In today’s classroom, there are various teaching styles a student could encounter. All of these styles fall somewhere on the continuum of technology-based learning presented in Tony Bates’ book Teaching in a Digital Age (2015). On one end of the continuum there’s face-to-face where the delivery involves no technology and on the other end of the continuum there’s online distance learning where the delivery is all technology. I teach algebra II for sophomores in high school so that is the audience my course is designed for. I have been teaching using a flipped classroom model, which falls under the blended learning hybrid, for the past five years. Since I have experience teaching a blended classroom where Google classroom is utilized as the learning management system (LMS), I decided to try designing an algebra 2 course that was fully online using a different LMS called Schoology.
Instructional Design Theories
I believe that the constructivist approach is the most beneficial for my students whether it is face-to-face or online. The constructivist theory is the idea that “meaning is constructed in the mind of individuals through discovery, with a focus on the process of assimilation and accommodation of knowledge” (Tan & Hung, 2003). It can be challenging to teach a higher-level math course through discovery. This is something I am still learning how to master, but to start, I have given my students reflection questions that make them think through why the math works the way that it does. The mathematical process may be taught through a video lecture, but they are discovering the why on their own through the reflection questions.
UbD Plan Implementation
I started my course by using the backwards design template from Wiggins' and McTighe's book Understanding by Design (UbD)for each unit. This template allowed me to think through my overall goal for the unit which in turn helped me to form the reflection questions used to guide them through their own thinking.
Importance of Online Learning
Providing online learning is vital for our students in today’s society where technology is constantly advancing and careers are ever-changing. Even the education field has changed due to technology. New positions are opening up in schools specifically to help teachers incorporate technology. Online learning provides students the opportunity to learn how to be resourceful in order to discover knowledge on their own. This is a skill that will benefit our students greatly in their future careers. Online learning also provides students the ability to learn at their own pace which greatly benefits a classroom of diverse learners.
Enduring Understanding
After creating an entire course online, I’ve realized the value in backwards design as it helped me to think through the purpose of the content which in turn allowed me to create reflection questions that will allow my students to think about why the math works the way that it does. I’ve also realized that I find it challenging to build rapport with students through a fully online class. While it was beneficial to gain the experience for creating a fully online course, if my audience is going to be high school students, I believe a blended learning approach would be best so that I can still interact with my students face-to-face and build that rapport. If my audience becomes adults for professional development, then a fully online course would be best so that they can manage on their own time with their busy schedules.
References
Bates, A.W. (2015) Teaching in a Digital Age: Guidelines for designing teaching and
learning (Chapter 7). Retrieved from https://opentextbc.ca/teachinginadigitalage/
Tan, S. C., & Hung, D. (2003). Beyond information pumping: Creating a constructivist e-
learning environment. Educational Technology, 42(5), 48–54. Retrieved
from https://repository.nie.edu.sg/bitstream/10497/4735/1/ET-42-5-48.pdf
Wiggins, G. & McTighe, J. (2005). Understanding by design (expanded second ed.).
Alexandria, Virginia: Association for Supervision and Curriculum Development.
This week I uploaded the second half of my course and included a syllabus. I've never taught a fully online course so I feel as though I may have missed some things that should have been included in my syllabus, but I'm not sure exactly what. Every year of teaching I have changed my syllabus, though, because this profession is one where you learn as you go and make adjustments as you learn. While this was very new to me, I enjoyed creating an entire course online, especially using a difference LMS than what I've used before. My school already has several courses available online; however, the math courses aren’t really available. We have them available through APEX for credit recovery, but they could be redesigned and used throughout the year for students trying to receive credit the first time. I believe math models and geometry would be great courses to start with! Math models is a course that has daily relevance for life after high school and geometry is extremely visual which is why I think both of these courses would do well online.
This week I focused on uploading the first half of my course as well as developing the outline of the second half of my course in more detail. I decided to break up the notes into smaller videos to help with engagement. I'm also looking for more ways to include more active learning activities. For one of my weeks in the first half of the course, I decided to have my students take a picture of a real-life conic and label all the pieces of the parabola as well as determine the equation of it. I also decided to save my syllabus for next week. I want to fully plan out the course before deciding all of the grading details and what not.
Copy and paste outline of final 50% of your course here:
Week 4
· Solving Quadratic Inequalities Algebraically
o Notes video
o Practice assignment
· Solving Quadratic Inequalities by Graphing
o Notes video
§ Solving Quadratic Inequalities by Graphing
§ A Hybrid Approach
o Practice assignment
· Linear Quadratic Systems
o Notes video
§ Solving Nonlinear Systems by Graphing
§ Solving Linear-Quadratic Systems by Substitution
o Practice assignment
· REFLECTION – How does solving a quadratic inequality compare to solving a quadratic equation? What connections do you notice between solving quadratic inequalities by graphing versus algebraically?
· Unit assessment
UNIT 8
Week 5
· Transformations
o Notes video
§ Function Families
§ Transformation Rules
o Practice assignment
· Solving Radical Equations
o Notes video
§ Solving Radical Equations Algebraically
§ Solving Radical Equations Graphically
§ Applications
o Practice assignment
· Solving Equations with Rational Exponents
o Notes video
§ Solving Equations with Rational Exponents
§ Applications
o Practice assignment
· REFLECTION – When solving equations with rational exponents, why does multiplying the exponent by the reciprocal work?
· Discussion question
Week 6
· Cubic-Cube Root Relationship
o Notes video
§ Inverse Relationships
§ Verifying Inverses
o Practice assignment
· Quadratic-Square Root Relationship
o Notes video
§ Domain Restrictions
§ Verifying Inverses
o Practice assignment
· Inverse Function Study
o Notes video
o Practice assignment
· REFLECTION – Explain the cubic-cube root relationship and the quadratic-square root relationship. Why are they inverses of each other? If quadratic functions and square root functions are inverses, why do their graphs look so different?
· Discussion question
· Unit assessment
Enter a detailed outline of the first 50% of your course using the space you need:
Intro to Schoology.
Intro to professor.
Vocabulary for each unit.
UNIT 6
Week 1
· Vertex and Standard Form
o Notes video
o Practice assignment
· Quadratic Functions from 3 Points
o Notes video
o Practice assignment
· REFLECTION – Why is it necessary to know the different forms of a quadratic? How come knowing just one of the forms is not enough?
· DISCUSSION – What skills are you specifically struggling with and why? Respond to two other posts to help your peers gain understanding.
Week 2
· Gravitational Parabolas
o Notes video
o Practice assignment
· Equations of Parabolas I
o Notes video
o Practice assignment
· Equations of Parabolas II
o Notes video
o Practice assignment
· REFLECTION – What real-world connections can you make with parabolas? Additionally, how are focus and directrix used in a real-world situation?
· DISCUSSION – What skills are you specifically struggling with and why? Respond to two other posts to help your peers gain understanding.
· Unit assessment
UNIT 7
Week 3
· Graphing and Factoring
o Notes video
o Practice assignment
· Completing the Square
o Notes video
o Practice assignment
· Quadratic Formula
o Notes video
o Practice assignment
· Quadratic Applications
o Notes video
o Practice assignment
· REFLECTION – Compare and contrast the different methods of solving a quadratic equation.
· DISCUSSION – What skills are you specifically struggling with and why? Respond to two other posts to help your peers gain understanding.
What is the acceptable evidence that learners have mastered the concepts in your course?
Students need to be able to perform the skills listed in the given TEKS. Evidence of mastery will come from regular unit assessments where students will demonstrate the know how to perform the mathematical skills. Evidence of mastery will also come from the weekly reflections where students should be able to demonstrate their understanding of how and why the math works and weekly discussions where students collaborate to help each other understand concepts that other students are struggling with.
What learning experiences and instruction are needed for learning to occur?
I believe the best learning occurs when reflecting on your mistakes as well as when you can teach others the content. This is why I have incorporated the weekly discussions where students reflect on what they need help with and then respond to others by helping to clarify those misunderstandings.
Introduction:
This online course is designed to guide students through the second semester of algebra II. Each lesson will contribute to the overall goal of broadening their knowledge of quadratic functions and systems of equations as well as studying square root, cubic, cube root functions and their related equations. Students will connect functions to their inverses and associated equations and solutions in both mathematical and real-world situations. Students will show evidence of learning through daily assignments, assessments, and reflections to show critical thinking.
Learning Goals:
2A.4A - Write the quadratic function given three specified points in the plane.
2A.4B - Write the equation of a parabola using give attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening
2A.4D - Transform a quadratic function f(x) = ax2 + bx + c to the form f(x) = a(x - h)2 + k to identify the different attributes of f(x).
2A.4E - Formulate quadratic equations using technology given a table of data.
2A.4F - Solve quadratic equations.
2A.4H - Solve quadratic inequalities.
Desired Results:
Students will be able to…
· Write a quadratic equation in standard form.
· Write a quadratic equation in vertex form.
· Write a quadratic equation in intercept form.
· Collect data and use technology to write a quadratic equation.
· Write a quadratic equation given the focus and directrix.
· Graph and solve a quadratic inequality.
· Solve a quadratic equation.
· Transform a quadratic equation from one form to another.
· Know which quadratic equation form to use given certain information about the graph’s attributes.
· Translate equations and inequalities from one form to another form.
Audience:
Texas high school students taking algebra II, mainly sophomores, preparing for the SAT and ACT tests. Students will have varying abilities, but should all have previously completed the algebra I course.
Outline:
UNIT 4
Week 1
· Vertex and Standard Form
o Notes video
o Practice assignment
· Quadratic Functions from 3 Points
o Notes video
o Practice assignment
· REFLECTION – Why is it necessary to know the different forms of a quadratic? How come knowing just one of the forms is not enough?
Week 2
· Gravitational Parabolas
o Notes video
o Practice assignment
· Equations of Parabolas I
o Notes video
o Practice assignment
· Equations of Parabolas II
o Notes video
o Practice assignment
· REFLECTION – What real-world connections can you make with parabolas? Additionally, how are focus and directrix used in a real-world situation?
· Unit assessment
UNIT 5
Week 3
· Graphing and Factoring
o Notes video
o Practice assignment
· Completing the Square
o Notes video
o Practice assignment
· Quadratic Formula
o Notes video
o Practice assignment
· Quadratic Applications
o Notes video
o Practice assignment
· REFLECTION – Compare and contrast the different methods of solving a quadratic equation.
Week 4
· Solving Quadratic Inequalities Algebraically
o Notes video
o Practice assignment
· Solving Quadratic Inequalities by Graphing
o Notes video
o Practice assignment
· Linear Quadratic Systems
o Notes video
o Practice assignment
· REFLECTION – How does solving a quadratic inequality compare to solving a quadratic equation? What connections do you notice between solving quadratic inequalities by graphing versus algebraically?
· Unit assessment
UNIT 6
Week 5
· Transformations
o Notes video
o Practice assignment
· Solving Radical Equations
o Notes video
o Practice assignment
· Solving Equations with Rational Exponents
o Notes video
o Practice assignment
· REFLECTION – When solving equations with rational exponents, why does multiplying the exponent by the reciprocal work?
Week 6
· Cubic-Cube Root Relationship
o Notes video
o Practice assignment
· Quadratic-Square Root Relationship
o Notes video
o Practice assignment
· Inverse Function Study
o Notes video
o Practice assignment
· REFLECTION – Explain the cubic-cube root relationship and the quadratic-square root relationship. Why are they inverses of each other? If quadratic functions and square root functions are inverses, why do their graphs look so different?
· Unit assessment
Materials:
· Guided notes videos
· Practice assignments
· Quizzes
· Test
· Reflection questions
· Useful resource links such as online calculators or apps and a math keyboard website to help students type the math symbols accurately.