Blog Entry #7

1. Reading over your previous six (6) blog entries,

a. which one was your ‘favourite’ entry and why?

My favourite entry that I had to write about was Blog Entry #5. I found it really fun to write to an old friend whom I have not spoken to in quite a while and tell her about the two videos I had watched on assessment in mathematics. I enjoyed watching the videos as they gave me a new perspective on how to assess students in mathematics. Having to write about these videos to my childhood friend also allowed me to reflect on my own experience as a student in mathematics and reflect on how we were assessed. This entry opened up my eyes to how I need to make sure I diversify my assessment strategies when I teach so that I do not fall back on how I was assessed. After writing this entry and going through the experience of pre-internship I have learned that not all assessment strategies work for certain subject areas, but it is all about trial and error and testing to see which ones do work for a mathematics classroom.

b. which entry would you most like to ‘do over’ and why?

I did not find an entry that I would want to do over because I feel as though I can see my growth throughout each of the posts. If I were to change one, I would not be able to see what I think is great progression as a mathematics teacher. However, now that I have grown as mathematics teacher, my first post about my mathematics autobiography would have to change because I learned so much through my pre-internship that I would have to add all the amazing things that I seen during my time in the classroom.

c. which entry did you learn the most about yourself as a learner and becoming teacher? Explain.

Blog Entry #6b allowed me to reflect on not only my entry before that about what my expectations were before entering pre-internship, but it also allowed to me take a look at my experience in the field and see how I had changed within that 3 week block. It was interesting to see that I did grow as a teacher during that time and that I could see the growth by responding to the post. When I look at that post it is nice to see that I took a bit of the theory that I learned in university, applied it to my teaching and then adapted it according to how the students responded. That post also clarified to me that I am in the right profession and I look forward to the road ahead as a teacher.

2. Create a blog entry you would like to have been asked to respond to but were not; after creating the blog entry question, respond to it.

How did the field change your perspective of mathematics teachers?

During my time in the field, I really tried to focus on two things: 1) how were students being assess now? and 2) how were students being taught? I noticed that for the most part, students were still being assessed in the same way as I was, through tests, quizzes and assignments. However, I did take notice that a couple of teachers were doing projects in their classrooms as a way to make mathematics more applicable. I found this extremely helpful to see because now I know for sure that there is more ways to assess students in mathematics and I have seen firsthand that these types of assessments can be very beneficial to students learning.

When I was in the field I wanted to see if teachers used differentiated instruction for their students to learn mathematics. I was sort of disappointed to see that the majority of lessons being taught were direct instruction, but I also saw the value in this. There are some topics that are not the easiest to teach any other way and teachers are under a lot of pressure to get through the curriculum on time, so this does not leave a lot of time to try a lot of variations of a lesson. I think trying a couple of new strategies every couple of months or so may be easier to do, but for the most part, teachers are relying on direct instruction because it gets students to learn the material. Do not get me wrong, I see the value in teaching differently because not all students learn in one way, but I think it would be silly to try 30 different strategies all the time.

3. Looking back on the EMTH 350 course this semester, describe two topics (areas of interest) you would like to have focused on more in this course that you feel would help shape your growth and learning in becoming a mathematics teacher.

Differentiated Instruction: I touched upon briefly in question 2 how I did not see much variation in the teaching strategies that teachers used during my time in pre-internship, which made me not as motivated as I thought I would be to try some new ones out. I feel as though if I had learned more about strategies that have been done in a mathematics classroom and have worked I would have been more enthusiastic about trying new strategies. It would have been nice to see more than just two strategies demonstrated in class (direct and inquiry) because I am a visual learner and I like to see something done first before I try it. I suppose in internship I will just have to take the plunge and try new strategies out without seeing them first because I want to make sure that I try new things during internship so that I get the most out of my experience.

Treaty Education: I feel as though this is still a topic that no one has answered for future mathematic teachers. Everyone has told us that we must teach Treaty Education in all subject areas, yet no one has given us the resources or a straight answer how to do so in mathematics. It would have been nice to learn about Treaty Education in this class because I feel as though mathematic teachers are slipping behind because no one will help us in trying to teach it, everyone just seems to dodge the question.

4. Looking ahead to internship in the Fall, describe two overarching goals you have (or want to) set for yourself. (If possible, connect these two goals to the learning you have had in this course or in your teacher education program in general.)

The first goal that I want to set out for myself is using a range and variety of teaching strategies and approaches. I have learned a lot of varied ways to teach throughout some of my university classes, it will just be a matter of testing them out and seeing which ones work best for me. During my pre-internship I felt crammed for time, so it was quite difficult for me to plan to teach in an unknown way. There are many strategies that I can try out and see if they do work for me as a mathematics teacher.

The next goal I have for myself is to be able to provide differentiated learning opportunities for all students. This goal goes along with my first goal and using a variety of teaching strategies. But I also think this goal goes deeper in the fact that it will make me really get to know my students so that I know how they learn best. I want to connect with my students in a way that they will feel comfortable enough to tell me whether or not a certain way I am teaching is working for them or not. Mathematics is sometimes a tricky subject in being able to really go away from the norm of direct instruction, but this is my time to try those new things because I will have my cooperating teacher there to help guide me.


Blog Entry #6b

When I look back to the blog post I had written before entering the field, I cannot help but look at questions 3 and realize that I was on the right track with it, but I was only touching the surface. Here is how I responded to question 3:

3. What do you already know now about being a mathematics teacher that is unlikely to change through your upcoming field experiences (i.e. fundamental beliefs, values, commitments, etc.)?

As I enter the classroom for my three week block I know that I have to keep in the back of mind that I was once where these students were. I was questioning the relevance of mathematics (though I still enjoyed it) and wondering where I would use it. I know that my students will be thinking similar things, so I know that it is my job as a teacher to make mathematics connected to their daily lives— that won’t change after my experience. Another thing that I know won’t change once I am finished my pre-internship is the fact that not all students learn the same way I did, or even learn similar to their classmates. I will constantly have to adapt and come up with solutions so that all my students understand my lessons, rather than just a select few. Even though I know these things won’t change after my experience, I am looking forward to the changes that I will see, both in myself as a teacher and in the way I choose to teach.

Now after completing my 3 week block I can look back on this response and know that there was not one or even two adaptations I could have made to my lesson plans that would have worked for all my students in my classroom in order for them to understand the material 100% of the time. I think I was naïve in thinking that I would be able to adapt my lessons on the fly so that I was touching upon each students specific needs. I learned quite quickly that many students do not even learn well in a group setting, I had a few students who needed the lesson re-explained to them at an individual level before they could fully grasp the concept I was trying to teach. As for connecting mathematics to students daily lives, I really struggled with one student who continually told me that what I was teaching (powers and radicals) was useless and that he did not care to learn because he would never need it. This particular unit seemed to be quite hard to relate to real life, so I struggled with making it applicable—especially for that one student who asked me every day where he would see this type of math. Pre-internship really opened up my eyes as to exactly how diverse students learning was and how I would need ten of me, just to teach one lesson in all the diverse ways. The 3 weeks I spent in the classroom really gave me a reality check as to how busy a teachers life is, but how worth it is in the end.

“Working with preservice teachers can be puzzling and surprising, particularly because they are students at the same time that they are learning to be teachers… I offer the following suggestions for teacher educators in assisting preservice teachers to discover their teacher selves. It is important to help students identify inconsistencies between their beliefs and practices and to discover counter examples to strongly held beliefs. In addition, preservice teachers must learn to assume personal responsibility for their actions and performance and not blame the students or others for their problems. To be a learner requires the consent of the learner (Loughran & Northfield, 1996). Therefore, it is essential that the learner is open to learning and seeing multiple perspectives. It is important that preservice teachers acquire a discovery, problem-solving mode that allows them to inquire and examine their teaching and the students’ learning through reflection and inquiry. I have learned that for the inquiry–reflection cycle to successfully become a habit of mind, it is important to help students develop the following attitudes and dispositions essential for reflection: open-mindedness, responsibility, and wholeheartedness (Dewey, 1933).”

Quote taken from: Freese, A. (2006). Reframing one’s teaching: Discovering our teacher selves through reflection and inquiry. Teaching and Teacher Education, 22(1), 100-119.

This quote seems to sum up quite nicely what my experience was during my pre-internship. I found that my cooperating teacher was extremely good at balancing me as a student, as well as me as a learning teacher. I felt that during my time in her classroom, she was great at letting me be the teacher who I thought I was in the beginning of the 3 week block, but then she would give me advice and possible strategies that I could try for the next time I was to teach. She never pushed me into any one way to teach mathematics, but she also let me know when something did not work very well so that I did not repeat my mistakes. When I was sick one day, my cooperating teacher left it up to me to still plan for the day, as if I was planning for a sub and I had seen this as something extremely beneficial because it not only put the responsibility of planning for someone else to teach my lesson on me, but it also made me realize how much a teacher is responsible for when they miss one day. Another aspect of the role of my cooperating teacher that I really appreciated was the fact that she let me first reflect on my lesson(s) that I had taught throughout the day first before she gave me her feedback. It was nice to have the opportunity to look at myself as a teacher and say this is what I did really well did and here is how I can improve for tomorrow. She would then share some of her thoughts and suggestions with me to better my teaching that much more. Overall, I feel as though I really got lucky when it came to who my cooperating teacher was. She showed me the value of sharing material with fellow colleagues, how to be a good reflector on my own teaching, and how using teaching strategies different from my own can only benefit me as a learning teacher.



Blog Entry #6 Part A

1. What, do you think, are the main purposes of (reasons for) field experience (i.e. pre-internship practicum, internship, etc.)?

I see the field experiences as a necessity for the education program. There is such a vast difference between theory and practice when it comes to education and without the experience of going into the classroom, I think many teachers would quit their first year of teaching, wasting a lot of money on a career they don’t even like. I know that when I first entered the program I started to question whether or not teaching was the right career for me, but as soon as I set foot in an actual classroom and started interacting with the students, I knew I had made the right decision. Another main focus of the field experience I think is getting to know yourself as an educator, rather than a student. I know that from my own experience, teaching at the university in my classes changes from who I am when I am teaching in the classroom. I find myself to be very cautious of what I am saying when I am teaching high school students as compared to when I am teaching my fellow classmates. I also notice that I can take control of a classroom if I need to, rather than quietly telling the students to focus— this was something I thought I’d be terrible at.  Without having the field experience apart of my experience in becoming a teacher, I don’t think I would have made it this far because I wouldn’t have been able to witness first hand that I can be a good teacher and I want to do everything I can to be a great teacher!

2. What role does (or, should) a university teacher education program play in the process of becoming a teacher?
When I first entered the program I expected it to be a lot different. I thought I was going to be taught how to teach. I expected to make piles of lesson and unit plans, learn how to teach mathematics inside and out, and interact with students. Though some of my expectations have been met, I still feel as though the program could have helped me in other areas more. For example, I think the program should have put a stronger emphasis on how to teach in each persons subject area. I feel as though I still feel unprepared in how to teach the mathematics curriculum. It would have been nice to have a course that refreshed new teachers memories in their specialty areas. Right now I am feeling as if I do not know how to even do some of the mathematics because it has been 3 years or more since I have taken a high school mathematics course. I think if there would have been at least one class where you learned what you would be teaching rather than left to figure it out on your own, I’d feel more prepared.

3. What do you already know now about being a mathematics teacher that is unlikely to change through your upcoming field experiences (i.e. fundamental beliefs, values, commitments, etc.)?
As I enter the classroom for my three week block I know that I have to keep in the back of mind that I was once where these students were. I was questioning the relevance of mathematics (though I still enjoyed it) and wondering where I would use it. I know that my students will be thinking similar things, so I know that it is my job as a teacher to make mathematics connected to their daily lives— that won’t change after my experience. Another thing that I know won’t change once I am finished my pre-internship is the fact that not all students learn the same way I did, or even learn similar to their classmates. I will constantly have to adapt and come up with solutions so that all my students understand my lessons, rather than just a select few. Even though I know these things won’t change after my experience, I am looking forward to the changes that I will see, both in myself as a teacher and in the way I choose to teach.

Blog Entry #5

Dear Lynnea,

I just have to tell about two videos I watched pertaining to assessment in mathematics! First of all, they were filmed in what looks like 90s, with their poofy hair, huge glasses, and out of date outfits. However, they did seem to give me some insight into how assessments can be quite valuable in a mathematics classroom. The first video I watched was called Teacher Insights 9-12 (High School), and it really opened up my eyes to see how assessment in mathematics should have been done in our high school years. If you watch the video you will see that assessment and evaluation is not just quizzes, tests, and homework assignments like we were given all throughout our high school mathematics, but students can actually be assessed on how well they work in groups (who knew you could work in groups in mathematics), self-assessing themselves to see what they understand and how they can adapt their learning so that they better understand concepts, and how they can show progress in their work. The first video really emphasized different teachers point of views on how they assess their students, whether it be through group tests, portfolios, student-teacher interviews, etc. This seemed quite unfamiliar for me to see in a mathematics classroom as I am sure you know we only ever got evaluated on how well we did on a test, never given the opportunity to learn from our mistakes. I think this video would be a good one for you to watch because I know how much you enjoyed mathematics in high school and now that you also want to become a teacher, I think it would give you different ideas on how to assess your students. It is sort of a starting point and I am sure these teachers had to try a few things out before they found what worked best for them, but take a look and let me know how you feel about it.

The second video that I watched was called Beyond Testing and it sort of dealt with the same types of topics discussed in the first video, but focused more on how teachers can collect the evidence they need to assess students on and getting support from their administrators so that they can actually try out some of the new assessment strategies. I found it quite interesting in how involved the principal at the one school got. He sat down with the one mathematics teacher and discussed how she thought the assessment practices she was using were useful. I am not sure if any of our mathematics teachers ever did that, but I do know that we were never given the opportunity to show that we knew what we were learning other than through a test. Do you think we would have struggled more in mathematics if we were assessed differently, or benefitted from them? Do you think that our teachers would have had the time to try out all these types of assessments that I talked about from the first video on our class because we were always in split classes, so we never got the full attention of our teacher. It would be interesting to see how the teachers in these videos would adapt their methods to fit a class that contained five grade 11 students and 9 grade 12 students. I do not think that their group work would be as effective, also the group discussions would be kind of difficult as both groups would not be covering the same material.

Anyways, I encourage you to take a look at both of these videos, it is kind of neat to watch something completely different from what we experienced in high school.



Blog Entry #4

In high school I never knew that there was other forms of assessment besides tests and quizzes. However, my grade 11 mathematics 20 class introduced to me something new. I had a new teacher fresh out of university who was hired to teach all the high school mathematics courses. He started his very first class with us doing what seemed like this really simple quiz full of questions that came from the mathematics 10 course. I finished it quite quickly thinking to myself that this seemed like a silly way to begin the year. But as I finished up the quiz, I noticed that some of my classmates were having some troubles with it and that this new teacher was going around the classroom to help my fellow classmates solve the quiz. Once the bell rang we handed in the quiz to him and that was last we heard about it. The next day we jumped into the mathematics 20 course and began learning as we always did, the teacher stood up at the board and wrote notes, expecting us to copy them down word for word and making sure to stop him when we did not understand a concept. It has not been until lately that I realize what this new teacher was doing with that first day quiz, he was pre-assessing where his students were to know where they excel and where they need some help to improve upon. I think because I never knew what his intentions were for this quiz I had just seen it as a waste of time. If he had been more explicit about why he was making us do it I might have had a greater appreciation for it and him in the end.

There was not too much that I had not already known about self-assessment, it is when students reflect on their own learning and give themselves a mark based on criteria that is provided by the teacher. Some self-assessments are used for grades, while others are just used for the teacher to see where each individual student is at. I found that there are a pretty even amount of advantages as well as disadvantages. Some advantages of using self-assessment are: they allow student to monitor their own learning, they help teachers better understand where their students are at, and they make students reflect and connect with the criteria that is given to them. Some disadvantages are: they put a lot of the work load on students shoulders and some students may not bother with it, they need to be modelled correctly so that students understand what is being asked of them more clearly, and students with often mark themselves higher in hoping that their grade with be higher because they do not think that the teacher will also be assessing them. Self-assessments should go alongside teacher evaluations so that if their are any discrepancies between the teacher and the student, both have evidence to support their reasoning. I found a really good example on the internet for a daily self-assessment that students could use in mathematics, it can be found here.

Kaylyn researched portfolios and they were something that I had heard about, but not something I was completely familiar with. She described portfolios has having many different forms but the main purpose of the them was to collect students for the possibility to show student progress over time. They help students self-reflect and flexible enough that students can pick what they want to include in them. Setting goals is a way to track the students progress as it happens and it gives students a chance to discuss their progress with the teacher. However, they can take a lot of time to plan, evaluating them can be kind of tricky and they can be quite disorganized. They are helpful to use when wanting to track student progress, show students processes and products and they are great to show for employment.

Emily researched rating scales and rubrics, separating the two because though they were similar in some areas, they differed in many other areas. Rating scales are a tool used to assess the performance of a task, process, quality, skill levels, etc. They are similar to checklists but determine the degree of accomplishments. Teachers make qualitative judgements where the descriptive word is more important. Some advantages to them are: they are quick and easy to fill out, they are easy to design, they describe students mastery of content, and they give information for students to set goals. Some disadvantages are: they are highly subjective and they can be unreliable as people as people can interpret the ratings differently. They are good to use for self or peer assessment and self-reflections for teachers. You cannot use them for tests and should not use them to compare students. Rubrics are a set of criteria used to assess or evaluate student performance. They have a consistent fixed measurement and focus on quality rather than quantity. Students can use them as a guideline and teachers can use them as a guideline for quality student reference. They can be easily modified and allow students to see the progression of their learning. Teachers can have students involved in the process of creating them and they enable self-reflection for students. There can be difficulty in determining the set of criteria and are used for more group work.

Each of these performance-based assessment involve students in their own learning as they have to take the time to reflect on their processes and progress throughout a class. They are meaningful for both students and teachers as they track both how the students complete their work, as well as how the teacher sees that work being completed. Though they have some minor disadvantages to them, the advantages to them provide students with multiple ways of meaningful descriptive feedback, allowing them to progress further in their work.

Blog Entry #3

1) What/how you are learning about inquiry in this course (through your readings, our class activities, lesson planning, and lesson teaching)

As this class progresses I am now starting to see what Kathy is trying to show us through the readings she gives, the activities she plans and the lessons she has us plan. She wants us to experience first hand on how both the teacher and the student feel when learning through inquiry. As a teacher I have felt both frustrated and excited as I try to learn how to teach inquiry-based learning. I can relate my frustration to how Brea first felt about inquiry-based learning. She was willing to use it and change up her mathematics classroom, but felt as though she did not know it enough to fully implement it within her classroom consistently. As I become more familiar with inquiry-based learning I sometimes get caught up on how I was taught and I struggle to wrap my mind around on how to teach without being the main focus (not that I like being the main focus). However, after I taught my first inquiry-based lesson I became excited with the fact that I could do it, it was not as impossible as I thought it had first seemed to be. I also seen that working as a facilitator was more fun than just being a lecturer because I got to see how students work through a problem to come up with a solution. Maybe one downfall to inquiry-based learning is the amount of planning it takes to come up with just one lesson. The time and effort that my partner and I put into our lesson was rewarding in the end, but while planning, the end seemed so far away. Being a student in the activities that I have took part in has made me realize why this type of learning is being pushed —it is fun! It also allowed me as a student to give reasons and justifications fro why something worked, rather than just plugging in a formula. I really appreciate the fact that I have been able to experience inquiry-based learning both as a teacher and as a student because that does not happen often with many instructional strategies.

2) How/if the ideas in the article challenge or affirm your beliefs about mathematics teaching & learning (as described in your blog entry 2 creed).

In my mathematics creed my five statements were focused mainly on my students and how I think they should view mathematics, but I only mentioned actual teaching methods in my first one. However, I was not as specific to say that by teaching new methods in mathematics will require me as teacher to challenge my personal views of how mathematics should be taught. What I am used to is the more lecture style of teaching, knowing that most teachers go back to the way they were taught when they were a student. After reading this article I now realize that it is quite important in my career to challenge myself in how I teach and be willing to change my teaching methods for the benefits of my students. As the article says, “teachers could orchestrate their own change if they are helped to develop a ‘‘stance’’ of looking at their own practice by analyzing, adapting, and always challenging their assumptions, in a self-sustaining cycle of reflecting on their own theory and practice, learning from one problem to inform the next problem” (447). If I start to become critical of my own beliefs and teaching methods, I truly think that will only have a positive benefit on my students and I. If we as teachers expect our students to learn in ways they are not comfortable with (because no student learns the same way) then we should be experiencing our own discomfort in trying to accommodate all our students diverse needs. But changing is one thing, as a teacher I also need to believe that the change I am willing to take will benefit all parties that are involved. Chapman puts it nicely when she says “It requires not only a desire by the teacher to change but also the belief that alternatives that are more beneficial are possible” (456).

Mathematical Beliefs

I found that throughout the articles Why teachers matter by Merrilyn Goos and The importance of mathematics teachers’ beliefs by Kim Beswick, the authors both stressed on the fact that a teachers beliefs in mathematics influence how they teach. I strongly agree that how I feel about mathematics will rub off on how I behave in my classroom. It would be evident to my students if I did not like mathematics as my enthusiasm for the subject would be lacking. Knowing what I am talking about also relates to wanting to teach mathematics, I cannot expect my students to learn something  I do not understand in the first place, I would come across as a fraud. I need to understand the material clearly, but be critical of what my students are learning because I do not want them to be misled. But my students also cannot expect me to know everything as I hope to learn from them as well throughout our classes. Learning from each other can be extremely beneficial for both my students and me. Throughout my experiences in mathematics I have seen mathematics as being fun — not necessarily important — but fun. However, as I grew up I started to realize that mathematics was actually quite important in my life. I started to realize that what I was learning was benefitting my life in the “real world”. Being fortunate enough to have amazing mathematic  teachers, I did not see what some of the students saw in Goos’ article (page 10). They were not mean and only teaching mathematics because they had to, they wanted to be there as much as I did. It was through their influence that I seen that it is extremely important for a mathematics teacher to share their beliefs and values of mathematics explicitly with their students so that they know upfront why they are learning the material. I do not think that my students need to necessarily believe in my personal believes on mathematics, but I think they would understand my enthusiasm of mathematics more clearly if they knew my beliefs. In the end all I want for my students is for them to see the passion I have for mathematics and in order to do that I need to be upfront with them on why I think mathematics is so important to learn.

Here are five of my mathematical beliefs:

  1. I believe that mathematics should be taught differently throughout the semester. It should not all consist of one strategy, but should be mixed up to engage your students.
  2. I believe that mathematics is necessary in all students lives. They should engage in it every day so that it stays relevant and fresh.
  3. I believe mathematics needs to be more than just about grades. Students need to see the importance of mathematics in their lives.
  4. I believe that as a future teacher I need to help guide my students learning in mathematics when they do not understand it clearly.
  5. I believe that I need to take an interest in my students learning of mathematics and know how they feel personally about mathematics.