Two Final Exam Questions

The first final exam question I think would be appropriate is, explain, in your own opinion, what it means for you to teach (and learn) through inquiry? There are a few reasons why I think this would be a great question, and the first would be because there is a big push out there right now for us to teach though inquiry, and in order for us to be able to do that successfully, I feel that we need to make sure we understand what exactly inquiry is to us. In addition to this, we all know that everybody may have a different perspective or opinion on the significance of inquiry after we have learned about it, practiced it and have actually been taught using it. Secondly, inquiry has been something that we have discussed many different times throughout the semester, and as a result I have placed a lot of importance upon it. For instance, on our very first day of class we started out by doing an inquiry activity, then later in the semester we had discussions on inquiry, and also in some of our last few classes before pre-internship we actually received some practice teaching inquiry based lessons to the class. As a result of this concept coming up regularly, I think that it is important for us to start developing an understanding as to what role this instructional strategy may play in our future classrooms, and I think that by answering the above question we will being working towards figuring the this out.

The second final exam question I think would be appropriate is what types of values or beliefs do you hold that you think will influence your teaching practices? We didn’t spend a great deal of time discussing these ideas directly, but we did spend one class talking about what types of things may affect the way we teach. Therefore, I understand that it may not have been a huge focus of class material, but at the same time I think that our beliefs have played a huge role among everything we have learnt or taught this semester. I think that every time we were given an assignment, we were having a discussion or we were being taught something our beliefs or values would shine through. I think that at times it was very easy for us to question why someone would teach something they way they did, or why they would assess something in a certain way, and I don’t think many of us took the time to determining why we felt that way.  I don’t think many of us realized, or took the time to consider the fact that our opinions on the above issues were probably based on the beliefs or values we hold individually. As a result, I think it is important that we are able to start determining what types of beliefs or values we actually do hold; as if we are able to do this we will be able to start understanding why we may be experiencing certain situations, whether they occur in our classrooms, or other classes around us. I also think that it is important for us to come up with an answer to this question because it will enable us to see why we may not like some of the new instructional approaches there are out there. I don’t think saying we don’t like something is a good enough reason to not use something, rather I think it is important that we are able to give reasoning’s for our hesitations.

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Post Pre-Internship Reflection

Part 1

This is a reflection that will partly be linked to my previous post. Now that I have completed my pre-internship, I am going to discuss whether I think my opinions on the three big questions have changed, or remain the same.

First, when it comes to question number 1, I don’t think my opinions have changed all that much. I strongly believe that what I stated is the real purpose of pre-internship based on my opinion. I found that the experience was extremely beneficial for me, and I got to experience what it truly means to be a teacher. I enjoyed being able to plan many different lessons, and try out new things, even though they didn’t necessarily work the way I had hoped. However; after completing the three weeks I have noticed just how important it is to have your cooperating teacher watching you and make notes. I think that I learned a lot through her observations, as she was able to pick up on the little things I could change within my teaching that I wouldn’t have been able to pick up on, on my own. I didn’t realize things like the way you write fractions, or the way you write a question on the board could have an effect on the student’s comprehension of the material. Also, in relation to something I had mentioned in the post, I disagree with the fact that I felt a main goal of pre-internship was to see how much schools have changed since we have been there last. The reason for this is that in a way I don’t think they have changed all that much. There have been many little changes along the way, but after completing pre-internship I noticed that the classes weren’t all the different from when I was in school. This may just be the school I was at, as I am sure many other schools have changed drastically, but I think change is something we need to be prepared for in life, and not just for pre-internship. I think it is important to keep in mind that changes are a part of life, and we will experience them almost every semester, regardless of it being pre-internship or not. All in all, I think that the main purpose of pre-internship should be to get practice in the profession we hope to do some day as without this practice I think we would have no idea what would be required of us when we actually got a job in the future.

Second, when it comes to question number 2, I can now see just how important a teacher education program is. I think that without all of the knowledge I have received throughout the program, I would have struggled tremendously in my pre-internship. I found that I was relieved to have some practice planning, and some background information on classroom management, assessment, and instructional techniques. Without all of this information, I think that I would have just tried to teach the students in the same ways I got taught throughout high school, and this may not have been so bad, except for the fact that I am not completely sure that I liked how I was taught in high school, and so it wouldn’t have been fair to my students if I used those methods. After the three weeks, I have also found myself thinking about some things I don’t think the program prepares us for, and in particular, I don’t think I was really prepared to experience being in a classroom with a cooperating teacher who taught in a way I never thought you would. My cooperating teacher used many different methods that I didn’t really like at first, and I found myself questioning her a bit, however; after being in the classes for a while I was able to see why she did the things she did, and I found it extremely valuable to ask her questions, and hear her reasoning’s as to why she does the things she does. One of the biggest things I learned was to make sure you didn’t judge things too quickly, as you may be wrong.

Thirdly, when it comes to question 3, I was actually shocked to find out that one of the things I assumed I would do no matter what, was a lot harder than I had anticipated. After completing pre-internship I now realize just how hard it is to teach the students all the required material they will need to know before they move on. Throughout my experience I was able to see just how important it is to stay on track with when you wanted to have material taught by. I struggled greatly with this concept because I wanted so badly for all the students to understand what I was teaching them, but at the same time I knew that some of them were not ready to move on with the material just yet. I found myself wanting to spend a little more time on some material, but at the same time my cooperating teacher told me I needed to stay on schedule, and therefore I wasn’t able to make sure all of my students understood everything I hoped that they did. I struggled with the previous issue quite a bit, and I was actually a little upset that I had to move on when I didn’t feel I was ready to. However; in all other regards I think that my response for this question would generally be the same. I know that I still feel that everything I mentioned previously is important, and although this is the case, I am not saying that I am able to do all of these with ease. Pre-internship has taught me just how hard it may be to do all the things you hoped you could do. To give an example of this, I found it extremely hard to incorporate different instructional strategies, because I wasn’t always able to find places in which a different strategy would be beneficial, but I know I am going to keep trying. Also, I had mentioned in the question that I will always be available for help when the students need it, and during pre-internship I stayed for lunch every day and stayed a while after school, and after having experience with giving students extra help, and I have to say that it isn’t always easy. There were many times when I had other things I wanted to be doing during those periods of time, but no matter what, I knew how important it was for me to help the students out, and I never once found myself turning away a student in need. Lastly, there is one thing I never mentioned before that I wish I would have, and it is that I should have noted how important it is to learn the student’s names and build relationships with them.  I think that this I something I am always going to try hard to do, no matter the size of the classroom. I was amazed by how much more respect I was given once I was actually able to call upon the students by names, and as a result I think it is important to develop a method that will help you remember names as quickly as possible.

 

Part 2

“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).”

When it comes to the above quote, I think it makes a lot of sense, and I do agree that as pre-service teachers we need to be open to different perspectives, but at the same time, I think it is important that we are able to have our own perspectives on certain issues. I think that every individual holds their own beliefs, and I don’t think that it is completely necessary for cooperating teachers to try and change their beliefs. I think that a huge part of pre-internship is allowing us to have a trial run. By going through this experience we get to see whether our beliefs still hold true after we have completed the process. I understand that out cooperating teachers are supposed to help us on our journey to becoming a teacher, but at the same time I don’t think they should try and form us into the types of teachers they think we should be. Based on my past experiences, I know that people’s opinions can change, and I think we should be given the time to see if this may occur for ourselves. Also, I strongly agree with the quote when it says that we need to take responsibility for our actions. I know that a lot of the time it may be easier to blame others, but I think it is extremely important that we are accountable to what we do in the school setting. Even though we are not real teachers yet, everything we do or say is important, and I think we need to make sure we are always acting like professionals. Even though we are leaving after three weeks, I think we need to try our hardest to take the role of a real teacher seriously. Lastly, when it comes to the idea of making sure learners are open to many different perspectives, I think this is extremely important for us to be successful. However; I think that in order to use some instructional methods in the school setting we must spend time preparing our students for them or else they may not embrace them the way we had hoped. As a result, I think it is important that we don’t try to overwhelm ourselves throughout pre-internship by needing to try new things every day. I think that if we become overwhelmed as teachers, we will also overwhelm our students, and in turn hinder their learning.

Pre-Internship Reflection

Below you will find my response to three big questions that are related to field experience and the role of teacher education.

1. What is the purpose of field experience?

I feel that the field experience we are offered has multiple purposes, but to me I think the most important would be that it allows us to see what it is like to actually be a teacher out in the real world. I think that there is a big difference between learning how to become a teacher in the university classroom, and actually putting into practice the many things that we have learned, and by having field experiences we are able to try and implement them. I also think another important aspect of the field experiences is that they allow us to practice all aspects of being a teacher. We are able to see the importance of observing other teachers, lesson planning, unit planning, evaluating and interacting with students just to name a few. On a similar note, I think that by giving us experience in the classroom we could also find out if this is actually the job for us. Wanting to be a teacher isn’t always enough, and so through the field experiences we are able to determine if we are heading down the right path, or if we need to make some sort of a change before it is too late. Another purpose of the field experiences that may be overlooked by some is the fact that they allow us to get familiar with the curriculum documents. It is important that we are able to work with and understand the outcomes and indicators within the curriculum; otherwise we will not be able to do our job successfully. We need practice deciding how we are going to teach a concept so that we can assess it in a way that will relate to one of the outcomes or indicators. I also feel that another purpose of the field experience program is to allow us to build relationships with other individuals that are currently in the occupation we plan to have in the future. I think that it is important to see what other teachers are doing in their classrooms, as this will allow us to find out what kinds of things we like to see in the classroom, as well as the many things we may not be so fond of. We all know that it is within a teacher’s nature to take ideas from one another, and so I think these experiences provide the perfect opportunity to try and gather some tools for our future use. I think that the field experiences allow us to see how the schools have changed since we were there last. There is a lot of time between when we would have been in school, and when we will graduate from university, and so I think that it is important for us to be able to experience some of the changes that have been occurring in that time period. The last thing I want to mention is that I feel that through these field experiences we are able to develop into the teachers we hope to be in the future, and without these experiences we would never be able to develop or monitor our growth.

2. What role does (or should) a teacher education program play in the process of becoming a teacher?

I think that a teacher education program should help all of the individuals within that program gain experience in the teaching field, as well as provide them with the information they will need to know in order to be successful as a teacher.  I feel that we are required to take a lot of content area classes, that aren’t always the easiest to relate to what we are going to do in the future, and so I find it important that the education program will provide us with the real-world appropriate information that we will actually need to enter the classroom setting. I think that we should be required to gain the necessary content knowledge, but the education program should help us see how we are supposed to teach that information in a classroom. As I mentioned in the previous question, I feel that it is important for us to gain experience with lesson planning, unit planning, as well as evaluating students, and so I think that it is essential that the education program gives us opportunities to practice these three things. Although this is the case, I don’t think just creating these documents and wondering if they are going to work is a great idea. I know we are given a lot of time to create these types of documents and I do think that it is important that we receive education on how to create these types of documents properly, but at the same time creating these things can become a little less important if we never get the chance to try them out. By stating the previous, I don’t mean that we always need to be out in the field to do this; I think that it is important to provide us with appropriate amounts of time to teach in front of our classmates as well. When we teach in front of our peers we are given so much more feedback that we would have never received if we just tucked that lesson plan away for future use. I think that we may feel as though we have a great lesson plan, but it might not be so great when we actually use it, so why not find out the flaws before you use them in the real classroom. I also think that it is important for the program to provide us with information regarding what types of things are occurring in the classroom in the present day. We all know how we were taught when we were in school, and so I think it is important that we are informed as to what types of strategies are being used, as well as what the benefits are of using such strategies. Lastly I think that an education program has to inform you on assessment strategies as well. We may know our content knowledge, know how to teach the material, and know what we want to get them to do to show that they learned the material, but all of that doesn’t mean anything if we don’t know how to assess it. As a result, I think it is important that we are given the support necessary to determine how we can decide what kinds of grades a student deserves. All in all I feel that the education program is a key factor in how successful an individual will be in the teaching field.

3. What do you already know now about being a mathematics teacher that is unlikely to change through your upcoming field experiences?

One of the things I know won’t change in my upcoming field experience is the idea that everyone deserves an education, and so by saying this I mean that I will always try my hardest to make my classroom a place where all my students want to be. Math isn’t always a subject that is liked by a lot of students, and so I want to try my hardest to create a positive classroom environment no matter what kind of classroom or students I am given. On a related note, I want to make sure that all of my students know that at times it is acceptable to make mistakes in my classroom, and that these mistakes are essential to learning. I don’t want my students to be afraid to give answers, and so I will always make sure that my students know that aside from exams, their mistakes will not all be scrutinized. I also know the importance of being there for the students whenever I can and so as a math teacher I plan on making sure that the students can come see me for help whenever they need to. I plan on making myself available before school, after school, and at lunch. I know that I won’t always be able to be there when my students need me, but I know I will always try my best to meet the needs of all of them. Similarly, since I am fully aware that each student is going to have their own particular needs, I know that I am going to take the time to get to know each and every one of my students so that I can offer them the best experience I can in the math classroom. I plan on trying to incorporate different teaching strategies into my classroom, as well as a variety of assessment techniques. I am going to try my best to ensure all of my students live up to their full potential. Lastly I know that I want to make sure I teach my students all of the necessary information they are going to need to move on to the next class, or grade. I feel that it is really important to stick to the curriculum, and make sure you are teaching the appropriate information. This is because I don’t want to make the education experience any harder than it needs to be. Similarly, if I am teaching high school mathematics I plan on trying my hardest to prepare those students to move onto post-secondary education. I know it is important to make adaptations in order to have successful students, and that is ok, but at the same time I want my students to be prepared for the obstacles they may face once they have left high school. This means that I do feel having assignments, exams, projects and finals are important aspects of math classes at the high school level. The above paragraph describes a few of the things I feel won’t change after having field experiences. I know that my opinions on some of these things could eventually change, but I can’t see it happening in the near future.

THEN & NOW: You’ll Never Believe the Difference

March 5, 2012

 

Dear Kayla,

 

            Hey, how has it been? It feels like it’s been forever since we were sitting in a high school classroom, but you will never believe what kinds of things are going on in those classrooms today. Just the other day I watched two videos, and you will never believe what kinds of assessment strategies they say teachers should use in their classrooms now. I strongly recommend that you take a look at these videos if you have some spare time. The two videos can be found by going to this website, http://www.learner.org/resources/series31.html. If you scroll down on this screen you will find multiple different videos, but I have only been able to watch two so far. The first video I watched was number ten and it was called Teaching Insights 9-12, and the second video I watched was number eleven, and it was called Beyond Testing. I am going to give you a brief description of what I have learned, and I hope this information will encourage you to watch the two videos.

            I am first going to discuss the first video I had watched. This one was very neat because it discussed the many ways teachers in math classes are starting to assess their students, and you know what, it is not through tests like we seemed to always receive. Can you believe that they actually give out participation marks these days? When we were in school I always figured participation was a requirement, and it wasn’t necessary to assess these actions. I wonder why things have changed so much, do you know of any reasons why teachers are starting to mark based on participation? I would love to hear your thoughts. Also, if I were to hear the term, it’s time to write your test; I would have never thought it was possible to do it in a group, did you? Within this video it discusses the notion of using group tests. This means that you are allowed to work with other people when completing the test, but you are still all required to fill in the answers in the exam book. This sounds neat hey, I mean you would think that we would have received much higher grades in math if we could have worked on all those math tests together, don’t you think. But, beware, because within the video the teacher that uses group tests also mentioned that the questions he gave were generally harder, and so I’m not sure if I would have liked these group tests. And another thing, what if we didn’t agree on an answer, what would we have done then? I know that a test in math isn’t anything new, and so I am now going to discuss another method they use, it’s called formative assessment. I know, you’re probably wondering what this means, but to give you an example of it, it can be as simple as a teacher walking around the classroom and stopping to listen to what the students are saying. Can you believe it; you are being assessed and not receiving grades from it? For the longest time I always thought that assessments had to be translated into grades, and I am finding out that this is not the case anymore. Also, do you ever remember any of our teachers walking around the room and seeing what was going on? I don’t think I do, I just remember them standing at the front of the room and lecturing. Furthermore, the fact that they walk around and listen isn’t even the most important thing. They actually use the information they observe to see if they need to re-teach a concept. I don’t think that we ever experienced this. Our teachers always just kept going, and it was your responsibility to catch up. To finish, I want to fill you in on group work. I know we experienced group work all the time in other subjects like English or Social Studies, but never in Math. We always loved working together on projects, and so could you have imagined if our math classes would have allowed us to do projects, or group work, we would have had such a blast. I know that I have given you a lot of information to absorb from this video, but this is just a little bit of what the first video has to offer. You should watch it to see all the other crazy ideas teachers are coming up with these days.

            Next I am going to give you some details regarding the second video I watched. I previously discussed to you all the things that are changing with assessment, and now I am going to give you a bit of insight as to why these things are occurring. The video stated that assessment is changing because our view of how students learn is changing. It said that it is no longer appropriate to just give students information and see which students remember it and which ones don’t, we now need to know what sense the students make of the concepts they are continuously given. After reading the paragraph on the first video you may be thinking that assessment isn’t anything like it was when we were in high school, but I just want to clarify that this is not the case. Even though teachers are adding in all these methods, they most definitely are not getting rid of everything they used to do. In relation to this concept, one of the most important things I learnt from this video was the concept of equity, and when the video first mentioned this term, I wasn’t quite sure what it meant until they defined it, so don’t be worried if you don’t either, I will fill you in. Equity means providing the students the vehicle for being successful. I think this is an important concept because even when we were in school we always tried to be the most successful students we could be, and I don’t know about you, but I think that we could have been more successful in our math classes if the teachers were willing to alter their assessment and teaching methods. I don’t want to give away the whole video, because I think that you should watch it, but I am lastly going to discuss the idea of questioning. When you think of questioning in the classroom, what do you remember the most? Me, the only questioning I remember was answering a question on the board when the teacher asked one, or asking a question if I was confused. However; this is no longer the case. Now days, when a teacher talks about questioning, it generally implies that when a student gives an answer that is correct the teacher will then ask how they went about getting that answer, or if a question isn’t quite right, or completely wrong the teacher will then ask questions back in order to get the students on the right track. I wish I had this experience when I was in school, I think it would have been great to hear the reasoning’s of other students, and I would have loved the extra help in clarifying where I went wrong.

            After you finish reading this letter I hope you found the information intriguing and you plan on watching the videos for yourself. I know you are not going to be a teacher, and you may find the information irrelevant, but I will guarantee you that you will still enjoy the video. The videos are reasonable in length, and I would love to watch them with you if we ever get the chance. I look forward to hearing back from you, as I am interested to hear your thoughts.

 

Yours Truly, Alanna

Assessment Strategies

When I think about assessment strategies in school, I mainly recall being assessed through exams, and I usually did really well on exams; however I know that there were many individuals around me that didn’t do so well with exams. As a result of this, I have come to think a lot about the assessment strategies I plan to use when I am teaching some day. Although these tests were a struggle for some, I had a math teacher in high school that allowed for us to re-write an exam as long as we were willing to come in and get the help required to do the corrections on the exam. I only took advantage of this experience once, however it was one of the best experiences I had. There was one test that I wrote and I didn’t get a mark that reflected what I know I could have received, and so I went in for help and did all of my corrections, and was able to do the re-write. As a result of this, I got a much higher grade, and was happy that I got a second chance at the exam. Since I have seen this type of assessment used, I value it a lot, and I am sure that I would use a similar strategy when I am teaching in a classroom. I think it is important to allow students to have second chances, as you may not know the circumstances as to why they didn’t do well on the exam.

                My learning strategy for the class assignment was self-assessment, and the reason I chose to do this strategy was because I always wondered how successful it could be. I found out a lot about this strategy, but the most important thing I found was a quote, and it stated that “self-assessment is the most overlooked, yet possibly most valuable aspect of assessment for students at all levels and in all fields”. I never understood just how important this strategy was until I did my research on it. I am going to start by stating the definition of what self assessment is, and it describes the process in which each student evaluates his or her own progress or performance. There are many different ways to incorporate this strategy into the classroom, and a few are I can statements, learner contracts, reflections, portfolio reviews, blogs, journals and so on. There has also been research shown that states that self assessment has been seen to increase motivation among the students, and if that is the case, I think it is extremely important that we start incorporating this strategy. On the other hand, I was able to find one flaw in this strategy, and it was that even though some students are capable of self assessing themselves, there are still many students that don’t become engaged with this process, and it can be challenging for some people to self-assess themselves. One of the most important things I think this strategy will do for the classroom is allow both the students and the teacher to become aware of both the strengths and the weaknesses of the students, and as a result the teacher can figure out the needs of each student. The last thing I want to note about self-assessment is that it should be used as formative assessment, and should not be graded. This strategy should be used in order to provide feedback to the students, and that should be its main focus.

                The next assessment strategy I am going to discuss is interviews. I think interviews are a great assessment tool as they allow the student and teacher to have discussions with one another that may not occur in the classroom setting. I learned that the purpose of interviews is to observe and question students in order to get a better idea of their attitudes, thinking processes, level of understanding, ability to make connections, or ability to communicate or apply concepts. I also found out that there are different types of interviews that can be used in the classroom setting, and they are known as structured and open. I have been the most familiar with structured interviews, as this form is used to collect data based on students, and with this kind of interview all of the students are required to answer the same questions and the same order. With this interview style all students are given the same conditions and opportunities. The next style of interview I learned about was open, and I don’t think I was ever exposed to this form. In this case the format of the interview is very flexible, and the students are asked open ended questions. With this form of an interview the students can be asked different questions, and the interviews could go to different places. Although both styles of interviews can be successful in diagnosing a student’s strengths and weaknesses, there are a few things to note about them. They can be very time consuming depending on the number of students in the classroom, and you need to make sure that you are not teaching during them, as interviews are not a way of teaching new concepts; it’s a way of seeing where the students are at.

                The last assessment strategy I am going to discuss is pencil and paper tests, and the definition for this strategy is a written examination of an individual’s proficiency of knowledge in a certain subject or area. One of the most important reasons teachers use this strategy is to record marks. Exams can be empirically documented, and they are viewed as consistent when they are written by a whole class. Another important reason to incorporate tests into the classroom environment is because grades are used for admissions purposes down the road, and test scores are the easiest way to record and calculate a student’s mark. To some this form of assessment has also been perceived as fair, as the students have the same conditions and the same opportunities, however; some students struggle with writing exams, and I am not so sure that this is actually a fair form of assessment. The last thing I am going to note is a disadvantage of exams in the classroom, and it is that tests cannot measure certain things. For instance, an exam cannot measure things like creativity, and so this is why we need to incorporate other forms of assessment other than exams.

                Lastly I think that all of these forms of assessment can be extremely beneficial within the classroom. I think that it is important to include a variety of these strategies, as not one particular strategy will be able to work on its own. I think that because we have many different students in the classroom, we must be willing to give them different opportunities to succeed.  I also think that many of these strategies can be used formatively in order to help give students feedback, and learn more about how the students learn best. I think it would be important to use strategies like interviews in order to find out where the students are at, and monitor their progress. By doing this the students will build relationships with the teacher, and develop a strong community within the classroom. As a teacher, I think it is going to be important to include forms of assessment for, as and of learning. Many of these assessment strategies can be altered to fit into any of those three categories, and so I think it is important to find a balance among all three.

My Views on Mathematics!

What is mathematics? This is a great question, that has a different answer depending on who you are asking, and thus there isn’t one complete definition. If you look up the definition of mathematics, you will find that it gives you a definition similar to the one that follows. Mathematics is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. Although this can be viewed as an accepted definition, I am going to briefly discuss what math is to me. I think math is a part of life, and as mentioned in the article by Goos, I agree with the statement that refers to math as a tool that is important in our everyday and working lives. I think most students feel as though math isn’t important for their lives, and they are never going to use it after they are done school, and so I think it is important that we address this issue in order to show the students that they will rarely go a day without using it. For instance, when the students are calculating how much time they have to get to school, or when they are trying to determining whether they have enough money to buy something, they are doing math without even realizing it. When most people think about math they think of it as sitting in desks, and working with numbers, and even though this is an important part of math, I feel that there is so much more that math has to offer, and as educators we need to find a way to teach math successfully. 

Now, when it comes to teaching these particular concepts, I feel as though my beliefs are going to strongly affect the way in which I teach. Also, when I think about what has affected these particular beliefs, I can say with certainty that most of my mathematic beliefs have been shaped by my past school experiences. I have had many experiences with math, as I am sure everyone has, and through these experiences, I have been shown behaviors, assignments, and techniques that I do like, and also that I don’t. As a result of this, I know that these experiences will affect the way in which I will teach in the future. I think that math should be fun as much as possible, and I feel that it doesn’t need to be as boring as some teachers make it out to be. Through learning mathematics, students are required to keep their mind working, and they are constantly learning new things. This is why I think inquiry is becoming more and more important, and although I never grew up with this method of instruction, I believe that this is a way to get students more engaged in what they are learning, and it will allow them to get a deeper understanding of what is being taught. I guess I would say that I am part of the “content and understanding” cluster of teachers that were mentioned in Beswicks article. I feel that getting through all of the content is important within a class, however; if it is taught in a way in which the students simply just memorize things, we are doing more harm than good. This is why I think it is important that we teach the required content, but more importantly we need to make sure we are teaching the students the concepts in a way in which they understand.  When I was in school, I know that I got through a lot of tests or assignments by simply memorizing things, and not understanding the key concepts, however; throughout university I have come to realize that memorization doesn’t always work. As a result, I have changed the way in which I feel I should teach mathematics. I don’t want to be a teacher that simply gives the students formulas or processes, and requires that they remember them, rather I want to be a teacher that can explain to the students why these things are the way they are, in the hope that they will actually learn something from the class.

Also, I know that since my beliefs are going to affect the way I teach, I feel it is important that my students have an understanding of what my particular beliefs are. If I plan on teaching things in a particular way, I feel that it is important that the students are aware of it right from the beginning. On a similar note, I feel as though students need to have their own opinions, and their beliefs need to be heard as well. As a teacher I want what is best for my students, and if they have input, I will gladly hear it, however; I will make sure they understand that I make the final decisions. To sum this up, I would like to finish up with a quote from Goos article, which states that “teachers matter because we have the power to engage or alienate students in ways they will remember for the rest of their lives.” I want to be a teacher that is remembered for the good things I did with my math classes, and I don’t want people to remember me as a teacher that didn’t care, or wasn’t willing to make accommodations for my students.  

All in all, I loved math growing up, and I hope that I will be able to show my love of math through my teaching. If I am able to make one student love math as much as I do, I will be extremely proud of my accomplishment.

The video!!