Unit Plan & Lesson Plan

Battleground Schools

I found the history of mathematics education discussed in the article very informative. Although I knew that teaching biology and history is usually influenced by ideologies, I have never thought that the politics and ideologies, especially in countries that have democratic governments, could influence the mathematical education policies.   It was very interesting to learn that the politics of the cold war was responsible for the New Math program; a program that continued in Iran even during the years that I was a high school student despite the fact that its ineffectiveness had become clear long before that time and the program had been changed in the States where it had been originated.

I found the progressive/conservative dichotomy used to categorize the conflicting views on mathematical education useful. But what I really liked was the author’s awareness of the danger of oversimplification and the discussion of the shared views of these parties.

When I think about the math textbooks that are currently used in Canadian high school, I am reminded of the description of pre-reform math textbooks in the article. Unfortunately, the math that is taught is reduced to a series of algorithm to solve artificially created problems. Students are expected to master these rules and use them to solve problems that they are given in their homework and tests. Neither are they taught why these algorithms work nor the importance or the beauty of the problems that they are used to solve. I only can hope that the next reform pays more attention to the progressive views and incorporates more of Dewey’s ideas.

John Mason on questioning in math class

John Mason on questioning in math class 

I found Mason’s ideas interesting and applicable to inquiry-based learning. In particular, I think they provide useful insights in conducting p4c-style method of teaching that I’m especially interested in. The role of the facilitator in community of inquiry is to help the learners to ask themselves questions that lead them to the solution to the problem, rather to lead them to solutions by asking them questions that lead to answer. I found the distinction between “asking as telling” and “asking as asking” which is based on the distinction between “listening-for an expected response and listening-to what students are saying (and watching what students are doing)(p. 515)” insightful. This idea can help the facilitator in community of inquiry to find ways to engage the learners in such a manner that they lead to ask useful questions and in the course of answering those questions learn the subject that they are supposed to learn. Another interesting idea discussed in Mason’s paper is asking students “to construct examples of mathematical objects meeting various constraints. By carefully choosing the constraints so as to force students to think beyond the first (usually rather simple) example that comes to mind”(p. 516). I will try to come up with ways to use the method of formulating questions by students and constructing examples when I plan my lesson for the long practicum.

 

Reflection on micro teaching:

Based on self-reflection and the feedback, I think there purpose of our activity wasn’t clear and made students a bit confusing. We also could have allocated more time for the activity and engaging students in learning so that they could have had enough time to express their ideas and solution methods.

Lesson Plan for Micro Teaching

Shan, Amandeep, and Pari

Subject: Probability of independent event                      Lesson Number: 1 of 1

Grade: Grade 8                                                         Time: 15 minutes

Big Idea for the Lesson: Finding probability of independent event.  

PLOs:   Student would be able to learn about the following topics:

• Data Analysis - critique ways in which data is presented
• Chance and Uncertainty –To solve problems involving the probability of independent events    

Objectives:   Students are expected to learn about how to find the probability of an event by using the definition of probability.     

Materials: paper, pencils, and laptops or tablets.

Hook: (about 1 min)

Showing the 1-die situation using MIT Scratch

Introducing the pattern that all numbers increased together.

Development: (about 13 min)

·      Teacher-led: (about min 4)

*Demonstrate sample space, outcome, event, probability, experiment, and trial. (2min)

             Demonstrate the MIT Scratch simulation and the EXCEL simulation (2 min)

·      Class activity: (about 9 min)

* Inviting students to explore the 2-die situation and share their solutions. (4 min)

             

  More questions: (5 min)

  Toss a coin, toss two coins, and 3-die situation and their sample space.

Assessment: Students would be assessed on their participation and work throughout the lesson (Fist of five).

Closing: (about 1 min): Students would be advised to write down key points of the lesson on their notebook.

2 Column Solutions

Right Angles:
Given the number of sides of a polygon, what is the maximum number of
right angles it can have? (p.173)

Exit slip: Hewitt’s video reflection

The video we watched during the class showed me an interesting way of teaching math: a balance between the teacher-centered approach and the student-centered approach. By asking questions Hewitt engaged all students in learning math and by asking the whole class to answer at the same time made the class active and enjoyable. This way also allows the teachers to assess their students’ understanding as well. Long wait times and repetition help the teachers to make sure all students are on the same page.  

 

Arbitrary vs. necessary in the math curriculum

According to Hewitt, something is arbitrary “if someone could only come to know it to be true by being informed of it by some external means” such as books and teachers. That is, there is no further reason about why it is the way it is, thus anyone who wants to know it needs to be informed by external means. Arbitrary cases include, for example, naming conventions (calling squares, “square” or using Hindu-Arabic numerals for numbers). The arbitrary conventions are based on choices which have been made at some time in the past and they could have been different. In contrast, “the necessary is dependent upon the awareness students already have”. That is, the student should be able to work it out without the need to be further informed.

For a particular lesson, I will see if students do have the required awareness for the subject I am supposed to teach. If so, I will consider it necessary and introduce tasks that help students to use their awareness to work it out. Otherwise, I will consider it as arbitrary and explain the rules or terms.

Knowing what is necessary and what is arbitrary helps me make math more enjoyable for students.  Helping students to use their awareness to work out the math problems would let the student enjoy doing math (that is the most interesting part of learning math) and would not see math as a boring subject consists of numerous formula that need to be memorized.

Exit slip: SNAP math fair

I was impressed by the students’ presentations. They worked together and took turns in presenting their math puzzles to us. I really liked the stories behind the puzzles and the way that students related their puzzles to the artifacts in the museum. It made their puzzles more interesting and engaging.

I’ve also found it interesting to put students in the position of teaching and helping others to solve the problems as the best way to understand a concept/problem is to explain it to someone else; teaching is the best way of learning.

Math Fair

Math is part of our every day life. It is used to perform many different daily tasks such as packing a suitcase, planning a travel route, making strategic decisions.

Many students fear math and think they are not able to solve math problems successfully. Problem solving, which is practiced in math fair, is a great way to engage students with math in a different way from they way that math is taught in the traditional classroom. It could especially help those students who fear math.

Surely, I think it is possible to do a math fair at school. One way to do that could be finding other math teachers who are interested in doing math fair and set up a math fair in proper place at school. Another possibility could be setting up a math fair for each class separately. But the first one, I think, would be more interesting.

Nov 9.

Today, we (STs from UBC and SFU) had a meeting with the president and vice-president of Windermere. The purpose of meeting was to get more information about the school’s rules and regulations and to get familiar with each other.

Nov 10.

I’ve decided to do some inquiry about garden based learning in Windermere as I’ve heard from my FA that Windermere has a big garden. I toured around the garden. The garden includes a student-built 16' by 20' greenhouse, thirteen beds and a composting system. They have also sowed over-winter ‘cover crops’, which restore fertility and humus, and enrich the soil for planting next spring. The garden provides vegetables for school cafeteria.

Although this provides a great hands-on learning opportunity for students, unfortunately the leadership program is the only one that uses the garden.

Nov 12.

Today, I attended a food and nutrition class that had planed to cook Clam Chowder soup. Teacher distributed the recipe, explained each of the ingredients and explained how to find or select them. She also shared some tips and techniques regarding food and kitchen safety and hygiene. Students first were asked to observe how their teacher cooks to get ready to cook their own soup. It was a hands-on experience that helps students participate actively in cooking process. Each group used tools with different colors so that the teacher could recognize how each group did their job.

Nov 13.

Today, I attended a presentation on working with students with learning disabilities presented by the Special Education Department Head. A student who graduated from special education program at Windermere was asked to share her life experience with us. She is attending college and living her life independently, just with a small help from her family. That was an interesting presentation that showed us how students with different learning abilities should be taught. 

Nov 5.

Today, I have attended a food and nutrition class to see how students are taught cooking skills. However, I found that they were not cooking anything today. I talked to the teacher and I am going to attend this class again next week the day they will cook soup:)

I found the teacher supper organized and asked her to give me some tips on class management. Here are some of them:

Using folders with different color for each class

Keeping students assignments in different place while the grading is in progress

Planning detailed lessons

Having extra activities in the lesson plan in case there is extra time.

 

Nov 6.

Today, my FA came to Windermere to meet up with my SA and join me in a visual art (painting) class. The class included four different levels of students (grade 9,10,11, and 12). The teacher explained that having mixed class is not unusual in Vancouver. Each grade had and was working on different assignments. I found one of the assignments very interesting. This assignment was about identity and encouraged students to think about themselves, who they were and who they wished or wanted to be.

Nov 2. First day of short practicum:

 I got to school around 7:45 am and met other STs from UBC at schools’ office. We met the vice-principal in his office. After a detailed orientation, we toured around the school and met the staff and teachers.  They were very warm and welcoming. The school atmosphere was very friendly.

I have attended three different math classes including my sponsoring teacher class.  We have also planed what lessons I would cover during the second week. I also got free math textbooks :)

Nov 3.

Today, I have attended a Mandarin class as my SA recommended. That was an interesting experience. I didn’t know the language, but the teacher and students actions attracted my attention.

Nov 4.

In the education system I attended, we as students were assigned to a classroom and different teachers came to our classroom and taught different subjects. But here is the opposite of what I experienced. Students go to different teachers’ office for different subjects. I found it quite interesting that each teacher has an office. The teachers have the opportunity to design their classroom suited for their method of teaching and the activities they are going to conduct.

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