Math, Friends and Fun!

This week one of our module videos was about the importance of seeing math as a series of connected methods rather than seeing them as isolated concepts. Studies have proven that students who see math as being connected are more successful than students who don’t.

The more we learn, the more I realize that this idea of connection goes far beyond connecting between math concepts. Students are not only more engaged when they can connect the methods but they are more engaged when they can connect processes with other students as well as problems with the real-world.

What we are learning is that absorbing information becomes easier when we have a previously understood piece of knowledge to attach it to.

Even beyond just math we as new teachers are learning the importance in finding connections between subjects (ie. teaching cross-curricular to provide students with familiarity and knowledge), and between teachers (sharing resources with teachers in the school, in the board or across the world to gain perspective).

I think the biggest takeaway is we are always stronger in numbers (math puns!). In all seriousness, making connections allows ideas to become more clear and perspectives to be expanded, it allows for deeper critical thought and an increase in questioning. All of which help students to strengthen their grasp on a topic and build confidence in their knowledge of the concept in question.

Who Doesn’t Love a Good Game?

Another great way to encourage engagement in math is through play! For next week’s class we were tasked with reading an article about the benefits of including play in mathematics. Studies have shown that first engaging students through television shows or blended activities encourages students to develop a deeper curiosity for math and therefore allow them to be more successful long term.

Often I think new teachers are scared of the idea of differentiation. Not because they are too lazy to do it or because they don’t want to but because if we are being honest, teaching is a lot of work. There’s the preparation of each unit and each task, there are assignments to mark and learning skills to keep an eye on. However, if we really stop to think about it, differentiation is really just getting to know the needs of our students. This is very much inclusive of understanding their interests and finding ways to incorporate them into our teaching. However, although this may seem scary, especially when we have 30-35 students to get to know, it is really very beneficial to us in the long run.

If we can find ways to differentiate for our students by including their likes and dislikes in our lessons and learning to thoroughly engage them in the concept being taught studies have shown that we are improving the likelihood of success for our students. The more we adapt to their needs and interests the more their curiosity will pique and the easier it will be to keep them engaged.

A Lesson in Techknowledgey (and other things)

Today is a good day to laugh at myself, every day is.

Yesterday was a day to almost cry but then still end up laughing at myself, as you always should.

Yesterday I presented my first ever Webinar lesson (luckily I had an awesome partner to co-experience the stress with me - thanks Lauren!). Planning a lesson for your peers is already hard enough in teachers college. My peers are all very creative and deep critical thinkers. We have learned many of the same things and therefore sit on a lot of the same knowledge, it can be hard to teach them anything they don’t already know or sometimes even understand at a deeper level than they do. However throw a webinar into the mix and you not only have to start thinking about how expansive you can make the material included in the lesson, but oh no, now you have all the potential technological blips to worry about as well.

The day the webinar was introduced moans and groans filled the room. “We have to use technology?!” We all said with worry as we typed away on our macbooks and began researching on our iphones and ipads….

It was only as I sat down to write my blog this week that I realized just how funny this situation would have looked for a fly on the wall.

Yes Millennials (or Gen Y or where ever we fit in) , we, the golden age of technology, have to use.. that’s right… technology for a presentation.

Maybe I’m exaggerating the feelings in the room, or maybe I’m projecting my own feelings on my peers (if so, I apologize). However it seems to me that many of my peers share my love for ‘the old ways’: the smell of textbooks in hand, the calming feel of pen to paper and the personalized connection of in class lectures. Or on the other side, they perhaps shared the fear of technological errors: a wifi complication, a software crash or complexity outside of my techknowledge (see above my mention of the absolute ruler of user friendly devices, the ever trusted Apple product).

Fast forward to Webinar Presentation day…

All is going well. Google Hangout’s is working just fine, all of my peers have joined and we are halfway through the presentation. Nerves have subsided, activities are opening, softwares are co-operating, the technological sun is shining!

Presentation ends, we say goodbye to our peers, stop our Broadcast and a wave of relief washes over us. All that’s left to do is a simple copy>paste into Sakai and we are home free. However, when we check the video it only shows 32 minutes when we were certain our webinar lasted at least 52 (including the warm up). We check again, the thumbnail says 52 minutes. Phew! Home free again. However, when we open the video, only 32 minutes shows. Where did the rest of the video go? All of our hard work, gone. PANIC. Breathe. PANIC. We search for Dino, the resident tech genius at the Hamilton campus. As soon as we arrive at his office, I open the software to show him our issue, open the video and low and behold our webinar, in its entirety, appears on the screen. We submit it quickly and breathe once more. We have done it, technology crisis averted.

I, the student terrified of math and only concerned with pen and paper have completed a math webinar and believe it or not, enjoyed it!

One day later, I sit here with my cell phone beside me, once again typing on my laptop and laughing at the silliness of my initial worries. I am a part of the technological era, it is my everyday. Why should I ever let that scare me?

Jo Boaler's informative videos have taught us the importance of taking on these fears, whether in math or anywhere else in order to progress our minds. If we do not challenge our minds by taking on new and exciting tasks we will never expand our brains. When we set out to complete a challenge our brain has to work harder and by working harder it fires synapse that help our growth and expand our capacity to deepen our understanding.

Inquiry Based Learning tells us that providing students with an opportunity to be personally invested in an assignment or task (ie. by giving the athletic student a math student about the circumference of a basketball or allowing a music students to find the perimeter of a picture of an instrument) will make them more likely to work hard and stay engaged and therefore deepen their understanding.

This week I feel like I was the perfect example of how effective Inquiry Based Learning can be. I was provided with a topic I was interested in (*inquiry based learning*) but very few directions of what direction to go in. I was simultaneously given the challenge of doing something I am unfamiliar with (*teaching a lesson online*). However, I was unable to spend any time focussing on how scary the webinar would be because I was too engaged in the topic. In the end, not only did I gain a lot of knowledge about a topic I was interested in but I learned some really amazing techniques about how to use technology in a classroom.

This week’s reading talked about the importance of differentiating instruction for our students. How can we ever expect our students to be successful if we are not setting them up, based on their individual, needs for success? Differentiating is not just important for the individual, it is beneficial for the whole class. Inquiry Based Learning talks about the importance of classroom collaboration and reflection. If we can pair differentiated instruction with collaboration and group discussion we can provide the students with a variety of different perspectives to help them expand and refine their own thinking while also ensuring the success of every. single. student.

This is what we need to do for our students. This is what Inquiry Based Learning and Growth Mindset is all about. It is easy to say ‘have a growth mindset’ but we need to give our students a reason to be open-minded and positive and a pathway to be successful. We need to give them freedom and opportunities to show their passion and then challenge them once they have a reason and the resources to be invested. We need to show them that math is not all formulas and numbers and black and white understanding. It is creative and it is personal and it is everywhere.

Learning for Learning for Learning

I grew up in a sport focussed environment. I played soccer from the age of five, basketball from the age of eight, tennis from ten, volleyball from twelve, I took swimming lessons and did athletic camps; you name it, I played it. The old saying ‘practice makes perfect’ was not unfamiliar to me, it had become an inherent part of my understanding of everything.

While I was researching Inquiry Based Learning (IBL) this week I began to understand how this saying caused me turbulence rather than ‘success’. Success. What is it? This is the problem. The saying says practice makes perfect, which makes our focus this anomaly of perfection when we should really be focussed on the importance of consistent practice.

Eventually, I lost my desire to play sport. I had played competitively in high school but due to this desire to be the best I was terrified of failure. I hated making mistakes and developed an extreme feeling of performance anxiety. Even if I was playing for fun I hated missing a free throw or serving into the net and would continue to feel that disappointment and embarrassment for many minutes after it occurred. After a while I began to experience these same feelings in areas of my life that weren’t related to sport and it all surrounded around a fear of mistakes.

Inquiry Based Learning is a great demonstration of how to prevent this type of fear from developing in students. The saying shouldn’t say practice makes perfect but instead it should say practice is perfect or merely just PRACTICE.

What is Inquiry Based Learning?

IBL is surrounded around student centred learning. It is a move away from the traditional style of classroom in which teachers are the providers of information and students are the vessels in which they pour. Instead, IBL encourages students to play an active role in their own learning and therefore develop a sense of ownership over the development of their knowledge. In an IBL environment students are encouraged to ask questions and then even more encouraged to ask questions about their questions. They are to develop individual, group or full class inquiries that require critical, creative and collaborative thinking. The desire is not to answer the questions but to foster the idea that knowledge is forever growing. Instead of encouraging our students to find one ‘correct’ answer teachers are encouraging their students to find as many possible solutions as they can and to never stop expanding on their search.

This style of learning is not a magic bean to be planted and miraculously sprout overnight. Similar to anything, Inquiry Based Learning needs to be taught, or better yet scaffolded, to be successful in a classroom. The role of the teacher is to be a model for the students. They need to foster an environment in which they are proud of their mistakes and use them for opportunities of growth; demonstrate how respectfully challenging an idea can lead to even further expansion and discovery; and create opportunities for collaboration and creativity.

Most importantly Inquiry Based Learning requires an environment that is safe, open and welcoming. Students need to feel confident in the importance and benefit of their mistakes; they need to know the classroom is open to whatever contribution they choose to make (whether they are posing a question, challenging an idea or connecting to other topics); and they need to feel that they, for all that makes them unique, are welcome in the conversation.

Wait, Isn’t This a Math Blog?

Why, yes it is! Remember those feelings of anxiousness and embarrassment I was having about playing sports? Well, you guessed it, I had them about math too and I know I’m not the only one. Inquiry Based Learning is the perfect way to refresh the page on math. It allows us to remove all of those scary so called ‘facts’ we grew up with about math….

1. Myth: there is only one right answer

IBL response: wrong! Let’s try and find as many possible solutions as we can!

     b.   Myth: As long as the answer is correct, you’ve succeeded at math

IBL response: How about we explore all of the processes of solving this question, even the ‘incorrect’ ones so we can understand everybody’s thinking, build new perspective and hopefully learn for the future!

And foster an environment of positivity, creativity, curiosity and most of all inherent motivation to learn!

From Fear to Fruition

When I entered the first day of math class in year one of my teacher education I was beyond terrified. Not only was I never a confident math student but my experience with Elevate My Math leading up to first year demonstrated that my skills had not grown, and more than likely depleted since the last time I took a formal math class (let’s estimate that was in the Eleventh Grade). My only saving grace was the fear I saw mirrored in many of my fellow teacher candidates. We then did an activity that basically asked how we felt about being in a math class. This solidified my inkling that most people felt the same way, if not worse than I did. However, as the course went on my fear began to float away as my confidence grew. By the end of the course I wouldn’t say I was ready to be a math teacher but I was definitely more ready than I had been twelve weeks prior.

Flash forward to day one of math in year two of my teacher education. As much as I would like to tell you that I walked in full of jumping beans ready to tackle the year, I did not. Once again, I walked in with fear knowing how lucky I had gotten to not teach math in my placement in block one but also knowing that I would definitely be looking forward to a placement of teaching math in block two. Similar to last year we did an activity that asked how we felt about math and finally my growth from the previous year came back to me. I remembered that first day fear and how much more overwhelming it was; I compared it to my current state which was no longer drowning fear but nervous excitement. I looked around the classroom and listened to the details of the course to come and became eager to get going, to grow my confidence and to enter block two ready to make sure that none of my students leave their year with the fear of math I had developed when I was their age.

Watching the math module videos once again solidified my knowledge that the fear and nervousness that I have felt can go away, and will go away if I continue trying to open my mind and grow my mindset. The myths about the stereotypes of math vs. non math people made me remember the importance of ‘yet’. When my students tell me they don’t know the answer to a question, I’ll remind them they may not know it yet. Just like I may not feel like a math teacher YET but with perseverance and positivity I know I will.

Encore Encore! A Final Reflection of 8P29

           Summer 2016: The first assignment I received this semester occurred before the semester even began. I remember getting an email in late July or early August that said I was required to complete an online math refresher course before the first day of classes and being utterly terrified. First, I was scared of the workload; the program had not even started and we were already expected to have completed assignments. Second, at the time even mentioning the word math made me shiver. As many of my classmates also divulged on the first day of class, math was not my best subject. However, I quickly shoved those negative feelings under the rug, signed up for ‘Elevate My Math’, read the first few questions and… just as quickly pulled those negative feelings back out. ‘This is supposed to reflect Junior/Intermediate math!? What does this even mean!?” I couldn’t remember a single thing about math. Over the course of a week or so I managed to struggle (with lots of frustration) through the math course, printed off my certificate and vowed never to open it again. I would NEVER be a math teacher anyway…

          December 2016: This week we had our last math class (which also happened to be my very last class of first semester). We were asked to create a song, skit, rap, rhyme or any other creative expression of math that we could think of. As each group performed their silly creation I looked around the room at my fellow ‘non-math students’ and noticed how different we looked as a class. On day one we walked in scared and shy; we expressed our fear for the course and our awful math backgrounds. On our last day I could visibly see the differences this course had made for us. I was now surrounded by smiles and laughter, silly jokes about math but also an obvious understanding of what had been taught. Over the course of twelve weeks we had moved past our fears and learned how easy it is to enjoy math and even more importantly how to make math enjoyable for our students as math teachers.

          Throughout this course we’ve moved past our fears by learning that math really is for everyone as long as teachers let it be. We need to teach our students not one but many strategies for solving any and every problem. We need to encourage students to do what makes sense to them rather than sticking to a strict formula. We need to instill a growth mindset in our students by exemplifying those characteristics in all of our lessons. We should never let a student to feel like math is not for them or get discouraged because something is not right. Math is not about right or wrong as we always thought, it is about mistakes, discovery and growth. Both students and teachers need to use their mistakes to discover new things in order to constantly grow as learners and educators.

          This course has taught us the importance of variety. This is appropriate for all subjects; lessons, activities and tasks should be fresh and new. There should be a number of mediums used to demonstrate ideas not just to keep lessons engaging but to ensure every style of learner is able to be successful. On day one we were told that ‘no’ does not belong in a math class. Math is about saying ‘yes’ to our students and encouraging them to explore their thought process and ideas. The more we can help them explore, the more we will foster their growth mindset and ensure they never say ‘I hate math’ like so many of us thought we did before starting this course.

          We’ve also learned the importance of collaboration when teaching math or really when teaching at all. We should collaborate with our fellow teachers when creating lessons and units in order to make sure we are providing students with the most opportunities to succeed. We should ‘collaborate’ with online resources in order to introduce students to as many learning opportunities as possible. We should also learn to combine all of our new teaching techniques with the old ones in order to collaborate with parents. There needs to be a balance between the old and the new so parents are able and willing to help their child’s growth. We should teach in this new and inclusive way but include some of the old ideas and strategies so it is easier for parents to understand and therefore be involved with their students learning.

         This semester I have learned so much about teaching math but most importantly I have learned that there is still so much to learn. Just as we expect our students to always be willing to grow, we too must realize that we can always learn new and exciting ways to make math fun, accessible and enjoyable for ALL of our students.

Can You Guess What We Learned This Week?

          As a (pre-service) teacher we are constantly warned about taking precautions during our lesson plans. This means always remaining politically correct or unbiased, ensuring inclusivity and avoiding (some) pedagogy’s or tasks that me be an issue to parents/guardians. When I thought about these precautions I often associated them with subjects in the arts, for example talking about global issues, politics or religion. This week in math however, I was (once again) shocked by the precautions that need to be taken with some units, such as data management and probability.

©vecteezy

          I’ve learned this year that successful teaching is about getting your point across in a way that is interesting and engaging for the students. Often this means assigning tasks that seem like play but surround elements of the unit or topic being studied. For example, we’ve spent a lot of time this term playing and reviewing online math games that could possibly be used with our own students. When teaching data management and probability, one of the best ways to incorporate the elements of play is by using dice or playing cards. However, the use of these instruments can often be associated with gambling and therefore may cause an issue for some parents/guardians. This is not to say we should avoid using these tools altogether, as they can be very helpful. As teachers we just need to be ‘smooth’ about our practices. First, we need to get to know both our students as well as their parents (and family dynamic) before we begin testing any questionable boundaries. Second, we should learn to address these tools in a way that avoids the gambling issues. For example, we can use different names. Instead of dice, we call them number blocks, and so on as to ensure we are disconnecting them from their associating to gambling.

         

This is our Stem and Leaf data!

Pat consistently shows us the benefits of making small changes and altering typical activities in order to make them more fun and exciting. There are so many traditional games or tasks that have been done over and over throughout school and therefore can become less exciting for the students and in turn, cause them to be less engaged. One important lesson I’ve learned through this math class is we don’t have to break our brains trying to think of completely new activities, we just need to find ways to change old ones to make them more fun again. An example of this happened this week during class when Pat was talking about making estimates. Traditionally, this is done by talking about guessing how many jelly beans are in a jar. However for us, Pat used oreos in a jar instead. The activity remains the same and the educational aspect does not change, however it made it more exciting for us because it was something new!  Each member of the class estimated how many oreos were in the jar and then we used that information to make a stem and leaf plot. It was a great way to introduce a new concept!