Week 12 Reflection Post

Retrieved December 5th 2016 from: AdventurousChica

Hey guys! This is likely going to be my last math blog post for a while...we are getting ready to head into our placements, yay! (OK the thought is actually terrifying me) but I just wanted to talk about some of the things I have learned throughout the last 12 weeks.

I came into this math course unbelievably nervous that I was not going to do well because I would need to know how to do math...How wrong I was!!! I learned that you do not need to be a math whiz to be able to teach math, I've now learned through experience that it is OK to tell students "I don't know the answer to that right now but let me find it for you" or "why don't we find that answer together?". When I started teachers college I was so worried that teachers needed to know everything, that is the biggest misconception I could have had, teachers learn just as much as students do, we learn from each other.

I have learned through our assignments in this class that with a little bit of time and effort, putting together a lesson that is well organized and effective that you understand, is not all that difficult, sure it may seem daunting, but a little bit of time and effort goes a long way. I've also learned many tips and tricks for engaging students and having them learn while having fun! We have done things like Easter Egg hunts, number lines, and in my placement class we did a Pokemon Go scavenger hunt!

Throughout the past 12 weeks we have watched our classmates become more confident in their abilities as educators and it is because we have had great support with guidance through all the ways we can be effective in the classroom. Math is still a scary thought for me, I was speaking with a high school math teacher over the past weekend and listening to her talk about the projects her students were working on scared the pants off me. However, this doesn't mean that it is something I would not be able to do anymore, it just means I need to be flexible and have an open mind when it comes to myself and my students abilities in the classroom.

Thank you guys so much for reading over the last 12 weeks and I will try and keep you updated throughout my placement!

Week 11 Reflection- Effective Assessment in Math

Retrieved 

What a big week we had this week...we are winding down the semester with nearly all of our assignments done (yahoo!) and have finally now had a taste of what it is like to lesson plan. I don't know about everybody else, but I struggled with the assessment part of the lesson plan. I thought to myself, what is the point of teaching a lesson if we can't assess our students on it? 

My biggest challenge that I face when I think of assessment is being fair to all students and making sure that I am evaluating them all with the same opportunities and the same mindset based on their individual needs. We have learned over the last 12 weeks that there are three different levels of assessment. Assessment for, as and of learning...what are these, you ask? Let's take a look. 

Assessment FOR Learning

Assessment for learning is a form of assessment that is used to determine student progress. Teachers are able to adjust learning to the needs of the students and provide feedback. 

Assessment OF Learning

Assessment of learning is the use of a task or an in class activity to measure, record and report on a student's level of achievement. Are they getting it? 

Assessment AS Learning

This is a form of assessment that allows students to use assessment to further their own learning. Students can use this to reflect on their learning and to set personal goals for themselves. 

Something I did not realize coming into teachers college that assessing a students level of achievement could be so complicated! I think we all assume it's going to be nice and easy every day, that everything is going to go smoothly, but as I've started putting together lesson plans I have started to realize that could not be farther from the truth...I've got something else coming for me in the real world eh? 

The most important thing that we need to remember is that we need to be fair to all students, give every single one of them an equal opportunity to succeed. As educators, it is our job to mold and shape these children into who they are going to become. We will spend an extremely large chunk of their lives with them between the months of September to June so we better make sure that we ALL try our best. 

Thanks for reading again this week, that's me signing off. Toodaloo! 

via GIPHY

Week 10 Reflection...Data Management and Probability

Retrieved November 21st 2016 from: Vecteezy

Data Management and probability...Does that make the rest of you as nervous as it makes me? How the heck are we supposed to teach students about probability...I've come to learn after our presentations in class this week that the best way to do that, is by playing games! Who wouldn't have loved to play games in school and learn at the same time? 

Some of the best ways to have students gain a conceptual understanding of a certain concept is by having them experiment with real life activities. Things such as card games, money tossing and rolling a pair of die are great ways to have students become engaged in the lesson without having them "hurt their brains" trying to grasp a concept.

Students need to want to learn something to be able to grasp a concept. We as educators, need to make them want to learn, make it engaging, make it fun and encourage them to want to try new things. How do we do this? By making it encouraging, by providing them with as many opportunities as possible to succeed and to test their abilities.

Empowering students is something that we need to do as educators, making them confident in their abilities to succeed, not only in math, however in all subjects. Math is one of the more tricky ones that students might need a little bit more of a push in. Not every student is obligated to fall in love with math, we will always encounter students who really do struggle with it however we can't simply give up on those students because we think it is too difficult to get them to that next level or to pass that upcoming quiz.

I have yet to see the students in my placement take on the Data Management and Probability strand however I look forward to seeing how they will handle it and I look even more forward to seeing how I will learn through them. I have had the opportunity to see things through their eyes and it has opened my mind up to so many more possibilities in the world of education.

Retrieved November 21st 2016 from: Math 6 

Week 9 Reflection...Let's Learn About Measurement

Retrieved November 15th from: Mr.V's Three's!

This week I got to prepare a presentation for my class. Unfortunately, I was unable to present in front of the class, however I was sort of glad because instead, I presented in front of a smaller group of people so it took some of the intimidation factor away. I got the chance to see first hand what it was like to think of all the elements that need to be considered before presenting it to a class.

Measurement seems like such a complex unit, there are so many different branches of it. Our presentation this week for class (since class was online, lucky us, a Friday off!) talked about what is introduced to students at what age. Grade 3 consists of things as simple as using a ruler and beginning to understand how it works, reading time, recording the mass of objects and using those concepts to compare and order objects.

Grade 4 students start to measure length, introducing the idea of perimeter and the idea of area, time intervals, units of measurement (kg, L) and some more complex concepts. Grade 5 is where it really gets interesting, students will start using formulas to calculate perimeter and area of rectangles, they introduce temperature over time and start considering the volume and space of 3D shapes.


Retrieved November 15th 2016 from: via GIPHY

I won't continue to bore you with these fun facts, I just wanted to give you an idea of the integral introduction to the different elements. It might seem small to us, however when preparing a lesson, making sure you are incorporating all of those things can be quite the task. My presentation this week involved the measurement of area...I know right? where do we begin? It was very hard to come up with a starting point because, as an adult, I know how to measure area, L X W = Area...however students would not know that, miss Bunz stated in her presentation that we must not make assumptions about our students prior knowledge, take the time and go over things. After deciding to give the students the formula, I decided to have them put it into action. A suggestion was made to me that instead of providing the students with the formula, I should have tried to give them prompts to find it on their own, such as having them count the squares on grid paper and seeing if they can make the connection themselves before simply giving them to formula.

Doing this presentation was a huge learning opportunity for me, I need to start considering a mini lesson I will be teaching in my practicum, which will include teaching a twenty minute lesson to a group of about 6 children. How perfect that I got to dip my toes into something like this with my presentation this week? We were given the choice of doing a literacy lesson or a math lesson, who would have ever thought that I would pick math...? not me, that's for sure!

 
Retrieved November 16th from: via GIPHY

Week 8 Reflection- Geome-whaaaatt?

Retrieved November 7th 2016 from: Crafthubs

This week, our topic of conversation was geometry...what is the first thing you think of when you hear "geometry"? I think of triangles...however this unit is much more complicated than simply identifying triangles. It concerns the properties and relations of points, lines, surfaces, solids and higher dimensional analogs...what the heck does that mean right?

It has been difficult for me up to this point to really try and see anything in action, however this week during my observation day in my placement class, I had the opportunity to see the nitty gritty of a geometry lesson. The students were working on measuring angles, at the start of the lesson, my associate teachers asked the students "why are the angles on the 3rd page surrounded by a circle?" It was very beneficial for me to experience this because nearly every student in the class had a different answer, ranging from:
- Because the teacher wants to tell us the whole angle
- You can put the arrow anywhere you wish to create an angle
- Because a circle is a full 360 degrees and no matter what angle we put into the circle, it will measure somewhere in between 0 and 360.

I found this absolutely incredible, those were only some of the examples and each student that answered this question was able to reasonably justify their answer. Some of the questions that the teacher asked were simply used as a refresher tool for things they had learned the previous day, such as "what do we use to measure an angle?" (a protractor in case anyone forgets...) and "what types of angles are there?" (acute, obtuse, right and straight).

Being a part of this lesson really helped me overcome some of the fears I thought I would have going into a math lesson, many of the students were coming to me with questions and I found myself readily helping them without much hesitation and I enjoyed being able to help them finally understand how to measure and create angles. One thing I found interesting was that when the students were presented with minimal instructions to create an angle, they struggled with it; many of them wanted step by step instructions to facilitate the task. I would be interested to see how we could try and make students feel more confident in their abilities to complete the tasks on their own.

Retrieved November 9th 2016 from Dreambox

One other thing I wanted to talk about was the website the students were using during part of their math period. This website is called Dreambox, and it is used to help students build conception understanding and fluency. I personally am a strong believer of the saying "practice makes perfect" so when I saw how engaged the students were while using Dreambox it amazed me. It gave me so much hope for this younger generation that they can still find it in them to put forth their best effort if provided with the appropriate tools for today's day and age because if education is something that is always evolving, so should the way we teach. 

Would we want to have been taught the way we are teaching? Or would we want our children to be taught that way? That is one question I will ask myself regularly as I work my way into the profession and I think that more educators should consider these types of questions...just a little food for thought! 

Retrieved November 9th 2016 via GIPHY

Week 7 Reflection - Algebra

Retrieved via GIPHY

This Gif does quite a good job of depicting how I feel when I hear the word "variables". Today in class, we looked at some different strategies/activities to help us understand patterning and algebra. The first thing we looked at was patterning and the demonstration used was the Fibonacci Spiral and I had an extremely hard time understanding the relationship to math/patterning. Ironically, one of the themes we were asked to consider in class this week was "what strategies can you use to help ELL (ESL- English as a Second Language) students in the math classroom"?

After the Fibonacci Spiral presentation I tried to put myself in a student who may not have a great understand of the English language's shoes. I struggled with this concept being someone who has spoken English my entire life, I could not imagine how someone who is new to the language would try and grasp this concept. I started trying to think of what I could do that would make this a little bit more simple to understand? The first thought that occurred to me was "too many words". I was confused as to how this theory was related to math and I feel like if there had been more numbers shown and what exactly these numbers are related to, it would have given me a better idea of what I was doing with it.

Retrieved from MathBlaster

I find that students almost always need the most simple form of something that we can give them. If we don't understand something ourselves, or we don't understand the purpose of something, how can we justify teaching it to our students?

The next concept we looked at today was my favourite term "variables"...solving for X or Y or whatever letter you choose to use as your unknown variable.The photo on the right side of this post depicts how to solve a simple algebraic equation solving for X. You would simply take the unknown variable, move it over to the other side of the equal sign and do the opposite equation to find your answer. Miss Bunz also showed us a neat strategy to help give students a way of visualizing how they might also find the answer for the variable. I personally liked this method and it is something that I foresee myself using in the classroom. If you were to take the same equation, x+8=10 and simply cover the x with your hand and ask your students "what plus 8 equals ten?" it can help take away all of the thoughts of remembering which way you need to move your numbers and what equation it has to become.

This week I feel like one of the most beneficial things I took away from our session was to keep things simple for students, try to avoid over complicating things and to always provide alternative methods for learning and teaching based on your student's needs and comfort levels.

Thank you for reading and I do hope this provides some insight as to how we can all work together to create the next generation of mathematicians!

Week 6 Reflection, Ratios and Proportions

 

Let's talk about Ratios

Retrieved October 2016 from: Wikipedia

What is this interesting little symbol you ask? This is what we talked about this week, ratios. What is a Ratio? According to "Making Math Meaningful" a ratio is a multiplicative comparison between two numbers. To explain that in more "English" language terms, if we look at the ratio on the right, it can be read as four to three, which can also translate to, there 4 four girl bathrooms for every 3 boy bathrooms. When I was younger, if I were to look at this I would have been extremely intimidated. If I must admit, even during our math refresher course that we had to take, I did struggle the first time through with the ratios and fractions section.

Retrieved October 2016 from: Pixabay

How have I become to feel slightly more confident with these? I have had to observe many different ways of trying to interpret ratios now. This week in class, we had the opportunity to observe our fellow classmates presentations and one stuck with me. I really enjoy cooking and baking and one of my classmates incorporated baking into her activity which really helped me grasp the concept. I personally find that if I can relate something to a real life situation, I will understand it better and remember it better in the future.

I feel like this realization has been personally extremely beneficial and it is something I will strive for in the classroom as a teacher. If students can relate what they are working on in the classroom to something in their every day life, it may help them grasp the concept and be able to create a mental image of something to help them work their way through the problem. I personally feel like this will help students gain a conceptual understanding of ratios and proportions.

Throughout the course, we have to complete 3 forums where we play a math learning game, and then we write about what we thought of it. Coincidentally, I had picked to do mine this week not knowing ahead of time that it would be based on ratios and proportions. Am I ever glad that I picked this week, not only did it give me the opportunity to practice, but it showed me what is available out there as learning tools for students nowadays.

I don't necessarily think that this is a game that I would play as a teaching tool, however I do feel that it could be extremely beneficial in helping students with their speed at determining equivalent fractions. One thing that I am a firm believer of is that practice makes perfect and if students can play games like these, enjoy themselves, and practice their fractions, ratios and proportions at the same time, it is a win-win situation.

Retrieved October 2016 from: Arcademic Skill Builders

Thanks for reading and I hope this will give my fellow teacher candidates who might be slightly apprehensive about math a little bit of an encouragement, because if I can do it, honestly anyone can!

Math Reflection Week 5

Let's Talk About Integers!

Retrieved October 8th, 2016 From: SparkNotes

This week we had the chance to talk about integers and do some activities in class using some manipulatives to better understand them ourselves. As we worked with the manipulatives, I was able to see how much easier it was to solve problems with the concrete, visual aid. However, I can see that it would be very easy to become dependent on those manipulatives which could be problematic because we need to know how to solve problems without always having them at our fingertips. How can we be sure that our future students won't become dependent on these manipulatives?

This is a tricky subject because we live in a day and age where people are used to having many different things available to them. Everyone has a calculator on their phone and children are getting them younger and younger, so how do we make sure our students can solve problems without relying on their devices or manipulatives? I personally believe that being a visual learner is beneficial, being able to picture something in your head to get the help you need was always enough to get me through. 

On page 352 of Making Math Meaningful, they talk about what appropriate manipulatives would be, there is a great list of helpful tools that can be used to sort of "replace" the calculator. Things such a number lines might be easier to be less dependent on as it would be easier to picture a number line in your head and jump the numbers. 

Making the calculator less available to students might help them become less and less dependent on the manipulatives because they would be learning how to work their way through their problems step by step and and learning the necessary processes. 

Making sure your students gain a conceptual understanding of concepts is also an important step because they may be able to complete an activity or solve a problem, but they may not know why or how they're doing it. Exponents are one of the more tricky concepts to grasp, there is a common mistake that when a student sees 5 to the power of 2 --5(2)-- they think it is 5X2 and not 5X5. I personally feel like one of the easiest ways to explain this dilemma is to have the students write them out completely, 5(2) would become 5X5 or 5(4) would become 5X5X5X5 as you have 5 multiplied by 5, 4 times. 

Retrieved October 8th, 2016 From: Learning with Math

This image depicts how I personally like to break down exponents. 

This last couple weeks has given me the opportunity to become much more confident in my ability to not only teach math, but to understand math as well. Opening yourself up to new concepts and new ideas can be extremely beneficial and having the necessary support and tools provided to me has made it much easier to become open to new ideas and ways of doing things. 

Having a bad experience in math class can really affect how a student looks at it for the rest of their lives. Let's change the negative "stigma" that surrounds math, make it fun and encourage students in the right ways to always express their feelings and ideas in the classroom! There is no wrong answer when someone can justify the reason they came up with the answer they have come to!

Week 3 reflection, I'm not in Kansas anymore...

Things are getting real...

Every week we have a sort of "information overload" trying to sort through everything that needs to be done as Teacher Candidates. I have now had the chance to observe a fifth grade classroom which has greatly helped "open" my eyes when it comes to teaching math. Let's just say, the thought of teaching math doesn't quite scare the pants off me anymore...OK let's not get ahead of ourselves, it is still slightly intimidating, but not as bad as three weeks ago.

This week, our readings that were assigned talked about when it was acceptable to estimate something and which elements matter when you make the decision which strategy to use. When you want to estimate something, the factors to consider are the context and the numbers and operations involved. Chapter 11 talks about the use of manipulatives to model algorithms for addition, subtraction, multiplication and division and what appropriate manipulatives are considered to be. I've had the opportunity to see the kids in my placement class use manipulatives now and I find it very interesting that some students need the visual aid to solve a problem, and others can simply solve the problem using mental math.

Retrieved September 29th, 2016 from: Wikipedia 

I found Chapter 11 to be extremely interesting especially as we were working on our problem solving activity this week. It talks about all the different algorithms possible for the four mathematical procedures, addition, subtraction, multiplication and division. Having two children answer two questions each for my problem solving activity gave me an opportunity to see that there are several different ways to come up with the correct answer, it is personal preference for that student/child.

One thing I really enjoyed this week during our math class was that our peers each had to do a presentation and teach a "mini" math lesson. I appreciated having the opportunity to see that everyone has a different teaching style however I didn't find any less successful than another. We also had the opportunity to work in our table groups while doing these activities and it was interesting to see everyone's different strategies for coming up with the answer.

Every week I have the opportunity to learn something new and see something new, this week I saw the students in my placement work with DreamBox. If you have a minute, take a look at the link and check it out, it is a resource that children can use to play games and learn math at the same time...I could not believe how engaged they were during this activity!

I find myself getting excited about going into my placement to see what new technique my associate teacher will use that week to help her students grasp new things...it is wonderful to be in my position and have someone experienced to learn from and I have definitely been taking notes!

Hope you all read again next week, signing off for now.
Bye!

Week 2 Reflection, Let's Talk About Math

Let's Talk About Math

Let me start by asking this question: do you think there is a negative opinion of mathematics in todays society? This is something I have personally always struggled with because I've "disliked" (for lack of a better word) math nearly my entire life. I have always found it difficult and have never put in as much effort as I should have because I never felt like I had the support that I needed to really just get something. I believe that kids of this generation have a negative opinion of mathematics simply due to the way it is presented to them, you start off being forced to take it, at a very fast paced, sometimes in a classroom with 30 or more other students and it can all become very hectic. There is also the question about how much mathematical knowledge teachers have in todays society, in an article we were provided this week to read, there is a very interesting opening statement that says "With all the talk of teachers’ weak mathematical knowledge, we begin with a reminder that the problem on the table is the quality of mathematics teaching and learning, not—in it- self—the quality of teachers’ knowledge. We seek in the end to improve students’ learning of mathematics, not just produce teachers who know more mathematics" (Simmt, Elaine and Davis, Brent. Canadian Mathematics Education Study Group. 2002). 

For more information regarding this article, please visit this page. 

I personally found this article very beneficial because it states that teachers do not need to know every math equation per say, however they need to know how to teach these equations, which are two different things. 

In class this we were presented with a task, Miss Bunz asked us the simple question "if there are 22 people in the class and everyone was to shake everyone's hand, how many total handshakes would there be?". This seems like a fairly simple question right? So we thought, however there were a few elements that needed to be analyzed before jumping into finding the appropriate solution, you couldn't shake the same person's hand twice, so my hand shake with Miss Bunz would only count as one, hers to me would not count. Troubling right? Right away my brain jumped into, let's look at this as if you're on the outside of a bubble and everyone else is on the inside, if everyone has a turn outside of the bubble, 22 people will have the chance to shake 21 other peoples' hands. 

After having done this activity, we had the chance to go around the room and look at the equations everyone else came up with to solve the problem and I was very surprised to see that nearly every group had come up with the answer a different way, however every group had the same answer. 

This made things quite clear to me when I ask myself "what makes an excellent mathematics teacher?". Being able to accept more than one way to solve the same problem. I believe that teachers who aren't open to change aren't necessarily as flexible when it comes to trying to explain something to a student who may just not be getting something. To finish things off today, I think the big picture is that you can do it, even if you're scared, you just need to be willing to accept new things and change your way of thinking in this never ending evolution. 

Miller, J. Howard. "We Can Do It!" poster (1943). Retrieved from: Wikipedia 

My First Math Blog! EDBE 8P29

Hi everyone!

Who ever thought I would be writing a blog about math? (Not me, that's for sure) But here I am! I want to start by admitting how nervous I am about taking this math course, however after being in lecture for the first time last week, it most definitely did help settle my nerves, at least a little bit.

I was never strong in math, it usually took me a little longer to catch on to what was being taught in the classroom and I always felt pressured to be done as quickly as everyone else because I wasn't as smart as them if it took me a little longer, and let's admit, it can seem embarrassing to a young child in a full classroom!

Retrieved September 14th 2016 from: Pinterest

Having said that, I did have some wonderful teachers throughout my years of schooling who seemed to really just "get me". They could tend to my learning needs and explain things in different ways which helped tremendously on those exhausting problem solving activities. This was not always the case as everyone has their own personal teaching style, but I found those teachers who were passionate about math to be the most helpful throughout my years. 

I am hoping to come into this math course with a fresh mind and no previous "misconceptions" that may hold me back, I need to keep in mind that I have not personally been in my own math class since the 10th grade (8 years ago, yikes!). I want to have an open mind because it is never too late to take on something new and try and conquer something that you previously had difficulties with, because honestly nothing feels better than doing well at something you've previously struggled with!

The readings that were assigned this week were also a sort of "eye opener" for me, as Miss Bunz said in our first class, "you don't need to be a math wiz to be able to teach math", I feel strongly about that, I feel like you just need to be open to change and have a willingness to learn new things. Like it says in the curriculum document we were assigned to read, "the development of mathematical knowledge is a gradual process", I take that as meaning there is always new things to learn. 

The second document proved to be most useful for me, as it is stated in Toward a practical Based Theory of Mathematical Knowledge for Teaching, "what many teachers lack is mathematical knowledge that is useful to and usable for teaching". This point is what I am most looking forward to learning throughout this course, what going to be most important and practical when teaching a math class.

I look forward to sharing my learning experience with you throughout the year! Let's have some fun!