Today, Etienne and I looked at the curriculum for calculus 12 (taught in high school).  We looked at the content material and the way in which the curriculum was structured.

First of all, the content was similar to the one Peri and I had studied in our high school calculus classes.  The main focus of the material is on differentiation and integration.  However, there were some novel features.  The material included a section dealing with the historical foundation of calculus.  Students were expected to know about the different mathematicians who contributed substantially to the material presented.  Newton, DesCartes, Leibniz, and others, are studied.  This brings history into the context of mathematics.

Another feature of the curriculum was its emphasis on assessment of the material taught.  The curriculum provides criteria by which the students can self-assess their own or others' work.  The assessment criteria are specific to each section of the curriculum.  Students are expected to work out problems on their own or with others, and to develop innovative ways to both answer problems and to self-correct their own problem-solving skills.

Lesson plan

Subject: Saffron

Time: 10 minutes

Big Idea or Question for the Lesson: why saffron is the most expensive spice in the world?

Objective: Students will be able to explain why saffron is the most expensive spice in the world.

Materials:  Saffron and Saffron ice cream

Assessment Plan: The entire students should be able to answer the big question.

Hook and Introduction: (1 min)

Check for prior knowledge

Opening up by asking if anyone taste or smell saffron

Development: (about 8 min)

Teacher-led: Present some information

Independent Work: Students smell and taste saffron

Group Activity: Students work in pairs to see what part of plant saffron come from and share their ideas.

Closing (1 min):

Check for understanding by sharing observations with the class, taking it a step further to ask students to think if there is any benefit in using saffron.

 

 

 

 

The Giant Soup Can Puzzle

The real soup can has dimensions of 10 cm (height) and 3.5 cm (radius). So the ratio of its height to radius is 10/3.5

My bike (as an average bike) has length of 175cm. Based on the picture, it seems that the length of the tank is 2.5 times longer than the length of the bike.

So the length of the tank is estimated to be 2.5*175= 437.5 cm ~ 4.30 m

Using the above ratio, the tank’s radius is estimated to be 150 cm ~ 1.5 m.

Thus, the volume of the tank is estimated to be 30 m³.

Two imaginary letters

Dear Ms. Ghazi,

This is Elli from your math 9 class. I am writing to you because one of my Profs at the university reminds me of you. He, like you, speaks in a flat monotone voice. I am really struggling in this class as I did in yours. I know you did care about our learning. You were trying to do your best to make mathematical concepts as simple as possible for students to grasp. I really appreciated it, but your monotonous voice often made me fall asleep in the math class. I had to self-teach myself and even sometimes had to ask for help to understand the material completely. I hope this criticism helps.

***************

If teachers can’t be heard, they can’t effectively teach their students. Voice is one of the most effective tools that a teacher has. Expressive voice can catch students’ attention, make the subject interesting and inspire them to learn. This letter indicates that I need to work on my voice to be able to use it as an effective teaching tool.

Dear Ms. Ghazi,

This is Sara from your math 8 class. I am writing to you to thank you because of your wonderful class. Your way of teaching not only improved our reasoning skills, but also helped us learn how to use these skills in our everyday life. I really enjoyed our activities in which we practiced giving and asking good reasons, making good distinctions and connections, making valid inferences, discovering assumption, generalizing, asking good questions, using and recognizing criteria, and judging well. I’ve learned to seek and examine reasons in order to accept any claim and I’ve also learned how to make my own choices and judgments based on reasons.

These skills prepared me for adulthood. They have enabled me to identify and to refuse to accept irrational and unreasonable arguments made in public debates. These skills also have helped me to protect myself from believing what others want me to believe without adequate inquiry, to embrace my responsibilities, and so on. Using these skills makes my every day life more meaningful and enjoyable.

***************

It is important to help students to use their reasoning skills improved by math in their every day life. From this letter, I take that students appreciate math and see it’s importance if we as teachers be able to teach math in a way that enable students to use their reasoning skills in their every day lives. 

Reflection: Math/Art Project

Math is not just about formulas and logic, but also about patterns and beauty. Math has been described as the science of patterns. It has also been described as the language of the universe. Math and art have a long historical relationship. Math can be perceived in arts such as music, dance, and architecture. Since ancient times, mathematics has been used to create beautiful designs in the architecture and decoration of palaces, cathedrals, and mosques. Many patterns in music can be also described by mathematics.

Transformations and symmetries are fundamental concepts that play an important role in both math and art. We enjoy looking at symmetrical things because our brains have a tendency to find meaningful patterns within our everyday experiences. We like geometrical shapes for the same reason, and these often form a basis for dance. Symmetry and geometry are used in dance to improve performances and make them visually appealing.

I think math-dance is an interesting way to physically engage students in math class, a way to bring movement, collaboration, and fun into math class. It helps students be active, enjoy learning math, and also see the connection between art and math. I believe that this project can go deeper with other mathematical concepts and be used in many math lessons.

Reflection: Mathematics for Social Justice

It is important to remember what the purpose of learning math is. Unfortunately, the purpose of math, unlike the study of humanities, seems to be not clear in Western system of education.

The Greeks moved away from a very practical approach to mathematics – a subject created by the Egyptian and Babylonian civilizations as a response to their practical problems and was based on experience – to a more abstract approach. They realized that mathematics dealing with numbers and figures can be dealt with in the abstraction. In fact, they found the connection between mathematics and reasoning.

Consider the following from Plato’s Republic (Book VII):

“The knowledge at which geometry aims is knowledge of the eternal, and not of anything perishing and transient. Geometry will draw the soul towards truth, and create the sprit of philosophy, and raise up that which is now unhappily allowed to fall down. Therefore, nothing should be more sternly laid down than the inhabitants of your fair city should by all means learn geometry.” Although this is from ancient source, one can find the similar idea for example in Morris Kline’s Mathematics for Liberal Art, a 20^th century mathematician and math educator.

The importance of this major step in advancement of mathematics should never be forgotten. It was this step that let to tremendous growth in knowledge in both math and science in sixteenth and seventeenth century.

 

Despite this, in western educational system, mathematics is often seen just as a useful means. As Thomas Teloar put it “ The honing of reasoning skills—a critical component of a liberal education—is often downplayed or completely neglected in mathematics education. The cohesive structure of mathematics is often discarded to more quickly get to the ‘useful’ results, but then these ‘useful’ results are often useless because this language of mathematics is without its cohesive structure.”

 

I  disagree with the author idea of connecting math with social justice because first, it is not the purpose of teaching math to teach social justice as it is not the purpose of, say, social sciences to teach math. Second, it could distract students from what the need to learn in a math class.

Dishes puzzle

My plans for the Oct. 23 Pro-D conferences

I am still looking for a conference or an activity in Vancouver. If I can’t find any, I will be attending the Northwest Math Conference in Whistler.

My own most- and least-inspiring math teachers

All my math teachers, as long as I can remember, had at least three things in common. They were serious, very organized, and knowledgeable in their teaching subjects, however some of them were better lecturers. 

Although my math classes lacked the excitement, I really liked math and solving puzzles during my elementary years. Among different math courses, I had during my secondary years, I found myself interested in geometry and the new math problems because I found them like puzzles. But I hated algebra and trigonometry because they didn’t make any sense to me. My teachers always were surprised at my grades: two of them were high and the other two were very low.

However, I can say the most inspiring teacher for me was my grade one teacher whose influence I still can feel on my life. I still remember a classroom full fun, exciting science activities, and a lovely teacher who cared for her students.