Math Week 6: The End Is Near

Hello teacher friends!

Wow..for the final time this year I am blogging about mathematics! Unless of course I am exposed to some wonderful ideas during practicum, but I have just discovered that I will be teaching FSL again! Woo! This means that unfortunately I cannot bring all of the fantastic ideas I've gathered throughout the course, PDs, modules, and from YOU lovely TCs into my classroom, since I am limited to teaching a language (you can imagine all the time & energy that takes!). However, if I am directed to any great resources while I am there, I will definitely be back to share them with you!

To do a quick round-up of what I have learned this week: Math is Everywhere.We practically live, breathe and eat math. It makes up so many of our thoughts and then proceeds to seep into our actions. Because of this, a question to ask ourselves is: How can we improve motivation, interest, and attention in the elementary mathematics classroom? Knowing how dictating and accessible math is, there are plenty of ways and tons of opportunities for some cross-curricular connections as well. Teachers can improve student achievement by turning their attention to resources and strategies that pique students' motivation, emotion, interest and attention. Since math can be discovered in every corner - the daunting task of ours to design enticing lessons shouldn't be that daunting after all. This week's module revealed that math is overarching in nature. We very seldom recognize that animals use math as a necessary means of survival - to construct their habitats, to gather food, and to find their prey. So fascinating! I think it would be interesting to have each student conduct research on a specific animal to inquire how they interact with math. 

"Mathematics in the Natural Sciences." 17, Oct 2017. Retrieved from: https://www-tc.pbs.org/wgbh/nova/blogs/physics/wp-content/uploads/sites/2/2015/04/sunflower_620.jpg

Having our students connect math to real-world applications is highly beneficial. Not only will it forge a more positive attitude towards the subject, but it will help form a lasting interest, ultimately shaping our students' future. Perhaps transferring the classroom outdoors and having them physically interact with the math that is observable around us will produce the greatest results in terms of encouraging the growth mindset we hope to see in mathematics! I LOVE nature so this is something I definitely plan on incorporating!

Another module we watched this week touched upon math apps and games. When considering the aspects of a "good" math app or video game, it is important to note that the game or app is relevant and enhances the expectations that the student is learning. I remember last year we were given the task to critique different games on www.exploregizmos.com for our science course. As educators, we should continue this reflective way of choosing resources in the ever-evolving 21st century. In my opinion, the app should encourage deeper, critical thinking and problem solving skills in a fun and engaging way. I also think it is important for the game to provide various levels, so that the student can recognize that it is indeed possible to succeed in math, but further, that they can make connections between levels of difficulty and build on their previous skills; guiding them to higher-order thinking. What techniques allowed them to pass the previous level? Students can fine tune their learning by analyzing this, and LEVEL UP with the level. Finally, math apps and games should emphasize the practicalities rather than the technicalities of the creation. The more practical the app is, the more likely a student will make real-world connections and retain what they have experienced.

"The Math Learning Center." Oct 25, 2017. Retrieved from: https://www.mathlearningcenter.org/sites/default/files/images/GB_product_shot_small.png

Well..that's all folks! I've really enjoyed learning more about mathematics with you all! Hope every one has a very fulfilling block 2 experience!

Until next time,

Have a beau-tea-ful day,

Mlle Capano

Week 5: MatheMAGICAL Ideas!

Hello teacher friends,

Hope you are all enjoying your much deserved break! Since we did not have regular classes last week, I want to discuss other math adventures I got up to. First, last Monday was webinar day for my partner, Mohamed and I! We touched upon Financial Literacy, a newly separated branch in mathematics that addresses numeracy in our society. We wanted to express how important it is that each individual be financially literate because it is a skill that equips us in making decisions that can affect us for the remainder of our lives. It allows us to be self-sufficient and independent as we learn to manage money matters like budgeting, saving, spending, and consumer awareness. All of our information is available on Sakai, but I wanted to provide you with a few quick tips & tricks when beginning to integrate financial literacy in your J/I Math Program.

 Steps to integrating financial literacy:

1. Research! Ask yourself: How much do my students know already? (prior

knowledge) What do they need to know at their age? (appropriateness) What finance education is your school currently delivering?(curriculum)

2.Plan! What do you want to achieve and how are you going to do it?

(learning goals + process) How will they learn best? (resources, environment, learning style/multiple intelligences)
 

3.Differentiate! (This is pretty self-explanatory at this point. Include opportunities for visual, kinesthetic, auditorial components, etc.)

4.Assess the Impact! What have students learned & how did they respond? (reflection)

If you did not attend our webinar but would like to see what else we discussed in greater detail, watch it below!

Now, for the other math venture.. I attended a PD workshop, hosted by the Ontario English Catholic Teachers' Association (OECTA) last Wednesday. The topic was extremely intriguing, as it promised fun, interactive, and communicative math techniques, hence its name, "Mathemagical Ideas." We were introduced to SO many neat resources. Before this workshop, I had no idea how many storybooks related to mathematics were available! Literature would be a fantastic way to enrich our math lessons, especially if you are an avid book reader and literature lover like myself! Here's a compiled list of the mentioned books:

One is a Snail, Ten is a Crab by April Pulley Sayre and Jeff Sayre

12 Ways to Get to 11 by Eve Merriam

Mission Addition by Loreen Leedy

Subtraction Action by Loreen Leedy

Two Too Many by Jo Ellen Bogart

10 for Dinner by Jo Ellen Bogart

Five Creatures by Emily Jenkins

The Doorbell Rang by Pat Hutchins

Six-Dinner Sid by Inga Moore

Ten Times Better by Richard Michelson

The Best of Times by Greg Tang

2 X 2 = BOO! By Loreen Leedy

Amanda Bean’s Amazing Dream by Cindy Neuschwander

 Although most books are geared towards P/J expectations, I believe we can still use these books as a great entry point and conversation starter surrounding certain mathematical concepts.

As for my favourite game that was played...we were introduced to a game called "Last One to School." All markers begin in the little houses. Students, in pairs, practice their doubles by rolling a 10-sided dice or using cards. If the double is rolled, the student places their marker in the "school." The first one to school, wins! This game is simple yet engaging enough for students to practice their multiplication skills. To increase the difficulty, have your students do "double + 1", or "double -1", including new elements.

Photo taken by me. Oct 4, 2017.

That's all for now! Make sure you're back next week for my final math blog post for the year! (Wow, where has the time gone?!)

Have a beau-tea-ful day every one!

Miss Capano 

Week 4: Get Rich!

Hello teacher friends!

This week, we focused on the growing need to implement mathematically rich tasks for our students. Rich, how, you ask? Rich in content, rich in objective, rich in accessibility, rich in its multiple representations, rich in assessment, and rich in the learning outcome itself. On top of every thing else we need to remember as pre-service teachers, this may seem a little overwhelming. So, how can this be accomplished?

In the guidance document "Mathematics at Key Stage 4: developing a scheme of work", the Secondary National Strategy describes a rich task as:

• accessible and extendable,
• one which allows learners to make decisions,
• involving learners in testing, proving, explaining, reflecting and interpreting,
• promoting discussion and communications,
• encouraging originality and invention,
• encouraging 'what if' and 'what if not' questions,
• enjoyable and contains the opportunity for surprise.  

"Tried and True Teaching Tools." Mathematics Mindsets, p.90. Retrieved from: http://www.triedandtrueteachingtools.com/2016/08/rich-mathematical-tasks.html

In class, we worked through a set of problems to assess whether they were credible for a rich task or not. Some were lower-order questions, focusing on the same mathematical topic, and some were more challenging - ones that required higher-order thinking. We considered things like openness vs. closed-ness (open questions promote deeper thinking - look for the Why?), feasible questions vs. infeasible (feasible questions ensure the question is possible in the sense that it is realistic and can be applied to every day life), and equality vs. inequality (was the question fair in its approach; considering all levels and learning modes of the student?). Most questions seemed to rank on the lower-order question spectrum, and not surprisingly so, seeing how a lot of textbooks do not address these type of questions. Teachers must then develop and create their own.

In smaller groups, we discussed what else might make a rich task effective. Casey, Kursten, and I collectively agreed that it is important to assess students' prior knowledge and their base of fundamental skills before rich tasks are even introduced. Since creating our own rich tasks requires plenty of planning, knowing our students' abilities and baseline will guide us in the development. We can therefore improve student achievement by turning our attention to resources and strategies that pique students' motivation, emotion, attention, and interest.

Photo taken by me. 09/28/17

Speaking of, some resources we explored in class that I'd like to make note of are: 

-https://nrich.maths.org/   (a main hub of teacher resources and notes related to mathematically rich tasks)

-https://nrich.maths.org/2526  (the Square It game! This game challenges students to form a square using a grid and dots while competing against an oppenent. The possibility thinking reinforces the notion of an open-ended task.)

-http://wodb.ca/    (the "Which Object Doesn't Belong?" game offers many entry points for students. What one student may observe as different, another may not. Rich discussion surrounding these perceptions will thus ensue. More than 1 correct answer = open-ended = rich task!) 

 Later this week I'll be attending a mathematics workshop, hosted by OECTA, called "Mathemagicals." I am curious to see if other methods regarding rich tasks will be discussed. Sooner than that, however, is my math webinar with Mohamed. We will be touching on the topic of integrating financial literacy in the curriculum.

Stay tuned for the details!

Until next time,

Have a beau-tea-ful day every one!

Miss Capano

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

Math Report: E.L.L. Students

Hey teacher friends!

This week's math class was full of all kinds of insight! I particularly enjoyed how Rebecca gave us the opportunity to discuss strategies by which we could assist English Language Learners in mathematics. The possibility of having ELL learners is always present, and I liked how Rebecca never limits our class discussions to topics surrounding mathematics but more so how to infuse mathematics as a "support system" in other areas of education. 

In choosing to take the Teaching Internationally online course here at Brock University, teaching English Language Learners is something I have been recently exposed to in research. I have had plenty of time to reflect on how I would cultivate inclusivity with specific teaching strategies. So...prepare for lots of advice coming at ya!

Red Pepper. "Welcome Mosaic with ESL Students". Online photo. (2008, June 25). Retreived from: https://www.flickr.com/photos/27984836@N07/2610991927/

Supporting English Language Learners is our current Ontario Ministry Document that is essential at having at our disposal as it focuses on a three-pronged approach to increase our student's success: understanding our English Language Learners, working as a school community to support the English Language Learners, and the adaptation of the Ontario Curriculum to increase student academic success. This document provides heaps of insight into the importance of understanding our E.L.L students (including their needs) so that we may make appropriate accomodations to ensure individual success. Highly recommended!

When I was completing my undergraduate studies at York University, I discovered a love and fascination for linguistics. This led me to enrolling in Second Language Acquistion and Discourse Analysis Courses - probably my most favourite electives that I chose during my time at York! I can recall reading a very interesting article written by John H. Schumann, titled Social Distance as a Factor in Second Language Acquisition. 

The article explains both good and bad learning situations for groups desiring to learn and teach a second language. There are certain societal factors that can either promote social distance or proximity between the second learning group (2LL) and acquiring the language of a target language group (TL group). So, as teachers of the English language, we would be considered the target language group. We must cultivate a reciprocated positive attitude with the second learning group so that they will intend to remain in the target language area for an extensive period of time. This way, enriched learning is achieved. Schumann expresses that the greater the social distance is between the two groups, the more difficult second language learning will prove to be. Therefore, we must achieve a sense of “low enclosure” which promotes the least amount of distance and steer away from “preservation” which is the greatest form of social distance. As leaders in the target language group, we must also carry a “non-dominant” attitude and level ourselves at their current learning status. Furthermore, remaining empathetic towards their cultural patterns (involving lifestyle and values) will encourage them to slowly assimilate into ours.

Enokson. "ESL Door Hanger." Online photo. (2006, June 12). Retrieved from: https://www.flickr.com/photos/vblibrary/4396314887/

An additional resource I would love to share with you all is found on the Brown University website, features a section dedicated to Teaching Diverse Learners. This of course includes the instruction of E.L.L students. It is a great resource that we may consult for suggestions in elementary literacy, teaching and learning strategies, policies, as well as assessment strategies – which are also extremely important to consider for E.L.L students because their rate of learning varies. Culturally responsive teaching is a category on the website that provides insight into how we can synthesize a celebration of culture in order to shape their attitude of learning and indulge in equitable access of material. 

It lists the characteristics of a culturally responsive teacher, including:

• ·      Positive perspectives on parents and families
• ·      Communication of high expectations
• ·      Learning within the context of culture
• ·      Student-centered instruction
• ·      Culturally mediated instruction
• ·      Reshaping the curriculum
• :   Teacher as facilitator 

Banlon 1964. "English Time Bulletin." Online photo. (2009, September 22).  Retreived from: https://www.flickr.com/photos/banlon1964/3945638242/

The resource additionally suggests we provide support for the child outside of the classroom which I found to be interesting. One particular recommendation that I loved is to involve the parents of the E.L.L student in translation activities. For example, having the parents participate in a culminating cultural event where they can help translate certain books that are relative to their native background. This is a wonderful way to integrate communication not only between differing cultures of students, but among different generations, too.

Now, in terms of making a student feel confident and comfortable in mathematics class, I think the same technique rings true across all subject areas and classes: incporporating visual elements. Students of learning English primarily rely on seeing and listening; it is the easiest way for them to take in information before they speak, read, or write. Perhaps including culturally relevant models, such as learning fractions with pizza if E.L.L students immigrated from Italy, or modifying my Ratio and Proportion lesson using ingredients that make up tortillas so that indigenous Mexican students can better connect to the material. In making simple adjustments, E.L.L students will feel more "at home" while feeling welcomed by all in a new community.

Confident ELL student: Challenges and Strategies. Taken Friday, October 28, 2016.

Rebecca also encouraged us to reflect on teaching strategies collaboratively within groups. Given the challenges of certain levels of E.L.L students: Early Stage, Foundation, Confident, and Fluent, we were then instructed to provide strategies that would align well with them. My group was to brainstorm ideas regarding the confident students, therefore, different challenges are presented with such students: errors in writing may occur (syntax), improper use of vocabulary, checking for understanding, and having high expectations of written and spoken language. The strategies we suggested were to have students keep a dictionary as well as a hand-made dictionary (the student can add new vocabulary to their own if new words pop up), encourage students to continue verbalizing written text but also allowing sufficient processing time, and assigning tasks that need to be expressed in different ways to exercise various skills.

All in all, I am feeling more inspired than ever to teach E.L.L students, perhaps even abroad one day! I think it would be extremely rewarding to be able to teach students learning my first language. Connecting with immigrants would resemble that "international feel" I would seek by teaching internationally. The student(s) would bring forth their own culture, heritage, values, and traditions in the classroom, which is what I think I essentially crave to experience because I am an endless learner at heart.

Until next time,

Have a beau-tea-ful day!

Miss Capano