Final Reflection

Editor: CHEN Feifeng

WEEK 1 : Introduce to the course.About TPACK and SAMR model

1.Know the Miro that is a famous online collaborative whiteboard.

2. I learned how to integrate technology into education.

[Two famous frameworks: TPACK model and SAMR model.]

3.I learned that What is the Bloom's Taxonomy.

4.We can combine both TPACK and SMAR together in the lesson design process. And learned that how to design a math lesson using blended ladder(A group class assignment about it looks like this).

Reflection of the blended ladder:

When we design the lesson, need to specify the level of target students.
And when we use e-learning tools, we need arrange how to use e-learning tools and in what stage is this tool used?
We must pay attention to the detail of the lesson plan.

WEEK 2 : Various pedagogy theories and LMS

1.I learned what is LMS.

[LMS means learning management systems.There are many popular LMS, such as Canvas,Google classroom ...]

2.I learned what is Google classroom and how to make our Group Log using Google Sites.

[Google classroom:It has a deep integration with other google services, e.g. Google Doc, Form, Sheet, Slide, Site, YouTube, Hangout and so on.]

3.I learned some pedagogical models that might be useful for the lesson design, e.g.Inquiry-based learning,Experiential learning,Collaborative learning,Variation theory,Flipped classroom...

4.I learned how to use the patterns of variation to design a lesson for teaching the object of learning(A group class assignment about it looks like this).

Reflection of using the patterns of variation to design a lesson:

we need identify the object of learning and its critical features.
When we use four patterns of variation to help students discerning the critical features, we should have an accurate understanding of the concepts.

WEEK 3 : A course in GeoGebra

I known GeoGebra and learned how to use GeoGebra for teaching math lesson.

[As a dynamic geometric algebra software, GeoGebra can establish geometric objects and maintain the relationships between them. It can be used to quickly experiment with mathematical ideas, observe graphic changes, or create simple animations and create teaching demonstration materials.]

WEEK 4 : A course in Desmos

I known Desmos and learned how to use Desmos for teaching math lesson.

[Desmos can draw images online, and can also design interactive links, etc.]

WEEK 5 : A course in ChatGTP

I known the applications of ChatGTP in mathematics education.

2.I learned how to use ChatGTP to design the lesson plan better（A group class assignment about it looks like this）.

Reflection of using ChatGTP to design the lesson plan:

we can have some specific ideas(like the use of some teaching strategy).

WEEK 6、7、8 : Design a math lesson using Desmos and GeoGebra and make a group project presentation

Reflection of designing a math lesson:

1.When we want to better design a math lesson , we should think about the following questions:

What are the number and the learning characteristics of the students in the classes you teach? Is the content designed appropriate for them?
What are the teaching objectives of this course?Is it achievable?
How to mobilize students to participate in teaching? What do students do? What do I do?
What teaching resources should be used to design good teaching? Among them, the teaching classroom can make full use of e-learning tools for teaching, such as GeoGebra, Desmos, etc.
Based on different educational backgrounds, student needs and teaching goals, which teaching models should we adopt to achieve the best results?

2.When we make a presentation，we should:

We should focus on teamwork, behave generously and naturally, express fluently and clearly, and have communication and interaction.

WEEK 9 : A course in RStudio/Shiny

1.Learn that what is Shiny: Shiny is an R package that can turn an R script into an interactive webpage. It is fantastic for dynamic data visualization and statistics teaching.

2.Know that how to make Shiny to help teach.

3.Do a Group task：A Shiny app for probability distributions.

Refection: Several questions can be designed to guide students to discover the normal distribution and its characteristics, as well as the influence of parameters on the shape of the normal curve.

WEEK 10、11、12 : Group project and Group presentation on designing an interactive statistics website using RStudio/Shiny

Refection: During the production process, I encountered some challenges. First, I need to be familiar with the syntax and functions of RStudio/Shiny, which is a learning process for me. Secondly, I want to understand the teaching logic of normal distribution so as to help students use it to better understand its concepts and applications.After listening to the opinions of classmates and professors after the group report, I think that：

1.It's better that include task about letting students explore the effect on the probabilities if they change the prior probability , likelihood etc.

2.It's better that show the math formula properly in the Shiny, can use latex formula to generate it. To reflect the rigor of mathematics.

3.Must have a clear understanding of the teaching content in order to better complete this group project.

WEEK 14 : Wrap up

Refection: One of the highlights of this course was exploring the TPACK (Technological Pedagogical Content Knowledge) model and the SAMR (Substitution, Augmentation, Modification, Redefinition) model. Understanding these frameworks helped me grasp the importance of effectively integrating technology into teaching practices. Additionally, the concept of the Blended ladder, which combines both models, provided a holistic approach to leveraging technology in education.

I appreciated the exploration of pedagogical approaches such as behaviorism, constructivism, social constructivism, liberationism , and connectivism . These approaches shed light on different perspectives and helped me understand the diverse ways in which students learn and engage with mathematical concepts.

The course also introduced various pedagogical models, including inquiry-based learning, experiential learning, collaborative learning, variation theory, and flipped classrooms. Each model offered unique strategies for teaching mathematics effectively and engaging students in meaningful ways. I particularly enjoyed learning about math games and mathematically rich tasks as practical strategies to enhance student learning.

Moreover, the course exposed us to a plethora of e-learning tools that can enhance mathematics instruction. From learning management systems like Canvas and Google Classroom to collaborative whiteboards like Miro, these tools provided avenues for creating interactive and engaging learning experiences. Math-specific tools such as GeoGebra, Desmos, and R with Shiny proved to be invaluable resources for visualizing and exploring mathematical concepts.

Dr. Albert Ku also emphasized the use of AI tools like ChatGPT as a means to facilitate learning and provide additional support. These tools showcased the potential of AI in enhancing educational experiences.

However, the course was not without its challenges.Especially in the process of making Shiny, I found that I had deficiencies in my knowledge of Bayes' theorem, so I needed to continue to learn and make up for the deficiencies; and in the process of completing the group, I was also learning R programming, and learning R knowledge was also a process. It's not easy, it requires patience.

In conclusion, MAED 5511 has been an enriching learning experience. It has deepened my understanding of the effective integration of technology in mathematics education and broadened my pedagogical repertoire. The course has equipped me with valuable tools, strategies, and frameworks that I can apply in my future teaching endeavors. I am grateful for Dr. Albert Ku's guidance and the opportunity to explore the digital age's potential in mathematics education.

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