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Learning Journey Week #3
*January 30, 2014*

*Posted by jennienorgaard in Learning Journey.*

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In this class we talk about assessment and how it is continual feedback that teachers provide their students with that inform them how well they are doing. However, from this I am struggling to understand different ways in which we can assess our students in a math classroom apart from the traditional homework checks, quizzes, exams, and projects. To an extent, I believe that this isn’t a fair way in assessing our students at all because not all students are good at writing exams; there should be more appropriate ways in which students can express their knowledge and what they have learned in the class than through exams. It is one thing to be able to memorize the process/steps in how to do different problems as opposed to actually understanding how to do it on your own. In this class, we also emphasize the importance it is to have an ongoing assessment instead of a one-shot assessment at the end of each unit through exams.

From my EMTH 200 class, Rick always emphasized the importance it was to teach to the bottom 2/3 of the class and monitor/look after the top 1/3 of the class. This is important because we want to ensure that all of our students understand the knowledge they need in the appropriate grade level they are in so that they don’t just get pushed through the system in the end. In saying this, it is also important to make sure to give the top 1/3 of your class material that they can work on that both challenges them and increases what they already know so that the class isn’t a waste to them. This goes along with the quote we were given in ECS 410, “When a teacher tries to teach something to the entire class at the same time, chances are, one-third of the kids already know it; one-third will get it and the remaining third won’t. So, two-thirds of the children are wasting their time.” -Lillian Katz. So from this we can see how important it is to know where each and every one of our students are at when it comes to learning so that we can make our lessons based on all our students and not just the majority of them.

In this class, we talk about the importance of ongoing assessment and providing our students with feedback to help them understand what they are doing well and what areas need improvement. So my concern to this is how does this happen in a math class if the only forms of assessments are through homework checks, quizzes, exams and the occasional project?

Apart from doing ongoing assessment, we also learned the difference between formative and summative assessment throughout this class. **Formative assessment **aims to discover *what* the learner knows, understands or can do with intent to inform our teaching or learning as a result. **Summative assessment **aims to discover *if* the learner knows, understands, or can do a predetermined thing.

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Chapter Six – Involving Students in Classroom Assessment
*January 30, 2014*

*Posted by jennienorgaard in ECS 410.*

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This chapter talks about involving your students when it comes to assessment. Not only does this engage the students more in their own learning but they also start to understand what is important while they learn. Six key strategies where learning is the main focus include: involve students in setting and using criteria, engage students in self-assessment, increase the sources of specific, descriptive feedback, assist students to set goals, have students collect evidence of learning in relation to standards, and have students present evidence of learning in relation to standards.

When I think of assessment in the math classroom, I believe it can guide instruction in the sense that it allows the teacher to understand what their students are struggling with, what needs to be reviewed, what needs to be talked about more, how to change your teaching style to aid more students, what needs to be done differently and what works well. When a teacher incorporates different assessment strategies and different teaching styles in the classroom their students are more likely to be engaged and learn more. I think that allowing the students to decide as a class how the grades should be distributed can lead to a better learning environment. For example, if your students are not the greatest at writing exams then they can make exams worth less of their final grade, as this would be an insufficient way of assessing them on what they have learned.

However, I haven’t really come up with different ways in which we can assess students in math classes apart from quizzes, homework checks, test/exams and projects. At this point, the only other assessment styles I can think of in a math classroom apart from the typical paper and pen/pencil style would be to have a conversation with your students. From the reading, engaging students in self-assessment would be a process in which could help the students understand what is expected to be learned. For example, providing the students with acronyms such as SUNA could lead the students in the right direction of what is expected from them. This process allows students time to absorb what was being taught and learn the proper material. Students will learn more based on the different kinds of feedback they get, so it is essential for students to get feedback from both their peers and teachers. Another way of involving your students in classroom assessment would be to increase the sources of specific and descriptive feedback. The more feedback we provide for our students the more they can learn from their mistakes. They can then see what they are doing well and what they need to improve on. Also, assisting students to set goals would be another form of classroom assessment that your students could be involved in. So, the students identify what they would like to be able to achieve by the end of the semester and work towards achieving these goals throughout the semester. From here, students can identify what they are struggling with and what they are learning. These are some ideas in which we can involve our students in classroom assessment, but I still have a difficult time understanding how we can assess our students in a math classroom apart from the traditional paper and pen style.

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Chapter Five – Evidence of Learning
*January 30, 2014*

*Posted by jennienorgaard in ECS 410.*

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This chapter talks about the different kinds of evidence teachers can collect that provide them with an understanding of what their students are actually learning. The learning outcomes may be the same in the end, but different teachers will collect different kinds of evidence. These forms of evidence vary from teacher to teacher but also from student to student as each student learns in different ways, at different times and provide different ways of representing their learning. This chapter talks about the “three general sources of assessment evidence gathered in classrooms: *observation* of learning, *products *students create, and *conversations *with students about learning. It is important to allow your students to explain their learning journey and essential to give your students the appropriate feedback as teachers to let the students know how they are doing well and what areas need improvement.

I believe that providing students with evidence of their own learning is important so that students can build on from there, know what to do differently next time, and can see what they are doing correctly. As teachers, it is also important to allow students to provide their learning in whatever style/way they want. This is important because everyone learns differently and it is essential to provide every student with the same chance to represent their learning in whatever way they are most confident and comfortable with. We are limiting our students from expressing everything they have actually learned when we don’t allow them the opportunity to represent their own learning in whatever way best suits them. This way it also allows teachers to provide the best and most effective feedback to the students when they are given the opportunity to express their learning in their own way.

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OCRE
*January 26, 2014*

*Posted by jennienorgaard in Learning Journey.*

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On January 23rd and 24th I took part in an On Campus Research Experience with my fellow math majors. Due to OCRE I had to miss a presentation for ECS 410 that I believe would have been pretty helpful to take part in. However, during OCRE I took part in a variety of activities with all the math majors and we brought in five different guest speakers that were very helpful. The guest speakers included: a high school principal, a first year math teacher, a first year teacher teaching abroad in England, an aboriginal math professor and three city police officers. From these presentations I took in a lot of information that will be very beneficial for my journey to becoming a teacher and for the hiring process in the years to come. All of these speakers had interesting presentations that provided us with different information that will be useful for us and allow us to grow and become better as teachers. Along with all the guest speakers and professional development that occurred during these two days, the bonding our group of math majors did brought us closer together as a group.

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Chapter Four – Describing Success
*January 23, 2014*

*Posted by jennienorgaard in ECS 410.*

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In chapter four, it talks about the different ways in which success can be looked at. It talks about the idea that if teachers are not clear with what reaching success is suppose to look like for their students, how will they ever know/determine when their students have been successful? It emphasizes the importance it is for teachers to provide their students with a variety of different learning examples so their students can meet and strive for these standards. Students always ask questions like; “what do you expect to be done”, “is this good enough”, or “what does excellence look like?” These are all questions that relate to standards and learning outcomes. As teachers, I think it is extremely important to provide your students with a variety of samples demonstrating the criteria that is needed and expected for each assignment. If the criteria aren’t clearly set out for our students we are not allowing them the potential to achieve success. It is important to have a clear criteria set forth for the students so they can demonstrate their learning to their full potential, and samples are also a great way to give the students ideas of what is expected from them. This chapter deals mainly with different samples in which you can use in your classroom, which are most effective in different situations, how to use them and how they can help your students. I think that providing your students with these samples is one of the best ways to explain how you want things to be done. It is also a great source of feedback for your students and it helps the students understand how they can improve from these different samples that are provided for them. By providing these examples, it allows your students to demonstrate/represent their learning in ways they feel more confident and comfortable with. This way students don’t feel obligated to do an assignment in a certain way if they learn better or can demonstrate their learning more effectively in a different way. This way it doesn’t limit the ability to demonstrate what they know.

From the hiking boots in this chapter, it asks us to collect a range of samples and analyze them to help our students recognize the importance of them and what to focus more on. I believe that providing students with different samples of work is one of the best ways to help them identify what is expected for the assignment. From these samples, the students can get a better understanding of what is expected for the assignment, get an idea of how long the assignment should be and get an idea of different topics/ideas they can do their assignment on. From this, the students can then identify if their thinking process is along the same lines, if they need to change what they were going to do or if they should take a totally different approach to the assignment than what they had originally had in mind. Apart from providing students with different samples of assignments I think it is key to include the feedback from these samples as well. This way students get a better understanding of not only what is expected but they also get an idea of how they can improve from these samples. This is a great way of providing a risk free environment in your classrooms! This way we are not providing barriers for our students and their learning abilities. Instead, we are guiding them in the correct direction to help them succeed in their learning.

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Chapter Three – Beginning with the End in Mind
*January 23, 2014*

*Posted by jennienorgaard in ECS 410.*

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This chapter talks about how the first question a teacher needs to be able to answer is: What do I want my students to learn? It states, “When teachers and students know where they are going, they are more likely to achieve success.” (p.25) This chapter emphasizes the importance it is for teachers to be able to use a variety of differentiated teaching strategies. Along with being able to use different teaching methods we also have to have different forms of assessment since every student learns in a different way and at their own pace. The main focus of this chapter is on how can we develop a clear description of our learning destination that we want to be able to achieve. It emphasizes the importance it is to ensure that students know what they will be learning, what learning can look like and what the goals the teachers want the students to be able to accomplish in the end (begin with the end in mind).

There will be a wide range of different learning levels in our classrooms, along with cultural backgrounds that teachers need to document throughout the year in order to give every student the same potential to succeed. It is important to establish these things in the beginning of the year so teachers know how they should be teaching, where all their students learning levels are at, and what instructional methods they need to incorporate in their classroom. Two challenges come along with being able to teach your students in a variety of different ways. The first challenge is being able to have a deep understanding of one subject area, in order to provide different instructional methods and in order to help your students learn the material. The second challenge is being able to teach small groups of students within the classroom as opposed to teaching the class as one large group. I believe that being able to teach small groups in the classroom will be more effective than trying to teach a large group all at once. This way **all** the different learning needs can be met instead of the majority of them, you get to know your students at a better level and your students will be achieving more success when given different opportunities to learn. By teaching students in smaller groups, you will be able to have a discussion with more of your students, and be able to get your point across about what you intend your students to learn and how you are going to assess your students on these things.

I think it is important to keep in mind the quote from the textbook, in order to get a better understanding of beginning with the end in mind. This quote is, “If you don’t know where you are going, every road will get you nowhere.” -Henry Kissinger (p.31)

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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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Assessment Vs Evaluation – Week #1
*January 16, 2014*

*Posted by jennienorgaard in Learning Journey.*

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After the first week of ECS 410 I have gained a better understanding of the difference between assessment and evaluation. Prior to this class, I had always thought these two things were the same. I thought that assessment and evaluation were just the “terms” used for how teachers gave you a certain grade/mark for each class. Instead, assessment is the feedback/comments in which you get for your work on how you did while evaluation is the grade/mark you get for your work.

After reading chapter two, I also learned that there are two different kinds of feedback that we can provide our students with. The first one being **descriptive feedback**, which “gives the learner information about their learning that helps them self-reference and plan their next steps.” This type of feedback usually: “comes during or after the learning, is easily understood and relates directly to the learning, is specific to help students improve, is an ongoing process/conversation about the students learning, and it deals with the performance of the work and not the person writing it. (p.17) The second type of feedback is **evaluative feedback**, which “tells the learner how he or she has performed compared to others (norm-referenced assessment) or as compared to what was to be learned (criterion-referenced assessment). (p. 17) Evaluative feedback is usually expressed by grades, numbers, checks, or other symbols. This type of feedback informs the students of what they understand and what they need to improve on, but it doesn’t tell the student **how** they can improve.

I think this is a topic that needs to be discussed more in other Education classes since clearly, there is a significant difference between assessment and evaluation. And if it weren’t for this class, I probably still would have thought these two things were the same.

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Chapter Two – Building the Foundation for Classroom Assessment
*January 15, 2014*

*Posted by jennienorgaard in ECS 410.*

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This chapter talks about the idea that you have to build relationships with your students first and foremost, and then you can start to establish what the classroom agreements should be for how everyone will work and learn together. This all starts by providing your students with a safe school environment in which they can learn. When this safe school environment is made, students are then more likely to take the risks needed in order to benefit their own learning. Assessment for learning happens when “everyone knows that mistakes are essential for learning, understands feedback, takes time to learn, and recognizes that success has many different looks.” (pg.15)

This chapter distinguishes the different between descriptive feedback, which tells students about their learning and evaluative feedback, which tells the learner how she or he has performed as compared to others or as compared to what was to be learned. (pg.17) I learned from this chapter that the best feedback of the two is clearly descriptive feedback. The chapter emphasizes the importance it is to get your community involved with your students learning. Students are going to learn more if we as future teachers take the time to get to know these students more through their parents and guardians. Getting the parents and guardians to be involved in their child’s learning is also very beneficial to providing the child with the best learning experience possible for them.

The information provided in this chapter is very useful to help out our students in their learning journey. If we provide our students with very thorough and descriptive feedback for their assignments they will understand what they need to do differently next time and learn from these mistakes. However, if we were just to give our students evaluative feedback this wouldn’t benefit their learning in any way. In fact it might affect their learning in the sense that the do not like the mark they got on an assignment and don’t know what they did wrong or was lacking in it. Without the descriptive feedback the students don’t know what the expectations are of the teachers for their next assignments and will not know how to learn from their previous mistakes. Therefore, it is really key to ensure that as teachers we provide as much feedback and comments as possible to our students when marking and evaluating them on assignments. The students need to know what they did well and what they need to improve on so they can change for future assignments. If students don’t know what the mistakes are that they made how will they ever be able to improve? Therefore, the feedback in which we choose to provide our students with has a huge impact on how we will be judged as teachers. If we provided the feedback needed to help students improve from their mistakes they are more likely to enjoy what they are learning and be more interested in broadening their learning from this success.

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Chapter One – Making Classroom Assessment Work
*January 15, 2014*

*Posted by jennienorgaard in ECS 410.*

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In the beginning of Chapter 1, it begins by describing the difference between what assessment is and what evaluation is. It goes on to say that, assessment is “gathering information about student learning that informs our teaching and helps students learn more” while evaluation is when “we decide whether or not students have learned what they needed to learn and how well they have learned it.” (p.1) After this explanation, Anne Davies, proceeds with giving us an example of a research paper that the students have a week to complete. She then goes on explaining in detail different ways/steps in which this paper can be assessed and how we can go about evaluating from there. This chapter also emphasizes the importance it is to get your students involved in the creating of the criteria for which they will be evaluated on.

In my EMTH 350 class we have been talking about different instructional practices such as the student-centered group and the teacher-centered group. I can say I have a pretty clear understanding of what the teacher-centered group is since that is how most of us have been taught. However, I cannot say that I have ever experienced or encountered a student-centered teaching approach myself. So I wouldn’t really know how to go about dealing with this kind of a teaching approach. After reading this chapter, it has gave me a better understanding of how to go about dealing with a student-centered teaching approach. This chapter talks about the fact that “when the students are involved from the beginning, they are more ready to learn.” (p.5) I think this is important as the students need to know from the beginning what is expected from them so they can achieve their full potential and learn everything they need to know in order to be successful. I also like the fact of how it talks about including your students in the process of making the criteria for the class so that students are maximizing their learning more than if the teacher just created the criteria themselves. This not only enhances the students learning but it also gets the students involved with what they are interested in learning as well. Another important aspect that is talked about in this chapter is how we as future teachers need to take advantage of peer assessment and self-assessment as much possible. It is important for teachers to assess students but it is also important for peers to assess one another. It is beneficial to gain different perspectives from each other. The teacher ultimately does not hold the golden key to learning. We all do!

Some thoughts I have now after reading this chapter are will student-centered teaching be very beneficial in the future? I think a student-centered teaching approach is a great way to help your students get more involved in their learning. This way you also have an idea of what it is your students want to learn and be evaluated on. But at the same time how will you be able to monitor every student’s needs/learning abilities and evaluate every student equally when all your students are at a different learning level? How beneficial is a student-centered learning approach then if 100% of your students are not benefitted from this approach? Then my final question is how do I go about teaching and evaluating students in the best possible way that benefits all students equally?