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Final Entry
*April 12, 2014*

*Posted by jennienorgaard in EMTH 350.*

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After reading over my six different blog entries in this class I would have to say my favourite blog entry would have to be the fourth one on assessment. I would say this is my favourite blog because I learned a variety of different ways to be able to assess students in a mathematics class apart from the traditional homework checks, quizzes and exams. We each researched different assessment strategies and had to explain them to our peers. From these presentations I learned a few other ways to assess students in a math class such as entrance and exit slips, oral reports and presentations, open-ended questioning, checklists and much more. Not only did I learn a variety of different assessment strategies that I can implement in my math class but these strategies also make assessing students more fair and accurate. I say this because not all students are good at writing exams or tests. I think the more variety you put into assessment for your students the more your students will enjoy the content, be engaged in class and they will be able to demonstrate their learning if they are provided a variety of ways to do so. I think it is extremely important to provide students with a variety of ways to demonstrate their learning as everyone learns differently and not all students can provide everything they have learned in certain kinds of assessment strategies.

Looking back at my blog posts for this class I don’t think there would be any blog that I would redo. I say this because my autobiography on math has not changed over the course of the semester and my creeds are still the same. My blog on assessment wouldn’t change either because these are the different assessment strategies I learned about that we could implement into a math classroom. I didn’t know some of these assessment strategies before I made that blog post or before this class. I don’t have much to change about my thoughts on the two videos I watched and had to blog about. I haven’t done anything after creating this blog post that would make me want to change my mind or opinion on those particular things. Prior to this class I didn’t know much about inquiry teaching if anything so there is nothing that I can say I would change about that blog post. As for my post 6a and 6b there is nothing more that I would change about them either. My thoughts on education and the program are the same. Plus on blog 6b we were asked to redo one of the questions after pre-internship, which I did. So realistically after looking at all my blogs I created in this class the only blog I would change would be 6b, which I already have by answering one of the questions again that I already answered in a prior blog.

The blog that I learned the most about myself as a learner would have to be blog 6b, which was created after pre-internship. This would be the one I learned the most because I would have to say I learned a lot of new things in and throughout my pre-internship experience! I learned a lot of things during this experience such as things that I should be doing in my classroom, how to adapt lesson plans for students, and things that work well and are not the best to do in a classroom setting. I learned a lot when I was actually given the opportunity to teach students of the appropriate age group as opposed to teaching university students the content they already knew. It was also very beneficial to learn how to adapt lesson plans for different students when I actually had students in my classes that I had to adapt lesson and assignments for them. In general, pre-internship was an amazing learning experience! I would also say I learned the most in this blog because prior to pre-internship I wasn’t entirely sure if becoming a teacher really was what I wanted to do. But the experience I had at pre-internship was so amazing and I enjoyed it so much that it has changed my opinion on becoming a teacher for sure. Through this three-week experience I learned that I do indeed enjoy teaching and that it is just the university classes that make me second-guess my decision on becoming a teacher. When I am actually out in the field teaching I love it.

To be honest, I don’t think there would be any other blog entry questions that I would add for this class. I think the questions that we were asked throughout this course hit all the points that we learned and discussed in this class. There really was nothing else that we did in this class that we could associate with another blog post. Everything that was done and discussed in this class we had a blog post to follow it. So I don’t think there are any other relevant questions to make and respond to for this class since we more or less covered all the things we did in this class in our blog as well.

After taking EMTH 350 this semester I wish we would have talked and learned more about providing different assessment forms in a math classroom and creating and implementing inquiry lessons. I think it was great that we learned about different assessment strategies but I think it would have been more beneficial to actually see some of these be done in a classroom. It would have also been beneficial if we could have learned how to use and incorporate these different assessment strategies properly in a classroom. For example, we talked about anecdotal notes and records but I have no idea how to incorporate this into a math classroom. I don’t even really understand what this assessment strategy is to be completely honest. The second thing I wish we would have went over more was if we could have done some more inquiry activities such as the activity we did on Tuesdays class with algetiles. It was great learning about how we could do an inquiry lesson with algetiles that taught the completing the square topic but why couldn’t we have done more or these types of activities throughout the course of the semester? I think if we would have done more activities like this throughout the semester it would have been more beneficial for us in becoming mathematics teachers.

Two goals that I have for myself in internship include trying to use a variety of different teaching strategies in and throughout my classroom. In pre-internship I did use a few different teaching strategies but it would have been better if I tried more. For example, it would be great if I could incorporate an inquiry lesson during internship since I didn’t get the chance to incorporate one into one of my lessons during pre-internship. Another goal that I would like to try and accomplish in internship is to be able to incorporate treaty education into my lessons. I find this extremely hard because you can’t simply incorporate algebra with First Nations objects. I also find it really difficult to incorporate this content into the material I am teaching as I am trying to be as respectful about this culture as possible.

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Professional Development Journal Response
*April 7, 2014*

*Posted by jennienorgaard in EMTH 350, Uncategorized.*

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After my three-week field experience has been completed and I look back on the 3 big questions I answered before pre-internship the one question I would answer differently would be the first question on the main purposes of field experiences. I still think that field placements are a great way to experience things first hand such as if teaching is really what you want to do and if you enjoy what you are doing. After my three-week block I would say that these placements are more than just that as well. These field placements are a great time to learn things in the field with your co-op teacher and make as many mistakes as you can. These experiences and mistakes I made in my class broaden my learning from what we talk about in my university classes. However, apart from the hands on experience I got from this placement I would have to say I learned more from watching other teachers teach and my partner teach than when I was up at the board teaching alone. I got to observe and see how different teachers managed their classes and how they interacted with their students. Just from watching this I was able to take away some valuable things to do when I teach. In this experience I also learned that everything I learn in university through the Education Program doesn’t always get implemented in a classroom. For example in University you learn about how to deal with different situations as they arise in your classroom. But sometimes things don’t work out the same in your classroom as the scenarios we learn and talk about in university and you have to do things a bit differently. I also think that being able to experience these things first hand and not just read and talk about it in class is totally different. You will never fully understand the importance of why we have to do certain things a certain way until you actually experience it in your own classroom. When I was observing my partner teach and other teachers teach was when I was able to pick out the little things that we should be doing in our class as we teach. I think that the university programs are helpful but it is more beneficial when you can see these things happen in real life either from observing other people teach or even when you teach yourself. So in general, I think the university programs are a great start in helping you understand different things that can occur and how to deal with them in a classroom. But ultimately the best way to learn is from actually experiencing these situations in a class for yourself and being able to talk about it afterwards with your co-op teacher and partner. So in the end, the main purposes of these experiences are for you to actually go out in the field and experience the things you learn and talk about in university classes. It is one thing to talk about them in class at university but it is another thing to actually see the things take place in your own classroom. Apart for realizing if teaching really is for you through these placements, they are also a way to help your have a better understanding of the different things you talk about and learn in class throughout university. I also found that some of the things we talk about in university were not the best way to go with some things. For example, we always talk about a student centered learning style to try and take on. But from my experience, the students learned better when it was a teacher directed type of lesson. When I had a cooperative learning/jigsaw activity for the students to take part in they were not sure what to do and how to do things without being instructed by the teacher. So I think in the end the things we learn in university can very well be beneficial but it all depends on the group of students you have in your classroom!

In this quote it talks about how “preservice teachers can be puzzled and surprised because they are students at the same time they are learning to be teachers.” I found this to be very true! The transition from being a university student to being the teacher to the grade 9 students was a struggle to try and overcome. It took a couple of days to get use to it but after that things were better from there on out. In the beginning I found it difficult to try and teach the grade 9 students this new content that they were not familiar with when I had just come from the same end of the spectrum where I was the person trying to learn what the teacher was teaching not that long ago. As a preservice teacher I had to start doing things differently then what I normally do as a university student. I was now responsible for my own actions **and** I was also responsible for the students learning as well. Just like it states in the quote, “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 found this to be very relevant as well considering the fact that when I was a preservice teacher I was in charge of teaching the students this new material and I had no one to blame for any of the mistakes that I made along the way. If things didn’t go as planned I had no one to blame but myself because I was responsible for all the things in the lessons being taught. Now that I am done being a preservice teacher, I am finding it extremely hard to come back to university for a week where I am now the student again. I find it difficult to transition from being the teacher to having to be the student again and study for finals.

Pre-internship overall was an amazing experience where I learned a lot and it made me realize that teaching really is what I want to do! The university aspect of becoming a teacher has always got me second guessing myself about whether or not I really truly want to be a teacher in the end. After this field experience I can say I am more confident with the idea of becoming a teacher.

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Field Experience and The Role of Teacher Education
*March 15, 2014*

*Posted by jennienorgaard in EMTH 350.*

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I think it is important that all students taking education should get the opportunity to experience what it is like to actually be out in the field. You will never know if teaching is actually what you want to do until you go out and experience it first hand. Going through university and studying everything required to get an education degree is totally different than actually going out and getting a feel for teaching. If you don’t actually go out and take part in field experience you will never be certain if teaching really is for you. Field experiences are a great way to interact with students, gain experience, gradually get into the routine of how it is to be a teacher and learn as much as you can about teaching. They are also a great way to learn things such as what you should be doing, how you should be doing certain things and an opportunity to make mistakes when there are co-op teachers there with you to help you along the way.

University teacher education programs are supposed to help students develop the knowledge, experience and understanding they require in order to be successful teachers. Apart from these, university programs also deal with things that you shouldn’t be doing as teachers in your classroom and they also go through some possible situations that could arise within a classroom and how to properly deal with them. University programs are there to help you learn as much as you can about the curriculum and teaching without actually being in the field. They are also there to help you develop your mind and thinking about teaching. You learn how to switch your thinking from being a student all through grade school to start putting your teacher hat on and thinking like a teacher. University education programs are also designed to help you learn how to develop a safe, risk free and non-judgmental environment. We learn the process in how to teach the subject area we are majoring/minor in, different strategies that we can and should be utilizing, the different learning styles that are out there and most importantly we learn that we teach people and not just the content. University programs are the first steps to take that guide the students in the right direction of how to be a successful teacher. University teacher education programs also gradually allow students to get into the field and see how it is to become a teacher. For example, the first field experience you get in the university program is just observing other teachers and how they operate their classroom. They don’t just throw you into a classroom and expect you to start teaching from day one. They gradually progress from a semester of observing, to teaching one class in the afternoon to pre-internship where you start teaching one class a day and gradually get to the point where you are expected to teach three classes in a day. I think it is crucial that all students should go through this process when becoming a teacher because if you get thrown into the field right away and are expected to teach not many students will be successful. Becoming a teacher is like teaching someone how to swim; you don’t just throw them into the deep end right away and expect that they can swim. You have to teach them step by step the important points and then gradually progress from there.

I believe that a mathematics teacher has to be passionate about what they do in order to be successful in the end. If a teacher isn’t passionate about what they do then the students they are teaching will not like mathematics either. I believe this because I think that if a teacher isn’t passionate about the subject they are teaching then they won’t try and make the material fun and engaging for the students. Apart from the passion a teacher has on a subject, I also believe that what the teacher believes and value about the subject will in turn reflect how they teach as well. I believe that if teachers can show students the importance of mathematics and that it is utilized everywhere outside of the classroom then maybe they will learn to appreciate it more. With all this, I also believe that mathematical beliefs and values can change as time progresses and as you experience different things in and through a math class.

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Assessment in a Mathematics Classroom
*March 3, 2014*

*Posted by jennienorgaard in EMTH 350.*

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Dear best friend,

I was just watching a video on high school mathematics and it was talking about how high schools are currently at the midst of a dramatic change for the way in which the approaches to mathematics should be. For example it is asking the students to begin to go beyond the mimicry/regurgitation and memorization in math classrooms. Instead they want students to start to investigate the complex problems they are given, communicate their ideas with their peers and teachers and to then become critical thinkers. I think this is a great idea that needs to be implemented as I clearly remember in high school how we use to all try and remember the process in how to do the problems prior to the exam. We never actually went beyond the process of how to do the problems in math class. I think this is mainly because we were marked only on homework checks, quizzes and exams. Due to this, memorizing was one of the best ways in order to get a good grade in the end.

Another topic that was discussed in this video was the idea that the way in which students are evaluated needs to evolve as well. For example, it talks about how evaluating groups is just as essential as evaluating individuals. The video talks about how this can be implemented through group tests. However, group tests are not a way to look for evidence of process. There are other ways to mark for group process such as participation quizzes. These look like group tests but the assessment goal in the end is different. This is because in a participation quiz the teacher is more interested in the quality of the conversations. Participation quizzes allow for the in-depth discussions to occur. I think this is important to do, as sometimes the quality of the conversation is more important than the process in how to do the problems. I say this because when teachers can listen to these different conversations taking place, this is a great way to assess your students based on what they know and how they are dealing with the problem. Whereas teachers cannot really assess their students as well based on the process in how they approached the problems. This video talks about more essential ways to mark for process such as in homework, class participation, class response, tests as this allows the teacher to see if the students are grasping the concepts that he or she is teaching.

The video also talks about how assessment doesn’t always result in a grade at the end. There are different forms of assessment such as assessment cards where students give suggestions on how to improve for their peers. This is a way for the students to go back and improve before handing in the final result. The video also talks about how it is more important if a student can go up to the front of the class and explain/present the questions they did in front of their peers. This is also more valuable than asking your students to do questions on a piece of paper and then hand it in. I also agree with this because I remember in high school how some students were scrambling last minute to try and get the answers for some of the questions from their classmates or from their friends. This way they are not learning anything at all. They are just copying the answers from their friends to make sure they get a good mark in the end and that it is completed. When really this isn’t very smart, as how much the students know will reflect on the exams that they write. This way if students have to go to the front and talk about the process they did for their questions, this ensures that all students are responsible for doing their own work and they are contributing to their own learning. This is also a good way for the teacher to assess the students when they go to the front and discuss their problem to their peers. This process also allows the students to ask questions to the presenters.

Lastly, the video talks about the importance it is for high school math teachers to change the different forms of assessment provided. The changing of assessment will offer students better instruction and build a greater self-confidence in their ability to do math in the end. I think in the end this will be very beneficial as it will start steering away from the idea of students copying assignments off their peers and not necessarily learning or contributing to their own learning in any way. I also think that if students are provided with more forms of assessment they could have a different view on mathematics if they are excelling at it.

I think that you should take some time and watch this video as it has a lot of information on here that could help you understand mathematics at a different level. It could help you get a better understanding of math instead of always just memorizing different concepts and finding math to be useless and not important in our lives. It is also more beneficial to actually see these different things being implemented in a classroom as opposed to just reading about it.

Another video that I watched was called Beyond Testing. This video also talks about how assessment is changing because how children are learning is also changing. It talks about how learning is now based on the process of making sense or making meaning of math, whereas learning use to be all about acquiring information. Students are now also expected to be able to make connections between mathematics and the real world. Due to all these changes, teachers have to change the way they assess their students on what it is they are doing and instead start evaluating their performances. I believe that this is really important as what students come up with for the final answer shouldn’t be as important as how they got there. By being more concerned about how the students got to their final answer makes it easier for teachers to assess the students. Not only is it easier to assess, but also teachers can see how they need to change their instructions if students do not understand how to do the problems properly and so on. After all, assessment is based on the different perspectives the students can have and not just about what percentage they get in the end. The video emphasizes that assessment affects and **drives** instruction. What we assess and how we assess communicate to a teacher certain skills, practices and knowledge that are very important. The video emphasizes that it is important to assess students in a variety of ways as they all learn in multiple different ways. I think this is extremely important as in high school we were only assessed through exams and quizzes. I don’t think this is fair at all considering the idea that not all students do well on exams.

The video talks about how we should begin to utilize performance based assessment more. This gives you more information from different perspectives, you can hear the students’ explanations of their ideas, you see how they can response to particular questions and you can see how they solve problems. By allowing for this type of assessment it allows for a more complete and balanced conception of students as well as promote equity in the classroom. Equity is the vehicle for being successful. So as a teacher you need to offer the opportunity for students to demonstrate what it is they know and you also need to be flexible so that you can recognize that there are different ways of demonstrating this knowledge. I agree with this, as I don’t think it is fair to be assessing students on things that they are not comfortable with demonstrating. For example, if students are bad at exams don’t assess them strictly on exams as that is not fair and doesn’t provide the opportunity for your students to demonstrate all that they have learned.

This video goes on to explain the four broad purposes of assessment. These include: monitoring student progress, making instructional decisions, evaluating student achievement, and evaluating programs. Assessment allows teachers to see if their students understand what they are learning and if they have to change their instruction to meet the needs of the students. It is important to involve your students in the assessment process. Assessment is also a form of improving teaching in the classroom. I think assessment needs to be utilized more and provided in a variety of ways in a classroom. I know this was not always the case in high school as there were rarely any forms of assessments apart from the exams.

This is another video that you should take a look at, as it can give you a better understanding of how assessment can be changed in a classroom and how it can be both beneficial for both the students and the teachers in the end. This video is also a great visual on how assessment can be used apart from the traditional exams. Instead this video streams away from the exams and uses a variety of different methods to assess the students. I hope these two videos and this information was enough to help you understand the importance it is for teachers to provide the proper assessment to their students. I also hope that you begin to understand the importance behind each of these different assessment forms and understand that mathematics shouldn’t just be about how well you can memorize concepts and regurgitate them on exams. Mathematics is way more than just that!

Hope this all helps!

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Assessment
*February 24, 2014*

*Posted by jennienorgaard in EMTH 350.*

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From my own high school experience I cannot say that I have experienced many different forms of assessment especially through mathematics. The only form of assessment we had for mathematics was the traditional paper and pencil exams and quizzes, to the occasional homework checks. Most of our assessments were based on the many unit exams we had and the weekly hand-in assignments we were assigned. Apart from mathematics I cannot say that I did experience a variety of assessment forms to begin with. We had the odd journal writing, oral reports and presentations for big projects and things like heritage fair, to some self and peer assessment. It wasn’t until university when I first encountered entrance and exit slips, open-ended questioning, rating scales and rubrics, to reflective prompts.

Through my own research on oral reports and presentations I learned a few things about this form of assessment that I didn’t know. I always thought these had to be in the form of a speech or paper, but learned through my research that it can also be incorporated through audio-visual aids such as: posters, slides, movies, models, or other demonstrations. Before this research process I had never thought oral reports and presentations could be done in a mathematics classroom. However, now that I think about it, if it were utilized in the correct way it could indeed be beneficial to consider. In a math class oral reports could be used to inform the teacher on what their students already know, what they didn’t understand about a unit, what they liked about the unit, what they didn’t like, to what they wish they would have learned. From these reports teachers can also learn how well they taught a unit, what they need to change for next time and what their students are still struggling with after the unit. Now that I think about it, I think an oral report or presentation can be more beneficial at times to use instead of an exam or test as not all students excel at writing exams. This way it allows the students to critically think about what they have learned in the class, what they wished they would have learned, and things like what they are still struggling with, instead of trying to regurgitate everything that they memorized the night before for an exam that takes anywhere from half an hour to an hour and fifteen minutes. This form of assessment strategy also allows students to explain what they know in a paper if they cannot explain it in mathematical language. These are some of the advantages I found for this assessment strategy through my research, but like anything there are always disadvantages to things as well. Some disadvantages for this assessment form in a math class could be the idea that not all students are good at explaining in depth what they have learned in a paper as opposed to a conversation, and it may be difficult for some students to reflect on their learning in a paper for a math class.

From listening to other assessment strategies I learned that open-ended questioning is a form of assessment that has a variety of ways to answer and not just one correct answer. This is a great way for students to explain how they arrived at their final answer and why they chose to do their question in this manner. This form of assessment allows for students to represent their own learning and ideas in whatever way they want. There is no correct way in how you are suppose to answer or go about answering a question which allows for more students to willingly share their thoughts and ideas as they are not afraid since there is no one correct answer. This form of assessment allows students to share their ideas and thoughts more frequently in the lesson and it allows for students to make different connections to create a deeper understanding for themselves and their peers. I think this would be a great form of assessment to use at the beginning of the year to see exactly where your students are at and what they know. Just like anything there is also disadvantages to this form of assessment as well. Another assessment strategy I learned about in our sharing activity was anecdotal notes and checklists. The purpose of this assessment strategy is to provide information about the student’s development over an extended period of time. This form of assessment also allows teachers to identify the instructional needs of their students and it is a form of assessment ** for** learning. This strategy can be used at any time to record all and any observations of our students. Anecdotal notes and very focused and brief. They also provide a very accurate description of the situation and comments or questions that may be a guide for further observations. This form of assessment provides information such as the strengths and weaknesses of our students, which can help educators change or focus their lessons on certain areas. In order to develop a complete profile for students’ language abilities, interests and attitudes it is important to comment and record during different times and during different activities throughout the day. Although I learned a lot about anecdotal notes and records, I cannot fully say I understand how to utilize this assessment process. It is still a bit confusing and uncertain to me in some areas.

I think it is important to incorporate a variety of forms of assessment in a classroom as not all students excel at the same thing. By this I mean that some students may be able to demonstrate what they learned more accurately if teachers provide them with a variety of ways to do so. As teachers we also can’t assess our students accurately and fairly if we do not provide all of them with the same opportunity to express and demonstrate all that they have learned in whatever way is most beneficial for them. I think it is our jobs as educators to find the way that is most beneficial for our students to demonstrate their learning as in the end it is all for them anyways.

These different forms of assessment connect to assessment* for* learning in the sense that they are all a way of determining the progress our students are making during and throughout a unit. From these different forms of assessment teachers can identify different areas of their classroom in which they should change in order to benefit their students more and of course through these assessment strategies students are given valuable feedback on their own learning. These are all also a form of assessment *of* learning in the sense that all of these forms measure and record students learning levels in some way. Lastly, these are also a form of assessment* as* learning as they all give students an equal opportunity to further their own learning through the feedback they are given. Through these different assessment strategies students are given an opportunity to set their own personal goals and determine what they would like to work on and do better on for next time. In general, all these different forms of assessment are a great guide to help students understand what they are doing well and what they can improve on. In the end it is all about helping students learn all that they can in the best way that suits them so as educators we need to utilize a variety of different assessment forms along with all the different instructional strategies we are encouraged to implement. There are so many different assessment strategies out there for the simple reason that we all learn and understand things in different ways so we should take advantage of this as much as we can!

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Inquiry-Based Teaching
*February 12, 2014*

*Posted by jennienorgaard in EMTH 350.*

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The first time we experienced an inquiry-based lesson in EMTH 350 was when Kathy gave us the lesson on circles. She brought up the idea with a problem she had with finding certain angles on her bicycle wheel. From there we worked on an activity where we, the students, came up with the concepts of the circle. We discussed amongst our groups while trying to answer the questions provided to us on the worksheets. This was the very first time we learned/experienced an inquiry lesson. From here, we learned more about inquiry lessons throughout our required readings in the textbooks, the different articles we had to read, the activities we did in class and the Teaching Mathematics Through Inquiry (TMTI) assignment we have been working on with our partners for the last couple weeks. Apart from this, I found that when we watched our videos of our own inquiry lessons that we presented to the class and critiqued our lessons it helped me to get a deeper understanding of the significance of the project. After the lesson I thought it had went well apart from the fact that we thought we were out of time and didn’t get to end our lesson like we had originally planned. However, after watching the video of it, I started to pick out things that could have been done differently to improve the lesson even more. Not only did I notice things that could have been done differently in my lesson after watching it, but it also states the importance it is to do this in the article, *Understanding change through a high school mathematics teacher’s journey. *This article states, “Schön (1983) suggest that 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 reflection on their own theory and practice, learning from one problem to inform the next problem. Reflection enables practitioners to assess, understand, and learn through their experiences.” (p. 3) By doing this, this ensures that the future lessons you make on the same topic are that much better! From the article, we learn that inquiry is “learner-focused, question driven, investigation/research, communication, reflection, and collaboration.” (p.4) Through this article, we learn that inquiry lessons brought a different idea of what Brea’s role as a teacher really was. It talks about how she “transformed her classroom discourse by listening to students differently, as described in her story. She began to give voice to, or recognize the voice of, students, thus empowering them. She shifted her concern from being the expert voice to a concern for the authenticity of students’ voice. (p.11) From here we begin to understand that inquiry based teaching is all about student based learning and helping students connect with mathematics in a deeper way. This way students are not just memorizing concepts/ ideas and just regurgitating information on exams to do well in school. They actually start to understand the concepts and can transfer this new knowledge outside of the math classroom.

After reading this article, I still strongly believe that the way a teacher presents a lesson is based strongly on his or her own mathematical beliefs. These mathematical beliefs are strongly influenced by the different math experiences one encounters in their life. For example, you are going to teach lessons based on how you learned the different concepts and what you enjoyed about math in and through school. Teachers normally won’t attempt to teach a subject in a way that they could not learn the material themselves when they were the students. Usually whichever method gets your point across the quickest and in the simplest way is what we strive for. My beliefs about mathematics teaching and learning are still the same as I stated that, it is important to understand how to properly do mathematics and not just know how to come up with the final answer. However, I did state that “so in the end, how we decide to go about teaching the material is ultimately up us and what our mathematical beliefs are.” which I kind of disagree with after reading this article. To an extent yes, we will be teaching what we want and based on our mathematical beliefs but ultimately it is important to teach to the students and not what we believe. This is crucial as we are there to help the learning of our students and not preach what we believe and agree with in mathematics. It is important to keep in mind what our own thoughts are about mathematics but I think it is more important that we teach to ensure our students are learning and understanding the concepts regardless if how we have to teach the content is not how we perceive math to be taught/learned. So in the end, my beliefs on mathematics teaching and learning are generally the same after reading this article. However, there are some key points I would add into my original thoughts on mathematics teaching and learning.

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Mathematics “Creed” and Beliefs
*January 21, 2014*

*Posted by jennienorgaard in EMTH 350.*

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Mathematical beliefs to me are strongly influenced by everyone’s different math experiences, which in turn affect our teaching practices. The beliefs that a person has on mathematics will ultimately have an impact on how they teach the subject. The article *Why Teachers Matter* by Goos talks about how “mathematics is a tool for thinking with, a unique and concise language, a way of investigating patterns and relationships, a part of our everyday lives.” (p.13) This quote can relate with what I learned in EMTH 200 with Rick and the idea that Mathematics is the vehicle to develop the mind. The article states that “our task as mathematics teachers is to help students make sense of this world and their experiences in it, in ways that engage them with powerful mathematical ideas and leave them feeling confident about their ability to learn.” (p.13) Therefore, it is important to understand how to properly do mathematics and not just know how to come up with the final answer. From the textbook, *Raymond’s model of the relationships between teachers’ mathematical beliefs and their teaching practice* state that teacher education program, past school experiences, and early family experiences all indeed have an impact on our mathematical beliefs and teaching practices. So in the end, how we decide to go about teaching the material is ultimately up us and what our mathematical beliefs are.

I believe that in order to understand mathematics you need to know more than just simply being able to come up with the correct solutions to different problems. Mathematics involves understanding all the different concepts, knowing the importance of why you are doing a problem and being able to explain how you got to your solution. It is one thing to come up with an answer by using a formula and another thing to actually be able to explain the process and thinking involved with coming up with that answer. Essentially everyone can do mathematics if they know the different formulas that they can use and just plug in the numbers but it is another thing to understand how to actually do the problem. It is important to realize how to do something, recognize if the answer is reasonable and then being able to transfer this knowledge to real life situations. Being able to bring mathematics into real life perspectives makes it easier to understand, more enjoyable and easier to relate to different things/ideas. From this, I believe that mathematics is an important and essential aspect to our every day lives.

Since we see mathematics everywhere I think it is important that teachers are passionate and actually care about what they teach. This way the students they teach can learn to understand the importance behind mathematics. If teachers are not passionate about what they teach, then students will hate doing mathematics as well. Therefore, teachers need to set a good example for their students. In order to do this, I think it is essential to utilize all the different teaching strategies that are out there. I mean they are out there for a reason so why not take advantage of them especially since everyone learns differently in their own unique way. I believe that if we can show our students how important mathematics is not only in school but how it also relates to many things in life then maybe they will learn to appreciate it!

Like I have said before, mathematics is important to learn because it is involved in our every day lives. We need to understand mathematics in order to develop our mind. I think we need to learn how to teach mathematics at different levels starting with helping students understand how to improve their thinking. When students begin to develop their minds in an through mathematics they start to develop a deeper meaning for it. From these deeper meanings they can start to understand the importance behind math, learn how to do it properly, and not always rely on the different formulas there are out there to help them get the ‘correct answer’. What good is the correct answer if you don’t understand the importance of how you got there, the necessary steps needed to get there and if you don’t know how to explain how you got to the final answer?

Therefore, the five ‘creeds’ I have created for mathematics are:

1) I believe that in order to understand mathematics you need to know more than just simply being able to come up with the correct solutions to different problems.

2) I believe that mathematics is an important and essential aspect to our every day lives.

3) I believe that mathematics teachers should be passionate and actually care about what they teach.

4) I believe it is very beneficial to utilize all the different teaching strategies into all of our teachings.

5) I believe that if we can show our students how important mathematics is not only in school but how it also relates to many things in life then maybe they will learn to appreciate it!

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Mathematics Autobiography
*January 14, 2014*

*Posted by jennienorgaard in EMTH 350.*

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Throughout high school I had a really good mathematics experience. This is one of the main reasons I wanted to become an educator and more specifically a math major. Apart from this, I also enjoyed helping my classmates out in the different math classes we had to take in high school. I also enjoy dealing with numbers and the different challenges that come along with math.

Mathematics to me is more than just numbers and knowing how to apply different operations to these numbers. Mathematics is something that you need to know how to do for your every day life! I believe mathematics is an important subject to learn, as it is an important aspect to our daily lives. Mathematics is a great way to work on developing the mind of individuals. I believe that more people should learn how to do mental math instead of always relying on the different sources of technology that surrounds us, such as cell phones, tablets, calculators, or computers. That being said, I also think that technology could have a huge impact on helping people understand and develop a better sense of mathematics. This could be done as long as everyone utilizes the technology that we have instead of always abusing it. It isn’t essential to take out a calculator right away when you are given a simple math problem to solve. I believe that it is more important to take a couple minutes and actually think about the problem we are given instead of referring straight to our different sources of technology. I think it is important to be able to teach mathematics in a variety of different ways instead of the traditional teacher lecturing students. I believe it is important to incorporate the three different learning styles as well as making learning as authentic as possible. I solely believe that if you can bring real life situations and problems into mathematics, your students will be more interested in the topic, more engaged in your lessons, and will be able to understand mathematics at a different level when they can relate it to real life.