Reflection on John Mason's Article

John Mason's article on questioning in Mathematics reminds me of what I have recently read in an award winning book "The Mathematical Mindset" that Mathematics is taught in a way that it seems we throw at students the answers to the questions they never asked. This perspective leads into asking why we don't let students ask questions before we begin answering their never-asked questions.

Questioning can be very effective in promoting inquiry-based learning, as it relies on students' explorations, their statements, and their ‘truth’. In inquiry-based learning, questions are genuine not rhetorical which is common in Math classroom, but not so useful in advancing students' learning as suggested by Mason.

I would like to extend the idea of questioning to dialogue, i.e. teaching Math via dialogue. I would love to have my students “talk” Math. Healthy back and forth discussions where the “talk” is based on understanding and exposure rather than facts and figures is a skill worth achieving.

In other words, creating a class atmosphere where learning is not about getting the right answer, but the procedure and the thought process, i.e. encouraging students to share their ideas, thoughts, and understanding without the fear of being wrong. The focus should be on justifying responses and backing them up with understanding rather than certainty, as Mason describes in the article.

The quickest response to incorporating Mason’s ideas into unit planning for the long practicum is asking the self, i.e. asking questions like what might go wrong in implementing a certain idea, how would the students react if presented a certain problem, and how can I make smooth transitions from one topic/activity to the other.

Lastly, ending the lesson in ways that genuinely raises students' curiosity and interest in the topic covered rather than having them answer forceful questions that seem to have no benefit in their eyes. Having them seeing me getting un-stuck when stuck, and allowing them to solve 'their-way' are other ways of having students see the creativity Math has to offer.

Microteaching !! Reflection

Based on self-reflection and the thoughtful feedback and comments we (me and my teammates) have recevied from our collesgues, there is definitely room for improvement in the lesson plan and its delivery. The participatory component of the lesson plan could have been better, as it would have been nice if we had incorporated a more intriguing and engaging “hook” into the lesson. It was a good opportunity to put into practice what we have been learning about student-centerd approach and problem based learning for teaching Mathematics.

However, it was suggested that we should have spent a few minutes solving and explaining the problem we posed via what we call the traditional teacher-centerd classrooom instead of asking the students to solve it. The “perfect” balance between the teacher-centered approach and the student-centered appraoch will become natural with practice and time. I look forward to implementing and improving my lesson plan and teaching procedures based on the feedback I’ve received!

Microteaching !!

Applications of Quadratic Functions

Subject: Math

Grade level: 11

Duration: 15 minutes

Prescribed Learning Outcomes:

 It is expected that students will be able to:

-C4: Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph, including: vertex and to solve problems

-C5. Solve problems that involve quadratic equations

Objectives:

Students will be able to:

-Learn how to analyze and solve real-life problems involving quadratic functions

-Identify the relationships between maximum/minimum problems and quadratic functions

Materials/Resources:

-white boards in the classroom

-Handouts of the word problems

  

Lesson Plan
Introduction	5 minutes	-Divide the class into groups of three -Handout the “hook” question to each group and encourage the students to come up with the dimensions that would enclose the largest area without using algebra A rancher has 800m of fencing to enclose a rectangular cattle pen along a river bank. There is no fencing needed along the river bank. Can you guess which dimensions would enclose the largest area? (HINT: the dimensions are integers)
Entry	5 minutes	-Go over the rancher question on the board, using algebraic method Ask one or two students to  come to the board and present their solutions. Encourage those students that think they've made mistakes. This is to promote mathematical thinking and that mistakes are part of the learning process.
Development	~4 minutes	-Ask the students to work on a similar problem individually You are trying to build a rectangular dog fence in your backyard using 600cm of fencing material. Since your dog is relatively big, you goal is to make a fence with the largest area possible using the given material. What should the dimensions of the fence be?
Closing	1 minute	-Go over the solution together.

Adaptations and Modifications:

-Allow students to work in groups

-Provide more time for work if needed

Assessment/Evaluation:

-Go around the classroom while the students solve the problems together in groups on the board to check their understanding

-Observe the students while they work independently and identify what the most commonly made mistakes are

2-Column Puzzle

Exit Slip - Mon, Nov 23

The video we watched reminds me of Silent Way, one of the methods used to teach pronunciation. It doesn't make sense when we first think about it, as pronunciation is teaching sounds, segmentals, and suprasegmentals that are to be taught by modeling and getting students exposed to the correct models, but it makes perfect sense when we begin to think beyond the surface. I made this link between Math and teaching English pronunciation via Silent Way, as I found the video did exactly that, i.e. the students were well engaged and actively participated without the typical and traditional pencil/paper approach. I look forward to using this approach with slight modifications depending on the topic/subject of course in my classroom.

Moreover, the video demonstrated long pauses when the teacher posed a question. This is something that I think all educators should consider to allow enough thinking time for students to get their cognitive processes working. 

Arbitrary vs. Necessary in the Math Curriculum

This article allows its readers to think about things that we generally tend to ignore under the umbrella of ‘that’s the way it is”, or ‘that’s the convention’, or even ‘true-because-teacher-says-so’. My question if what if I let the students break the convention. For example, what if I let them write the y-coordinate before they write the x-coordinate. Would it be looked upon as breaking the rules, or would it give the students some power or control over Math, I wonder. Moreover, I wouldn’t want to answer ‘the-why’ questions from the students via ‘that’s the convention’. I would like to support their curiosity and get them explore ‘why that’s the way it is’. However, there is a fine line between satisfying curiosity, and exploring for purpose and getting confused, i.e. as an educator, I’d need to be careful for not getting the students confused by sharing too much information and getting them exposed to it without support.

One of the ways for defining arbitrary and necessary is by considering what can/cannot be solved. In other words, ‘arbitrary’ is information (or “received wisdom”) that may not be be worked out and is in the "realm of memory", whereas ‘necessary’ includes the properties and relationships that are in the "realm of awareness", and can be worked out, as described in the article. The decision of what’s arbitrary and what's necessary can vary from topic to topic. The question of what arbitrary and necessary are under a given topic can be responded to by considering the answers. For instance, the aspects of the lesson that can be summarized as “symbols, notation, and convention” are arbitrary, and the properties and relationships that carry good explanation to satifsy the ‘why’ are necessary. However, if one excels at explaining the ‘why’, what’s arbitrary can become necessary, as Hewitt outlines why New York is New York.

Furthermore, the differentiation between arbitrary and necessary of course influences the lesson plans, as this decision would greatly impact how much time should be spent on what and why. As teachers, we don’t want to spent too much time to what's arbitrary. Instead, our focus should be on problem based and inquiry based learning within the given topic. It's related to what's we talked about previously regarding regarding instrumental and relational thinking. We want to teach the students to think mathematically under the given topic.

SNAP Math Fair Field Trip - Exit Slip

Firstly, thanks so much Susan for giving us the incredible opportunity to work with kids outside the classroom setting where the kids are the experts, and we’re the guests. Secondly, I’m more happy than surprised to see the expected outcomes of SNAP Math Fair becoming a reality. For instance, the students delivered and communicated their projects in such a professional way; they were confident, ready, and well-prepared and having fun at the same time.

Thirdly, I love the connections educators are establishing to make Math more relevant and fun. I personally never thought of anthropology as a source of creating Math fun problems/puzzles to solve. Me and my group members (Jordan and Mandeep) had a chance to ask the students where they got the ideas from for the problem/puzzle they were presenting. The ideas of course originated from the artifacts/displays at the Museum of Anthropology, but the connections the students made with Math was fascinating!

I’m glad to be part of the profession where there’s so much room for creativity and inquiry. However, making creativity and inquiry part of the Mathematics education for the general public to appreciate is yet to be achieved.

SNAP Math Fair

I’d absolutely love to organize the SNAP Math Fair. However, I’m not sure if I can organize it during my extended practicum, as surviving the long practicum is a challenge on its own, I think.

Nevertheless, once I officially become an educator/teacher, I’ll definitely incorporate such activities/fairs into my teaching. I have a few ideas that are discussed below.

One of the ideas is to get two schools involved in the Fair. It can either mean that students from both schools present/display the problems the same day one after the other or collaboratively, or it can be broken down into two days, i.e. students from school A display their problems and are the hosts, whereas the students from school B are the guests and they come and solve the problem and vice versa. The both streams have pros and cons. For instance, having students from 2 schools at one place requires more space/organization, etc. On the other hand, having 2 schools work on it collaboratively can help strengthen connections between educators and students, hence the community.

Another challenge could be convincing other Math teachers or principal/administration to organize the Math Fair in the first place. For this to work out, we can’t afford to leave gaps and have to be on top of things in terms of organization and preparatory work required for the fair.

Response to BattleGround Schools: Mathematics Education

This article was able to put things into perspective for me. I was aware of different approaches and varying attitudes towards teaching and learning Mathematics, but the dichotomies: the Conservative and the Progressive helped me categorize and structure the diversity that exists around teaching and learning Mathematics. This will of course affect almost all Math teachers. Some of us will fall under the umbrella of the conservative approach, while others will lean towards the progressive way, and some of us will be blending one into the other.

One of the titles ‘The New Math’ caught my attention. I found it intriguing that the mathematics education became the focus of national anxieties in the United States in the 1960’s. It’s very interesting to see the initiation of this new Math movement and the associated challenges for both Math teachers and parents. I can only imagine the stress and anxiety the students, the teachers, along with the parents went through.

Likewise, the title ‘Math Wars over the NCTM Standards’ and the content under it reminds me of what one of my instructors in this programs said, i.e. ‘schools are a political system’. It will be naive to not consider the politics and the national interests involved that directly or indirectly impact our education system.

Lastly, we, as educators and Math teachers, should be ready and are expected to teach what we think we’re not comfortable teaching. We should be ready to embrace these challenges as learning opportunities and risk-taking experiences.

Microteaching 1 Reflection

Teaching Henna Tatoo was a great experience, it generally went well. However, comments/feedback from my colleagues allowed me to focus my attention on the aspects that I wouldn’t have noticed otherwise. For instance, one of the comments from one of my colleagues reads as the following:

“Overall the performance is very good but if you could help the students make the mehndi with us.”

On a side note, mehndi is another word for Henna which is widely used in countries like Pakistan and India. The above comment is a great suggestion and a deep observation.

My initial plan was to have the students see/observe me designing henna before asking them to try it. However, I changed my plan on the fly for time restrains. Also, I now realized that I could have the students watch a mini video/lesson on designing henna before asking them to try it.

Similarly, I noticed I’m given a ‘2’ on assessment aspect of the lesson planning by almost all of the teammates. It’s an indication that I need to work on that.

Likewise, one of the other comments reads:

“It would have been nice to see real example of Mehndi being used on people’s skin.”

Absolutely, I agree with the above! I hesitated to allow the students design henna on their hands for safety reasons, as it comes with chemicals that may be reactive for certain skin types. In the future, it could be made possible by ensuring that the containing chemicals are not reactive and asking students if they sensitive skin.

Microteaching 1 - Henna Tatoo

Giant Soup Can Problem

Imaginary Email II

Nov 13, 2025

Dear Ms. Javed,

I hope this email finds you in the best state of health. I just graduated from the Masters of Applied Math program. Allow me to introduce myself in case you don’t recall, I’m Jane Witson from the very first Science 10 class you taught. I was also in your Math 11 Honours and Math 12/AP Calculus class. Additionally, I was part of the team for Kwantlen Science Challenge that you lead in 2019.

I’m writing this email to say both sorry and thank you. I want to say sorry for having to judge you based on what I’ve now learn to call and consider stereotypes. I’m not sure if you ever noticed, but I didn’t like you for who you are initially. However, after having spent more than three semesters in your class, you became my favorite teacher and someone I respect a lot.

Also, I’m a regular reader of your blogs. I hope we can publish something together.

I look forward to seeing you soon!

Sincerely,

Jane Witson

RESPONSE TO THE EMAIL

Hi Jane,

Yes, I remember you of course. I'm happy to find out you're on your way becoming a successsful and inspring mathematician. Don't be sorry, being judgemental is also being human.

Thanks for the taking the time to read my blogs. Yes, absoutely, I look forward to seeing some of your writings and that which you would like get published.

Take care,
Iqra Javed

Imaginary Email 1

Dec 15, 2025

Dear Ms. Javed,

Hope you’re as lively and positive as you’ve always been. I’m Aneela Jan from your Math 12, 2023 class. Firstly, I wanted to wish you a very Happy Birthday. I found out it’s your birthday, so thought I’d take the opportunity to wish you and congratulate you for your success as an educator and a Math teacher.

Secondly, I wanted to thank you for being an amazing role model for me and other students. Aside from teaching Math, you taught us how to embrace challenges in life, and how to be positive in the most negative situations. I’ve always been a huge fan of your optimism!

Also, I still remember your risk-taking analogy that you would use to solve a Math problem/puzzle, and I use it on daily basis.

Lastly, you’d be happy to know that I’m currently majoring in Math with the combined Bachelor of Science and Education program at UBC. I choose to become a teacher so I can make a difference in other people’s lives just like you made in mine.

I hope I can come see you sometime if you’re still working at the same school.

Sincerely,

Aneela Jan

RESONSE TO THE EMAIL

Hi Aneela,

Your email made my day. I'm glad to know I was able to make a differene in your life. I wish you success in your current program and all you future endeavours.

Take care,
Iqra Javed

Math/Art Project Reflection

Firstly, it's been a pleasure to be part of the team that I was. We got to know each other a little better and had fun via this project.

Secondly, the task was to create a polyhedra using binder clips. It was challenging to get started as the online resources were limited to basic written instructions without tutorials or videos. One of our team members got started by making a star, then we all made stars. The plan was to make enough stars, so we can combine them into a sphere/ball. However, some of us hesitated to go ahead with the polyhedra for time constrains, and there were no clear instructions/tutorials to be sure.

Regardless, we continued making the stars that were then put together. It got harder to combine the stars as we proceeded. The last star was almost impossible to put in, but one of the dedicated team members decided to embrace the challenge and succeeded.

In terms of assigning this project to Secondary school students, I'd definitely consider exposing them to the union of Math & Art, as it'd allow them to think of Math beyond calculations and numbers. However, I would like to give the freedom to choose based on their interests, as it will psychologically make them feel more involved in their learning.

Chinese Dishes Problem

My first step would be to see what I can do with the given information, i.e.

‘every 2 shared a dish of rice’ = 1 dish/2 guests

‘every 3 shared a dish of broth’ = 1 dish/3 guests

‘every 4 shared a dish of meat’ = 1 dish/4 guests

Furthermore,

dishes/guests = ½ + ⅓ + ¼ = (6+4+3)/12 = 13/12

Lastly, there are 65 dishes in total:

65 dishes * 12 guests/13 dishes = 60 guests

I’m not sure how cultural context wil affect/modify the solution or the problem itself except that we word the problem differently. For exmaple, use ‘bowl/portion/plate’ instead of ‘dish’.  However, the cultural context is one of the improtant components of this problem in terms of interpretration. For instance, sharing and/or serving food may not be a ‘norm’ in some cultures, and it might have different and unique implications. The students belonging to the culture where sharing and serving food in dishes in not normal may find interpreting the problem a bit odd. Nevertheless, this problem could be their exposure to the culture(s) where sharing/seving food in dishes is normal.

Moreover, there can be numerous interpretations of the term ‘dish’. It can be thought of as plate/bowl or a big pot in which food is cooked.

In additon, if the problem is presented as 'Chinese Puzzle' or 'Chinese Dishes Problem', the mind automatically shifts to thinking about culture and its implications on the solution. Some students might also think that the problem needs to be solved in the context of culture.

Pro-D Day Plan

Hello!

I'll be here: https://www.eply.com/BCTESOL2015

EDCP 342A - Commentary on Mathematics for Social Justice

My first reaction after reading the topic “Linking Math and Social Justice” was “I love it”. I felt I finally found something I’ve been wanting to read about. It definitely is a unique and rare combination. The first thing people usually think about Math is numbers or calculations, or that it’s irrelevant to practical life.

Moreover, one of the excerpts from David Stocker reads: “The main aim of education should be to produce competent, caring, loving, and lovable people”. It is probably the first time I’m seeing the words ‘caring, loving, and lovable people’ in the context of Math. It fascinates me to see there are Mathematicians that see connections between human emotions and Math.

Furthermore, his work is admirable, especially the connections he withdraws between Math and practical life. I feel he’s using his expertise, i.e. Mathematics to make a difference via one of the strongest tools - writing. Such writing pieces are rare to found.

Additionally, there definitely are topics in Math that are related to the issues of social justice, we need the lense to integrate them together. For instance, Stocker relates the algebraic equation and violence as follows: “Antonino can figure out his daily paper route salary using an algebraic equation but he can’t use a pattern to show how violence on television and aggression in the world are related.”

Lastly, mathematical thinking is what I call a way to go about life in general. It is the devotion, commitment, and not giving up that allow us to reach a solution while solving a Mathematical problem. The same applies to life holistically.

EDCP 342A - Previous Learning Experiences

Studying Mathematics has always been fascinating for me. However, I wish I could look at Math during my Elementary and Secondary school years the way I look at it now. Furthermore, thinking of test/exam during my high school years, it is still fresh in memory that my friends would lose marks on content-based mistakes that require explanation, but I would lose marks on silly mistakes out of text/exam anxiety and nervousness. This, as a result, affected my confidence in learning Mathematics. However, it is interesting to note that I would enjoy challenging myself with difficult Math problems and loved solving them outside of exam settings. My confidence was renewed during my undergrad when I finally decided to specialize in Mathematics.

As of my best Math teacher, I had him in grade 10 and grade 12/AP Calculus. One of the reasons I liked his class was the way he communicated information/content. He was clear and inspiring. I also wanted to be in his class for Math 11, but had a jolly teacher. It was fun to be in his class, but didn’t learn much. He also had strong bonding with the class in general, but I had trouble understanding him. I would count this as my not-so-good learning experience.

EDCP 342A - TPI Survey Results

Based on the TPI survey results, my dominant perspective with the score of 38 is Nurturing. I found it intriguing. I consider myself a caring person, but never thought this trait/characteristic would dominate my profile/personality. Also, the other four perspectives including Transmission, Apprenticeship, Developmental, and Social Reform are recessive, and I scored about the same in these four perspectives. This doesn't surprise me because I'm usually open to trying and exploring new things. Furthermore, I have always thought there is more than one way to learn/teach/express/communicate. Teaching/learning is multifaceted with numerous dimensions. 

On watching the video about TPI from the website, I found it inspiring that TPI is considered a conversational tool rather than a diagnostic tool. We, as Teacher Candidates, will explore and develop our own philosophy of teaching/learning as we progress in the BEd program. I look forward to seeing how my teaching philosophy establishes and teaching perspectives change over time.