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
Alice's Blog
Wednesday, December 16, 2015
Monday, December 7, 2015
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.
Thursday, December 3, 2015
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.
Saturday, November 28, 2015
Wednesday, November 25, 2015
Monday, November 23, 2015
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.
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