Happy New Year!


It’s that time of year again where we welcome our students to a new school year! Whether it’s elementary, high school, or higher education, it is important that we not only get to know our students but that they get to know each other in order to build relationships and a sense of community in the classroom. This is usually done through games, icebreakers, and interest inventories. How about using technology to get to know your students? Here are 10 tools you can use to build a positive classroom climate and relationships using technology:

  1. Flipgrid: have students record a response to any number of prompts (e.g., favourite book/summer memory/TV show/movie/band etc, “If a movie was to be made about your life, who would play you and why?”, “Which 3 famous people would you invite to dinner and why?”,  “What is your dream job?”, “If you could guest star on any one TV show, which one would it be and why?”, “Who do you admire?”, etc).  How about having students interview each other and they respond to questions posed by their classmates? I’d even recommend having administration and support staff (ESL teacher, Special Education teacher, office staff, custodian, lunchroom supervisors, etc) record a response for your students because it’s important for them to get to know the adults in the building, and not just their teachers. In order to feel like a school community, it is vital that students build relationships with the entire school staff. (https://flipgrid.com/)
  2. Canva: have students create an All About Me graphic in the form of a poster, flyer, brochure, or bookmark; the possibilities are endless! Or better yet, pair up students, have them interview each other and they create a graphic all about their partner! Depending on their age, you can get them to select that number and generate a list they can use to create their graphic – for example, if they are 13 years old, they have to come up with 13 things they would like to share about themselves. (https://www.canva.com/)
  3. Instagram: this is a great tool for high school and higher education students. After you get to know your students and they get to know each other, post a picture (or a collage) that represents each of the students and have them guess the classmate. It’s even great in terms of getting familiar with your surroundings. Take pictures around the school/campus and have students go searching! You can also design it in the form of a scavenger hunt where you create riddles for  students to answer in order to find the spot in the photo! This is especially great for students who are new to the school. (https://www.instagram.com/?hl=en)
  4. Goosechase: Speaking of scavenger hunts, Goosechase is a fun tool to use to create your own scavenger hunts! Place your class in teams of 3-4 and have them go hunting for places and people around the school or campus; students post a picture of themselves completing the challenge and gain points – of course, whichever team has the greatest number of points at the end, wins!

  5. Kahoot! – students of all ages love this game-based platform! I have even used it with teachers when delivering PD during staff meetings and workshops and they love it too! You can use this tool in several ways: (a) students respond to questions about themselves and get to see the responses from other students in terms of commonalities and differences, (b)  provide questions that can help you with planning the year (e.g., “What do you think we need to add to the classroom?”, “How do you like to learn?”, “What questions do you have about this upcoming school year?”, “Are there any extra-curricular activities/clubs you would like to see added this year?” and (c) create a class quiz; in other words once students get to know each other, come up with one question/answer for each student and see if the rest of the class can guess to whom you are referring. The student who scores the highest can even get a small prize! (https://kahoot.com/)

  6. Google Forms – generate a list of questions to use as an Interest Inventory for students to answer (e.g., “What kinds of books do you like to read?”, “If you were an Olympic athlete, what sport would you compete in?, “What country would you like to travel to?”, “Would you rather watch TV or listen to music?”, “I wish my teacher knew….”); depending on the questions, the features of this tool will allow students to see similarities and differences amongst each other. You can also use the their answers to target learning to their interests and curiosities.
  7. Twitter: Twitter is another great tool for communication, collaboration and learning. Students have to be 13 to create their own account so those in middle and high school as well as college/university can create their own academic account. You can post a series of icebreaker questions for students to answer so that a thread is created where they can see the responses from their classmates. Better yet, create a series of poll questions for students to answer. For younger students, you can ask questions such as, “If you could follow 10 people, who would you choose? Why?”, “What would your bio say?”, “What would you add as your header? Your profile photo? Why?”. There are also many ways you can use Twitter for learning; here is a link to my blog posts about Twitter in the classroom (https://techdiva29.wordpress.com/2015/07/05/social-media-in-the-classroom/ and https://techdiva29.wordpress.com/2015/08/16/twitter-in-the-classroom/)
  8. Mentimeter: this tool is similar to Padlet in that you can pose questions for students to answer and you get to select the format in which the responses appear (e.g., word cloud, graph, open ended, etc). I like to use the word cloud format because the more popular an answer is the bigger that word appears in the word cloud. You could ask a question such as, “What is the most important factor to ensure success in the classroom?” or “I wish my teacher knew…..”. If you use the word cloud option, the most consistent answer will appear the largest, thus telling you what students think is important for learning.  (each question you generate will have its own individual code that students will use in order to respond). Of course, you can generate some fun questions as well to get to know students.
  9. Tiki-Toki: this is a cool tool for students to use to create a timeline of important dates in their life; students can post visuals and links to enhance their timeline! It’s also a great tool to use for history, science, and geography! (https://www.tiki-toki.com/)
  10. Infographics: infographics are great because they represent information in a visual manner. Students can use any number of tools to create an infographic about themselves (e.g., piktochart https://piktochart.com/, Venngage,https://venngage.com/, Snappa, https://snappa.com/, and canva, https://www.canva.com/). You can give a list of questions for students to use in their infographic or you can allow for some freedom and have them create their own based on what they think it important for their classmates to know about them. As mentioned before, you can have students interview each other so they are creating an infographic about a classmate instead of themselves.
  11. GIFs: I love GIFs! They are fun and engaging and I love to use them when I am interacting with my followers on Twitter or just texting with friends! Generate a list of questions for students (e.g., “What do you like to do for fun?”, “How do you feel about broccoli?”, “What is a hidden talent you have?”, “How would you spend a rainy day?”, etc). Have them find and/or post a GIF that represents their answers or feelings towards the question; this can get pretty funny and is a light hearted way to get to know students. (https://giphy.com/). For example, my answer to “How do you feel about broccoli?”, is….


Whichever tool(s) you decide to use, be sure to remind students about responding appropriately – these are supposed to be fun and engaging tools for students to get to know each other (and for you to get to know your students) so being respectful and considerate is essential to ensure a sense of belonging. Equally important is to ensure that you continue to get to know your students throughout the year through games, challenges, and icebreakers. Usually we spend the month of September building community and climate and then move onto the curriculum, but it should not stop there – continuing to get to know our students is vital to sustain community in the classroom, so be sure to integrate these types of activities throughout the year. After all, as we grow, we change and it is imperative that we are aware of these changes as the year progresses. Students will be willing to learn and take risks when they know their teacher cares about them and knows them as individuals. Have fun and have a fabulous year ahead!


February: Black History Month and The Olympics

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For those who have read my blog and/or know me, will know that I am a proponent of inquiry based and personalized learning. My journey with inquiry started over 10 years ago and my thinking has evolved tremendously due to new knowledge and what my students were telling and showing me in the classroom. If you haven’t had a chance to read my previous blogs on my journey with inquiry, you can read them here http://bit.ly/2dENLbe (Part 1), http://bit.ly/2gaaXiX (Part 2), and http://bit.ly/2fyQJf8 (Part 3).

A special event or occasion should not be the invitation to welcome inquiry into your classroom – this kind of learning should be infused throughout the year. In other words, it should be a regular part of your classroom, where students are allowed to explore their passions, ask questions, be inspired, think for themselves, have conversations with others, make effective use of technology, and problem solve, just to name a few. For those who might be new to inquiry, there are different frameworks and stages to support your students in this type of learning. I think of inquiry in four stages: (a) Structured/Guided, (b) Blended, (c) Independent, and (d) Personalized (more to come on these stages in my next blog post). Furthermore, I always include the lens of: (a)  Universal Design for Learning (UDL), (b) social justice and equity, and (c) integrated curriculum, which I will also explain further in subsequent blog posts.

February is Black History Month, a time where educators and students alike explore their history – the injustices, the struggles, and the successes. In theory, these types of months might seem like a great idea (there’s also Asian Heritage month in May) to highlight and explore issues related to different races and ethnicities but in reality, these issues need to be embedded throughout the year, not just for 28 days before moving on to the next think we have to “check off” in the curriculum (that’s another blog post all on its own!). So, how can you use the curriculum to infuse issues of social justice and equity into teaching and learning on a daily basis? I often ask educators these three questions:

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In my opinion, the curriculum needs to be more flexible to allow for students to explore, investigate, and play around with ideas, topics, and concepts (again, an entirely new blog post!).

For now, I will leave you with some sample questions you can ask your students based on Black History Month and the Olympics, happening this month in Pyeongchang, South Korea. What do they think? Why? All these questions are open ended (i.e., no one right answer), thus lending themselves to the exploration of inquiry in your classroom.

Black History Month

  1. Who had the greatest impact in history in the fight for justice and equality?
  2. Which important events have been squashed in history? Which one do you think is the most important one for others to know? Why? Why do you believe this event was concealed?
  3. What are some of the most significant events in Black History that we do not know about? Which one in the most important? Why?
  4. Who do you believe is the most important person furthering the cause of African-Canadians today? Why?


  1. Which country actually performed the best? (This might seem like an odd question since there are usually 1 or 2 countries that always perform the best but if students were to think about this question, there are many factors and criteria that need to be taken into consideration such as: (a) how many athletes were represented?, (b) how much funding goes into training?, (c) Who is training the athletes?, (d) what do we know about the economy and geography of the countries and how does that relate to performance?
  2. Which country should get a chance to host the Olympics? Why?
  3. Was it right for the NHL to decide that NHL players can not participate in the 2018 Winter Olympics?
  4. Was it right for Russia to be banned from the Olympics because of doping and cheating? (even though Russian athletes are competing, they are competing as OARs [Olympic Athletes from Russia] and any medals they win will not count towards Russia’s medal count).

Hope some of these questions will pique the interest of your students and lead to some interesting conversations!

Any questions, please ask!

Until next week!

Happy New Year!!!


As I think about the start of the school year tomorrow, I can’t help but reflect on my years in the classroom. I’ve taught almost every grade level from K-8 and enjoyed each and every grade level for a variety of reasons. Each grade taught me different things and as I think about my friends and colleagues heading back into the classroom tomorrow to welcome their new students, here are my top ten thoughts to get the school year off to a great start!


    1. Names: nothing is more important than learning to pronounce their names correctly. Take the time to ask them how their name is pronounced. I often had my students tell me “It’s okay” or “Don’t worry about it.” I never listened and asked them to tell me how their parent(s)/guardian(s) said their names. Due to my East Indian background, pronouncing most of my students’ names correctly wasn’t an issue but I know how challenging it can be to pronounce some of their names. Learning to pronounce their names properly goes a long way because it demonstrates to your students that you care. I know this might be difficult because of the different linguistic rules and norms of languages but as long as you put the effort into it, your students will appreciate those efforts.
    2. Daily Greeting: to get their day (and yours) off to a great start, be sure to greet them at the door; whether you have them line up at the door or come into the classroom as soon as they are ready, be sure to say “hello” and ask them how they are doing. Being in the hallway as they gather their materials for the day is a great opportunity to see how they are doing and asking them if they had a nice evening. Again, this shows them that you care about them as a person.
    3. Classroom: I know we spend lots of quality time setting up our classroom for our students so they feel welcome. This includes the physical arrangement of the classroom, bulletin boards, and materials/resources. I’ve learned over the years that less is more. Purchasing those colourful pre-packaged bulletin boards from the teacher’s store might make the classroom look pretty, but students will not refer to them because their is no ownership in those bulletin boards. They did not create them, hence there is no investment. I left my bulletin boards empty and had my students create them – they referred to them much more often! In addition to the bulletin boards, let them choose how they want their classroom setup. How do they believe the desks should be set up? Should there be different areas for different purposes? If so, how? Why? Where should resources and materials go? What about technology? Where should it be stored? How should it be used? It is their learning space and they should have a voice in how their space is setup to allow for maximum learning and engagement.
    4. Rules: The first day and week of school is also spent discussing and generating classroom rules and norms. Have students generate these norms with the consequences. Students need to realize that certain behaviours have consequences. You choose a behaviour; you choose the consequences. Hence, it is important for students to brainstorm consequences (within reason) along with the rules. Send home a copy to parents to sign and have students sign as well. This way, everyone is on the same page and there are no surprises.
    5. Expectations: This is an extension of classroom norms. To ensure a successful year, it is important to start off with expectations. What do I, as your teacher expect from you as a learner? (e.g., I will do my best., I will ask for help when needed., I will be a good peer to my fellow classmates, etc). What would be your top three? It needs to go the other way as well. What do I, as your student, expect from you as my teacher? (e.g., Believe that I can succeed., Show me you care., Show me that I can trust you.). What do you think your students would say? Why?
    6. Relationships: Nothing is more important than getting to know your students. You need to build relationships with your students so that they can trust you and come to you with their problems, whether personal or academic. This is becoming increasingly important as students struggle with wellness, mental health, and a jam-packed schedule. There are many ways you can get to know your students, such as: (a) Interest Inventories, (b) Parent Questionnaires, (c) Games, (d) Icebreakers, (e) Community Circles, and (f) Community building activities. Even though this is concentrated in the first month or so of the school year, these activities should be ongoing because it not only keeps it fun but it also allows you to continue building those relationships.
    7. Gift Bags: organizing and putting together small gift bags for your students for the first day of school can get them excited about their year of learning. It doesn’t have to be overly complicated nor does it have to take a long time. Simple items such as pencils, erasers, markers, a bouncy ball, and chocolates/candy can be included in these Welcome Back to School gift bags (e.g., Ready, Set, Go! Or It’s A Treat to Have You In My Class!).
    8. Student Records: Looking at each student’s file in the office is something that is on our ‘to do list’ during that first week or so of school so we can get some background information on our students. I found that looking at them too early can gave me some preconceived notions about the students in my classroom. Hence, I stopped looking at them until I had formed my own opinions about their abilities, strengths, needs, and interests. It was interesting that there were several occasions where I was surprised at what I read in their file after I had a chance to get to know them. Not looking at their files for at least a month was one of the best changes I made to my practice.
    9. Nurture Curiosity: I know we are bound by the curriculum but it is important to nurture their curiosity through the curriculum. This can be done through inquiry and open ended questions (some of my previous blog posts) but also by showing them the curriculum. The curriculum is not a secret; it’s readily available online. So, why not show them the curriculum for a variety of subject areas and ask them these three important questions: (a) How do you want to learn this?, (b) What questions do you have?”, and (c) Where do you see yourself represented in the curriculum?” Another way to look at your classroom/classes is to ask, “If my classroom/course was optional, would students sign up?It is so important that we develop a passion for learning in our students and this can be done by giving them more choice and voice in what they learn, how they learn it, and how they share their learning with a wider global audience (more to come on this!).
    10. Support Staff: and last but not least, be sure to thank your support staff for working hard over the summer to make the school clean, safe, and welcoming. This includes custodial staff and the office staff who worked hard to ensure a smooth welcome and transition for staff and students for the new school year!



Wishing all of you a great first week back and an awesome 2017-2018 school year!

Digging into the Curriculum


So, I just realized it’s been almost six months since I’ve blogged; it’s amazing how time flies! Well I am back and I want to dig deeper into integrated curriculum and inquiry.

If you’ve read my previous 3 posts on inquiry, you know that I am passionate about integrating curriculum with an inquiry and social justice lens.

Today, I’d like to talk about intentionally using curriculum expectations, learning goals, and success criteria when creating tasks.

As I’ve mentioned previously, one way to approach inquiry is select a big idea/concept related to the curriculum and generate an essential or driving question that is open ended for students to explore. Students may be exploring and investigating the answer to their driving question, but explicit teaching is still happening in the classroom. Inquiry does not mean we let the students go without playing a role in the learning nor does it mean we relinquish complete control over the learning environment. When we talk about “letting go of the control”, we mean allowing students the freedom to go in different directions, based on their questions and interests. This is what we mean by honouring student voice and choice; it allows students to take their learning in new and exciting directions.

Our explicit teaching during the inquiry process starts with examining the curriculum expectations; it tells us what to teach but not how to teach it. In other words, based on the big idea and driving question selected, what skills do students need to develop in order to successfully respond to the driving question? In order to successfully communicate their thoughts and opinions related to the driving question? One can say, that communication is a skill in itself and that is correct; students need to be taught how to analyze, evaluate, judge, justify, organize, compare, contrast, and the list goes on. They don’t magically hone these skills without teacher support.

This past year, I started to look at curriculum expectations in a new light. As an instructional coach, I have had the opportunity to attend many PD sessions and workshops and many of them started with a Know, Do, Be Framework in terms of goals for the day. Here is an example:

Know: Deepen our understanding of instructional practices and how they might affect the decisions we make in support of the students we have (i.e., what is the outcome of student learning?)
Do: Intentionally selecting and implementing practices based on our learners’ profile
Be: Reflective and responsive educators based on student learning needs

The lightbulb went off and I made a connection between the Know, Do, Be Framework and our curriculum expectations. When deconstructing an expectation, it can be broken down into a Know (Content), Do (Skills), and Be (Habits of Mind). Even though I consider myself pretty familiar with curriculum expectations in terms of content and skills, I never thought of breaking it down to its nuts and bolts in this manner.


Curriculum Expectation (Grade 4 Math): collect and organize discrete primary data and display the data in charts, tables, and graphs (including stem-and-leaf plots and double bar graphs) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, simple spreadsheets, dynamic statistical software).

Know (content): charts, tables, graphs (different types; titles, axes, scale, etc), primary data

Do (skills): collect and organize

Be (habits of mind): not always present, however, as the teacher you may generate a “be” such as “critical consumers” (however, this may fit with another data management expectation)

I didn’t realize until about a month ago after reading an article, that Susan Drake, a professor at Brock University had done some work around this framework; I would love to get in touch with her to have a deeper dialogue about curriculum and student engagement and achievement.

Based on this framework for interpreting curriculum expectations, I created a chart not only to organize my thinking around the overall and specific expectations but also to assist teachers in determining what exactly they would like their students to know and do. From there, teachers can generate a “be” if they so choose. This “know” and “do” then helps to create learning goals and success criteria. which can also be connected with the four categories on the achievement chart and 7 processes in the mathematics curriculum (*note: these processes span all subject areas; not sure why it’s only in the mathematics curriculum).

(I’ve attached a PDF document with the Know/Do/Be framework at the end of this post)

Using the curriculum expectation from above, a learning goal could be:

“We are learning to collect and organize data and select an appropriate type of graph to represent the data.”

What mathematical processes do you see in the above learning goal?

So, now, we need to create a rich task and generate success criteria for the task based on the learning goal. (I will be talking more about rich tasks in my next blog post). Our next step, as teachers, is to think about an instructional strategy that aligns with the learning goal and task, which will help students to be successful. This is where your explicit teaching comes into the picture. What instructional strategy will you use? Why? How will you use it? These are questions you need to think about when selecting a particular instructional strategy. So, what instructional strategy can you use to assist students with organizing, collecting, and displaying? I’ll leave you with that question to ponder 🙂

How will we know whether students are successful in achieving the learning goal? We will know because we will assess student work based on the success criteria we generated and then provide descriptive feedback to students to help them to create next steps in their own learning.

Students will be able to use this learning when working on their inquiries; for example, if their inquiry includes displaying data to prove their point, then they have learned the skills to do so through the carefully crafted tasks designed by you, which includes the learning goal and success criteria!

Therefore, in very simple terms, we need to:

1. Start with the curriculum expectations
2. Break it down into the Know/Do/Be components
3. Create a learning goal in student friendly language {keeping in mind the 4 categories of the achievement chart and 7 (mathematical) processes}
4. Create a rich task
5. Generate success criteria (aligning with the learning goal and task)
6. Provide descriptive feedback to students

There is much more to the above steps but it is a basic structure of how we need to re-examine the curriculum and the work we do with our students.

Thanks for reading and I’ll be back next week (I promise!) when I talk about rich tasks not only in mathematics but also across other subject areas through an inquiry lens.


Mathematical Thinking: No Pencils Allowed!!!



So the good news is that I successfully defended my dissertation and am now a PhD; the bad news is I haven’t blogged since February! This seems to be the recurring theme for the last year; writing a blog post and then becoming busy again with work and completing my degree requirements. Hopefully, now that I have completed my PhD, I will be able to blog once a week.

This week I’d like to talk about a topic that has been a focus in my role as an Instructional Coach this past year – that of mathematical thinking, reasoning and proving. I supported teachers in my schools in these areas and it has been great to see students develop and demonstrate their mathematical thinking, aligned with learning goals and success criteria.

When students reason and prove in mathematics, they are explaining their thinking and providing the evidence in a systematic manner using a variety of representations.

Many times, it is difficult to understand what a student is showing in his/her work. Before I provide some suggestions, we need to understand what reasoning actually is; what is reasoning?

The Ontario curriculum states:

“The reasoning process supports a deeper understanding of mathematics by enabling students to make sense of the mathematics they are learning. The process involves exploring phenomena, developing ideas, making mathematical conjectures, and justifying results. Teachers draw on students’ natural ability to reason to help them learn to reason mathematically. Initially, students may rely on the viewpoints of others to justify a choice or an approach. Students should be encouraged to reason from the evidence they find in their explorations and investigations or from what they already know to be true, and to recognize the characteristics of an acceptable argument in the mathematics classroom. Teachers help students revisit conjectures that they have found to be true in one context to see if they are always true. For example, when teaching students in the junior grades about decimals, teachers may guide students to revisit the conjecture that multiplication always makes things bigger.” (Ontario Ministry of Education, p. 14).

What key words stand out in this definition? I’ve bolded and underlined what I feel are the important terms and statements when it comes to reasoning. Students need to be able to make conjectures based on their prior knowledge and then provide proof/disproof of that conjecture depending on the question being posed. They need multiple opportunities to practice demonstrating their thinking in a variety of ways and developing their ideas in group settings and individually.

So, when do we reason? I know I rely on my reasoning skills when I am presented with a new problem or when logical thinking is required. For example, I was presented with this problem recently:

You are in a cabin and it is pitch black. You have one match on you. Which do you light first; the newspaper, the lamp, the candle or the fire?

I used logical reasoning and decided to light any of the items, you had to light the match first!

Now this  might not be a math problem but you get the idea; here’s one for you to try:

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So, what number is the car park on? How do you know? (Feel free to post your answer in the Comment Section).

We also have to look at the context when we are reasoning; think of the “bus problem” that I am sure several of you might be familiar with. I don’t remember the numbers that were used in the original problem but it goes something like this:

“The Grade 6 classes were going on a school trip, there were 78 students altogether and one bus can hold 22 students. How many buses needed to be ordered?”

Many students perform the standard algorithm and divide 78 by 22 to get 3.5 and their answer is 3.5 buses without using reasoning to understand that you can’t have half a bus, so we really need 4 buses. In this case, the context helps us to reason through our answer and explain our thinking.

When students are given a problem, whether it is open- routed or open-ended, they have to deconstruct and understand the problem in order to determine which strategy to use; this requires reasoning since they need to use the information given in order to select a strategy to answer the question. Sometimes, there is information missing from the problem and students need to realize what information is missing and how to fill those gaps in order to solve the problem.

Last but not least, students will use their reasoning skills when dealing with open-ended questions. These types of questions have multiple answers and multiple pathways to get to the answer. They will need to use their reasoning skills to determine the best path to get to an answer.

As I said previously, sometimes when we are looking at student work, it is hard to decipher their thinking, evidence, and reasoning. This is where conversations and observations are powerful. As educators, we recognize the importance of triangulation of data, so when we don’t understand what a student has written, follow it up by a conversation with that student with some probing questions or better yet, observe students while they are working and ask those clarifying questions in order to better understand their thinking process.

Here are some probing questions you can ask:

  1. How did you do this step?
  2. How did you know to…..?
  3. Tell me more about…….?
  4. What happened when you……?
  5. Why did you…..?
  6. How is this like….?
  7. How is this different from….?
  8. Can you find another way to solve the problem?
  9. Does your solution make sense? How do you know?
  10. Can you explain…?

Finally, in order to track and support students’ mathematical thinking and make it more visible, here are some suggestions:

  • Use Markers. When students use a pencil, they erase their mistakes and start over. This deprives us of seeing their thinking and how it evolved as they solved the problem. I have my students use markers and if they make a mistake, they place a line through it and continue underneath. This allows me to clearly see their thinking and have richer conversations with them, when looking at their work. This also supports growth mindset because students begin to see mistakes as valuable.
  • Give them the answer. Math can be stressful for many kids. This is why I would regularly (not every day) provide the answer to the question (e.g., the answer is “47”) and tell them to “prove it.” This allowed students to explore and investigate more freely and without a lot of stress. It has worked really well.
  • Modify the Question. Sometimes, I would modify the question for students in a “yes” or “no” format, (e.g., “Shelly says the answer is 2.5. Is Shelly right?” OR “Shelly says the answer is 2.5 but Jason says the answer is 3.5. Who is right and why?”). This also allows students to explore, investigate, and develop ideas but in a different way, especially with the latter example because students have to prove why either Shelly or Jason is wrong.
  • Convince a friend. Can they explain their reasoning to a friend? Can they answer their friend’s questions effectively?
  • Convince a skeptic. Can they explain their reasoning and thinking to someone who is not quite sure? Can they answer his/her questions effectively? Do they manage to convince the skeptic their line of thinking is correct?
  • Trade with a classmate. I’d often have students exchange their solutions with a partner and see if the other person can follow their line of thinking. Can Student A understand what Student B has done on paper? If not, what can/does Student B need to do in order to make their thinking more visible and explicit? The same goes for Student A. This is another great way for students to communicate as well as seeing the different strategies used to solve the same problem.
  • Group by strategy. Students can also be grouped by strategy and work together to show their thinking. After presenting a problem to students, let them get started individually; walk around and make a note of which strategy each student is using and then stop the class after a few minutes and pair them up (or groups of three; I don’t recommend groups of 4 since one or two students will end up taking a backseat), have these small groups continue working on the problem using their shared strategy and then share solutions as a class.
  • Take the paper away. There are many ways to solve a problem on paper, yet we often don’t emphasize other ways to solve the problem, without the use of paper. My suggestion is, take the paper away and challenge them to show their thinking in another way; what about acting it out? Going outside? Using manipulatives? Can you think of other ways students can demonstrate their thinking without the use of paper?
  • Marker for each student. In my first suggestion, I talked about having students using a marker (or pen/pencil crayon) to do their work; if students are working in small groups, give each student a different coloured marker so you can track individual thinking (a placemat can work well here).

I hope you find some of these suggestions helpful and effective!

I also recommend ThinkFun games for students to practice their reasoning, logical, and spatial thinking skills. These are fun and engaging games to support mathematics in any classroom. My 5 year old nephew is hooked on Rush Hour!

Here are a few titles:

  1. Rush Hour
  2. Gravity Maze
  3. Blokus
  4. Shape by Shape
  5. Block by Block
  6. Circuit Game
  7. Tipover
  8. Laser Maze
  9. Robot Turtles
  10. Brick by Brick

Visit their website at: http://www.thinkfun.com/

Next week, the plan is to continue talking about mathematical thinking and reasoning from the lens of assessment; in particular learning goals and success criteria. It is important that we assess what we are supposed to be assessing and this is where the difference between success criteria and task requirements come into play.

Until next week!



Ministry of Education (2005). The curriculum: Grades 1-8: Mathematics, 2005. The
curriculum: Elementary. Retrieved from

Financial Literacy in the Classroom


It’s amazing that’s it been almost five months since my last blog post but life was busy as I was adjusting to my new role as an instructional coach, working on writing chapters 4 and 5 of my dissertation, and instructing Additional Qualification courses in mathematics.

Now that I am back, I want to start off the year talking about financial literacy. While it is true that we have seen our scores in mathematics decline and therefore, are now focusing our attention on ensuring students having a deeper understanding of this discipline by exploring strategies to develop skills such as spatial reasoning, proportional reasoning, number sense, number fluency, and relationships and connections between concepts and skills, I feel that we also need to examine ways in which to teach our students about finanical literacy.

Financial literacy is about understanding how money works and how to manage and invest that money. More importantly financial literacy is about making wise choices and informed decisions about money. Because of advances in technology, which allows service providers to reach their consumers in more ways than ever, we need students to be aware of the manner in which these providers can entice and convince them to make poor choices. The popularity of online shopping, different payment options, and credit cards, have given the illusion that money isn’t “real”. In a time when unemployment rates are high and debts are increasing at the same time that cost of living is increasing, children of all ages need to be taught skills related to financial literacy in order that they are effectively equipped to grasp concepts related to personal finance. Stats Canada (2016) states that students who have completed a bachelor’s or master’s degree owe $26,000 while those who earned a doctorate degree owe approximately $41,000 (Statistics Canada, 2016)(and it’s only going to get worse as the cost of higher education increases). Combine these factors with an uncertain global financial market, and it should be obvious that teaching financial literacy skills to our students is imperative. We not only need to teach our kids how to handle personal finances but we also need to teach them the principles of economics in order to assist them to be well informed citizens who understand the important financial issues facing our nation and the world.

It needs to start at a young age when children first begin to receive an allowance. It needs to start with something as simple as the difference between a “need” and a “want”, which can lead to rich discussions about the value of saving. I always started my financial literacy unit with this concept and then each student randomly selected a job (e.g., hairdresser, plumber, interior designer, engineer, teacher, fire fighter, etc). The look on their faces when they were doing their monthly expenses always made me laugh because they were shocked at how much money was deducted from their paychecks in the form of tax (each of my students selected a job/profession from an envelope and then conducted research on that job); thereby teaching them the difference between gross pay and net pay. They were also visibly surprised when they realized the interest rate on their credit cards – yes folks, credit cards doesn’t mean free money 🙂

I started to teach financial literacy about 6 years ago after a couple of real life experieneces:

1) Those of you who know me, know I love my shoes! Aldo was having a sale and I was looking at a pair of beautiful stilettos, I happened to overhear the conversation occuring beside me between two high school girls. They were looking at a pair of boots and they were 30% off. One girl said to the other, “I have no idea what 30% off means for these boots?” to which her friend replied, “What makes you think I know?” I cringed and decided to intervene. I approached them and told them the answer and they looked at me as if I had two heads. “How did you figure that out so quickly?” one of them asked. I then proceeded to give them a 10 minute lesson on percents right there in the store. As I was helping them understand the concept of percentages and the relationship between percents and decimals, I could see the lightbulbs going off in their heads – what a grand moment! They were so happy that they finally got it and they couldn’t thank me enough. I left the store without buying any shoes but with a sense of accomplishment that I had done a good deed. 🙂

2) I went to purchase some blinds to cover the windows of the door that led out to our balcony from our kitchen. I had someone come in to install them for us and as he was putting them up, I heard him mutter under his breath, “Well, I’ll be damned, it’s right.” I asked him what he meant and he turned to me and said with a straight face, “This is the first set of blinds that I’ve installed where the measurements are correct.” He went on to tell me how all the other window coverings he had attempted to install weren’t possible because the owners hadn’t taken accurate measurements. I, needless to say, was floored. I thought he was joking but he clearly told me that it was no joke.

3) I’ve had many experiences where a high school student and/or a university student couldn’t give me exact change when their cash register wasn’t working. Almost every single time, I would have to tell them how much they owed me in return. One example was when I gave the cashier $20 on a purchase of $16.45 and he gave me $4 back. Now, some people might just take the $4 and go on their merry way but me being a math geek gave it back and told him he actually owed me $3.55. He was a bit embarassed but like the Aldo incident I took it upon myself to give him a quick lesson on mental math strategies and thankfully he was thankful 🙂

These three incidents combined caused me to reflect on what I can do differently in my math classroom. I, therefore, took it upon myself to start developing my own financial literacy unit. As I mentioned above, it started with a discussion around weekly allowances, needs vs. wants, and then assigning them a job. From there, they were given weekly assignments and tasks that gave them a better and deeper understanding of money and financial literacy. I even gave them opportunities to research and discuss topics such as the stock market, financial portfolios, pension and retirement plans (this was in my Grade 8 classroom).

This topic can and should be linked to our Ontario curriculum. We looked at proportional and spatial reasoning by exploring and examining such things as floor plans, shopping, redecorating, and the stock market. We looked at expenses and cost of living through number talks and we made connections between financial concepts and our seven mathematical processes. In other words, teaching financial literacy should not be an add-on but viewed as a natural integration based on the overall and specific expectations in the curriculum. 

Many adults make poor choices with their money and it’s because they were not taught effective ways to manage their money or make informed decisions. They need to have these important discussions with their children; parents shouldn’t be afraid to share their experienecs, good and bad, with their children because in essence they are sharing their knowledge and their persepctives about money matters. I am one of the lucky ones as my dad started a finanial portfolio for me when I was in elementary school and he was the one who taught me the value of saving and investing, which is another reason I want to pass on the knoweldge I received from my dad to my students. These conversations need to be supplemented in the classroom where teachers guide students through a variety of topics and concepts that have direct links to our curriculum expectations, the four levels on the achievement chart, and the seven mathematical processes.

If financial literacy programs are implemented in education and we have a continuum of concepts from K-12, then perhaps the next generations will not only learn to start saving and investing in high school but also graduate with less debt in order that they can have the same benefits as their parents when it comes to retirement.


Statistics Canada (2016). Graduating in Canada: Profile, labour market outcomes and student debt of the class of 2009/2010, 2013Consumers making wise choices. Retrieved from


Part Three: Inquiry in the Classroom


Calvin and Hobbes is one of my favourite comic strips and the one above demonstrates how the education system focuses too much on facts and less on the development of skills. Inquiry not only helps students to acquire skills such as critical thinking, analyzing, and evaluating but it also helps with growth mindset. By asking essential questions, which are open ended such as the ones I have done in my class, students begin to realize that there isn’t one answer to a question and that the answer isn’t clear. This is where inquiry starts with students asking even more questions. Now, I want to take a minute to point out the difference between wondering and inquiring. Wondering leads to one right answer. For example, we might wonder why dogs can’t eat chocolate but there is one correct answer to this question (it’s because of the compound theobromine found in cocoa), so it can’t be considered real inquiry. Inquiry leads students in different directions, with each student answering the question based on what they learned, their experiences and perspectives. For example, when my grade 8 students were studying cells, the big idea was “ethics” and the essential/driving question was “What role should ethics play in science, technology, and medicine?”. It was amazing to see the process unfold as my students flip flopped while we were discussing stem cell research. As they attained more knowledge and discussed these issues with their classmates, their perspectives changed, which led to thinking differently and ultimately asking more questions. I remember one of my students who ended up researching stem cell guidelines in different countries and how it impacted their communities, which led to a great discussion during one of our community circles. Because the inquiry process might be new to many students, they will ask you what you think. I always refrained from giving them my opinions and views because mine didn’t matter. The purpose is for them to go on their own path of learning and not be influenced by your views because traditionally students have always looked to the teacher for the “right answer”.

I think one of the best things about this unit was our literature circles. I found several novels that pertained to biotechnology, stem cell research, and cloning. I remember how surprised my students were when I introduced the novels; “You mean we’re reading fiction in science class?” <cue confused looks>! This was not only a great way to integrate language into my science class but also gave them a great introduction on how to ask questions (close and open ended) by using the Q-chart. I did not have them rely on this chart for questioning as it can be limiting but it was a good way to introduce them to the art of questioning and assessing their questioning skills.

I always get questions about how to assess inquiry units. My answer usually takes the form of how inquiry is a great way to assess through triangulation of data (i.e., observations, conversations, and product). When I have conversations with my students, I always ask prompting questions, which are open ended such as:

  • Why do you think that?,
  • what else have you discovered?
  • What questions do you still have?
  • Tell me more.
  • So what if…
  • Why do you say that?
  • Can you explain that?
  • Can you give me an example?

Giving students time to think (i.e. wait time) and not judging their responses are two other key factors when engaging in conversations with students. By asking open ended prompts and not judging by saying things like “That’s right.” or “That’s great. Good job” will allow the learning to continue and students to carry on by digging deeper and asking more questions.

My observations are done by completing a form for each student, which involves certain indicators (e.g., doesn’t give up easily, attempts several approaches, and brainstorms other solutions, etc) with space to write down my comments. I complete these observational forms for both their research process as well as how they interact with their peers during group discussions (e.g., asks appropriate prompts to ask questions, speaks in a respectful tone, accepts other alternatives even though might not agree with them, etc).

In terms of products, we generate success criteria as a class for the many ways in which we can demonstrate our learning (e.g., essay, movie trailer, podcast, website, speech, newspaper article, etc). This does take time but once it is done, it is accessible for the rest of the year. In terms of products, my students choose three tasks from a tic-tac-toe board I create such as this one:

podcast PSA brochure
speech movie trailer commercial
persuasive essay comic book story website

Sometimes I let students choose any three to make a tic-tac-toe pattern or I tell them they have to do the centre square and then choose any two others to complete the pattern.

Finally, I have students complete regular self-reflections once a week, which also helps with the learning skills portion of report cards. This takes the form of journal responses where I ask students:

  • How are you progressing? How do you know?
  • Has your opinion changed? Why or why not?
  • Anything I can do to help you with your learning?

In addition to triangulation of data, I also ensured that each of my assessments was based on at least one of the four levels on the achievement chart (i.e., knowledge/understanding, application, thinking, and communication) as well as the seven processes in math because those can be applied across the curriculum (i.e., representing, reflecting, connecting, reasoning, proving, selecting tools, and computational strategies). It does take a lot of planning and preparation and with time and experience it will become seamless; I have done this for almost 7 years and I am still learning, adapting, and changing things!

These inquiry units are a great introduction to personalized learning, which I will be talking about in a future post.

Again, as always, feel free to leave comments and questions!