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