My math students struggle with planning their methods before working through problems. I always ask questions in class to help them create plans, to think about how to work through something. I will use a flow chart with my AP Calculus students to help them decide which derivative rules to use before finding the derivative. This entire activity revolves around making decisions without completing any computations. I provide instructions here and am excited to see what happens. 

     I teach many different types of learners and am always looking to find new ways to reach them. I like to have each student come into my classroom with a fresh start, but they do not always feel that way. Students struggle with math and struggle to make meaning of the math they learn in school. I want students to see that the content may not be the most valuable math lesson; learning how to learn and approach problems is the fundamental skill. Learning how to learn is individual and different for every student. So, while I show students one way to problem-solve, I always welcome new ideas, talking through them to ensure those methods work consistently. But many students will not make this effort. They try to fit new information into pre-existing schema instead of creating a new schema to make space for the latest information. (Walden University, 2015e)

    In my math class, I want students to work together to make sense of the content and develop personalized problem-solving methods. When I teach trigonometry, and we create the unit circle, students always ask if they have to memorize the information. I tell students that I want them to find ways to remember the material; memorization is temporary, and this is the knowledge we will need for the course and math courses to follow. I give them time to look over the unit circle, find patterns, and see what connections exist in the material. I have seen students color code their unit circles, underline certain information, and create phrases to help organize the material. I enjoy watching them make this personal and meaningful without my help. (Rob & Rob, 2018) This year, I shared a website with students to test their knowledge of the unit circle. As students felt ready, they clicked on the website I had posted in Google Classroom and tested themselves to determine how well they knew the unit circle. Some students competed against each other for the fastest time, and some competed against themselves. Through mistakes students made on this website, they could adapt their methods to remember the information better for the next time. Having computers ready and available for students to experiment, not just watch and listen, supports the constructivist learning theory. (Rob & Rob, 2018) Throughout this process, I act as a facilitator (ISTE, 2016), helping students become problem solvers, using technology to check and explore their methods. (ISTE, 2007)

    Today, my Calculus students learned how to find a derivative of an exponential function using the chain rule. Students were trying to identify the parts we needed to start the problem. I had a student who thought he had found another way to find the derivative of our first example. I let him work through the problem on his own and then challenged him with another to see if his method worked. It did not, and he was able to figure out why. Pitler, Hubbard, and Kuhn (2012) discuss this type of discovery as a way to deepen students’ understanding of the material. This student worked with another classmate to talk it through together; what a fantastic way to start my day!

    Constructivism and constructionism are closely related, and the differences are subtle. When trying to decide which theory best describes my classroom, I struggled - having multiple sources to read helped me identify both views within my classroom. In my pre-Calculus class, students are working on proofs that have numerous pathways. The focus is on the methods, and processes students use (Orey, 2001) as opposed to answers. I often give my Calculus students a challenging problem after we have practiced the necessary skills and have them work as a class to complete the work. I may ask a question as they work, but they are responsible for creating the process. This knowledge construction comes from conversations and interactions, as described by changingminds.org.

    My favorite discovery was that Seymour Papert, along with his theory of constructionism, developed Logo. I remember using the turtle on the computer screen to make shapes. Eventually, we used the Logo programming to connect vehicles made from Legos and were able to move the vehicles around the classroom using the Logo programming language. I did this in middle school, and I remember it so vividly. I want students to have this same experience from the projects they create during our Genius Hour time. I want students to explore and build on their knowledge, adapting as they move through the process. (blog.cccatconference.org)

    Each year, I want students to leave my classroom with a newfound respect for math. If I can have students move on to future endeavors with their own problem-solving methods and the ability to collaborate with peers to the same end, I will know that students found success in my class. 

References

Walden University, LLC. (Producer). (2015e). Constructionist and constructivist learning theories [Video file]. Baltimore, MD: Author.

Rob, M., & Rob, F. (2018). Dilemma between constructivism and constructionism: Leading to the development of a teaching-learning framework for student engagement and learning. Journal of International Education in Business, 11(2), 273–290. https://www.proquest.com/docview/2154592910?accountid=14872 https://doi.org/10.1108/JIEB-01-2018-0002

International Society for Technology in Education. (2016). ISTE standards for teachers. http://www.iste.org/standards/iste-standards/standards-for- teachers

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. http://textbookequity.org/Textbooks/Orey_Emergin_Perspectiv es_Learning.pdf

International Society for Technology in Education. (2007). ISTE standards for students. http://www.iste.org/standards/iste-standards/standards-for- students

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.

Dave If you like what you are reading. (2022, October 7). Constructivism vs. constructionism. Connecting, Collaborating, and Celebrating the Art of Teaching. Retrieved November 29, 2022, from https://blog.cccatconference.org/2022/10/constructivism-vs-constructionism.html

Constructionism and constructivism. (n.d.). Retrieved November 29, 2022, from http://changingminds.org/explanations/research/philosophies/constructionism.htm 

 My Advanced Pre-Calculus class took a virtual field trip to NIST (the National Institute of Standards and Technology) to learn where Pi is used in the real world. As we begin our study of Trignometry, students are thinking about where this math applies. Here is what they discovered: 

Behaviorism in the Classroom

         Teaching math to high school students brings many challenges. I have genuinely advanced students working five steps ahead of me at all times. I see students who absorb every word I say and every example I do, waiting to regurgitate it back to me at any moment. I teach students with such negative views of math that I have to find ways to give them a fresh start every day. My ultimate goal is to teach all my students how to learn math, approach a problem, and feel successful even if they do not find a correct answer. I am fortunate to teach students who want to be in school, for the most part. Behavior, in the traditional sense, is never an issue. When students are in class, they work together, discuss problems, and focus on the task. I worry about what happens when they leave my classroom and how to have them continue those behaviors when I am not watching.

        Most of my students are 11th and 12th graders, and by the time they get to my class, they have created study habits for themselves. What I want them to be able to do is decide if those study habits (I’m going to call them behaviors moving forward) are creating their desired outcome. They learned these behaviors over time and through practice. What if they are not the best for the student? Those kids have no idea, and I would love for them to see that they could “unlearn or relearn” (Orey, 2001) their behaviors.

        I could create a Google Form that students would fill out each day at the beginning of class. I would ask them simple questions about how many homework problems they completed the night before, how many they finished, how many were correct, and how many they did not know how to do. Once a week, I could provide an “effort rubric” (Pitler, Hubbell, & Kuhn, 2012) for students to reflect on how they approach math class and their attitude toward practicing math. The Google Form collects data into a spreadsheet and provides a private way for students to answer questions. After a quiz, I would compile the data for the students and show them their results at once. We would continue this process with the hopes of students seeing progress, or lack thereof, and connecting their practice outside of class with their achievement in the classroom.

        As I collect data with the students, I will be able to provide instruction to help my students achieve their goals. (ISTE, 2016) I can guide students on how to make changes to find success, reminding them that improvement is always possible. (Campbell, Craig, & Collier-Reed, 2020) A tangible record of time, effort, and achievement will help hold students accountable. When students see how their action impacts achievement, they can set learning goals and have ways for technology to guide their work. (ISTE, 2007)

        As students become accustomed to using a digital log, they will use a similar record for the goals in their genius hour project. Students will share this document with me in the Google Suite, and I will provide immediate feedback and encouragement. When students see their work is noticed and reinforced, they will know that what they do makes a difference. (Yussif, 2022) The underlying goal of the genius project is for students to feel motivated to work on a project because it interests them. A little positive reinforcement to help spark motivation (Western Governors University, 2021) can fill in gaps when students struggle.

        Students want to do well in school, do the right thing, and be appreciated by people around them. While the behaviorist learning theory cannot be the only learning theory used in the classroom, it has a place. Behaviorism can help students develop a growth mindset when used to promote student achievement, opening them up to more experiences and success. 

References

International Society for Technology in Education. (2016). ISTE standards for teachers.                        http://www.iste.org/standards/iste-standards/standards-for- teachers

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. http://textbookequity.org/Textbooks/Orey_Emergin_Perspectiv es_Learning.pdf

International Society for Technology in Education. (2007). ISTE standards for students. http://www.iste.org/standards/iste-standards/standards-for-students

Yussif. (2022, October 10). Behaviorism learning theory in the classroom. Classroom Management Expert. Retrieved November 15, 2022, from https://classroommanagementexpert.com/blog/behaviorism-learning-theory-in-the- classroom/

Western Governors University. (2021, March 23). What is the behavioral learning theory? Western Governors University. Retrieved November 15, 2022, from https://www.wgu.edu/blog/what-behavioral-learning-theory2005.html#close 

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD. 

M^3 (Making Math Meaningful): Which One Doesn't Belong? ... for Calculus

M^3 (Making Math Meaningful): Which One Doesn't Belong? ... for Calculus: In February,  Christopher Danielson  released his shapes book : Which One Doesn't Belong? It is fantastic for all ages and if you haven&...

Math was my favorite subject in high school. Incredible teachers taught me, and I excelled. I always knew that math was not that way for everyone, and I got into teaching math to help remedy that. My goal is always to have students feel better about math, understand more, and have fewer negative feelings. When students enjoy math, that is a bonus. I worked to ensure student understanding for the first two-thirds of my career. I honed my examples and my explanations of skills. Since technology has become a mainstay in our society, I must focus on engagement too. I always wanted students to be engaged, but it was never a focus in my lesson planning. In recent years, student engagement has become the biggest challenge in the classroom, and technology is part of the solution.

Throughout this course, I have tried Web 2.0 tools that I had never thought to apply to the math classroom. I created a blog and some podcasts, which pushed me out of my comfort zone, seeing the math classroom from a different perspective. I enjoyed the new experience of writing and recording for the classroom. The exposure to new technologies allows me to add tools that I will now be open to using in my classroom. I am most proud of the wiki I created and am excited to use wikis in my classroom this year. As they use the class wiki, I look forward to watching my students hone their “collaboration and negotiation skills” (Richardson, 2010). As we all become more proficient with working with wikis, I believe students will feel a “sense of responsibility and ownership for the site” (Richardson, 2010), contributing to a true collaboration amongst the class.

Learning new tools in this course has given me new ideas for my classroom. I will work this year on implementing wikis in my classroom. I have already begun with my AP Calculus students and will use what I learn from their experience to include my other classes in wikis. I have two goals for transforming my classroom environment to incorporate Web 2.0 technologies. One goal is to have students contribute to a blog post each day with something they remember learning from the class period before. I will initially have students practice doing this as an entrance slip on paper. Once students are in the routine, I will change the process from an entrance slip into a Jamboard. The class will maintain one document, each student adding a sticky note so that they can see what other students have written. The final step will be creating a blog for the class and having students record their learning as a blog post. As I work with students on this process, I will learn how to adjust so the transition from entrance slip to blog post becomes quicker, allowing more time to create more content in our class blog. Blogging will be integral to my math class within a couple of years.

I want students to create a podcast for each course I teach. As I introduce students to podcasting in math class, I would start with having them explain how they completed a problem. The following podcast topic will have students reflect on their success at the end of a unit. The final podcast topic will have students offering advice to next year’s class. When the next school year begins, I will have the new students listen to the podcast and tell them that they will do the same thing at the end of their school year. I think students do not expect podcasts to fit into math class, but I want to show them that connections with technology exist anywhere at any time.

I have always had “faith in the ability of technology to improve learning outcomes” (Chand, Deshmukh, & Shukla, 2020), and my experience in this course has strengthened my beliefs. I know that I have not used technology to its fullest potential. Throughout the research, readings, and experiences I have had in this course, I know that “[s]uccessful technology use and integration … has the potential to provide more access, promote learning outcomes, and preserve the investment of technology.” (Gaddis, 2020)

My most significant barrier to overcome is that the way I have used technology in my classroom is to “do things differently [not] do different things.” (Walden University, 2015k) This course has helped me begin to break down that barrier. I now have new tools to employ with my students to help them learn and see math differently. While they are learning math differently, they will also learn necessary skills for productivity in the 21st Century. The work I bring to my students will help develop their communication skills, collaboration skills, critical thinking, and problem-solving. (Walden University, 2015b).

This year, I will bring wikis, blogs, and podcasts into my classroom. The integration will be slow so that I can proceed with intentionality. I want my students to “develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods.” (ISTE, 2015a) The computers we provide for students at my school are much more than they seem. I must help students tap into their creativity using technology in math class.

Two goals motivated me to pursue my MSED for technology integration in the classroom. First, I wanted to learn more to teach students more about the technology they use. Students are comfortable with technology but do not know how much more they must learn. The second goal is to become a technology specialist in a school. I want to become a leader in technology in my school. This coursework allows me to “seek out opportunities for leadership to support student empowerment and success and to improve teaching and learning.” (ISTE, 2015b) The skills I learned and will apply in this course will give me the experience I need to achieve my professional goals.

References

Chand, V. S., Deshmukh, K. S., & Shukla, A. (2020). Why does technology integration fail? Teacher beliefs and content developer assumptions in an Indian initiative. Educational Technology Research and Development, 68(5), 2753–2774. https://doi.org/10.1007 /s11423-020-09760-x

Richardson, W. (2010). Blogs, wikis, podcasts, and other powerful web tools for classrooms (3rd ed.). Thousand Oaks, CA: Corwin.

Gaddis, M. L. (2020). Faculty and student technology use to enhance student learning. International Review of Research in Open & Distance Learning, 21(4), 39–60. https://doi.org/10.19173 /irrodl.v21i3.4600

Walden University, LLC. (Producer). (2015k). The emergence of educational technology [Video file]. Baltimore, MD: Author.

Walden University, LLC. (Producer). (2015b). Skills for the 21st Century [Video file]. Baltimore, MD: Author.

International Society for Technology in Education (ISTE). (2016a) ISTE standards for students. Retrieved from https://www.iste.org/standards/for-students

International Society for Technology in Education (ISTE). (2016b) ISTE standards for educators. Retrieved from https://www.iste.org/standards/for-educators

     This blog will be used to show students that math is more than textbooks, lists of problems, and tests. Math is problem-solving, which is something we do every day. We decide how to prioritize our day, how to get from one location to the next, how to navigate relationship challenges, and the list goes on and on. Creative problem solving is not limited to the outside world. I want this blog to be a space to showcase student creativity.

    "We live in an era dominated by online media." (Thompson, 2018) This blog will provide my students with an introduction to the "mathematical blogosphere [which] is alive and well." (Thompson, 2018)

    In this blog, I will highlight student work as they "develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions" and as they "communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals." (ISTE, 2016a) I will provide prompts and assignments for students to show how they can do math differently, and I will post work on this blog to brag about my students.

    As an educator, it is my job and my goal to "continually improve [my] practice by learning from and with others and exploring proven and promising practices that leverage technology to improve student learning." (ISTE, 2016b) I have classes full of students with so much to teach me, and this blog is a space for all that work to come together. I want my "students to positively contribute to and responsibly contribute in the digital world. (ISTE, 2016b) This blog will start our collaboration, and perhaps we will grow and create class and student blogs. The possibilities are endless!

References

International Society for Technology in Education (ISTE). (2016a) ISTE standards for students. Retrieved from https://www.iste.org/standards/for-students

International Society for Technology in Education (ISTE). (2016b) ISTE standards for educators. Retrieved from https://www.iste.org/standards/for-educators

Thompson, K. (2018). A survey of the math blogosphere. Journal of Humanistic Mathematics, 8(1), 125-139. https://doi.org/10.5642/jhummath.201802.09