For my micro-teaching lesson, I taught my peers to make fruit/vegetable sculptures based on Saxton Freymann's picture books. Initially, I had wanted to make giraffes out of bananas but decided against it since it was too complicated to finish in 10 minutes. Hence, I simplified the lesson to using bell peppers and adding lively features such as eyes and a smile. Overall, I think the lesson went well and everyone enjoyed this fun activity.
In my first micro-teaching lesson in another class, I ran out of time so I wanted to be extra careful not to plan too much. But in this case, since the activity had been simplified and everyone was cooperative, we were left with a few minutes to spare. I expounded on the picture books I showed them in the beginning. In hindsight, I would have elaborated more on the sculptures themselves, such as adding other distinctive elements on each bell pepper or ask the students to brainstorm other extension ideas. Moreover, I intended the "take a photo of your final product" to be the assessment part but it may not have come across clear enough because some feedback indicated a lack of thorough assessment.
Monday, October 26, 2015
Response - Battleground Schools reading
For this blog response, please comment on the fraught history of mathematics education in North America and the ways that you think this might affect your own situation as a math teacher.
I was surprised to discover so much contention in the history of mathematics education in North America. Progressivists had thought of and Dewey attempted to implement inquiry-based learning in the last century with little reform in the general scene of math education. However, the university-level math curriculum gained ground in response to the space race between the former Soviet Union and the United States. I started to consider where I fit into this history that unfolded in the US. As an elementary student in California, I remembered learning math in a basic, traditionalist way. When I moved back to Taiwan, I experienced an even more "conservative" approach to teaching mathematics but at a higher level. The international ranking of different countries eighth graders' mathematical ability heightened the emphasis on math education in North America and thereby influencing NCTM Standards.
For my future career as a math teacher, I will certainly encounter parents and other teachers who are math-phobic. In addition, there will be ongoing "math wars" and revisions to the current math curriculum. I believe that the students should come out of the math classroom feeling accomplished about the sense-making and practical applications of mathematics, not merely the drill and skill of accurate computation.
Wednesday, October 21, 2015
Lesson plan for micro-teaching: Food for thought
Teacher: Jessica Chen
Topic: Food for thought
Topic: Food for thought
Objective
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Teach students that you can play with your food, using fruits and
vegetables to make interesting, everyday objects.
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Materials
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Bell peppers, beans, exacto knives.
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Prior Knowledge
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Safe use of exacto knives.
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Intro/Hook
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Materials prepared in front of each student. Ask “What can we make
out of this?”
Show the picture books by Saxton Freymann. |
2-3 min.
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Development
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1. Teacher
demonstration.
2. Individual
student work.
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5-6 min.
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Assessment
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Students take photos of their creations.
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1 min.
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Closure
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Remarks about ways you can have fun with your food.
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1 min.
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Monday, October 19, 2015
The giant soup can puzzle
I think everyone will have different points of measure so the answers we come up with will be different. I also noticed that the camera angle of this photo, the way the bike is positioned, and the partially buried portion of the water tank can alter the results. With that said, I estimate from this picture that the water tank's diameter is 2 times the bike's height.
From a simple Google search result, "The dimensions of a typical bicycle are a handlebar height of 0.75 - 1.10 m". I will estimate that Susan's bike is 1 m, or 100 cm. Therefore, the diameter of the water tank is 100 cm × 2 = 200 cm, and the radius is 100 cm.
According to the other picture of the Campbell soup can and my own measurement of one at home, the ratio of the height of the soup can to the diameter is 1.51. For the water tank, the length can be determined by 200 cm × 1.51 = 302 cm.
The volume of the water tank is estimated to be (pi)×(radius^2)×(height)=pi×(100 cm)^2× (302 cm)=9488000 cm^3 = 9488000 ml = 9488 L.
The volume of the water tank is estimated to be (pi)×(radius^2)×(height)=pi×(100 cm)^2× (302 cm)=9488000 cm^3 = 9488000 ml = 9488 L.
Tuesday, October 13, 2015
(Imaginary) letters from future students
Dear Ms. Chen,
I was in your math class in grade 10. To this day, I always tell other people that I love learning math and you are my favorite math teacher. Why? It's because you really care about the students' learning. You would make the effort to explain a concept several times by showing different examples. I enjoyed doing the fun in-class activities that engaged me in mathematical thinking and working with my peers helped me understand better too. Whenever I felt like I needed extra help, I know that your classroom is a warm door for me even after school. Thank you for inspiring me in such a unique subject as math and genuinely caring for us students.
Dear Ms. Chen,
You might not remember me in one of your grade 11 math class. I sat in the back of the classroom where you probably don't notice much. Sometimes I had trouble hearing your voice, especially if you were speaking too fast. I didn't like my partner when we worked in group activities because he always got the answer right away so I didn't feel like trying to solve the problem. Doing the math project was fun but that's because I prefer anything other than quizzes and tests. I am sure I learned quite a bit in your class but math is still a difficult subject for me.
Reflection:
I hope to implement interesting activities in my math classroom so that it is not just pencil and paper. Also, caring for students in every aspect is one of my main goals. I will make myself available and approachable for extra help after school.
I am afraid that I may not be aware of speaking too fast or too soft in class. I hope to walk around the classroom so that I'm not always in the front talking. In addition, I would like to make different types of assessment in math such as a math project. Another thing that I'm worried about is how to pair up students, those with similar or differing levels of math together, and how to carry out group work.
Math/Art project: 60-card polyhedron
For the math/art project, my group created a deltoidal hexecontrahedron out of 60 playing cards using the template provided by George Hart. I have always been fascinated by the art seen in geometrical shapes and solids but using playing cards to construct polyhedra is a new idea to me. The slits on each card must be cut accurately since the construction is made by interlocking the cards together without tape or glue. The most difficult part was to figure out the 3-fold lock which required a little bit of bending to create the equilateral triangle with each point above the next. This task was easy for only one group member who is a very visual learner. It took the rest of us about 30 minutes individually to learn to do the 3-fold construction.
Rather than putting together 60 cards randomly, we arranged the cards in a specific pattern. Each layer is the same suit of cards in ascending order and the layers are alternating between red and black suits. This required more careful planning when we were constructing the cards but our final product looked awesome. We can explore shapes and patterns in this 60-card polyhedron. For example, we can ask students, "How many pentagons are there? How many vertices are formed by 3-fold locks?" These questions can lead to lessons in geometry about platonic solids and various other kinds of 3-dimensional models.
The fire alarm incident during our presentation gave us an opportunity to experience "teaching math outside the classroom." I think our classmates tried their best at the activity but it was more difficult than we had planned. Getting everyone's attention outside with many distractions around was not an easy task. I believe it is important for teachers to adapt to changing environments. Sometimes, unpredictable circumstances will require us to relate the material to the surrounding or give insight into other perspectives. I will continue to examine math in an artistic way, endeavor to discover/create art in math and bring these new points of view to my students.
Wednesday, October 7, 2015
Dishes puzzle
We know that every 2 guests shared a dish of rice, every 3 shared a dish of broth and every 4 shared a dish of meat. What is the smallest number of guests that can fit this scenario?
If we only take into account the first two conditions, that is, 1) every 2 guests shared a dish of rice and 2) every 3 guests shared a dish of broth, then we need at least 6 people for this to work (since 6 can be divided into both 2 and 3). Now, for the multiples of 2, 3, and 4, let's see where they share a common multiple!
Listing out the multiples:
2, 4, 6, 8, 10, 12, ...
3, 6, 9, 12, ...
4, 8, 12, ...
So 12 is our friend here. Let's consider the case where there are 12 guests. How many dishes of each type would there be?
12 ÷2 = 6 dishes of rice
12 ÷3 = 4 dishes of broth
12 ÷4 = 3 dishes of meat
6 + 4 + 3 = 13 dishes in total
The question has 65 dishes. (65 ÷ 13 = 5)
Since we multiply 13 dishes by 5 to obtain 65 dishes, we also multiply 12 guests by 5 to obtain our final answer: 60 guests in total.
I think cultural context certainly would have an effect on the problem or the attitude of students towards solving this problem. If put into a Chinese context, a student with a Chinese cultural background may be more likely to tackle the problem without much thought. Another student without this background may not be familiar to the idea of so many people sharing multiple dishes, therefore be a bit confused when solving this problem. I found this same question on the NCTM facebook page using Mexican food as the cultural context. This shows that math puzzles can be tailored to meet the specific needs of certain students/community.
If we only take into account the first two conditions, that is, 1) every 2 guests shared a dish of rice and 2) every 3 guests shared a dish of broth, then we need at least 6 people for this to work (since 6 can be divided into both 2 and 3). Now, for the multiples of 2, 3, and 4, let's see where they share a common multiple!
Listing out the multiples:
2, 4, 6, 8, 10, 12, ...
3, 6, 9, 12, ...
4, 8, 12, ...
So 12 is our friend here. Let's consider the case where there are 12 guests. How many dishes of each type would there be?
12 ÷2 = 6 dishes of rice
12 ÷3 = 4 dishes of broth
12 ÷4 = 3 dishes of meat
6 + 4 + 3 = 13 dishes in total
The question has 65 dishes. (65 ÷ 13 = 5)
Since we multiply 13 dishes by 5 to obtain 65 dishes, we also multiply 12 guests by 5 to obtain our final answer: 60 guests in total.
I think cultural context certainly would have an effect on the problem or the attitude of students towards solving this problem. If put into a Chinese context, a student with a Chinese cultural background may be more likely to tackle the problem without much thought. Another student without this background may not be familiar to the idea of so many people sharing multiple dishes, therefore be a bit confused when solving this problem. I found this same question on the NCTM facebook page using Mexican food as the cultural context. This shows that math puzzles can be tailored to meet the specific needs of certain students/community.
Monday, October 5, 2015
Mathematics for social justice
After reading the excerpts from David Stocker's Maththatmatters, I have gained a whole new perspective on the teaching of mathematics in school. Through thoughtful planning with the goal of engaging students' interest, the teacher can transform ordinary math lessons to topics that address social and environmental issues in the world. I was impressed by how often we take a "real-life" problem to do math operations when instead it may be more beneficial to apply math skills on issues that matter to the society. In this context, Stocker's topics would not necessarily be considered as "neutral" because he does incorporate his own point of view. This kind of approach tends to raise concerns over the bias of a topic but I believe it is also our duty to encourage students to think critically.
Even though Stocker's book focuses on middle school mathematics, I am positive that these topics can be tailored to teach secondary mathematics as well. Secondary students may be able to take a stand strongly on these issues or going further, to develop some topics into their own research projects. This will definitely be more time-consuming but ultimately the students will learn math in more depth, consider social justice matters and eventually take actions to make a brighter future.
Even though Stocker's book focuses on middle school mathematics, I am positive that these topics can be tailored to teach secondary mathematics as well. Secondary students may be able to take a stand strongly on these issues or going further, to develop some topics into their own research projects. This will definitely be more time-consuming but ultimately the students will learn math in more depth, consider social justice matters and eventually take actions to make a brighter future.
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