John Mason- On questioning in Class

1) One of the examples that were given in this article was that in Japan, teachers ask mathematical questions differently than we ask in Canada. They ask their students, "in how many different ways can you solve this"? This question is inquiry based and can very well be used in secondary-school mathematics learning. However, the rest of the techniques that John talks about such as, asking a genuine question instead of asking as telling and not asking as asking; I will not consider them to be helpful to encourage inquiry-based learning because they are not prompting a thought process that is initiated by the students themselves. In this process, there is a big role that the teacher plays hence not really inquiry based learning. On the other hand, where John talks about intervening when the student is stuck on a problem and knowing when to intervene and how often to intervene is a great example of inquiry-based learning.

2) I had a really good short practicum where both my FA and my SA's were really happy with my first lesson. However, one of the things they told me that I need to work on is "asking questions". According to them I ask too many questions by probing them too many times. I realized right away what they were talking about and I had to fix this about my teaching. As John mentions in his article that asking as telling may not be the most efficient technique which I completely agree with. However, the biggest change that I am going to make in my unit plan after reading this article is by adding things like, "how many different solutions are possible for this problem?" or "what do you do when you get stuck" and have problems on my lesson plans where the most students will get stuck. Also, the technique of the teacher getting stuck him/herself is really impressive which I will try to use during my long practicum.

Micro teaching Reflection

My micro teaching experience was not so great. There were a few things that could have gone better as a lot of our evaluation forms talk about having a rough start with a weak hook. Also, we could have used some sort of props in our activity to make it more interesting. Doing two examples to teach the lesson was not vey effective as it came across as a lot of talking to some of our peers. We did good in terms of timing and engaging the students. I think the activity had an interesting touch to it as it was called the lifespan card activity which got people interested in it. Also, our plan did not include an extension in case we had extra time so I made that on the spot bu adding a few new things to the activity. 

Lesson Plan- Micro Teaching

I had this done yesterday as a group but forgot to post it on my blog.

Teachers: Jessica, Mandeep, Simran

Topic	Intro to Percentages
Grade level	8
PLO	A3 demonstrate an understanding of percents greater than or equal to 0%
Objective	Students will be able to use the given percentage to find the required information. Students will be able to find percentage of two given whole numbers. Students will have the understanding of the percentage sign.
Materials	White board and marker. Lifespan cards.
Prior Knowledge	Students know division and multiplication.
Intro/Hook	4 mins	Percentage sign %, no calculations here. Discuss how many pennies make up a dollar. (nickels, dimes, quarters). Each group still represents one dollar. On the board, draw out a circle representing a dollar and then fill in 25% to represent 1 quarter.
Development	4 mins	Finding a percent of any number with respect to another number (comparative number) Here percent represent the fraction with denominator 100,While the number represent the amount. Example1 -  if i have 40  halloween  candies ,i gave  10 % of candies to my son ,then what is the number of  candies i gave to my son? Solution- Here, 40 is comparative number    10% of 40 candies = 10/100* 40 =  4 candies to my son Example 2-   If i have 40 halloween candies ,i gave 10 to my daughter,then what is the percentage of the candies i gave to my daughter? Solution-       10/40*100 =25 % of  the total number of candies to my daughter
Activity	3 mins	-Give each student a “Lifespan” card - Ask them to fill out the blanks on the card, their age etc - Explain the question on the card and tell them to do their calculations on the back of the card - let the students work in pairs of two for 2 minutes - go around and make sure everyone's clear on the activity
Closure	1 min	go over the idea of percentage and how it can be used in daily life. For ex: at the shopping mall, calculating the time you have left before you have to get ready for school or dividing your food into portions and eat a certain percentage at a time. It becomes very easy to picture what's gone and what's left if you convert things into percentage.

----------------------------------------

BC Math 8 and 9 curriculum guide

A3 demonstrate an understanding of percents greater than or equal to 0% [CN, PS, R, V]

• provide a context where a percent may be more than 100% or between 0% and 1%
• represent a given fractional percent using grid paper represent a given percent greater than 100 using grid paper
• determine the percent represented by a given shaded region on a grid, and record it in decimal, fractional, and percent form
• express a given percent in decimal or fractional form
• express a given decimal in percent or fractional form
• express a given fraction in decimal or percent form
• solve a given problem involving percents solve a given problem involving combined percents (e.g., addition of percents, such as GST + PST)
• solve a given problem that involves finding the percent of a percent (e.g., A population increased by 10% one year and then 15% the next year. Explain why there was not a 25% increase in population over the two years.)

Two column solution- The Leap Birthday

Please see the attached for my two column solution

Exit slip- video

The videos that we watched dring class were exceptionally good. A few things that stuck with me were:
- learning is now about being told, it's about exploring and getting to the point where the "aha" moment happens.
- I do not want to be a teacher; I want to be a facilitator.
- using classroom as tangibles is a great idea as kids will remember the classroom where the learning happened for the rest of their lives.
- sometimes less is more. Letting go of control can help students learn faster and better at times.
- a lesson plan should not be about what the teacher is going to do in the lesson, it should be about what the students will be doing during class and how the teacher helps them do that.

Arbitrary and Necessary

This article is one of the finest articles I have read so far about teaching Mathematics. The author says it very clearly that arbitrary is something that students have to be informed by an external mean; whereas, necessary is something that students can become aware of without any effort made by an external source. Arbitrary part of your lesson is that is very definitive and cannot be changed as it has been set by someone a long time ago. For example, teaching students about locating hypotenuse and the opposite side on a triangle is teaching them arbitrary part of the lesson. Necessary part of the lesson would be something that students may discover on their own based on all they knowledge that is given to them. For example, students may figure out on their own that when doing fraction cancellation, one may start with any common factor first and continue cancelling instead of always starting with the biggest common factor.

This article was an eye opener for me in terms of thinking, before teaching or even planning, about what to put in your lesson and what to leave for the students to figure out on their own. My lessons so far have been very heavy on examples. I will  be teaching one Math 8 challenge class which I think will benefit from only learning arbitrary things from my lesson and it would be better if I leave necessary things for them to figure out for themselves. As the author mentions that if a teacher decides to teach something that is necessary then a student may take it as a 'fact' and decide to memorize it. Whereas, if this concept is taught through awareness, which is by letting them figuring it out on their own, it would sit in their minds as a necessary concept that they came up with on their own and they do not need to memorize it. 

Experience at the SNAP Math Fair

My experience at the SNAP Math Fair on last Wednesday was memorable one that I will always look back at and reflect upon when or if organizing a Math fair in the future. It was a fortunate and unfortunate at the same time that I could only spend time with one of the groups presenting at the fair. I failed to walk around and stop by as many projects as I could in the given time, however, I spent all my time working with one set of girls presenting a problem on patterns and its relation with Fibonacci series.  

They had a set of blocks laid on the ground in a certain manner and the guest was supposed to flip it within the given number of moves. They had three different set of blocks which I was able to do fairly quickly. However, they had an extension to their problem which even they did not know the solution for. I decided to take on the challenge and started to work on the extension problem. Within minutes these two girls who were presenting the problem, got so interested in what I was trying to do that they decided to help me find the solution. I was trying to look for a pattern in the problem so that we could figure out the relation of this problem with Fibonacci series. These girls went beyond what they had in terms of supplies and used their shoes and my pen and my phone as additional number of boxes that they needed in order to find out a solution to a particular series. 

Unfortunately, I was not able to find a relation between the problem and the Fibonacci series but the whole experience with the girls trying to find the solution that I will remember for the rest of my life. I was able to build a relationship with the girls bu the end of the session that they wanted to take my contact number in case I come up with a solution so I can keep them updated on that. I told them that I will get in touch with their teacher in case I come up with a solution. Overall, it was a great experience to be able to connect with these two girls and have them so interested in doing Math.