ETEC 533 e-folio

Assignment 1: Framing Issue

My first touch of technology in classroom

My first touch of keyboard happened when I was a primary school student at year 3, that was mid 1990s where computer was just introduced to Asia. The primary school I attended was an international private school in Shanghai, China whose teaching resources and gadgets were advanced if compared with other local schools or public school. 

My first time experience for basic programming is DOS system, Disk Operating System, when i was in elementary school. DOS is a family of computer operating systems that were widely used in the early days of personal computing.  DOS operates in a command-line interface, meaning users interact with the system by typing commands rather than using a graphical user interface. It lays the foundation of basic programming logic in a black and white interface and machine learning – we learn how to use DOS system to make a simple snake eating game. 

Technology stayed in computer class and it was a completely independent subject. Maths teacher probably knows nothing about programing and English (as foreign language) teacher use chalk and blackboard to teach us grammar with no tech background. Technology is isolated from rest of the subjects.

Slideshow, powerpoint, movie and other multimedia were introduced into classroom but manual lecturing, physical textbook, paper and pencil were still the main media for educators till my college graduation in 2009.

What is a good use of technology in math and science classrooms?

Good use of technology in math and science learning environments can be demonstrated from different facets and share the same goal as to facilitate students' understanding of abstract concepts and more importantly, stir up students' curiosity to explore new knowledge themselves. The tools are meant to be easy to use (accessible), enable students to explore geometric relationships and algebraic concepts dynamically for example, motivate students and enhance their learning experiences through challenges and rewards (gamification), create an interactive virtual community to express their findings, thoughts and inquiries freely. Use of technology also enables students with disabilities equally accessible to knowledge, discussions and database. 

Form my personal experience, graphs are easier to understand than words. Animation helps more than graphs to understand STEM concept. Key point is to utilize transmedia and multisensory stimulation to help understand the concept, internalize the concept and make the whole learning process engaging, interactive, fun thus stir up students' interest to explore new knowledge by themselves.  

Case 2: Math Secondary

Graphic calculator was one of the main digital gadgets back to my middle school era so I chose case 2 because it resonates my personal learning experience of maths. Echo with Teacher F’s point that graphic calculator mitigates the limitation of accessibility issue given the limited access to computer lab (back then) and high cost of the software.

The good use of technology of STEM class allows the students to explore the repeated rules by playing with digital gadgets by themselves, help develop the patterns and to generate new questions by themselves. Technology pushes the students’ knowledge boundary through self-exploration and self-study process. The utilization of technology in STEM courses plays down the importance of answer itself and emphasizes on problem solving process. This also increases the sense of achievement and satisfaction level of students compared with knowledge obtained via lecturing.

Limitation：

The use of calculator plays down the importance of answer itself but seems to be a blackbox for students who would be intrigued to know how the answer was derived by the calculator and alternatively, whether answers can also be generated by students’ own calculation. 

Case 3: Physics Secondary

Key message to deliver in class is to develop the transferable skills include managing resources including technology, lecturer, peer intelligence and apply the knowledge acquired in class to daily life.

The role of educator becomes more transactive, less transitive. More important than physics knowledge is to help students develop skills e.g. cooperate and work with people you don’t like, manage time, set goals and achieve them. 

Interview: Never stop learning, even for educators!

I interviewed my middle school maths teacher in Shanghai Ms Xu who has been teaching maths in middle school for the past 20+ years. Ms Xu now focuses on course design and still lectures on 2 maths courses per week for Grade 9 students. 

When I was middle school students, Ms Xu was one of the pioneers to employ multi-media for teaching – slideshows, animation/movie, onsite visit to science museum etc to stir up students’ self exploration interest for science.

We conducted interviews via wechat video call at 5pm HKT on Sunday. Wechat is one of the most commonly used instant messaging tools in mainland China (equivalent to whatsapp while whatsapp is banned in mainland). It ran about 30 minutes with a few interruptions from my sons. As we conducted the interview, we are amazed by how many changes have been made in teaching methodology for the past 20 years and all the new technologies employed in classroom that never heard of during my students’ era. She shared the fun, challenges and differences to teach 80s vs. 2000s kids. As she is one of the core members for teachers re-education and sits on course design committee, she also shared her thoughts on challenges poses on educators nowadays.

1. What are the main differences of teaching method compared with the time when I was middle school student? 

Nowadays students receive tailor made homework from a robot, who scanned user’s face to detect identity of the student and print out homework based on the student’s past performance in quiz. During the quiz, all the students now use smart pens equipped with mini cameras which recorded not just their answers but also mindflow as how they work out the answers. From an app on smartphone or PC, a maths teacher can see the performance of each student and design homework, class questions or pick up from school system’s pool of questions. After finishing homework, students put the homework back to robot who can quickly mark via digital reader. The teacher can view result from smartphone and auto generate follow up assignments accordingly.

The whole process largely releases educators from wasting time to score quiz. This is especially helpful when comes to STEM courses where only very limited portion of questions would be open-end and most are just right or wrong. This auto-marking system also reduces the possibility for human error when grading and evaluating students. According to the latest announcement, the Ministry of Education in Shanghai requires schools to reduce homework for students. The system helps reduce unnecessary repetition for homework and locate the knowledge blindspot more accurately.  Smart pens can only be used in school with a particular device for charging. While there are no other functions of the smart pens but to record and detect homework workout process, the concern that digital gadgets would potentially distract students from study has been largely addressed.

1.     

2.       2. What digital tools or software do you find most effective for teaching mathematical concepts? Why do you prefer these tools? 

Ms Xu acknowledged large variety of AI tools which focus on visualize maths concept are available which indeed helps students understand the abstract concepts of maths and learn maths interactively. It largely saves educators’ time to produce graphics and animations by themselves and output is much more neat, professional and intriguing.  Since 99% middle school students now carry smartphone to school, we do not prohibit students from using smartphones to learn . Rather, recommend apps e.g. photomaths, to let students learn with interest.  WolframAlpha is a powerful tool that students can basically learn everything by themselves after being equipped with basic knowledge of science and social science. Videoscribe is a commonly used animation maker which is a virtual whiteboard to turn ideas into eye-catching animated videos.  “Manim is good. “said Ms Xu. Manim also created a community and maintain a library for creating maths animations.

-          User friendly -          easy to access -          low cost or reasonably priced -          progress tracking -          instant feedback mechanism -          visual aids/transmediation -          less reliance on educator’s programing background -          integration to curriculum

3.  What kind of professional development have you pursued to improve your use of technology in math instruction? 

Coursera is a resourceful virtual place for educators. Coursera provides free online courses (while some charge but tuition is reasonable) with almost every topic. Content contributors are of good quality. I have strongly recommended my colleagues and peers to learn from Coursera based on individual’s need.  “Some useful courses I would like to implement in regular teachers advancement and re-education scheme.” Ms Xu is thinking to create an online virtual community where teachers are encouraged to exchange latest useful tools that help them improve teaching efficacy.

Self study requires higher level of self-discipline, even for teachers. While learning programming from scratch might be too much for full time job worker, keep updated to latest technology progress especially those applicable to daily lecturing is necessary.  It is recommended schools to provide regular courses for educators, to encourage students and teachers exchange information and promote a culture of learning.

Module B: Instructional Framework - TELE

Feature	T-GEM & Chemland	Anchored Instruction & Jasper	SKI & WISE	LfU & MyWorld
Focus	Chemistry & Scientific Inquiry	Math & Science Problem-Solving	Multi-Disciplinary Science Inquiry	Geography & Environmental Science
Technology	Simulations (Chemland)	Multimedia Narratives (Jasper)	Web-Based Inquiry (WISE)	GIS Tools (MyWorld)
Learning Process	Cyclical (Generate-Evaluate-Modify)	Linear (Problem-Driven)	Scaffolded Inquiry	Motivation-Construction-Refinement
Real-World Connection	Scientific Phenomena	Real-World Problems	Integrated Science Concepts	Geospatial & Environmental Issues
Student Role	Hypothesis Testing & Experimentation	Problem-Solving & Collaboration	Knowledge Integration	Data Analysis & Exploration

Each framework has unique strengths and is suited to different educational contexts and goals. All the frameworks emphasize inquiry-based learning and constructivist principles, where students actively engage in exploring, hypothesizing, and constructing knowledge rather than passively receiving information.  Teachers should design lessons that encourage students to ask questions, test hypotheses, and refine their understanding through iterative processes (e.g., T-GEM’s Generate-Evaluate-Modify cycle).  Technology should be used to facilitate exploration and experimentation, such as through simulations (Chemland) or geospatial tools (MyWorld).

Frameworks like Anchored Instruction (Jasper) and LfU (MyWorld) highlight the importance of embedding learning in real-world, meaningful contexts to increase engagement and relevance. Teachers should integrate real-world problems and scenarios into their lessons, such as using multimedia narratives (Jasper) or geospatial data (MyWorld) to anchor learning. This approach helps students see the practical applications of science and math, making learning more engaging and impactful.

Frameworks like SKI and WISE emphasize the importance of scaffolding to guide students through complex inquiry processes without overwhelming them. Technology can be used to provide adaptive feedback and resources tailored to students’ needs.

T-GEM and LfU both emphasize iterative learning, where students continuously refine their understanding through cycles of hypothesis testing, evaluation, and modification. Teachers play as facilitator to invite students to engage in critical thinking, collaboration via interactive technology based learning modules rather than lecturing, and encourage students to link the theories into real world. These four foundational technology-enhanced learning environments compliment each other to provide an effective course design guideline. 

Embodied Learning

Have you ever wondered how the teacher can draw a perfect circle on the chalkboard so easily?

Winn (2003) emphasizes the importance of embodied cognition in learning, arguing that abstract concepts in math and science are often grounded in physical experiences. The body serves as a medium through which learners interact with and make sense of their environment. For example, gestures, movements, and spatial reasoning are critical for understanding mathematical concepts like geometry or physics principles like force and motion. Winn suggests that learning is not just a mental activity but a whole-body experience, where physical actions (e.g., manipulating objects, drawing diagrams, or gesturing) help internalize abstract ideas.

Donnelly-Hermosillo et al. (2020) explore how graph technologies in K-12 education can enhance science and math learning by leveraging embodied cognition. Their research highlights that interactive graph technologies, such as touchscreens or motion-sensing devices, allow students to physically manipulate data representations (e.g., graphs, charts, or models). For example, when students use their fingers to adjust the slope of a line on a graph or drag data points to observe changes in a scatterplot, they are engaging their bodies in the learning process. This embodied interaction bridges the gap between abstract concepts and concrete experiences, making it easier for students to grasp complex ideas like rates of change, correlations, or scientific trends. 

Tran et al. (2017) investigate how embodied cognition supports mathematical thinking through both nondigital and digital approaches. Their research demonstrates that physical activities, such as gesturing, moving through space, or manipulating objects, can enhance students' understanding of mathematical concepts. The authors also highlight the potential of digital tools, such as virtual reality (VR) or motion-based games, to create immersive, embodied learning experiences. In a VR environment, students might "step into" a geometric shape to explore its properties or use motion controllers to simulate mathematical transformations. These digital tools extend the body's role in learning by providing new ways to interact with abstract concepts, making them more tangible and intuitive.

Questions:

What concept you have taught in class can employ embodied learning teaching concept?

Do you prefer physical body movement or immersive artificial virtual environment to understand the same concept, why?

 

References

• Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition, and Learning, 1(1), 87-114.

• Donnelly-Hermosillo, D. F., Gerard, L. F., & Linn, M. C. (2020). Impact of graph technologies in K-12 science and mathematics education. Computers & Education, 146, 103748.

• Tran, C., Smith, B., & Buschkuehl, M. (2017). Support of mathematical thinking through embodied cognition: Nondigital and digital approaches. Cognitive Research: Principles and Implications, 2(1), 1-18.

• Pastor Thom (2022) A perfect circle? https://morethanuseless.com/archives/8039

Knowledge Mobilization

Why role play is rare in STEM and why RP shall be promoted

Role-playing (RP) is common in humanities (e.g., historical reenactments, mock trials) but rarely used in math and science education because math and science are often framed as disciplines of fixed truths, not interpretation or empathy. Role-playing might seem irrelevant when the focus is on formulas, data, and logic. Many educators assume abstract concepts (e.g., calculus, quantum mechanics) can’t be "acted out," unlike historical events or literature.

STEM curricula prioritize efficiency—solving problems quickly—over experiential learning. Standardized tests don’t measure creativity or perspective-taking, so RP is seen as a distraction. 

However, role-playing can highlight underrepresented figures (e.g., a student playing Katherine Johnson calculating Apollo 11’s trajectory), affirming diverse identities in STEM or students role-playing as competing species in an ecosystem (predator/prey dynamics) grasp emergent patterns better than through equations alone - Just two examples on top of my head to showcase why RP could help in STEM class. RP visualizes the abstract concept relationship and invites students to change their role from an outsider, an observant to a participant, a player. 

This RP TPACK bridges the gap between technical skills and real-world application. Calls to rehumanize mathematics –connecting math to everyday life and to a global history – echo calls to action accompanying antiracism efforts, the establishment of culturally-relevant pedagogy, and the study of enthomathematics (D’Ambrosio, 2001). Students could role-play as 9th-century Arab scholars debating al-Khwarizmi’s algebra, or as Mayan astronomers calculating celestial cycles, disrupting the myth that "Western math" is the only valid tradition. RP could simulate real-world applications—e.g., students as city planners using statistics to argue for equitable school funding, mirroring data activism like Million Dollar Blocks.

Before equations, explore the people behind them (e.g., the Navajo "sheep counting" system vs. Fibonacci numbers). This rehumanize maths and relate maths to learner's cultural background. Role-playing in math isn’t just a "fun activity"—it’s subversive. This aligns with D’Ambrosio’s call for math education that "respects the cultural roots of knowledge" while empowering students to critique its uses.

If we want math to be for everyone, it must speak to everyone—and role-playing is one way to shout that message. Would love to hear your take: What math topics that could most benefit from RP?

Reference:

D’Ambrosio, U. (2001). Ethnomathematics: Link between traditions and modernity. Sense Publishers.

Eglash, R., Babbitt, W., Bennett, A., Bennett, K., Callahan, B., Davis, J., Drazan, J., Hathaway, C., Hughes, D., Krishnamoorthy, M., Lachney, M., Mascarenhas, M., Sawyer, S., & Tully, K. (2017). Culturally Situated Design Tools: Generative Justice as a Foundation for STEM Diversity.

5 step T-GEM course design

My personal experience and research studies have consistently shown that trigonometry is one of the most challenging topics for students in Grade 11. This is due to its abstract nature, reliance on visualization, and the need for strong foundational skills in algebra and geometry. Trigonometry involves abstract concepts like angles, unit circles, and trigonometric functions (sine, cosine, tangent), which require strong visualization skills. A study by Weber (2005) found that students who lack proficiency in algebra (e.g., solving equations, manipulating expressions) often struggle with trigonometric identities and equations. A study by Cetin (2015) found that students struggle with understanding the unit circle and the periodic nature of trigonometric functions. 

The T-GEM (Teach-Guided Inquiry-Exploration-Modeling) cycle is an instructional approach that helps students construct knowledge through inquiry and exploration. For teaching a trigonometric concept (e.g., understanding the sine function), a 5-step T-GEM cycle can be designed as follows:

1. Teach: introduce concept  

Display a unit circle with a point moving around it, and simultaneously plot the corresponding sine graph in real-time (e.g., using GeoGebra).  Highlight the connection between the angle (θ) and the sine value (sin θ).

2. Guided inquiry - explore the concept

Encourage students to explore the concept through trial and error by using GeoGebra and find the pattern by themselves. Request to manipulate the sine function by changing its amplitude, period, and phase shift. Pose questions like "How does changing the period affect the graph?" "What happens to the graph when the amplitude increases or decreases?"

3. Modelling - apply the concept

Provide a real-world scenario, such as modeling the height of a Ferris wheel rider over time or the motion of a pendulum. Show a video or animation of the real-world scenario (e.g., a Ferris wheel rotating) alongside the corresponding sine graph. Use a graphing tool to overlay the student-generated sine function on the real-world data.

4 Reflection - students reflect on their understanding and identify gaps or misconceptions.

5. Based on their reflections, the teacher revisits the Teach phase to clarify concepts or introduce new ones (e.g., cosine or tangent functions). The cycle repeats, allowing students to deepen their understanding and apply their knowledge to more complex problems.

 

Reference:

1. Weber, K. (2005). Students’ understanding of trigonometric functions. Mathematics Education Research Journal, 17(3), 91–112. https://doi.org/10.1007/BF03217423Links to an external site.

2. Cetin, N. (2015). Understanding the unit circle and trigonometric functions. International Journal of Mathematical Education in Science and Technology, 46(4), 553–563. https://doi.org/10.1080/0020739X.2014.990530

Final Analysis

Reflecting on questions I have posted, the concept of teaching shift from content to process, connect abstract concepts to real-life scenarios. Focus on trying to discover a pattern of valuing students' voice, exploration and mistakes as learning opportunities. By developing a 5 step T-GEM class, I got the chance to think, how to mobilize the concepts learned during the course and integrate inquiry based learning approach. I was encouraged to shift from teaching as telling to teaching as facilitating understanding. The biggest change might be a willingness to slow down, listen to students’ thinking, and adapt rather than just "cover" content.

The big breakthrough is to be convinced metaphor and role play can be introduced in STEM class where traditionally, STEM class means factual, abstract and direct.