Week 4: September 26

Hello Everyone!

Left to Right: Pigeon HeadWaters Provincial Park, Tractor Pull at Lindsay Ex,
Pigeon HeadWaters Provincial Park, Sunset at Lindsay Ex.
Katic, K. September 24, 25, 2016. 

Welcome back to this week's blog post! As you are well aware of, it's October in only 2 days! As
such, with the program we've been extremely busy with lesson planning, conducting lessons, webinars, unit planning (to only name a few)! As such, as I have said many times before, it's always important to become mindful during our day, and to remember those quiet simple joys in our lives that we find pleasure in. Throughout this week, I reflected back to this past weekend and the incredible amount of joy I get from going to Local Fairs and on long, peaceful hikes. The Tractor Pull at the Lindsay Ex was EXTREMELY loud but I would highly recommend it, it was super exciting! In conjunction with exploring Pigeon HeadWaters Provincial Park, I keep those positive memories close to me when going through stressful moments. Just as I celebrate my successes with scaling a slippery rock slope while hiking, I too believe that in the context of the classroom, we must be hypersensitive to the importance of celebrating the success of our students, not just in math class but in all other subjects! This promotes a positive classroom environment for everyone, and is something that I wish I had when I was a student.

This is where the importance of Differentiated Instruction comes in! Fundamentally, as math teachers we must have a thorough, extensive knowledge of the Curriculum and be able to identify exactly what we are trying to teach, the Big Ideas behind our lessons. However, D/I is equally as important; we have all heard this term many times throughout college, however, it isn't simply a term we can just *shrug* off, we must actively incorporate this in our classrooms to ensure our student's success. This is where the discussion of Rich Tasks comes into play. These tasks, comparably to Parallel Tasks that we discussed earlier, are great for engaging our students as they accommodate for a variety of levels of our students and provide everyone with the opportunity to succeed. However, as teachers, rich tasks are difficult to create until you become good at it. This is where carefully constructed examples of Rich Tasks can help us greatly. One such example I have included below; we explored this Grade 4 level Rich Task in class and I thought it was a great task!

~ Rich Question From Class ~

A group of students are participating in a project where they are trying to determine how many students in their class are active during lunch time. There are 24 students in the class. Half of the students in the class like playing soccer, one quarter like playing adventure playground, one sixth enjoy sitting around, and the remainder like playing tag. Then they decided to ask the teacher and she also liked sitting around.

What percent of students are active during lunchtime? Show your work.

Katic, K. (Sept. 24, 2016). "Vine to Victory".
Lindsay Exhibition.

We proceeded with this question through using a "placemat"; everyone at our table groups shared one piece of paper to show our work with this question. While I understood the purpose behind this activity (to see our peers' work), some found it fantastic! .... Others found it to be slightly anxiety-inducing should one get intimidated by seeing others' work before writing down their own. As such, accommodation is required in our classes, such as providing extra scrap paper before writing on the group placemat.

This conversation about the importance of Rich Tasks reminded me of a really well-done poster board that I saw at the Lindsay Fair this past weekend, and while it isn't explicitly mathematically related, there are many ways this can be used in our math classrooms. This poster board inquires about how to successfully grow a Giant Pumpkin, and it was created by a local Grade 4 student. This can lead to many various discussions in our classrooms, and I think that any Grade 4 student would be curious about how to grow a Giant Veggie! Mathematically related questions can include relations to temperatures, weight, area and perimeter, the possibilities are endless!

Kelly, E. (Sept. 25, 2016).
Pigeon HeadWaters Provincial Park.

In addition, we can create our own Rich Tasks by using the world around us! Like I stated in the section above, I went on a really great hike this past weekend, and this got me thinking about the picture I have included along side the text. I am sitting at the top of the "Lookout Post" in this park, and in the picture there are 8 stairs. We could ask our students to estimate how tall they believe the Lookout Post is in comparison to my height sitting down, if they're curious as to where it is, they can do some research in regards to calculating the area of the park, how long the trails are in the park in relation to other parks in the nearing neighbourhood, once again the possibilities are endless! It all depends on the level of engagement that your students have, as well as how effectively the Mathematical Processes are being used for the tasks at hand. Just as a reminder, the Mathematical Processes that we constantly refer to are: 

• Reasoning & Proving 
• Selecting Tools & Computational Strategies 
• Connecting 
• Representing
• Communicating 



Katic, K. (Sept, 30, 2016).
Various Resourceful YouTube Videos. 

• Problem Solving

Finally, there were a variety of video resources this week that completely changed the way that I view mathematics! I have included links to all of them below in the references section. The first video asks simple question:

What is 18x5? 

No Calculators. 

At first, this question seems daunting! I thought to myself, 18x5 without a calculator? Then I thought about it, ok it can't be that hard, 10x5 is 50, and 8x5 is 40, add them together it's 90. Then I decided to see if there was another way to do it, and there is! In fact, the second video discusses the various ways to calculate this in our minds, and the last solution discussed is my favourite! Finally, the last video takes us on an interactive Mathematical Tour, and quite honestly this completely changed the way that I viewed math. I saw math as being an interconnected subject where all of the strands are connected and relatable to everything that we do in our lives. I would highly recommend this video, especially for people who are transitioning towards a growth mindset. 

I hope that you learned something from reading this post today! If you have any questions or comments please feel free to leave them in the comments section below. Remember, it is important that while we experience stress in our lives, we must remember those quiet, joyful moments in order for us to be healthy in our minds, bodies and spirits. I hope that the image I have included below inspires you as much as it does me. Thanks for reading! 

Katic, K. (Sept. 26, 2016).
Pigeon HeadWaters Provincial Park.

References 

Lesson 4a. (June 12, 2014). Lesson 4a. YouTube Video. Retrieved From https://www.youtube.com/watch?v=kTn_KNjItZ8&feature=youtu.be
Lesson 4b. (June 12, 2014). Lesson 4b. YouTube Video. Retrieved From https://www.youtube.com/watch?v=LHtIBt3ootM&feature=youtu.be
Lesson 4e. (June 12, 2014). Lesson 4e. YouTube Video. Retrieved From https://www.youtube.com/watch?v=LKmk9MnBumQ&feature=youtu.be
Lesson 4f. (June 12, 2014). Lesson 4f. YouTube Video. Retrieved From https://www.youtube.com/watch?v=q8hzzv4a_8Y&feature=youtu.be

Photos. 
Katic, K. (September 24, 2016). Tractor Pull at the Lindsay Ex©; Sunset at Lindsay Ex©; "Vine to Victory".© Photographs. 
Katic, K. (September 25, 2016). Pigeon HeadWaters Provincial Park©. Photograph. 
Kelly, K. (September 25, 2016). Pigeon HeadWaters Provincial Park©. Photograph. 

Week 3: September 19

Hi Everyone!

K, Katic (Sept. 17, 18, 2016). Relaxing After Birthday Fun and Apple Picking!
Nana and Papa's; and Pingle's Farm Market in Hampton.

Welcome back this week, it's hard to believe that this week is the official start of autumn! By far summer is my absolute favourite, however, I am really starting to welcome the joys that this season has to offer, like apple picking, pumpkin pies, warm socks and sweaters, cozy fireside evenings and, of course, lots of hot coffee. It's so easy to forget about these simple pleasures with the intensity of University, however, as I have stated in my previous posts, those small joys are so important in our lives to remain healthy and happy. Just this past weekend served as a great, simple reminder for me that spending quality time with family brings me immense joy! We celebrated an entire weekend of birthday festivities complete with a large dinner and some farm fun apple picking, and let me be the first to tell you that nothing tastes quite as good as farm fresh Ontario apples...delicious! Yet the emerging teacher in me never really seems to leave as I was asking the kids to do some simple math problems with the apples...which leads me into my discussion this week about some fundamental concepts!

Katic, K. (Sept. 19, 2016). I Have...Who Has?
In Class Ice-Breaker, BrockU.

I have...Who has? 
We began class this week with a great icebreaker, minds-on activity since it involves EVERYONE in the class and, as no calculators are allowed, it's an excellent review of concepts. This can be adapted for every single age, grade and individual, shy or outgoing, everyone is involved and everyone loves it. I love this strategy as an introduction to multiple math lessons in multiple units, I really experienced having my brain get warmed up with math before the lesson began, and this is something that would help our students feel ready to learn, create and explore.

Katic, K. (Sept. 19, 2016).
Parallel Tasks Activity: Anna Laman's Group. BrockU. 

Parallel Questions
This concept during this class time was new to me, I had never heard of these types of questions, but upon exploration of them, I really do think these types of questions are crucial to teaching math to our students effectively. Parallel Questions or Tasks are sets of two or three tasks that are designed to meet the needs of students at various developmental levels, but meet the needs of those students through the same big idea and are close enough in context so they can be discussed simultaneously, as a whole class. This integration of all students at all developmental levels is critical as it is inclusive, accommodates everyones needs, and creates an overall positive environment where challenging math can be created and explored freely. In addition, As Pat, our instructor stated, "We're looking for rich discussion in these open-ended questions, these parallel questions, in order to support what you have to say!" Pat, September 19, 2016 in class. This point, of encouraging rich discussion through parallel questions, is so critical in order for our students to holistically, deeply, and fully understand math.

Here is a great example of one of those types of parallel questions we discussed in class: 

Choice 1: Jane & Brad delivered flyers. Brad delivered three times as many as Jane. Together they delivered fewer than 20 flyers. How many might each have delivered? Open set of answers. 

vs.

Choice 2: Jane & Brad delivered 81 flyers. For each four flyers that Jane delivered, Brad delivered five flyers. How many did each deliver? There's only one answer.

While these might not be the best choice together, the overall expectation is about getting a ratio out of a word problem.

Parallel questions are all about exploring the same concept in a variety of ways, and I personally think it's an absolutely phenomenal way for us, as teachers, to be able to accommodate every single one of our learners. These types of questions allow everyone to feel successful, and they are able to accordingly select a variety of starting points depending on their current comfort level with the concepts. I wish I had been given more of these opportunities as a student! To the right I have included an image of an activity we completed in class, where we were given a set of parallel questions and had to come up with a set of Common Questions and Scaffolded Questions in order to support all of our students and have them challenged while still being able to be successful (I credit this gorgeous chart to Anna Laman's Group, great job guys!). Scaffolding Questions are questions that aid in supporting our learners with completing the problem while Common Questions are questions that allow students to explore the question more in depth and understand concepts deeply.

Katic, K. (Sept. 20, 2016). Various YouTube Videos, Screenshot.

Lastly, below in my references section, I have included links to various videos we viewed this week, videos about the importance of allowing our students to make mistakes in math, and be encouraged to take their time in order to understand concepts by asking questions and make connections. You will discover upon viewing these videos that those are the two main messages being discussed, however there are lots of other great facts and encouraging tidbits in these videos that I highly recommend.

Thank you for reading everyone! If you have any questions or comments, please feel free to post them below. Remember those small, simple joys that we have in our lives and continue to live inspired and freely!

Katic, K. (Autumn, 2016). Warm Socks and Hot Coffee Fireside.

References 

College of Natural Sciences Video. (Oct. 19, 2012). The Second Element of Effective Thinking: Make Mistakes. https://www.youtube.com/watch?v=Txq-bsbbhaY&feature=youtu.be 

Sue D. (July 20, 2016). Lesson+3a 360p, How to Learn Math for Students: Mistakes. YouTube Video. Retrieved From 

https://www.youtube.com/watch?v=kGV0HQujmKs&feature=youtu.be

Sue D. (July 20, 2016). Lesson+3b 260p, Mistakes and Life. YouTube Video. Retrieved From https://www.youtube.com/watch?v=_GoYi3hfiBg&feature=youtu.be

Sue D. (Sept. 13, 2015). Lesson+3c 360p. YouTube Video. Retrieved From https://www.youtube.com/watch?v=ElzFq-G1QmU

Images 

Katic, K. (September 17, 18, 2016). Relaxing After Birthday Fun and Apple Picking!© Nana and Papa's; and Pingle's Farm Market in Hampton. Editing Face Tool: https://www.facepixelizer.com/ 
Katic, K. (Sept. 19, 2016). I Have...Who Has? In Class Ice-Breaker, Brock University. 
Katic, K. (Sept. 19, 2016). Parallel Tasks Activity: Anna Laman's Group. Math Class, Brock University. 
Katic, K. (Sept. 20, 2016). Various YouTube Videos, Screenshot.  
Katic, K. (Autumn, 2016). Warm Socks and Hot Coffee Fireside.©  

Week 2: September 12

Hello Everyone!

Puppy Sitting for my Boss!
Katic, K. (Summer, 2016). Rosedale.
Left to Right: Hooch, Flower, and Stone.

Can you believe that we're almost at the half way point of September? It's hard for me to believe that autumn is almost here, it feels like summer was just yesterday! As the pace continues to increase during this school year, I will constantly be stressing the importance of finding the small things in life to keep your mind at ease. It's so easy to get overwhelmed and stressed with our schooling, and those small things help to keep us in check. As I have said before, I love being outside, weight-training and yoga, but I am also a huge animal lover! For me, the perfect break from getting overwhelmed with school this weekend was to have dinner with my boss and our significant others. Her Great Dane puppy Stone just turned 6 months, and he is just the sweetest boy (you can see him in the picture above from when I was puppy sitting in the summer). He always makes sure to give great sloppy kisses when I'm feeling a bit stressed out, so remember the small, simple pleasures and this will ensure that you get through your school year with minimal stress and great success!

Screenshots of Videos from Week 2.
Left to Right: Mindset, Messages About Math, Messages About You.

This week, there were many concepts from class that I found to be great! They really challenged my thinking and I truly believe that it has changed my mentality about math. All three of the videos that had to be watched on the Online Module really affected how I viewed math and the mentality that I have about it. The three modules this week discussed Mindset, Messages About Math, and Messages About You. I have set up the links for each video for easy viewing. While there were many great take-away's from all of these videos, I have narrowed down two important things that each teacher should know.

The first is the importance of maintaining a growth mindset as opposed to a fixed mindset. A growth mindset believes that you can succeed and increase your intelligence with hard work, practice and dedication. It has been proven that having a fixed mindset, the belief that someone is intelligent or not and no matter the amount of work intelligence cannot increase, it truly detrimental to our students and ourselves; this limits the potential for success in every area of our lives! By maintaining a growth mindset and constantly challenging ourselves, great things will happen! The second take-away is that we must encourage our students with positive feedback and ensure they know that we believe they can succeed in order for them to achieve at the highest levels possible. As teachers, we must avoid using phrases such as "smart" to describe students as this has been proven to lead to a fixed mindset due to those "smart students" being fearful of failure. Instead, we must use words of praise such as "great job for working so hard, I believe in you!". These types of encouraging words will lead to students trying harder and great success!

Studying for my Stats Exam, Year 2 at McMaster.
Horsley, S. (April 25, 2013). Hamilton.

From my own personal experience, I have had both growth and fixed mindsets, as well as teachers who really didn't believe in me as a student. I have had growth mindsets with every area of my life, with the exception of math. I constantly got frustrated because I really didn't understand the material, and yet by constantly having negative feelings internally I discouraged and hindered myself. Here's a (really embarrassing) throwback picture that my friend took when I was extremely frustrated during exams. She took this picture for me to look back on when I was finished my exam and feel that overwhelming rush of relief...but it didn't happen that way; my math problems followed me all the way to my Undergrad when a Statistics Course was mandatory, which was this exam I was studying for. I truly thought that I was going to fail, I ended up passing my course but not with the grade I wanted. If I had only adopted this growth mindset mentality, then maybe I could have done better. However, with a Professor who really didn't care about the students and with not understanding certain concepts and having my friends say, "It's easy what don't you understand about it?', it was very discouraging. Therefore, with my own personal experiences I have had with math, I will do everything in my power as an educator to ensure my student's success with positive words of encouragement and constantly enforcing a growth mindset.

I hope that you have enjoyed reading this post, and I hope that I have offered some insight about how we can further improve our math classrooms. If you have any comments or questions please feel free to post below, and remember, enjoy the small things that breath life into all of your passions and endeavours! "Be fearless in pursuit of what sets your soul on fire". Feel free to post any questions or comments below!

Glute Bridges Personal Record!
Katic, K. (September, 2016). Lindsay. 

References 
Sue, D. (July 20, 2016). Week 2a: Mindset. Retrieved From https://www.youtube.com/watch?v=fuf1LzY5thM&feature=youtu.be 
Sue, D. (July 20, 2016). Lesson+2b: Messages About Math. Retrieved From https://www.youtube.com/watch?v=cuFHBwAgqjU&feature=youtu.be
Sue, D. (July 20, 2016). Lesson+2c: Messages About You. Retrieved From https://www.youtube.com/watch?v=_9q0paQoZa8&feature=youtu.be

Photos 
Horsley, S. (April 25, 2013). Studying for my Stats Exam, Year 2 at McMaster.© Hamilton.
Katic, K. (Summer, 2016). Puppy Sitting for my Boss!© Rosedale. Left to Right: Hooch, Flower, and Stone.
Katic, K. (September, 2016). Glute Bridges Personal Record.© Lindsay. Editing Tools: Photos on MacBook Air, PDF annotator, and http://www.quickpicturetools.com/en/blur_edges/

Week 1: September 8

Exploring the Local Sites.
Kelly, E. (Summer 2016). Emily Provincial Park.

Hello Fellow Readers and Bloggers!

I am so to be here! I have this amazing opportunity to complete my second year of Teacher's College! I am so fortunate that the program at Brock University - Hamilton Campus, is small, and have had many opportunities to collaborate with all of my colleagues, however for those of you who do not personally know me, I am going to include a short background of who I am before going into a discussion about the materials for this week's Junior/Intermediate Mathematics Course.

Enjoying Waterfall Jumping!
Kelly, E. (Summer 2016). Burleigh Falls.

Nothing Better Than Summer Sunrises
and Coffee.
Katic, K. (Summer 2016). Balsam Lake.

My name is Kathlene Katic and I am currently in my second year of Teacher's College at Brock University, Junior/Intermediate program. I am extremely passionate about teaching and ensuring that I reach every single student through engaging, relevant, and life-applicable material. Additionally, I am extremely passionate about yoga and weightlifting, as a healthy body goes hand-in-hand with a healthy mind and spirit. I love spending time outdoors in any way possible, and am constantly looking for ways to integrate my passion for fitness and the outdoors into my classroom. I was fortunate this past summer to spend every single day outside working and exploring the Great-Up-North, Kawartha Lakes region and beyond, and with this rejuvenation of mind, body and spirit, I am extremely excited to be back here at Brock!

Above: Stanford Myths and the Brain 2. YouTube Screenshot.
Below: Jo Boaler: The Brain Science on Growth Mindset. YouTube Screenshot.

Back to math, this week we were having a discussion over the importance of math in the classroom, and how stereotypes, fears and held beliefs affect our student's success in our classrooms. Personally, I fall under the category of people who dislike math, and as demonstrated this week through our resources, I can attribute this to many things stated: our students don't understand how many is applicable to real life situations, while some students may be good at it sometimes they really don't like to do it, and math making people feel unintelligent if they do not understand it immediately. In addition to feelings of discouragement comes stereotypes within math that are very clear. There is the perception that math is something that you have to have a genetic pre-disposition to be intelligent in, that some people are just math people and some aren't... these stereotypes are incorrect yet they are everywhere, whether that be in social media, written texts, social interactions and especially within our schools. Fundamentally, we are all born with the innate ability to do well in math, however, one's success within math is highly dependent on the beliefs that you have and your personal experiences. Experiences help to grow the brain, and the more that you revisit to ideas and concepts, the more deeply the synapses in your brain become and, therefore, you learn concepts deeply and holistically (see Stanford Myths and the Brain 2 and The Brain Science on Growth Mindset videos for more information).

This is where our roll as educators comes into play. Those stereotypes mentioned above, regarding students being fearful of math and some students not being "math people", are stereotypes that must be addressed within our classrooms appropriately. We must encourage all students that they can do math, with encouragement and by abolishing those negative stereotypes. Alarmingly, test results such as EQAO do discourage students in math as they realize that they are not meeting up to the Ontario Provincial standards, as discussed in this article. This puts an immense amount of pressure on students who are already fearful or uninterested in math as their government is now telling them that they must do better in this subject. Once again, this is where our roll as educators comes into play. Those types of results are opportunities for us to grow as educators in order to encourage our students to be successful! As a student, I wished that I had had math teachers who cared about my success and used relevant, applicable examples in the classroom. However, what I didn't have as a student is something that I will give my students, as my goal is to make a traditionally scary subject become enjoyable and eventually for them to have a more positive outlook on this subject. We must ensure that math class for all students is a safe place where mistakes are encouraged and accepted, and success celebrated. Additionally, furthering our professional careers through taking innovating math workshops is something that should be encouraged by our School Boards and Government to ensure our students success.

I hope that this discussion about math for this week has been helpful! Throughout this course I will be posting reflexive blogs about different topics within math, and how we can further this discussion in the future. However, the most important piece of advice that I can offer from this post is that when life gets stressful, always remember the simple quiet pleasures to regroup, refocus and resume. Below I have included one of my favourite happy places that helps my mind, body and spirit, and as this year progresses, I encourage each and every one of you to find those quiet, small things that breathe life into your passions and endeavours. Happy exploring, and feel free to post a comment below!

Finally Reached the Top!
Kelly, E. (Summer 2016). Eagle's Nest, Bancroft. 

References 
genConnect U. (2015, August 6). Jo Boaler: The Brain Science on Growth Mindset. YouTube Video. Retrieved From https://www.youtube.com/watch?v=s4xqzgBy-lM 
Toronto Star. (2016, September 5). Falling Math Scores Send Out a Loud Warning Signal: Editorial. The Toronto Star. Retrieved From https://www.thestar.com/opinion/editorials/2016/09/05/falling-math-scores-send-out-a-loud-warning-signal-editorial.html  
Williams, Tracy. (2014, August 10). Stanford Math Myths and the Brain 2. YouTube Video Retrieved From https://www.youtube.com/watch?v=JDhu53IrmnM&feature=youtu.be 

Photos
Katic, Kathlene. (2016). Nothing Better Than Summer Sunrises and Coffee©. Balsam Lake. 
Katic, Kathlene. (2016, August 2). Sunrise on Balsam Lake©. Background Photo.
Kelly, Ethan. (2016). Enjoying Waterfall Jumping!© Burleigh Falls. 
Kelly, Ethan. (2016). Exploring the Local Sites.© Emily Provincial Park. 
Kelly, Ethan. (2016). Finally Reached the Top!© Eagle's Nest, Bancroft.