Micro teaching class

I am going to teach garba dance which is a traditional dance form on Wednesday for microtechnology  lesson class.

Math Art Project Journal reflection entry

As a group, we have chosen Sharol Nau’s math artwork “How Many Triangles Do You See” for our Math art learning project from the Bridges Math & Art 2019 Conference Gallery, as a resource. All members of our group have been actively involved in the project. I have shared my method and strategy with the group.  Karmdeep has prepared Base-5 triangles model for the math art project by using two different colors for the up-facing triangle and down-facing triangle. Ziyad has prepared handouts for the interactive activity to engage our classmates. Anwar has guided us on how to present the project step by step in the class.

My experience with the project:

First of all, I have tried to understand the project through the reverse engineering strategy.  I mean, I have tried to understand the project by participating in a learning activity and by analyzing what I have noticed and experienced from the activity. First, I have counted how many triangles I can see on Base-2 triangles, on Base-3 triangles, on Base-4 triangles, and Base-5 triangles. I have noticed a certain pattern for Base-n triangles where n = 1, 2,3,4,5.

I have noticed the following pattern for the Base-5 triangle:

For the Up-facing triangles, there is 1 triangle of Base-5, 1 + 2 = 3 triangles of Base-4, 1 + 2 + 3 = 6 triangles of Base-3, 1 + 2 + 3 + 4 = 10 triangles of Base-4, and 1 + 2 + 3 + 4 + 5 = 15 triangles of Base-5.

For the Down-facing triangles, I count from the smallest base. For the smallest Base-1 there are 10 triangles, the next smallest Base-2 there are 3 triangles, the second next smallest Base-3 there is 0 triangle, and the pattern continues.

The total of the numbers Base-5 triangles is 48. Therefore, T (5) =48.

This sequence is 1, 5, 13, 27, 48, 78, and so on. 

I have reviewed the math curriculum on https://curriculum.gov.bc.ca/curriculum/mathematics.

I have found that the project is directly connected with "Patterns", "Geometry", and “Series and Sequence” Math concept. 

The project takes place in Grade 5& Grade 6 (for Patterns content), Grade 7 &Grade 8(for geometry content), Grade11&Grade12 Pre-calculus( for "Series and Sequence” Math concept). It generates an opportunity for students to understand the concept through the interactive learning experience. In other words, how does a sequence help to identify certain patterns by arranging an ordered number, and how does a series help to find out the formulas or equations through the activity.

Wordy Puzzle

I have broken the puzzle down into the smaller pieces and drew the diagram from the person who is speaking.

I do not have Brother and sister. That means, that man’s (Brother) father.

Is My Father’s son! Here, the son is a brother. My father is a father who is speaking. And that man is my son.

My Father=========My Father's son======== that Man

My Father=======me

 

Myself (I) am that man’s father.

My Son is that man.

                                                                               

The locker problem puzzle

I tried a small sample of lockers, which was 1to 20 numbers of lockers.

I noticed that the numbers of locker which have odd numbers of factors those lockers are closed and the numbers of lockers which have even numbers of factors those lockers are open. Also, the perfect numbers of lockers are also closed.

Letters from my two future students in 2029

A first student who loved my class.

The student has mentioned in the letter that he enjoyed my teaching methods and he liked to share his opinions with the other students. My teaching method helps him to become a social person. As a result, he is doing well in his profession as a manager.

A second student who didn’t like so much my class.

The student has mentioned in the letter that he was straggling to share his ideas about math concept because he didn’t like to speak with other students. He wrote that she like to share her ideas one on one instead in a group. He didn't like my teaching methods because my teaching methods were based on group discussion.

After reading these letters, I am going to make some changes in my teaching styles so that I can make the balance between those students who like to get involved in the class actively and those students who do not feel comfortable to share their ideas about the math concepts. I hope this strategy helps me to enhance my teaching methods by taking care of both kinds of students.

Math and me

Math was not my favorite subject when I was elementary student, but I liked to solve problems in many different ways. Therefore, I started to do practice a lots. After sometime, I realized that I am enjoying math when I solve math problems in various ways. When I entered high school, I started to learn about different topics of math. I like to spend my time with numbers. Math is my passion and I  feel confidence about  my math ability.

The role of representations

In the article, two kinds of mathematical representations are included such as external and internal representations. Both representations are influenced by each other. The representations facilitate the students' ability to make a comparison. Students can formulate internal representations to solve problems and to understand math ideas. Besides, representations help us understand external manifestations of math concepts such as graphs, algebraic equations, charts, and tables. Only teacher-oriented presentations are excluded from this article.

The representations include many activities. Social activities enhance students’ ability to interpret, communicate effectively through external and internal representations so that students can understand the process and its products. The activity Pictures theory, the use of visual and concrete modes of representation, and culture activities help students to understand math concept through their own experience. Moreover, students have the opportunity to interact with one another and the teacher due to these representations. Representations play an essential role in understanding math. 

I can use arrays multiplication concepts of a mathematical representation (from grade 3) that might be helpful for students in developing understanding. Arrays are useful representations of multiplication concepts.

For example, the array has 4 rows and 5 columns. Students notice that the groups in each array are equal and think of the rows as equal groups. My students will use equal groups to multiply 4 by 5. Students have 4 groups of counters and each group has 5 counters, students will add them together they have a total 20 counters. 

Questions for group discussion of Skemp article:

Questions for group discussion of Skemp article:

1.  It’s depends on the topics. If students are learning basic foundations of mathematics, teachers have to teach those topics through the instrumental math. However, if they are learning an advanced math topics, teachers have to teach the topics through the relational math.

2. It’s again depends on the topics and on the classroom requirements.

3. We have to connect the learning topics with the real life events as mathematics teachers so that some students who have anxiety about the mathematics and are able to tackle it with confidence.

Skemp : Mathematical Understanding

            As a future teacher, I totally agree with the issue Skemp has raised in this article about the instrumental understanding and relational understanding. There are three things that make me think about this, the role of Devil's Advocate, Theoretical formulation, and situational factors. 

First of all, the Devil's Advocate mentions three advantages of instrumental mathematical understanding. As a teacher, I am not going to deny the benefits of the advantages. In fact, the most of students and teachers both give priority to instant outcomes rather than the deep understanding of the math because of situational factors such as the there are limited questions going to be asked in examinations, over-burdened syllabi, and difficulty of assessment. As a result, students learn math for the short term. They do not think beyond it. They would give up the subject at some points due to instrumental understanding.

However, the four advantages of relational understanding are far more beneficial than instrumental understanding because of the theoretical formulation. I am thinking about how to encourage students and teachers both to give importance to learning relational mathematics rather than to stick with the fixed plan to learn mathematics. I believe that learning relational mathematics provides more flexibility with effective outcomes throughout students' school life. In other words, students can learn how to apply these concepts during learning math if they understand the foundation of math. They would like to pursue learning math with enthusiasm due to relational understanding.  

Hello,

I am Hemlatta Engineer.