Micro teaching topic

I am going to discuss the benefits of exercise in our daily life, and going to demonstrate some basic exercises for healthy living.

Wordy puzzle

From the first sentence we get to know that the person who is describing the puzzle has no brother and sister as he says, "brothers and sisters have I none". From the second sentence we get to know
that the man who is describing the puzzle is talking about himself and "that man" is his son.
The way in which this puzzle is described is very confusing as well as interesting.

Reflection on presentation

We selected the art work by Sharol Nau for our presentation. We found this art work very interesting and engaging. This art work is about "how many triangles do you see" in the given 5 base triangle. This is a very good brainstorming exercise for students. Usually when we see these type of problems, we feel curiosity to get the answer, and our mind starts thinking critically. Therefore, we thought that this art work would engage the classroom, and encourage students to think critically.

After selecting the art work, we first helped each other to completely understand the whole concept. We started thinking about the shape of the triangle, tables and patterns we can use to solve the problem, and the formula that can be used to solve this problem. Once we ourselves were cleared, we all brought different types of ideas to make this project interesting for students. We first selected the 5 base triangle for our activity, then we thought about starting from base 1, then 2 and so on, to help students understand the basics of the whole activity. Basic knowledge is very important to easily understand the whole concept. When we have the total understanding of the concept, we can solve all the other related difficult problems very easily. Then, we decided to explain the concept through table method where students only needed to calculate the upside and downside triangles on different bases, observe the pattern, and then add them together to get the answer. We also did rehearsal before our presentation where we decided who will perform which part.

I decided to make this art work on paper chart. To make it more artistic and easy to understand I choose two different color of papers to separate upside triangles and downside triangles . Each triangle is equilateral with sides 4.5cm and angles 60 degree. We can also make the same project for isosceles triangle. While making this art work I realised that how geometry can be taught to students through this project. They can learn about the properties of isosceles  triangle and equilateral triangle, base of the triangle, patterns followed to solve the problem, triangular numbers through this project.

During our presentation, I realised that we were successful in engaging our class with our presentation. Everybody was able to understand the concept and to find the number of triangles in 5 base triangle.

Locker Problem

Letters from two of your future students

One loved your class!

Hi Karmdeep,

You were my favourite teacher because you were very creative, and always brought something new to learn  in class. I never found your class boring. You increased my interest in maths. You were always there to help me and other students. You were always smiling and very friendly to all the students, I never felt hesitation before asking anything from you.

The other, not so much

Hi Karmdeep,

I didn't like your class because you always wanted us to focus on studies. You didn't  let us do  fun activities in the classroom.

I hope to teach all the students with love and care, so that they enjoy my teaching and learn good things form me. I am little worried about how students will react to my teaching.

Math and Me

When I was in school,
1) I love mathematics. Sometimes I spent my whole day just solving math problems.
2) My favourite teacher was maths teacher.
3) I used to help my friends, my brother and relatives in solving their math problems.
4) I think, I decided to become a math teacher because my friends always told  me that we can easily understand the topic when you teach us.
5) But I was never taught maths in the interesting way like through group discussions, and presentations. But I will try my best to make it more and more interesting for my students.

The role of representations in developing mathematical understanding

According to the author both internal and external representations are interconnected with each other. The examples given by the author to explain this theory convinced me in his argument. In case of internal representations we imagine the numbers and figures in our mind, and when we give them the shape on the paper they become external representations. On the other hand, when we have external representations, and we study and examine them in mind, then these representations become internal representations. Therefore, our mind analyse things internally and then visualize externally. The representational thinking depends on the individual's ability to interrupt, construct and operate effectively with both form of representations.

The article includes the base 10 blocks for multidigit addition, two different ways of presenting the same set of things, and seeing, imagining and analysing patterns of numerical values like Fibonacci series. It is explained in this article through example, one particular mode of representation does not improve student's conceptual understanding and representational thinking.  Students who use both analytical and visual representations are able to solve multiple types of problems.

 Mathematical representation of fractions is not included in this article. Fractions are very easy to understand through pictures. I will ask students what they can see in this picture. I will give them time to observe the picture. There must be different answers. Some will count the whole parts of the circle, some will count the shaded parts, whereas the others will count the unshaded parts of the circle. After that, to calculate the fractions I will ask them to observe how many parts are shaded out of total number of parts. In first case the answer would be 4 out of 5 is shaded, which is the fraction. We can do the same for unshaded parts. I will also explain the concept of numerator and denominator,

Richard Skemp on instrumental vs. relational ways of knowing mathematics

The first thing is that we can connect the concept of Faux Amis with mathematics. In mathematics the word understanding has two different meanings which are relational understanding and instrumental understanding. It depends on a person how he or she takes it. There are all kind of students in the classrooms, some of them want to understand concepts instrumentally because they just don't want to know all the explanation behind the concept. Whereas others want to get the depth-in knowledge of the concept.

Secondly, after reading the examples of instrumental understanding, it made me think that most of the time  I had been taught in the instrumental way. Only the formulas were given to solve the problems. After that I came to realise that why in school I liked some teacher's style of teaching more than other. Some of them teach relationally which was easy to understand, on the other hand, some just gave the formulas to solve the problems. In the end, there is a difference between learning the formula and understanding the formula. If you learn the formula, you may think that you have understand the formula, but in fact you haven't understand it. By learning formula you will only be able to solve similar type of questions.

According to me, instrumental understanding do have some advantages over relational understanding. As it is written in the article, there are some topics those are difficult to understand relationally. Otherwise, teachers should try their best to teach students relationally.

Hello everyone !

This is Karmdeep Bagri