personal Reaction: While this may look like a relatively simple simulation, the interactive nature and freedom to manipulate values is profound. Many students are visual learners and being able to see the direct correlation between changing values in the equation and the effect that they on the graph of that equation is priceless. When I first saw this display, I thought it was perfect this is for teaching this topic. I have taught this subject in the past by having student use their graphing calculator to make an educational inference on the relationship between equation and graph but this simulation sets up the equation and graph side by side so it is easier for students to process. In my opinion, using this gizmo in the classroom is the best way to teach students about translations and dilations of trigonometric functions.
Ease of Use: This Gizmo was extremely easy to use. Even though there are no clear instructions, its use is intuitive and I don't think the students will have any trouble figuring out how to manipulate the application. I love how the equation is shown, but I do think that it might be better if the numbers replaced the variables in the equation so that students could see that correlation as well.
Educational Value: This tool is perfect for teaching students how the graphs of trig functions are translated. In math, graphing can be a difficult concept for students to master, this visual simulation makes it easier for students to understand. Its very practical that students can switch between the sine and cosine functions as well as degree and radian measure. I also think the option to view any portion of the graph and the ability to see the amplitude and period calculations are extremely beneficial.
Age Appropriateness: This tool is very appropriate for high school level students. Students have the motor skills and cognitive ability to manipulate its use and apply their learning this Gizmo.
Applicability to Theme: This simulation is designed for Trigonometry students which is a High School math course that I teach. Therefore, this Gizmo applies to the theme of my final project and would certainly be used in a high school math classroom.
Ease of Use: This Gizmo was extremely easy to use. Even though there are no clear instructions, its use is intuitive and I don't think the students will have any trouble figuring out how to manipulate the application. I love how the equation is shown, but I do think that it might be better if the numbers replaced the variables in the equation so that students could see that correlation as well.
Educational Value: This tool is perfect for teaching students how the graphs of trig functions are translated. In math, graphing can be a difficult concept for students to master, this visual simulation makes it easier for students to understand. Its very practical that students can switch between the sine and cosine functions as well as degree and radian measure. I also think the option to view any portion of the graph and the ability to see the amplitude and period calculations are extremely beneficial.
Age Appropriateness: This tool is very appropriate for high school level students. Students have the motor skills and cognitive ability to manipulate its use and apply their learning this Gizmo.
Applicability to Theme: This simulation is designed for Trigonometry students which is a High School math course that I teach. Therefore, this Gizmo applies to the theme of my final project and would certainly be used in a high school math classroom.
Vector Addition Interactive Software
This applet is available on the PhET interactive simulations website and offers students a wonderful opportunity to develop a clear understanding of vectors, vector components and vector addition. The interface is easy to use and applicable to upper level high school math students.
Crash Scene Investigation Simulation
This is a detailed, realistic simulation that allows students to learn about the math and science that go into police work, specifically into a crash scene investigation. The entire simulation and materials are rather lengthy but it can be scaled back to meet the needs of a math or science course.
Personal Reaction: I was so impressed when I first found this simulation. I love how realistic it is and I think it offers a unique learning opportunity for students. Students are always asking the question, "When am I ever going to use this in real life?" This simulation helps answer that question and makes the math applications very real for students.
Ease of Use: The program is easy to navigate and does a good job of guiding students through the calculations. The instructions are explicit and well defined throughout the entire simulation. My only critique is that the simulation is quite lengthy and not all of the material seems to relate directly to math curriculum. When I use this in a class, I would most likely curtail it to include just the calculations and conclusions sections.
Educational Value: This simulation would be a wonderful project for students to do after learning about vectors. This application helps students solve real world problems involving velocity and other quantities represented by vectors as well as model functions that describe real relationships between quantities. The calculations are not overly difficult but the concepts are and these concepts are made real for students during this learning activity.
Age Appropriateness: This simulation is clearly designed for older students. The content of the material is written for students of higher levels of math and science education and the intense nature of the crash itself should only be taught to high school students. This simulation is very appropriate for upper level high school students taking precalculus or calculus.
Applicability to Theme: The use of this Crash Scene Investigation activity is definitely applicable to a high school math class. I would integrate this simulation into the curriculum following the study of vectors and applications of trigonometry. This unit tends to be taught in the springtime around the same time as spring break and prom. Therefore, not only would this learning activity hold educational benefits for math but it may give students the insight needed to make responsible decisions in life.
Ease of Use: The program is easy to navigate and does a good job of guiding students through the calculations. The instructions are explicit and well defined throughout the entire simulation. My only critique is that the simulation is quite lengthy and not all of the material seems to relate directly to math curriculum. When I use this in a class, I would most likely curtail it to include just the calculations and conclusions sections.
Educational Value: This simulation would be a wonderful project for students to do after learning about vectors. This application helps students solve real world problems involving velocity and other quantities represented by vectors as well as model functions that describe real relationships between quantities. The calculations are not overly difficult but the concepts are and these concepts are made real for students during this learning activity.
Age Appropriateness: This simulation is clearly designed for older students. The content of the material is written for students of higher levels of math and science education and the intense nature of the crash itself should only be taught to high school students. This simulation is very appropriate for upper level high school students taking precalculus or calculus.
Applicability to Theme: The use of this Crash Scene Investigation activity is definitely applicable to a high school math class. I would integrate this simulation into the curriculum following the study of vectors and applications of trigonometry. This unit tends to be taught in the springtime around the same time as spring break and prom. Therefore, not only would this learning activity hold educational benefits for math but it may give students the insight needed to make responsible decisions in life.
Part Two: Resources
I created a Symbaloo webmix page to display a collection of websites and resources for high school math. The links include general education websites such as Edmodo and Teacher Tube as well as specific math resources or lesson plans. The teal icons are specific for Calculus and the orange icons are specific lesson resources for teaching students about the relationships between time, position, velocity and acceleration.
Resource Lesson Ideas
1. How Fast Am I Moving? - The interactive lesson allows students to investigate the relationship between motion and time. Students learn to use the slope of a position graph to find velocity. Since Calculus is the math of motion, this activity would be a good learning activity to introduce the applications of derivatives. Understanding the relationships between position, velocity and acceleration is a key objective in any Calculus class. The derivative function and its graph reveal a lot to the student about these quantities and this activity would help students conceptualize this topic.
2. Describing Velocity - This activity guides students through an exploration of the velocity function and its relationship to position and time. Even though the Concord Consortium website that it is found on identifies this lesson to be used in middle school, I believe it holds value for a regular Calculus class lesson. The concepts covered in this activity are a major component of the subject and understanding the foundations allows students to succeed at a higher level.
3. The Running Man - This Gizmo can be used with any math class exploring the concepts of position and velocity over time. I think this activity could be put to do good use for Calculus students applying their knowledge of derivative graphs to real world applications. This interactive tool allows you to change velocity over time, add an additional runner and also look at the derivative graph and the absolute value graph.
4. The Moving Man - This resource provides students or teachers with a great tool for exploring the position, velocity and acceleration of a moving body. Again, it could be used in a Calculus class when students are determining the relationships between these concepts and how these functions and graphs relate to the concepts studied in Calculus. The ability to watch the man move while the graphs are being charted is a major educational benefit.
5. ProProfs Flashcards - At the end of the academic school, AP Calculus students are preparing for the AP exam. This resource can be used by students to make flashcards to help them study for this comprehensive exam. This website can also be used with any other high school math class that is studying for a unit exam that is heavy on formulas or definitions.
6. Geogebra - This resource can be used a high school math class in a variety of way. There are countless materials for teachers to use for instruction. Teachers can use the Unit Circle demonstration to explore the many properties of this tools or Parallel Parking Optimization demonstration to teach a trigonometry class about an application of a trig identity. An algebra teacher can use the many applets available for teaching graphing lines. The are thousands of resources that can be used in a multitude of ways for teacher or students on this site.
7. Mathalicious - This is a great resources for incorporating real world applications of math into your lesson. This website is particularly interesting because it takes into account the events happening in the world to feature particular lessons. For instance, there are lesson about math and baseball in the springtime or bracketology around the time of march madness. You can look up lessons by topic, grade level or standard. The lesson ideas apply the math to interesting topics; there is a trigonometry lesson called "Sofa away from me" that asks students to calculate the optimum distance that a couch should be placed from the television using their trigonometry skills.
8. Real World Math - This resource offers teachers a variety of lessons that focus on real world application of math concepts. There are many free materials available for instructional use that cover both traditional classroom concepts such as scientific notation, volume, rates, and measurement and non traditional concepts such as fractals and topology. The integration of Google Earth helps make these lesson relatable and interesting for students.
9. The Futures Channel - Math doesn't appeal to every student. Some students are bored by the calculations and technicality of math problems. This resource is a great website for teachers to use if they are looking for an interesting video to motivate their students. There are many, many videos to choose from that can be shown to a math class that will peak a student's interest and perhaps influence future career choices. A favorite movie for most math teachers to show their classes is the movie, Stand and Deliver, there are additional resources here that could be shown to the class instead of or in addition to the movie.
10. Visual Calculus - Many students claim to be visual learners, since it is important to appeal to different learning styles, teaching math through the use of visuals is important. This resource is great collection of applets and demonstrations on every topic taught in Calculus. There are resources available to use teaching aids, drilling software, full tutorials, computer programs, calculator demonstrations and so much more. I find that the interactive applets, such as this one for optimizaiton, have been the most helpful for a teacher to use to enhance a lesson plan.
2. Describing Velocity - This activity guides students through an exploration of the velocity function and its relationship to position and time. Even though the Concord Consortium website that it is found on identifies this lesson to be used in middle school, I believe it holds value for a regular Calculus class lesson. The concepts covered in this activity are a major component of the subject and understanding the foundations allows students to succeed at a higher level.
3. The Running Man - This Gizmo can be used with any math class exploring the concepts of position and velocity over time. I think this activity could be put to do good use for Calculus students applying their knowledge of derivative graphs to real world applications. This interactive tool allows you to change velocity over time, add an additional runner and also look at the derivative graph and the absolute value graph.
4. The Moving Man - This resource provides students or teachers with a great tool for exploring the position, velocity and acceleration of a moving body. Again, it could be used in a Calculus class when students are determining the relationships between these concepts and how these functions and graphs relate to the concepts studied in Calculus. The ability to watch the man move while the graphs are being charted is a major educational benefit.
5. ProProfs Flashcards - At the end of the academic school, AP Calculus students are preparing for the AP exam. This resource can be used by students to make flashcards to help them study for this comprehensive exam. This website can also be used with any other high school math class that is studying for a unit exam that is heavy on formulas or definitions.
6. Geogebra - This resource can be used a high school math class in a variety of way. There are countless materials for teachers to use for instruction. Teachers can use the Unit Circle demonstration to explore the many properties of this tools or Parallel Parking Optimization demonstration to teach a trigonometry class about an application of a trig identity. An algebra teacher can use the many applets available for teaching graphing lines. The are thousands of resources that can be used in a multitude of ways for teacher or students on this site.
7. Mathalicious - This is a great resources for incorporating real world applications of math into your lesson. This website is particularly interesting because it takes into account the events happening in the world to feature particular lessons. For instance, there are lesson about math and baseball in the springtime or bracketology around the time of march madness. You can look up lessons by topic, grade level or standard. The lesson ideas apply the math to interesting topics; there is a trigonometry lesson called "Sofa away from me" that asks students to calculate the optimum distance that a couch should be placed from the television using their trigonometry skills.
8. Real World Math - This resource offers teachers a variety of lessons that focus on real world application of math concepts. There are many free materials available for instructional use that cover both traditional classroom concepts such as scientific notation, volume, rates, and measurement and non traditional concepts such as fractals and topology. The integration of Google Earth helps make these lesson relatable and interesting for students.
9. The Futures Channel - Math doesn't appeal to every student. Some students are bored by the calculations and technicality of math problems. This resource is a great website for teachers to use if they are looking for an interesting video to motivate their students. There are many, many videos to choose from that can be shown to a math class that will peak a student's interest and perhaps influence future career choices. A favorite movie for most math teachers to show their classes is the movie, Stand and Deliver, there are additional resources here that could be shown to the class instead of or in addition to the movie.
10. Visual Calculus - Many students claim to be visual learners, since it is important to appeal to different learning styles, teaching math through the use of visuals is important. This resource is great collection of applets and demonstrations on every topic taught in Calculus. There are resources available to use teaching aids, drilling software, full tutorials, computer programs, calculator demonstrations and so much more. I find that the interactive applets, such as this one for optimizaiton, have been the most helpful for a teacher to use to enhance a lesson plan.
AECT Standards achieved: 1.2 Message Design, 1.4 Learner Characteristics, 2.2 Audiovisual
Technologies, 2.3 Computer-Based Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization
Technologies, 2.3 Computer-Based Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization