Math Week 3

Hello teacher friends!

Hopefully we have all returned to math class this week with more of an open mind and refreshed attitude towards the subject. I know I certainly have, especially after the main activity we participated in during class. This week's challenge was to recreate a common board game to one that would contain math elements; essentially navigating our own rules and expectations under the mathematics strand of our choice. After heading to the IRC with our creative juices flowing, Matt and I decided to alter one of the most beloved toys of young children - lego! I knew that we would have no trouble altering lego because there are so many STEM (science, technology, engineering, mathematics) components that lego may offer. I was employed for a day camp this summer at an elementary school, and one of the other camps we shared the space with was called "Bricks 4 Kidz." If you'd like to check out their own blog, I'll leave the link here: Bricks 4 Kidz. Although I didn't work for them specifically, I was fortunate to be exposed to their methods of teaching.

Retrieved from www.bricks4kidz.com

Bricks 4 Kidz is a day camp geared towards experiential and playful learning through building specifically-designed models with lego pieces. They believe that children of any age learn best through curiousity, creativity, and multi-sensory activities. Constructing objects, robotics, the possibilities are endless! For this reason, I knew Matt and I could creatively design our own lego game. Though we hadn't named it, our idea was pretty rad! We decided to plan our game around the "measurement" stream in mathematics. Since our box of lego was seemingly already a little different, containing dice and a timer, we planned to add these components as part of our game.



Our game's main goal was to create a building or structure with proper measurements. How are these measurements determined, you ask? Well, first students must role the dice. The numbers that are rolled will be added to form the sum of the area OR perimeter of the structure to be built. (Decide what you are rolling for.) For example, if the numbers 4 and 5 are rolled, you can either multiply or add those numbers to give you a larger sum. Let's multiply this time. 5x4=20. Therefore, the lego structure will need to have a perimeter of 20cm. Students are then required to "work backwards" in getting the other measurements. To assist with the process, students will be given some grid paper where they can plan out the design and measurements of the structure. Too simple? Add in the timer! Group your students and see who can construct their building with the correct measurements, the fastest! Give bonus points to the most creative or wacky design! We had so much fun creating this game and hope you have just as much fun trying it out with your students :).

Photo taken by me.

Games are a fantastic way to get comfortable with making mistakes - another huge topic discussed this week. When you're introduced to a new game, you're just beginning to understand the rules and expectations. Therefore, the whole trial and error process is prevalent and making mistakes becomes common. As we observed this week in the stage 3 module, mistakes are necessary, and should even be encouraged in the subject of mathematics, where mistakes are often avoided or feared. Based on scientific evidence, it is this process that allows our brain to "stretch" and grow. It is through the failed attempts where we analyze the hows and the whys of how we could have possibly arrived at the solution. I love comparing this notion to real life scenarios, because it is undeniably true! Only through adversity and struggles do we grow stronger as human beings. We store these life lessons in our minds, which then equip us with the tools and knowledge for similar challenges we meet in the future. This is exactly why mistakes should be encouraged in mathematics. Students will value the messy mistakes because it will carry them forward to a much more comfortable and confident place when solving problems.

Well, that's it friends! Hard to believe we are already half way through this course!

Until next time,

Have a beau-tea-ful evening!

Miss Capano

Week 2: Season of Harvest

Welcome back, teacher friends!

This week's module has directed our attention to our current "math mindset" as educators, and that of our students. Videos confirmed that to a degree, we all still struggle with having a completely positive outlook towards this subject. It's important to reflect on how we may be feeling, so that we may make room for a shift in our perspective. With the season upon us soon changing, so too, can our mindset. 

This past weekend, I had the lovely opportunity to attend a meditation retreat in Toronto where we honoured and welcomed the autumnal energy (despite this unsuitable hot, summer weather!) and began setting new intentions for the approaching months. As we gathered in a small, intimate circle, we were asked, "What are you harvesting this season?" Though the gentle whisps of the trees, the subtle chirps of the birds, and the harvested crops surrounding us on the farm may have inclined us to respond in a literal sense, we were called to look within, and respond in a way that would reveal our truest intentions. We were each given a sticky note and marker to record what we may have set out to do at the commencement of the year, the seeds we have planted, and are now "harvesting.'' Who or what supported us along the way to reach this season of harvest, and revel in its abundance? We then placed our notes into the basket and anonymously read someone else's note. Strangely enough, the note I read aloud completely resonated with me. It said "Seasons change. Crops flourish, others don't. But a new season will always come." Seasons change. Ah, yes. When I was a little girl, and still, to this day - I always perceived September as another "New Year." A time to reflect on the year thus far, and a time to set new intentions for the promised opportunity on the horizon.

Photos taken by me.

 Of course, being an educator, I reflected today about what this season can mean for students. Some students will enter this season with a renewed sense of courage and motivation to pursue a deeper understanding in their personal areas of weakness, the "unflourished crops." This could very well be mathematics - but it can also be language class, social studies, or science. What's unfortunate is that these new intentions can easily become distant if we meet them with poor language.

 Just as the "Messages About Math" video informed us, we must be careful with our words, for they hold so much power within them. If we praise our students for their intelligence, saying "You are so smart! You got this!", they may develop a fixed mindset where they will solely depend on correct answers, as opposed to completely understanding the question being asked. And although the seasons around us may change, a deepened understanding can remain with us, if it is reached. Therefore, it is extremely important we mindfully choose encouraging language that will best support our students through the challenges on their journey. We want our students to rise to the challenges given - not to avoid them for fear of how they measure up relative to others.

In class, an interesting activity was presented to us, the "dot" activity. This was to practice the concept of subtizing, the ability to see a small number of objects and know how many there are without the need to count. This is a fundamental skill students should grasp when learning to understand numbers. After all, dots are recurring in many games we play, such as dice for board games, concentration cards, or dominos. Dr. Mina showed us a photo of dots, but kept it on the screen for about a millisecond before skipping to the next slide.

We were then asked to estimate how many dots appeared. Encouraging us to design a "shape" in our minds, some drew them on the board. One person grouped the dots together in a way that made her visualize a lady wearing a hat, others visualized a sail boat. I think this would be a great diagnostic activity to do with our students, especially towards the beginning of the year, as it will prove that mathematics is a very creative and visual subject - every one perceives it differently. This means it can adhere to the diverse learning styles in the classroom; reassuring the students that there are indeed many paths that may lead to the same destination. In hopes that this will forge a growth mindset; one that is deeply rooted in acceptance of challenges and openness to possibility, let us remember, too, that the crops of the Earth never think of competing to those next to them. They simply find comfort and succumb to the conditions of the Earth - the soil, the water, and the care. We, as educators, must cultivate and fertilize this type of care, so that our student's knowledge and understanding in mathematics (and in every subject) can grow in abundance! There is always so much to learn from nature. As you can see, I am a firm believer in this.

What are you harvesting this season?

I'd love to hear your thoughts!

Until next time,

have a beau-tea-ful afternoon!

Miss Capano

Math (EDBE 8P54) Post 1

Hello teacher friends!

Why yes, I know..it has indeed been a while! I hope every one enjoyed their summer! But I am excited to be back for our second and final year, here in the Teacher Education program at Brock University. This just means we are one step closer to reaching our dreams! Or a very particular dream, I should mention; which includes inspiring the young minds for a brighter future.

We had our first mathematics part II edition this week. Insightful it was! Our instructor, Mina, opened the class with an intriguing card trick. With a few shuffles and flips of the cards, organized into 4 piles, the end goal was to reveal four cards of the same number. Seemed easy enough, but it still presented difficulties for my group. Eventually, with lots of trial and error and as we communicated with another group, we were closer to being successful. Once this activity was complete, Mina posed the question "What did I do wrong as a teacher?" We had to stop and give it a few moments of thought. She told us that initially, when introducing the activity, she said "This is a simple card trick." The tricky - pun intended - word being "simple." The language used can be condescending for students who, after the first few tries, do not succeed in the desired result. Further, the student(s) may feel devalued, suddenly lack confidence in their own skillset, or just be simply confused! It is best to stray from this type of language, so that students approach the challenge without a predetermined label of whether it is an easy activity or not. Remember - what we may find easy may be difficult for others! This is where the beauty lies of learning from one another. :)

Swister_p. "Cards?" Online photo. (2007, March 19). Retrieved from: https://www.flickr.com/photos/swister/426950151/.

 I also happened to notice that when first choosing a student to demonstrate the trick, she asked "Who is good at cards?" And while this may be a wonderful opportunity for a student to showcase and lead something they enjoy, again - the use of language may suddenly highlight the activities we aren't very good at. It can stir an insecurity within us. If a student who is not very good at cards, but has the willingness to participate, is present, then the opportunity to try and possibly improve in the activity would be amazing. Let a child step out of their comfort zone! I think this is especially important in mathematics, where a lot of these insecurities tend to loom. Give it a go -you may be surprised at what they accomplish.

I bring attention to these situations - not to criticize, but to welcome the "teaching/learning moment." I am constantly seeking these out, and appreciated how Mina encouraged us to analyze what could have been done differently.

Next, we played an online game called "The Game About Squares." Wow! This was incredibly fun, but also had its own challenges! It's essentially a game where you need to line up the squares to their corresponding dot (by colour). But the game is colour-blind friendly, so it is great to know that inclusive practices are prioritized in content creation. The square could only move in the direction that its arrow points to, so that is where the challenge was. The simple graphics and design are deceptive to its complexity as the levels increase.

Digital Vincent. "3 Squares." Online photo. (2014, August 17.) Retrieved from: https://www.flickr.com/photos/7699384@N07/14952667635/

Later, we discussed what helped us during this activity, and it was great to have the opportunity to pause and think about what strategies worked and what did not. Thinking about our own thinking - an important technique to consider when fostering that metacognitive piece for our students. Also, I believe this is an admirable education tool to use in the classroom because students are not given any prompts to direct them what to do. It's a chance to explore what the game entails, and what innate strategies students may gravitate towards. Are you a logical thinker? Does it take time to figure out a plan of action? Do you tend to seek help from others when stuck? What a great learning experience it can be. Here is the link for the game, incase you would like to check it out and make use of it in your own classroom: Square Game.


That wraps up class 1 of our mathematics course!

Until next time,

Have a beau-tea-ful day every one!

Giuliana