The purpose of this assignment is to serve as an introductory background story of what my feelings were towards math in high school, how it was my least favorite subject, and how I grew to love and appreciate math through the random things I experienced in life that led me to earn a degree in math. The objectives of sharing this story are: (1) for students to reflect on what their own feelings are towards math. (2) To have students think about their own personal interests and to start investigating how math ties into these interests. (3) To illustrate how problem-solving and logic, skills that are at the essence of math, can greatly aid in finding solutions to the random problems and situations a person encounters throughout life.
Instructions: For this assignment, watch the digital story “When Am I Ever Going to Use This?” by clicking on the link below. After viewing the digital story, take out your math journal and answer the following prompts:
- What are your feelings about math? Have you always felt this way? If not, when do you remember your feelings/attitude shift towards math? What do you think contributed to you feeling the way you do about learning math? How have previous math teachers you’ve had affected your attitude towards learning math?
- What are some of your personal interests? If you could do anything you wanted to do with your life, what would it be? Have you ever thought about or explored any connections that might exist between this and learning math?
- What does problem-solving mean to you? Do you think problem-solving is a useful skill to have? How could/can problem-solving help you in your day to day experiences? Do you see a connection between math and problem-solving? Do you think that learning math can help you refine your problem-solving skills?
Each of the three problems for this journal entry should be at least several sentences at minimum. The intent of this assignment is for me to better understand how you feel about math and to get a better idea of what your interests are so that we can begin to investigate how they tie into this course, Math Models, and the real world. It is my hope that through this process of exploration and refining your problem-solving skills, that an authentic understanding and appreciation of maths relevance and usefulness in your life now, and possibly into the future, can be better revealed to you.
This screencast is intended as an introduction for my Math Models students to the phET interactive simulations website that’s focused on math, science, and engineering. It is a website that is filled with a wide array of simulations that cover a lot of the topics covered in my Math Models course. This website will be used extensively with project and inquiry-based activities students will be assigned where it provides accurate simulations of real-world phenomena for students to conduct hypothesis testing and gather and interpret data.
The objective of the lesson that this introductory screencast is connected to is for students to try and predict how varying initial conditions can affect the path of a projectile when launched from a cannon. Students will be required through the use of the simulation to collect and analyze data on how the horizontal distance of a projectile(s) is affected by:
- Adjusting the height that the cannon is fired from
- Adjusting the degree to which the cannon is fired
- Adjusting the initial speed that a projectile is launched at
- Firing objects of various masses and diameters from the cannon
- Applying air resistance
- Analyzing velocity and acceleration vectors
- Determining what the optimal angle is to fire a projectile from a cannon for it to achieve its maximum horizontal distance
Students will be asked to record for homework the results of the data they collect from the simulation and to discuss how the height, angle degree, initial velocity, air resistance, mass/diameter affect their ability to fire a projectile and hit a target that is shown on the ground. Students will then be asked what they believe the optimal angle is to fire a projectile from a cannon for it to achieve its maximum horizontal distance. Students will share these results during the following class which will lead to further in-class explorations with projectile motion and discussion on how to calculate angular velocities of projectiles using trigonometry.
The purpose of this podcast is for students that are enrolled in a Math Models and Applications course to gain exposure once a week from a 5-minute teacher created/produced podcast that covers various historical figures and discoveries that have been made throughout world history that are directly related to math and science.
The objective of this recurring weekly lesson is for students to, after listening to a 5-minute long weekly podcast that covers a different historical mathematician and/or scientist, to reflect, analyze, and draw connections to the individual(s) and topics that are covered in the podcast.
The student will be expected to:
- Create a personal journal/blog entry that discusses the contributions that the historical figure has contributed to math and/or science.
- Answer 3-4 questions related to the podcast and the mathematics/science that was discovered or used that has contributed to society
- Research and list an interesting fact about the historical figure that the podcast covers that was not mentioned in the podcast
- Attempt to solve/answer a math and/or science problem study directly related to the historical figure covered in the podcast
A new weekly podcast assignment will be assigned every Tuesday for students to complete. Students will have until the following Sunday evening at 9pm to update their journal blogs for full credit and any related math/science problem that accompanies the podcast assignment will be due on the following Monday at the beginning of class. The blog/journal activities and problem studies that accompany the podcasts will cumulatively count for 15% of the student’s final grade in the course.
The tentative schedule for this semester’s podcasts thus far are:
- Week 1: Archimedes and the golden crown
- Week 2: Edison, the great American inventor of incandescent light
- Week 3: Pythagoras, the Pythagorean theorem, and the cult of Pythagoras
- Week 4: The Geometrical Discoveries of Thales
- Week 5: Eratosthenes, the Wise Man of Alexandria who measured the circumference of the earth
- Week 6: Leonardo DaVinci and his quest for flight
- Week 6: Fibonacci, the Fibonacci sequence, and the rabbit problem
- Week 7: Rene Descartes and the Cartesian plane
Though I’m a strong advocate for free educational resources, there are some educational resources out there that aren’t free and well worth the investment. This book happens to be one of them. Rethinking Mathematics is a compilation of articles and lesson plans geared towards teaching math and science concepts that bridges connections to social justice issues, real-world applications, and real-world relevance.
With topics and lessons ranging from students applying Algebra to explore issues concerning what a living wage really is or should be, to PBL based activities that have students investigate what the density of hazardous waste sites are in urban/suburban areas with data gathered off the U.S. Environmental Protection Agency’s website, to lessons on multicultural math, and so on, students not only gain practice and learn math concepts on a deeper level but also make genuine connections to maths relevance in their personal lives and throughout society.
Truly a great resource to consider using with students that exposes them to complex societal concerns and how math and science can be quite useful in analyzing and empowering students to make educated decisions on real-world issues that affect them and their communities.
In my support of open-course free educational content, I’d like to share the correlated lesson plan above that I co-authored that focuses on unit conversions and statistical analysis of data with categorical and quantitative graphs of Planets and Dwarf Planets of our solar system.
The lesson plan utilizes part of NASA’s educational website, Solar System Exploration, which offers a wealth of educational information for students to learn about our solar system, and requires students to collect data off the website in order to explore and gain practice in graphing categorical and quantitative data and unit conversions between astronomical units, miles, and scientific notation. Common Core and TEKS standards are listed within the lesson plan and an assessment is listed at the end that includes a key for grading.
This lesson plan should cover a 45-50 min class and requires student collaboration/group work. Please feel free to share, edit, and/or comment. Feedback is always appreciated!
There is so much to consider from this Ted Talk. How does a teacher ensure that technology tools that are introduced in a classroom serve their intended purpose, which should be authentic learning, and don’t just become another distraction? The key according to Preston is by creating learning environments that utilize technology to share information in such a way that the learner is a co-author of their learning experience and quality evaluation isn’t compromised.
What are examples of what this looks like?
Blogs are excellent tools for evaluation where a person displays elements of their personality, esthetic, and style. Having students collaborate with the use of technology, such as applications like slack, are ways in which technology can create networks and learning communities.
The idea is, for learners to take control of their own learning that extends beyond the teacher and reaches out to the teacher’s networks and sources of information. By encouraging students to send emails to authors they’ve read and to engage with experts in whatever field they are researching, learning goes beyond just the content and extends into process.
The crux of all this is that right now students have the capability of engaging with people and experts from around the world and yet by and large this ability is underutilized. Training students on how to engage with “thought leaders” around the world through online conferencing and digital tools are paramount to having students no longer be passive spectators in their learning but active participants.
How can we teach students to create their own opportunities to assess each other through peer feedback and through inquiry create their own curriculum and learning experiences that are meaningful to the learner?
By guiding students to the plethora of freeware and free digital educational content that exists and giving students “permission” to explore and learn. By doing so, students gain a sense of value in their learning process.
Preston states that “ultimately in our culture, entrepreneurship is a function of value, entrepreneurship is a function of taking personal responsibility for putting something out there and ultimately, if we encourage people to achieve their own value, to get referendums through online media, through social media, we have a better opportunity than ever in creating the sort of innovation that will get us through to the next century.”
Information has never been more available, its never been freer than it is now. The key is helping students tap into it and empowering them to utilize it to their full potential.
In the countless inspirational videos I’ve either stumbled across or been subjected to throughout the years, there hasn’t been anything I can think of that has left a more lasting impression than probably this video narrated by Alan Watts. It is a video and a dialogue I often think of when listening to students talk about their plans after graduation and what they want to do with themselves and when I think of my own children and what I wish for them. The premise, what do I desire is such an important question to ask ourselves.
If students could figure out what it is they really wanted to do in life early on where money wasn’t the overriding concern and instead genuine fulfillment in the work they committed themselves to was, wouldn’t the end result more likely be happier, passionate people that are more likely to be highly skilled in their area(s) of interest? Obviously, money is a necessity in our society along with material comfort but what is the life better lived?
I believe that one of the most important goals of an educator is to foster students natural interests and creativity and creatively help students find relevance in what they’re learning. Educators should strive to help students see the connections that always exist between what they are learning and their interests and most importantly to encourage students to pursue their inherent passions. Ingenuity, innovation, creativity, and quality are all end results of what people produce when they are truly immersed and passionate about what they do. Passion and support towards students dreams and aspirations are what should be cultivated. As the old adage goes, to thyself be true.