Unit Plan for Trigonometry

Here is my unit plan for IB11HL class on Trigonometry:
https://drive.google.com/file/d/0B4Z716GXspHySERKRklvaW1MZE1Bd2ZBcVhGWTBrRjltY1NF/view?usp=sharing

Here is my lesson plan:
https://drive.google.com/file/d/0B4Z716GXspHybUFPYkMtQmJtLXBIMVdyNnJVSGZNeVFkeTZF/view?usp=sharing

Here is the class worksheet I will be using:
https://drive.google.com/file/d/0B4Z716GXspHyTk9NLXpVWU5QRUgtSmdtY3l6OE1ybk8xekhr/view?usp=sharing

John Mason article: reflection on questioning

I agree with John Mason that asking good question promotes inquiry-based learning. We want students to question things. For math, we should promote students to question a theorem on not only how it works, but also why it works. Some questions may be very challenging to answer, and John Mason suggested that teacher need to help students develop resilience and resourcefulness. Everyone will get stuck some time, and it is important to encourage students. Just like the 2-column problem we did in class, we should value our thinking process, even the mistakes and the wrong turns. As teachers do examples in class, we can comment on our own experience when doing the problem, what mistakes we made and most importantly what strategies we used when we get stuck. Resilience is especially important in math and by modeling the process, it will help student overcome the anxiety in doing math. Math is not just for geniuses, if you work hard you will develop skills to be successful in math.

 “Teaching by listening” is also very important. Questioning not only guides students through a problem, it also gives teachers feedback. Listening to what the students are doing rather than just for the answer, teachers will better assess students’ knowledge. Another useful teaching strategies is to ask students create their own problem. When students create their own problem, they have to more thoroughly think through the concept, and really understand each step. To challenge students to the next step, teachers can add constraints to the problems they are creating, and make them to think in a deeper level and applying the concept.  Lastly, I would be very excited to have students asking me challenging questions or even question that I don’t know. I might ask them to come in at lunch time, look at the problem together and see what we can do together. Asking difficult questions shows me that they are thinking in a deeper level and I have done my job in teaching them the curriculum, challenging them to inquiry, and let them advance beyond my knowledge.

Reflection: Quasi-empirical Reasoning (Lakatos)

“Lakatos claims that mathematical theorems are not irrefutable true statements, but conjectures,” and this got me thinking about how my math knowledge was learned and how math is usually taught as schools. Based on my experiences, math was taught by assuming the theorems are correct, and my math classes focused on how the theorems worked and applied. At the university level, my professors would sometimes proof theorems, but I have never seen anyone in the class question the validity of the proof, or even propose a different way of proofing a theorem. I think this connects to inquiry-based learning where we should promote students to question a theorem on not only how it works, but also why it works. At secondary level, formal mathematical proofs may be too complex and challenging for students to generate themselves. However, I think if we showed the proof and pose good guiding questions while explaining the proof, it will really promote inquiry-based learning, let students have a deeper understanding in a theorem, and have a stronger mathematical way of thinking. Lakatos also said “conjectures can be a starting point of the growth of knowledge.” Relating to that, the IB program has an internal assessment where students investigate on an inquiry math project on a topic they are interested, and I think that is a great example of what the author wanted to portray. In a regular class, My SAs also work very hard in making good real-life projects for students to do, and that is also something I hope to continue when I am teaching in my long practicum.  

Reflection: micro teaching of Infinite Geometric series

Our micro-teaching lesson did not go as well as I thought it would and I want to thank everyone for those very constructive feedbacks with great suggestions. First, I do agree that we should have a better hook, and using the real life application, which we used as our ending, could have been a better introduction. Another suggestion was to have a prop, and I think having a basketball and showing the bounce could also be a better introduction. We asked a few questions on the geometric sequence in the beginning, and I thought checking students’ prior knowledge could be done better or in another way since most people did not feel like their prior knowledge was assessed. Our intention for the four questions as an introduction was to use the geometric series formula as reminder and checking students’ prior knowledge from last class, and letting students find the infinite sum, which they are seeing for the first time, as an exploration and inquiry by using calculator, the formula or any other method. Then, we built up upon the geometric series formula and used that to generate the formula for infinite geometric series and talked about restrictions. We were planning to talk about divergence and convergence before generating the formula, however, because a student asked a question, therefore we switched the order from the plan. The first parts were also taking longer than what we expected so we did not follow our lesson plan on having the 3 groups and have students come up to the board to write the solutions. Instead, we only had time to talk about one question. Therefore, our participatory activity was not as engaging, collaborative and involving team work as the 3-group activity that we wanted to do. Lastly, I feel like the time management in all parts could have been better.

2-column solution. "Reversals"

lesson plan for micro-teaching

Reflection: Hewitt’s teaching (video)

I like how Hewitt moved around the classroom, not just stayed at the black board. He shows a visual and physical demonstration of a number line, and it was easy for students to follow and participate. Moving around the classroom also helps students pay attention and stay focused. I find Hewitt uses more verbal scaffolding, and not writing everything on the board. I think this may be difficult to do in B.C because we have a very diversity population and many students are ELL. I find writing things down and drawing diagram help ELL student understand better. Hewitt also uses a lot of repetition, which I think is very important in helping any students to understand. He also pauses and allows a lot of wait time for students to think and answer. I find giving long wait time very hard for me as a beginning teacher and I hope to improve on wait time and time management in the classroom. It is also surprising to me how well the whole class participated. I also hope to engage the students and have everyone participate in the lesson like Hewitt.