Blog Post #10: A Reflective Farewell

Hello everyone!

Welcome back to my blog for my final post! I have learned a lot through using this blog as a reflective outlet within my educational journey in teacher's college. As my first year of teacher's college is coming to an end, I think it is the appropriate time to look back on my own posts as well as my peers blog posts to extend my reflection beyond just my knowledge. 

While reflecting on my peers blog posts, I came across a post that Shauna made that I found to be extremely useful and relevant. Shauna's post explored the variety of virtual manipulatives that are available to both students and teachers to be used in mathematics. I really liked this post because it allowed me to see the value of virtual manipulatives, especially given our current state with the world in a global pandemic. Having to learn in an online setting has posed many challenges to the education system in general. However, an online setting poses various challenges to both teaching and learning mathematics specifically. Without face-to-face learning, students who learn mathematics best in a hands-on way have been negatively impacted. However, with the use of virtual manipulatives, teachers can ensure that these students are still engaging with the mathematical concepts in an interactive way that provides them with positive learning experiences. I love the relevance of this blog post because it allowed me curate more resources and tools considering virtual learning will likely become a normality moving forward.

Another blog post that I came across was written by Sydney H. In this post, Sydney talked about recognizing her progress in both approaching and working through word problems. I think that it is so important to recognize how far you've come in any situation, not just in mathematics. While I was reading Sydney's post, I was able to recognize my own progress in my confidence when teaching mathematics. I did not realize how many times I successfully taught a mathematics lesson or concept throughout my first year of teacher's college. I taught a math lesson in two of my classes and led a problem solving session and activity in my math class! Given that confidence is something that does not come easily to me, I am extremely proud of how far I have come in just seven months! I believe that recognizing and reminding myself of the progress that I have made will allow me to keep progressing in this journey of becoming a great math teacher!

As this year approaches an end, I am happy that I have taken the time to reflect upon my progress and collect useful teaching resources that I can implement within classrooms of my own and during my placements. I am very grateful for the many learning opportunities I have been given over this past year of teacher's college and cannot wait to embark on my very first placement. 

Here are a few of my proudest accomplishments over this past year!

I created a digital word problem!

A virtual mathematics classroom (that's me)!

I taught a grade 12 probability lesson!

Part 1 of my Grade 12 Advanced Functions Activity!

Part 2 of my Grade 12 Advanced Functions Activity!

Part 3 of my Grade 12 Advanced Functions Activity!
(The Jamboard Component)

Well folks... that's all from me! Thanks for tagging along on this really fun journey with me. Take care and stay safe everyone!

Signing off, 

        Ms. Blackwell

Blog Post #9: What is Math Anxiety?

Welcome back everyone!

Today, I am going to be discussing a very important topic with you all - math anxiety. Math anxiety is a very real thing that students experience and it is often dismissed by teachers when they are teaching and evaluating their students. 

As you may have read in the photo above, math anxiety is different from a simple dislike of mathematics. For some students, the act of engaging in mathematics instills many negative emotions such as failure and fear within them. These negative emotions become overwhelming and thus, impairs students' ability to successfully perform. Math anxiety can impact students as early as first grade through impacts on their working memory. An individual's working memory is essentially like a mental notepad or sketchpad - something that comes in handy when keeping track of numbers in mathematics. Unfortunately, math anxiety disrupts the working memory and causes students in both elementary and high school to fall behind their peers. It is important that even students without math anxiety develop positive study habits that enable them to grow confidence as math becomes more complex. 

Now some of you may be wondering... how does math anxiety even develop? Math anxiety can target children and students in a variety of ways. Some causes of math anxiety may include:

1. The Influence of Teachers

Students can easily pick up on a teacher's feelings towards mathematics. For example, if a teacher is excited about math, the students may convey these same emotions. However, if educators are negative towards mathematics or certain units of it, the students may also pick up on these emotions as well. Additionally, if teachers neglect to recognize the presence of math anxiety in their classrooms, this can also worsen students' level of math anxiety. 

2. The Pressure Caused By Time Limits on Tests

Students can develop anxiety towards mathematics due to deadlines that timed tests impose on them. This time constraint causes students to forget concepts that they have studied and would have no issues remembering outside of the test time. This causes students' grades to decline and confirms their fear of failure. Testing is a vicious cycle that is difficult to be broken once the math anxiety towards tests has developed.

 

3. The Fear of Public Embarrassment 

Math anxiety within students can also be linked to negative emotions and experiences in their past. For example, if a student has experienced laughter or anger from others in response to getting an answer wrong, it can make their math anxiety even worse. 

Now that we have established some of the main ways in which math anxiety can be developed, it is important that, as educators, we understand what we can do to help our students cope with this anxiety. It is our job to understand this anxiety and help to reduce it as they progress through their mathematics journey. Some tips when engaging with students who have math anxiety during lessons or after school help include:

• Positive reinforcement
• Suggesting a tutor
• Make math fun and engaging
• Reassure students that there is not just one way to solve a problem
• Allow lots of opportunities for students to ask questions
• Encourage positive self-talk

These are all important tips for educators to follow when interacting with their students in math classes. However, there are also some tips to suggest for students to try in order to help them overcome their math anxiety. Some of these tips include:

• Confidence + Preparation = Success
• Ask Questions
• There is more than one way to solve a problem
• Overcome negative self-talk
• Read your math textbook
• Go back to the basics if you need to
• Use technology for assistance too

Something that I saw online while researching math anxiety that really caught my attention was a poster that I now fully intend to put up in my future classroom. This poster screams positive reinforcement and positive self-talk. It encourages students to be nicer to themselves and understand that their best is still good enough. 

I hope that once I am in my future high school mathematics classroom that I can conquer these feelings of math anxiety within my students and allow them to grow and overcome these feelings of fear and failure.  I hope I was able to teach you all a thing or two about math anxiety and the importance in recognizing it and helping your students overcome it. 

Until next time... 

Signing off, 

        Ms. Blackwell

Blog Post #8: Leading a Math Activity

Welcome back everyone!

It's been a couple of busy weeks for me but I have a lot to catch you all up on. This week I led a learning activity for my math class and I think it went very well. I wanted to reflect upon the process to think about what I can do differently next time or what I can add to the activity!

The activity that I ran was for a Grade 12 Academic Advanced Functions class. The unit that I covered was polynomial and rational functions, however my focus was on the key features and characteristics of the graphs of rational functions. My class really enjoyed the investigative approach that I took for the activity as well as my execution of the debrief prior to the activity. I provided everyone in the class with the following handout prior to engaging in any activity or debrief discussion. 

After going over the definitions of the different characteristics of a rational function's graph, I applied them to the basic rational function of f(x) = 1/x. After the example, I broke the class into groups of 2-3 and sent them off to apply their knowledge through investigating different graphs of rational functions. While each student was off working on investigating the features of these graphs, they were filling out this jamboard to help organize their observations. I found that this collaborative approach to investigating the key features of the graph allowed students to build on each other's thinking. Furthermore, having the handout open in the next tab allows students to refer back to the terminology and both check and reflect on their answers. Following the breakout groups, I brought the conversation back to a larger class discussion to consolidate student learning and go over the answers in the tables on the jamboard. This also provided students with the opportunity to ask questions and clarify their understanding on certain key features. 

Upon receiving feedback from my peers in my class, I was able to see what went well in the activity and what I could change for next time. My classmates really enjoyed the activity as a whole and expressed their liking for the layout of the jamboard as well as the handout. However, I did receive an insightful piece of feedback that really made me think. I was told that next time, maybe check with the students to make sure that when we are talking as a class, that they are still okay with me sharing my screen when pulling up their work. This was really eye-opening for me as some groups may have struggled and felt embarrassed that they did not have much of the charts filled out. I really appreciated this constructive feedback as it allowed me to really take into consideration the feelings of my students as I would never want to reinforce any feelings of math anxiety. 

Overall, I think that this learning activity went really well! I would definitely use this lesson in one of my future classrooms if I am lucky enough to ever teach Grade 12 Advanced Functions. I think it is always so important to reflect on how your lessons go as a teacher because it is key to know what to change for next time. Improving your lessons should be an expectation for all teachers as you are always getting new students in your classroom and it is important to strive to meet their learning needs.  

Anyways, that's it for me today! I feel like the next time I lead a math lesson or activity that I can better my approach in certain aspects through reflecting on this experience and utilizing the feedback that I received from my professor and classmates. There is always room for improvement when you're an educators so keep on reflecting! 

Until we chat again next time... 

Signing off, 

        Ms. Blackwell

Blog Post #7: It's Curation Time!

Welcome back everyone!

This week I want to discuss with you all a new term that I have learned this week in teacher's college. The term I learned is what it means to curate resources. At first, I was a little bit confused on the idea because I thought it just meant research, however I'm glad I was taught otherwise! Curating resources is so valuable for us future teachers! So let me explain what it means to curate resources....

Curate essentially means to bring together resources and share them as a collection. Combining resources into folders or files in a creative and organized way is referred to as curating resources. This is useful as an educator because you can collect an abundance of useful resources throughout your career to implement within the classroom. As we curate, we can ensure that we are always looking to improve our pedagogical approaches to the curriculum. Curating resources can provide teachers with a way to keep their lessons fun and engaging while also meeting the students in their zones of proximal development. So what are you waiting for? Let's get curating!

Now that I have explained to you all what it means to curate as well as the value in it, I would love to share two websites that I recently came across to help you start your new curation journey! I learned of this website just last week and I love it already. The website Cube for Teachers allows people to create an account and start curating instantaneously! As a future high school math teacher, I have started curating different resources that will enhance the quality of my lessons. Some of the resources I have curated include engaging worksheets, activities, tutorials, printables, and games that will add many more collaborative and interactive elements in my classroom. All it took was a simple search of "high school math resources" and I was amazed to see all the different resources that came up. With a simple click, I was able to add all the resources that I liked into my mathematics folder. 

There is also another website called EDWIN that allows users to curate resources. This website is a great curation tool because it even has a presentation embedded within the site that walks you through how to use it. EDWIN will enable teachers to search, collect, and share these resources in lessons or activities in the classroom. Just like Cube for Teachers, EDWIN promote the development of pedagogical approaches to constantly push teachers to enhance their lessons and unit plans. 

There is so much value that comes with curating resources that it is important we take the opportunity to start developing these folders and organizing them according to our wants. Starting early will push us to become better prepared for teaching in the classroom setting once we are officially teachers! 

Now, despite today being a slightly shorter blog post, it was definitely an important one! As future educators, we need to be constantly building our repertoire of resources through curation. Like I mentioned in my last blog post, even teachers need help and it is important that we take all the help we can get! Reflecting upon my university experiences through my undergraduate degree and my first year of teachers college so far, I can see the value in curating resources. As a future high school mathematics teacher, I want to be constantly implementing engaging elements to my lessons to keep students interested. I think that it is so important to keep up to date on different and innovative and creative pedagogical approaches when teaching the math curriculum. Curating resources is not an intimidating process once you become more familiar with the steps to do so. Take a look at the two curation websites I linked above to start curating resources for yourself. I hope this experience is as exciting for you as it was for me. Happy curating!

That's all from me for today. Until next time....

Signing off, 

        Ms. Blackwell

Blog Post #6: Even Teachers Need Help!

Hello everyone and welcome back to my blog!

Wow it's been quite a while since my last blog post, but I am back and ready to chat! Today I really want to dive into how important it is to ask for help. I feel like a common misconception about teachers is that we know everything. Well, let me clarify that we most definitely do not know everything despite how cool that would be! Even teachers need help and have things to learn so it is so important that we do so whenever possible. 

You see, being a teacher can create some really stressful and overwhelming situations. It is most definitely not your typical 9:00-5:00 job. Being a teacher does not stop. You wake up, go to school, and be a teacher just to come home and mark, lesson plan, and continue being a teacher! The silver lining is that if you love being a teacher, you are constantly doing what you love (I can't wait!). But of course I am not excited for this stressful and overwhelming feeling... so I am happy to share with you all the many resources that I have come across in teacher's college during my math course. These resources are websites that help math teachers immensely in enhancing their lesson plans and unit plans and provide teachers with new ideas on how to introduce different mathematical problems or concepts. 

This semester of teacher's college has only recently begun but I have already found myself reflecting a lot. My math course has really opened my eyes to all of the help and resources that are out there to help math teachers succeed in the classroom. We are not alone! So let me begin by sharing with you all some of my favourite websites that I have come across that have many free resources available for math teachers!

1. OAME Website

OAME stands for Ontario Association for Mathematics Education. I am still quite new to this website so I still have not gotten around to exploring the entire site, however I have explored enough to know how resourceful it is. At first glance, this website was really overwhelming on the eyes, but once you know where to go to find what you need, it is much less stressful. My favourite section of the website is under grade specific resources where you can click whichever grade you are teaching from K-12. These resources all include lesson plans, unit plans, classroom resources, activities for students, creative ways to introduce new concepts, etc. I would use this website while lesson planning or unit planning to enhance the quality of my lessons and maximize student learning. This is an amazing website for both new teachers who are learning to lesson plan as well as teachers who have been teaching for a while and need some new inspiration!

2. EduGAINS

Some of you may have heard of this website already as it is quite popular. This website has it all. I have known about this website for some time now during my undergraduate studies, however I have found more use from it throughout teachers college. This website has an abundance of ministry developed resources but we are going to focus more specifically on the mathematics section. This portion of EduGAINS allows you to select which curriculum document you are focused on as well as many different sidebar options to select leading you to different resources. TIPS4RM is an amazing resource that stands for Targeted Implementation Planning Supports for Math. This link provides teachers with various ways to support students in their mathematics using a more targeted approach to the concept. Lessons and Supports  is another section on EduGAINS that provides teachers with different teaching supports and resources such as apps, digital learning sites, and online manipulatives to help students learn. I would use this website for tips and tricks on how to enhance my lessons for math to better meet the needs of my students in more creative and engaging ways. Feel free to explore the EduGAINS website even further to see how many rich resources are available to us teachers!

3. Mathies

This website makes me feel like a little kid again! When I was in my fourth year of my undergraduate degree, I had to explore this website to investigate its usefulness. Mathies is one of my favourite websites because it not only provides help to teachers, but it also provides help for students and parents/guardians! Mathies has five main components for their website: games, learning tools, activities, additional supports, and home supports. All of the components are useful for teachers to integrate within their lessons as well as for students to engage in for extra practice. Furthermore, the home supports link on Mathies provides parents/guardians with information about what their child is learning in school and ways that they can help. This website is so rich in resources in its ability to reach such a large audience and meet the needs of students, teachers, and parents/guardians. I would use this website both in my classroom and through assigned work. This website is great because I can give students work periods in class to practice through activities and games or I can assign them these activities to work through at home. 

4. Math4TheNines

This website is very new to me however I find it to be particularly useful. Math4TheNines is a website designed specifically for grade 9 mathematics learning. I think that a website dedicated solely to grade 9 learning is so important because many students struggle with the transition from grade 8 to grade 9 mathematics. My favourite part of this website is the resources section where there are many rich tasks for students to work through for extra practice or for teachers to implement within their lessons. Additionally, the research section of this website greets new teachers with six different videos that include classroom experience from other teachers, different information from research, as well as Q&A sessions. I would use this website by taking some of the different rich tasks and implementing them in my lessons. By implementing rich tasks into my lessons, I will be able to observe my students' progress as well as prompt them if needed to keep their morale up. Feel free to explore more of this website as well!

5. Wired Math

This website is also quite new to me but I have to say I love it! This website is a great alternative to the traditional way of teaching and learning mathematics as it allows students to engage in mathematics using technology in a fun and interactive way. Wired Math is a website that offers a bunch of different games that are organized according to the unit it applies to (i.e. patterning and algebra). What is really great about the games on this website is that they provide you feedback if you get the answer incorrect. Additionally, it meets students at their level of learning when it asks them to select the level of difficulty that they prefer. This is great because students can gradually advance in their level of difficulty through more practice. I would use this website to encourage students to engage in fun and interactive math problems. This is a great way to get students practicing their mathematical thinking skills while playing games. 

There you have it! These are five of my new favourite math websites that help teachers enhance their lessons and can help students practice their math skills. Like I mentioned before, even teachers need help! There is no shame in asking for help because there is always something to learn. It is important that we, as teachers, always leave room for improvement and continuously try to better our approach to teaching because the education system is continuously changing. Let me know if you come across some more useful websites for a math teacher, I'd love to explore them!

Until next time...

Signing off,

            Ms. Blackwell

Blog Post #5: Ready, Set, Attack!

Hi Everyone and Welcome Back to my Blog!

In my last blog post, I talked about what we do when we get stuck. Well, now I have a follow-up question: What do we do when we finally become unstuck? The answer is actually quite simple... we ATTACK the problem. The answer may be simple, but realistically not many people know how to go about this phase of attack. But, that's what I am here for! Today we will be breaking down how we should tackle the attack phase when engaging in a mathematical problem. 

The first main component of the ATTACK phase is conjecturing. A conjecture is essentially a statement that appears reasonable, but has not yet proven to be true. When we are solving a mathematical problem, it is important that we conjecture because they form the backbone of mathematical thinking. Half the battle when it comes to mathematical thinking is getting a sense of the question and establishing what might be true and articulating these conjectures. When we form these conjectures, we are focusing our attention on useful components of the question. This allows you to ask what can be done by generalizing and specializing because when conjectures are made, a larger pattern emerges. Thus, we come back to specializing and generalizing being two very important aspects involved in conjecturing. Therefore, when we conjecture, we must become open to new interpretations of the problem and articulate, test, and modify our conjectures to form the backbone for our resolution. Just think... conjectures are kind of like butterflies. Like butterflies, conjectures are not easy to capture, but once one comes by, there are many to follow. 

The second main component of the ATTACK phase is justifying & convincing. This phase is all about seeking and explaining why. It is one thing to conjecture WHAT is happening in a question, but it is much more difficult to see WHY it is happening. Justification and convincing is necessary to frame an argument for your conjectures. Articulating the link between what you KNOW and what you WANT is the essence of one's justification for a conjecture. This can be done following three basic steps:

1. Convince yourself
2. Convince a friend 
3. Convince a skeptic

Justifying every step of your argument will convince both yourself and others behind the WHY of your conjecture. It is also important to develop your own internal skeptic in order to question your own steps allowing you to CHECK your work without the assumption that you completed your resolution without any errors. 

The only way to question and test the correctness of your conjecture is by attempting to refute it - be your own skeptic. This is just another way to sharpen your critical skills in looking at your own and other people's arguments to decide whether or not you are convinced. 

The last main component of the ATTACK phase is dealing with being still STUCK. Sometimes, when all else fails, we realize that we are still stuck with the problem we are facing. When we are working on a problem, we have to accept the fact that there is no way of getting around the work we need to do that is necessary to carrying out the problem. However, if you encounter still being stuck, there are three options you can choose from:

1. abandon the problem altogether;
2. put it aside for a while;
3. keep going. 

Here is what we can do when trying to push through being stuck:

• distilling the problem to a sharp question;
• intentionally mulling;
• more extreme specializing and generalizing. 

To distill the problem to a sharp question we must articulate as clearly and succinctly as possible the essence of the problem. Sometimes it helps to do this by explaining it to someone else. This will help us juggle the components of the question so that new combinations and connections can be formed. When we are able to make these new combinations and questions, we are mulling the problem. Lastly, to engage in more extreme specialization and generalization, we are altering the current problem that we cannot solve until we can solve it. Sometimes the problems we are attempting become clearer when stated more abstractly with the inessential details removed. 

It is important that we try to remove our hidden assumptions from the question because a changed perspective or insight may be exactly what you need to effectively ATTACK the problem. 

Well... now you know. This is what you have to do to ATTACK! Build on your mathematical thinking and keep going! I hope I taught you a thing or two in this blog post.

Until next time...

Signing off, 

    

            Ms. Blackwell

Blog Post #4: STUCK? I'm Here to Help!

Welcome back to my blog! 

Today's blog post is a really important one... it's probably one we could all benefit from reading! I'll start off with a general question; have you ever been stuck and not quite known how to overcome the situation/problem? I am pretty confident in saying that the vast majority of readers probably answered yes to this question. That is because getting stuck is a normal and a common feeling that people feel, however that doesn't mean it isn't a frustrating feeling. BUT... fear not! This blog post is all about how to get UNSTUCK!

Being stuck can be experienced in a variety of ways. For example, you may have experienced being stuck while:

• staring at a blank page, at the question, or into space;
• resisting a computation or some other action;
• growing tense or even panicking because you cannot make progress;
• feeling frustrated because nothing seems to be working

First things first... take a break! Sometimes all you need is a mental break from the question. Next, you might want to revisit the entry phase. Think about what you KNOW, what you WANT, and what you can INTRODUCE.  Engaging in your RUBRIC notes to track the steps of your work is beneficial to focusing the question on where you are stuck. Zooming in on the portion of the problem that is causing you to feel stuck may help in not getting overwhelmed and overcoming the obstacle you are being faced with.

Once you have completed the Entry phase, you can move onto the Attack phase to reflect on what you feel is blocking your progress in the resolution process. This will give you the power to assess whether or not you can avoid these obstacles. Doing so will allow you to extend your knowledge on the problem and give you the power to take control over the problem. 

Just remember... everyone gets stuck! In fact, it is beneficial to the development of our mathematical thinking skills because we are required to problem solve and extend our knowledge to get unstuck. It may be frustrating to be stuck, but I can guarantee that the feeling of being unstuck is so rewarding and so worth the struggle!

Oh, one more thing... BE CONFIDENT! Confidence in your mathematical abilities is such an asset when being faced with problems. Believe in yourself and don't give up. Persevere and be your own mathematical superhero! Discover the feeling of being UNSTUCK!

Thats all from me friends! Enjoy getting unstuck!! Until next time...

Signing off, 

            Ms. Blackwell