Emily Columpsi

"The art of teaching is the art of assisting discovery" -Mark Van Doren

Archive for the category “EMTH 350-2014”

Entry #7: Final Post

1. a) My favorite blog post was definitely entry number four, which was entirely about assessment in mathematics. For this blog entry we had to research a particular method of assessment, that was assigned to us by our professor, and then present our findings to the class. I rather enjoyed the presentations as we got the opportunity to learn about a wide range of assessment that we could potentially apply to our teaching one day. This blog post was very realistic and useful; therefore, aiding me in my pre-internship.

b) Looking back on all my blog posts, I can’t actually say, or choose one, that I would like do to over again. I mean when I wrote each response I felt like I answered the questions to the best of my knowledge and ability. If I was to write one over again, I know for a fact that my responses would not change significantly, or at all.

c)  I learnt the most about myself as a learner and a teacher when writing entries six a) and b). Both of these blog entries really made me think on what I have learnt, not only this semester, but in the past three years. In addition, my responses made me realize how much my professors, University classes, and fellow colleagues have helped me to become a teacher. Entry six a) was written prior to pre-internship and entry six b) was written after. As I reflect back on both of these responses I have a better understanding now of who I am as a future teacher, including what my expectations are and pedagogy. These of course will continue to evolve as I go through my internship, but they have started me on the path towards learning more about who I potentially want to be within the classroom.

2.  The blog entry that I would have liked to write is the following:

What other ways can you engage the students in your classroom besides inquiry?

I have found that learning is optimized when students are actively engaged in the learning. That being said, lectures can only engage students so much that teachers must find alternative ways to captivate the interest of students. For instance, teachers can encourage discussion by providing positive reinforcement to all the students that happen to participate in the discussion. These discussions can then turn into debates or think/pair/shares where all the students ideas and viewpoints are being acknowledged. Students become more involved and engaged when they are given the opportunity to comment on the ideas of others, whether adding additional information or correcting the initial response. Furthermore, when a lecture is taking place many students will zone out. Thus, breaking up the lecture into pieces by allowing three-five minutes of personal discussion between students will get students back on track and re focus them. I think that it is important to interact with not only ones peers but also the material in order to retain the information and become engaged in the learning.

Group activities can be seen as one of the best ways to involve students in the learning. In addition, when students are given the opportunity the create the assessment piece alongside the teacher, the more likely they will put effort into what they are doing as they know the expectations and the goals they have to reach. As well, teachers can make the project relatable to the students lives, resulting in more engagement and commitment to the overall project. However, when group work is being facilitated is it important that all members of the group are equally involved; thus, it is important to make sure that each member of the group has a role to play.

Another possible way to engage students is to spend a couple minutes at the beginning of class with a discussion about what is going on in their lives. For instance, a teacher could ask, “do you have any interesting news to share with the class today?” or “Anything exciting happen to you since last class?” Such questions allow the teacher to get to know the students on a more personal level, and the teacher can then become aware of problems that some students may be facing. As well, the atmosphere in the classroom becomes more relaxed and personal, which can be motivating for some students and get them engaged.

In general, content needs to be relatable to students; otherwise their engagement level will be low. Thus, letting students have some input into the assessment pieces or projects will boost their motivation and get them more involved in what they are doing. I find that all the above has the potential to engage students, that is if it is presented in a honest and interesting manner. Inquiry is not going to work all the time; thus, we need to be open to other ideas.

3. One area that I would have liked to focus more on in this course is Treaty Education. Everything that we do now has to in some way incorporate Treaty Education, and being a mathematics major I am still struggling to find ways to incorporate these topics into my teaching. It seems next to impossible, as everyone that I have talked to struggles themselves, resulting in them not willing to teach it.  That being said, some instruction on Treaty Education would have been, in my opinion, beneficial.

Another area that I would have liked to focus more on in this course is topics other than inquiry. This whole semester has been about this one approach to teaching. Well what if inquiry does not necessarily work for your students; other methods would, therefore, have to be incorporated. Thus, learning other engaging methods would have been nice.

4. The way teachers talk to their students, the manner in which they interact is crucial to both successful learning and teaching. Perhaps the most important point that determines how successfully students will learn is the way instructions/directions are formulated. As a result, one of my internship goals for the fall is to work on my directions, such that they are clear, precise and effective. When I am planning and/or carrying out a lesson I think it is important to  ask myself: are my instructions clear? Do they include information that is needed? Do I give verbal and written directions? Which information do the students need first? What must students know in order to complete the task successfully? I have come to the conclusion that in order for directions to be effective they must be kept as simple as possible and they must be logical: I need to avoid wordiness. However, body language counts as well; therefore, being aware of my gestures and posture is highly important. Lastly, to strengthen this professional goal, I can check for understanding by asking questions related to the instructions.

Questions play a central role in the overall learning process. Thus, my second internship goal for the fall is to improve my questioning skills and to have a more central focus on essential questions. When I am planning my lessons my goal is to come up with a variety of questions that not only guide students towards further investigation, but also allow for a deeper understanding of the concepts being stressed. That being said, I have to ask myself: Do I ask challenging questions during my lesson? Do I vary the level of the questions I ask? Are they thought provoking, clear, brief, open and purposeful? Do I allow time for thought? In addition, I desire to avoid yes or no (closed) questions. During my internship I want to encourage the students as much as possible. Thus, I hope to encourage the students to comment on the answers of their peers to keep the conversation and learning going.

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Entry #6B – Professional Development Journal Response

i) Now that my three-week block is complete I can reflect back on my initial responses to the three big questions that were asked in blog entry #6A. As I read through my responses to the first two questions most of what I said initially has not changed. Field experiences most definitely play a role in preparing education students to become teachers. Pre-internship provided direct experiences that helped to increase my confidence, teaching strategies, and classroom management.  Without these field experiences, I would struggle to apply the skills necessary for facilitating learning. In addition, what I said concerning University Teacher Education Programs has also not changed. The emphasis continues to be on methods and pedagogy, giving pre-service teachers the opportunity to learn, study and familiarize themselves with the educational necessities such as the curriculum and professional rights and responsibilities of teachers. I stated it in my last response and I will repeat it here. Lectures only do and provide so much for pre-service teachers. The real learning is when we are out in the field.

As I read my response to the third question, I realize that most of what I said initially has not changed; however, if I was to respond to the question again now, being that my pre-internship is over, my response would change slightly. First off, having been in front of the classroom for three weeks, I realized that the most effective form of instruction is a combination of both teacher and student centred instruction (not one or the other). My students outwardly expressed that they learn best when we go through the notes together as a class (teacher centred). To get some of the students involved, I would constantly ask essential questions to heighten the learning; however, there was many instances where my students would volunteer themselves to come up to the board to teach a particular question or concept (student centred). Furthermore, I did have a conversation with some students on inquiry based learning, and they all expressed to me that they would “absolutely hate it” as most of them would have no idea where to start, let alone do the activities. That being said, I now find that teacher centred instruction mixed with student centred instruction is in some ways the most beneficial for both parties. It is what everyone is comfortable with. Another idea that has somewhat changed for me after pre-internship concerns memorization. Yes, instruction should partly no longer be about memorization, but knowing the steps and what to do within a particular question is sometimes the most effective for students. Throughout these three weeks I have fortunately established positive teacher-student relationships with my students. That being said, I would ask them questions about their learning of mathematics, and most if not all of my students expressed that they need the steps to help them with the questions. They fully understand the concepts, but if they didn’t know the steps beforehand they would be completely lost. So should math  no longer be about steps? I don’t exactly know anymore. Before pre-internship I would have said no, but now I am not so sure as students seem to succeed more when the teacher goes through the steps with them, providing them with the opportunity to of course practice.

On the plus side, much of what I said prior to pre-internship has further developed. For instance, I strongly believe now that math is a fundamental area of study that can be applied to any field. Many of my students have told me that they want to go on to be pharmacists, doctors, carpenters, and/or physio/massage therapists, and they are all completely aware that they need math to help them get there. In addition, prior to pre-internship I stated that presenting content with integrity and honesty holds value, as the course content then becomes more relevant and useful not only for the present but for the students future lives. This idea has definitely developed further as I know see the connection between positivity, authenticity, and mathematics. The more authentic and interesting the instruction, the more likely that students are going to remember the content.

ii) This quote raises some very interesting points, most of which I have either seen or experienced while in teacher education. First off, Freese states that pre-service teachers are “students at the same time that they are learning to be teachers” (2006). Being a pre-service teacher myself, I can verify that this is a difficult position to be put in. While we are in out in the field, we must always remember to be in the mindset of a professional teacher. This is difficult to say the least, as when we are placed back into our regular education classes at the University, we must return to the student mindset, focusing on grades and discerning applicable information.

Freese also declares that pre-service teachers need to “assume personal responsibility for their actions and performance and not blame the students or others for their problems” (2006).  For me, this was partly obvious. I mean as teachers we should know not to blame others, such as students, parents or colleagues, for our problems. As professionals and adults, we are expected to take responsibility for our own actions. However, this statement can be partly problematic as well. If students are not working, being uncooperative and unwilling to learn, then some of the blame can be put on the students. As Freese said, learners must be willing to learn (2006).

Lastly, Freese declares that pre-service teachers must be open to learning and seeing multiple perspectives. This statement has the potential to be challenging as many pre-service teachers do not have a general teaching perspective to start from, such as myself. Throughout my teacher education, I have definitely seen multiple perspectives and ways of teaching, as exemplified from my own professors. However, to be honest, I was not as open to these perspectives simply because I did not know what to expect from them if and when they are applied to the real world and I was resistance to change. I like routine, thus,  I need to be comfortable with one way of doing something or anything for a long time before taking up or adopting a new one. Nevertheless, being open to new ideas and perspectives of teaching is a way to correct, or in some instances improve, the problems in your current teaching practice. That being said, all teachers need to be open to change.

 

Entry #6A -Field Experience and The Role of Teacher Education

In my opinion, field experiences (ex. pre-internship, internship, practicums etc.) play a major role in preparing education students to become teachers. “The primary purpose…is to help students learn how to apply theory and principles to work situations and to develop and expand professional skills and competencies essential to these tasks” (UofM). In addition, it provides, first hand, direct experiences that help to increase the understanding of the learning process. From personal experience, motivation, confidence, classroom management, and teaching strategies are the main focus areas of field experiences. It is through the field experience in the schools that allows pre-service teachers to see the meaningful development and merging of theory and practice. Without field experiences, pre-service teachers would struggle to apply the skills necessary for facilitating learning.

University Teacher Education Programs provide students with the professional education necessary to become certified teachers. Teacher education programs place emphasis on methods, standards and pedagogy; providing pre-service teachers with the opportunity to study, learn and familiarize oneself with the curriculum, student development, pedagogy, lesson planning, and the professional rights and responsibilities of teachers. However, lectures can only do and provide so much for pre-service teachers. Education students need to go out in the field and experience the realities of schools, classrooms, and students themselves. I personally find that I learn more by doing. 

Through my years as an education student I have come to believe that math is a fundamental area of study. Thus, what I already know now about being a mathematics teacher is unlikely to change through my field experience. In some of my previous posts I state how math is an important area of study because it has the potential to provide students with several fundamental or transferrable skills. Thus, it is important that I believe in what I am doing, not only seeing math as important but relevant. Presenting content with integrity and honesty holds value to me, as the course content becomes more relevant and useful not only for the present but for the students future lives. This belief is unlikely to change because it is an opinion that I have carried with me since I entered university, as I witnessed first hand the importance of relevant communication. Thus, I hope to apply this in my field experience.  In addition, I hold the belief that math should no longer be about steps and memorization, but rather it should be about and geared towards student-centered instruction and inquiry. This fundamental belief arose while I was in university and will unlikely change in my field experience. I am committed to the students. Thus, interacting with them in a positive and encouraging manner holds value. In addition, I am committed to relaying the content in an interesting manner, that is geared more towards direct application and student involvement.  

Entry #5 -Letter To A Friend

Dear Friend,

Recently, I viewed two short films both of which discussed assessment in high school mathematics classrooms. Both were very informative, to say the least. Therefore, I would like to share with you a short synopsis of each, highlighting what I learnt, its relevance, and why I think you should take some time to view these videos for yourself.

Within the first video, Teacher Insights (9-12), seven high school mathematics teachers discussed their methods for assessing student learning. Although all the approaches varied, the teachers were consistent. Some teachers focused on peer-assessment, group-assessment and self-assessment, while others were more directly involved in student interviews, the creation of portfolios or group tests. Within each assessment practice the students were able to think critically and personally reflect, which enabled higher levels of comprehension and understanding as they were steered away from mimicry and memorization. As a result, I noticed that many of the students exuded confidence in their abilities to answer questions or to present in front of their peers (as was shown in the presentations within the video).

The video pointed out that  “in high schools today we are in a midst of a dramatic change in our approach to teaching mathematics. [Therefore], we are asking our students to go beyond mimicry and memorization, to investigate complex problems, communicate ideas and to become critical thinkers. With these rising expectations there has been a growing awareness that the way we approach evaluation must also evolve.” As a result, instead of summative assessment tasks (tests or unit exams), which most students in high school mathematics are used to, teachers must also incorporate formative assessment or ongoing assessment tasks to better understand and more accurately assess student progession. Do you remember in high school mathematics when all we did was test after test after test? There was no projects, major assignments, or homework checks, and as a result our teacher had no indication of where the students were at with their learning. In contrast, within the video the students were carrying out a variety of tasks such as, presentations, group tests/assignments, and projects, which, after assessment, directed future instruction and learning since the teacher had a grasp of where each student was at with their learning. As a result, the students were able to feel more comfortable with the material that they were learning. If our mathematics teacher focused more on formative assessment tasks I wonder how that would have changed the dynamic, atmosphere and learning in our mathematics classroom.

I strongly suggest that you watch this video because no matter what your profession is you are going to have to assess either someone or something in one way or another. Yes, high schools are in a midst of a dramatic change, but so is our society. Therefore, no longer can we cling to outdated beliefs on assessment practices, school related or not. The ways in which we approach evaluation must also evolve in order to keep up with the ever changing society in which we live. I believe that you would get a lot out of this video. If you get the chance have a look at the video through this link and let me know what you think!

The second video, Case Study: Group Test, discussed the effectiveness of group tests. The premise behind group tests is to assess students mathematical knowledge while they are working together with their classmates. Group tests allow for discussion to deepen and further the learning process. In addition, it is important to note that everyone in the group is collectively responsible for the overall grade they receive. When we were in high school our teachers solely stuck to individual tests and assignments. Could you imagine completing a group test?  I personally believe that a group test would not have benefited me at all because I would be relying on others to give me the answers. Furthermore, due to the fact that the group is handing in one collective response, the teacher will have difficulty in determining which students are struggling with the material. What do you think?  Assessment is a instrument to communicate to the students what they are learning, but if students are asked to verbally share answers, is this type of assessment accurate?

While watching the video I noticed that the teacher was able to circulate the room in a more efficient manner. In addition, he could ask his students harder questions that he couldn’t ask them individually; thus, the students were able to bounce ideas off of one another to come to conclusions. One problem with group tests is that the teacher can explicitly give the answers to the students through the discussion; therefore, it is important that the teacher encourages the students to check their answers or ask them questions which can imply hints (scaffolding). In the end, when group tests are implemented the students have to function well together in order to learn the mathematics; they need to communicate.

If you have the time I suggest you watch this video. It demonstrated the effectiveness of communication and group work: qualities that are useful in all professions.

You can easily access both videos through the links that I provided. I am curious to know your thoughts and if you would ever consider using any of the mentioned assessment items in your profession. Hope all is well.

Emily.

Entry #4: Assessment

My assessment experiences in high school mathematics were frequently revolved around summative assessment tasks. In other words, my teachers would evaluate or ‘sum up’ the learning by distributing exams at the end of an instructional unit. Furthermore, final exams were held at the end of each semester to evaluate overall student learning. Occasionally, my mathematics teachers would hand out quizzes, ask questions, or conduct homework checks to monitor student learning. This type of assessment, often known as formative assessment, was minimally present in my high school mathematics classes. Throughout high school, I viewed unit and final exams (summative assessments) as having high point value. In other words, they were weighted more heavily than my homework and quizzes (formative assessments), which I viewed as having low or no point value. Thus, I can conclude that my high school mathematics teachers believed that unit exams or final exams were the most important part of a student’s overall grade. As a result, I worked harder and cared more about the exams than I did the quizzes.

The assessment strategies that I researched were rating scales and rubrics.

A rating scale is a tool used for assessing the performance of tasks, skill levels, procedures, processes, qualities, quantities or end products. They are similar to checklists except that they indicate the degree of accomplishment rather than just a simple yes or no. Rating scales are set up in such a way that they list performance statements in one column and the range of accomplishment in descriptive words (strongly agree, agree, disagree, strongly disagree), with or without numbers, in the other columns. In a rating scale, the descriptive words are more important than the numbers. Rating scales have many advantages. For instance, they are quick and easy to complete or fill out, they are easy to design, they can describe the student’s steps towards understanding or mastery, students can pinpoint specific strengths and needs, and, lastly, rating scales give students information for setting goals and improving performance. However, rating scales also have disadvantages. For example, rating scales can be highly subjective. In other words, teacher bias gives better marks to favourite students. In addition, if a rating scale was given as a self-assessment, students may mark themselves higher to receive a better mark from the teacher. Another disadvantage is that rating scales can be seen as unreliable. For instance, interpretations of terms may vary. Also, a single word doesn’t contain enough information on what criteria is indicated at each of the points on the scale. Rating scales should be used for recording informal observations of student learning, such as discussions, participation, behaviour etc. Furthermore, rating scales are effective for peer-assessments and group mathematics projects, but they should not be used to grade exams. Lastly, rating scales should not be used for comparisons amongst students.

Rubrics “are tools for rating the quality of student performance that identify the anticipated evidence that will be used for making judgments” (Goos). They consist of a fixed measurement scale and detailed description of the characteristics for each level of performance (distinguishes performance from one level to the next). Rubrics focus on quality rather than quantity and they function as a guideline for both teachers and students. Rubrics are commonly used with the intention of including the result in a grade for reporting purposes. The advantages of rubrics are the following: they provide guidelines for quality student work or performance, they are flexible in that they can be designed for many uses and/or ability levels, they can be easily modified, can increase the consistency and reliability of scoring, provide a way to both effectively assess student learning and communicate expectations directly, clearly and concisely to students (feedback is present), they allow students to see the progression of mastery in the development of understanding and skills, teachers can even involve students in the assessment process which allows them to know and see the expectations, and, lastly, rubrics allow for student and teacher reflection (guide for future learning or instruction). However, rubrics also have a few disadvantages. For instance, teachers might use predetermined criteria, rather than basing scores on examples of student’s work. Rubrics can be used for individual or group projects. Furthermore, self-assessment, peer-assessment and teacher reflection can be graded through a rubric. It is important that teachers hand out the rubric before the students get to work so that they can see what is expected of them. Teachers can even send a rubric home so that parents are aware of the expectations and assist students with their homework. Rubrics should not be used all the time. Although, rubrics are easy to fill out, it is important to change up the method of assessment. Lastly, rubrics should not be used to grade mathematics tests, quizzes or exams.

The activity conducted in EMTH 350 allowed me to learn about other forms of assessment.

Courtney discussed self-assessment strategies. Self-assessments are used so that students have the opportunity to reflect on their own work/learning. In addition, through this process students can confirm, consolidate and integrate new knowledge. Courtney stated that some self-assessments are used for grades, while others are used by the teacher to see where the student is at. While conversing with Courtney, I learnt that there are just as many disadvantages to self-assessments as there are advantages. The disadvantages are the following: if teachers do not model it correctly then students won’t understand its potential, some students may mark themselves higher to improve their grade thinking the teacher isn’t marking herself, some students will feel ill equipped to undertake the assessment, and additional briefing time can increase a teacher’s workload. The advantages are the following: student’s can monitor their own learning, encourages both student involvement and responsibility, allows students to reflect and enables them to look over the criteria again to see where they can improve, teachers see where the student is at and can offer extra help/assistance, and they focus on the development of student judgment skills. Teachers should use self-assessments alongside their own evaluations. Furthermore, self-assessments are beneficial for addressing and evening achieving personal goals. Teachers should not use self-assessments if there is no clear goal or criteria, as students might get confused on what they are assessing themselves on.

Hillary discussed exit slips. Exit slips, typically, are a written response to one or more questions that the teachers will pose at the end of a class. The questions usually address the material or concepts that were just learnt as a way to summarize the learning of that particular subject. Exit slips can take many forms. For instance, they can be completed orally, pictorially or in a written format. This range allows for students to respond in whatever way they are comfortable with. Some advantages of exit slips are: allows the teachers to see where the students are at with the material and if concepts need to be addressed again the following day, enables teachers to make the appropriate adjustments to the lesson to further students learning and comprehension of subject matter, teachers can self evaluate to see where they need to change their teaching style to better fit their students needs, and, lastly, exit slips allow for students to reflect on what they just learnt. The disadvantages of exit slips are that they are usually brief (not enough information is provided), some students may not take it seriously as there are no marks attached to the exit slips, and some students may respond to the exit slips anonymously, which poses a problem as the teacher wouldn’t be able to identify the students that are struggling and thus wouldn’t be able to help them. Exit slips should be used, obviously, at the end of class to summarize learning. They can, however, be carried over into the set (entrance slip) of the following day’s lesson.

The value/purpose of these forms of performance-based assessments is that they focus not only on the quality of the final product of a student’s work, but performance-based assessments also concentrates on the students learning process. In addition, through performance-based assessments teachers can track students work on a task, show them the value of their work processes and help them self-monitor so that they can use tools such as self-assessments more effectively. Performance-based assessments connect to the ideas of assessment for/as/of learning. For instance, all the above are used to collect information that will inform the teacher’s next teaching steps and the student’s next learning steps (assessment for learning). In addition, the above assessment strategies can be used to communicate progress towards standards, to students, parents, and teachers themselves (assessment of learning). Lastly, teachers can use self-assessments, rubrics or rating scales to allow students the opportunity to use assessment to further their own learning (assessment as learning). These forms of performance-based assessments allow students to reflect on their own learning and identify areas of strength and need; offering students the chance to set their own personal goals.

Entry #3 – Teacher Change

1) I see teacher change as inevitable. For instance, upon entering the Faculty of Education pre-service teachers, like myself, had a personalized view of what teaching should be or look like (based on our own experiences). However, each semester our beliefs and practices were challenged and/or questioned by colleagues, professors, cooperating teachers and/or students, resulting in a shift/change in our initial teaching approaches and beliefs. Even experienced teachers, as discussed in the article, encounter opportunities for change. Beliefs and there related tensions, as well as “a lack of intellectual challenge and satisfaction in dealing or engaging students with the mathematics” can promote or result in change (pg. 453) . I see change as healthy and realistic; however, “it requires not only a desire by the teacher to change but also the belief that alternatives that are more beneficial are possible” (pg. 456). Yes, “change is a challenging journey to a desired but undefined destination,” but teacher change can be a self-transforming journey (pg. 456).

My view of mathematics was very similar to Brea’s. When I was a student in high school math was made simple through formulas and steps; teachers would dominate the classroom simplifying math as best as they could “into little bits so the students could consume it and regurgitate it” (pg. 450). The focus/aim was to cover the curriculum. This was my experience; thus, I believed my job as a future teacher should be the same. Once I entered University this belief changed. I saw that math was no longer about steps and memorization, but rather it should be about and geared towards student-centered instruction and inquiry. At first, I had an inner struggle/tension with this concept as it was different and unfamiliar. However, through the various readings, class activities, lesson planning and lesson teaching exercises that I have undergone in my EMTH 350 class, I have become more open to this change. The first class activity that we did, which focused on understanding radian measure and circle trigonometric functions through a concrete representation, was my first ever experience with inquiry. After completing the activity, I realized how important it is for teachers to provide students with the opportunities to “…question, explore, notice, conjecture, prove/validate, and generalize” (pg. 455). Furthermore, the readings emphasized the importance of giving voice to, or recognizing “the voice of, students, thus empowering them” (pg. 455). I used to see teachers as being the expert voice in the classroom; however, my short experience with inquiry has made me realize that the “authenticity of student voices” are key to effective learning and understanding (both for teachers and students).

The article provides three different types of change: instrumental change, conceptual change and foundational change. I feel that as of right now I have only gone through, and continue to experience, conceptual change within my EMTH 350 class. Everyday I interact with my colleagues/peers in a way that enables me to view learning as collaboration with others. We question, explore, and conjecture together; facilitating each others understanding (of course with the guidance of our professors). In addition, as we build our inquiry lessons together we are furthering this type of change.

2) If you were to ask me this question two years ago I would have said that the ideas in the article definitely challenged, even contrasted, my beliefs about mathematics teaching and learning. However, now that I have had the experience to see and work with inquiry lessons, resulting in a change in both my attitude and approaches to teaching, I feel like I can say the ideas in the article affirm my beliefs about mathematics teaching and learning. In my pervious blog post I stated my mathematics creed: I believe math is a universal language, a discipline, a human endeavour, a science and a social activity.  These beliefs about math were definitely acknowledged within the article. For instance, Brea wanted to show her students that math “does exist in the world, that it is a ‘living discipline’, that it has bloodlines” (pg. 450). This connects to my belief of math as a discipline and human endeavour, as there are patterns, relationships, and quantities that connect to and are transferrable to the outside world enabling further understanding, learning and respect. My belief of math as a science is highlighted when the article states that “math presents itself as complicated, uncertain, and unfinished” (pg. 450). In my eyes the study of math and science are similar in the sense that both are a complicated, ongoing process, encapsulating comfort with uncertainty as well as teaching for understanding. My belief of math as a social activity was emphasized throughout the whole article. Inquiry-based teaching practices encourage discourse and conversations that are rich with questions, answers and insights; thus, enabling math to become a social activity among the students and teachers. Lastly, math as a universal language is highlighted and connected to all the above. All students have in some way or another a shared/collective understanding of mathematical ideas and concepts, which in the end is connected to and enriched by the social activity of the students.

In the end, I believe that my teaching practices and beliefs are going to continue to change as I progress in my profession. However, as of right now, as shown in the above examples and connections, my beliefs about mathematics teaching and learning hold true to the article. 

Entry #2

a) I believe that mathematics is at the heart of many successful careers and does contribute positively to our lives. As a result, mathematics is an important area of study because it has the potential to provide students with several fundamental or transferrable skills. Teachers need to acknowledge the fact that they play a significant role in the learning process of students. Therefore, referring to the articles and textbook chapter, I strongly agree that efficiency in delivering a lesson depends on both the beliefs, interests, and pedagogical content knowledge of the teacher. I believe that mastery of content knowledge can include teaching and learning strategies and student’s learning styles. As well, using appropriate teaching methods, resources and materials  can result in more effective teaching approaches, and potentially make concept understanding more achievable and/or clearer.

Furthermore, it is important that mathematics teachers believe that what they are teaching is beneficial and relevant. Teachers have to convince their students that there is value in the content. However, if mathematics teachers see the relevancy themselves then they will most likely teach accordingly. For example, if you have a teacher who believes in what they are doing, not only seeing math as important but relevant, then they can model that for their students by presenting their courses with integrity and honesty. As well, the course content becomes more relevant and “useful” not only for the present but for the student’s future lives. This is a reflection from my own math experiences. Every math class that I have taken, in both high school and elementary school, there was always a significant amount of students who said “why are we learning this?” Now if the teacher not only believes, but also communicates and teaches the importance and relevancy of mathematical content then students are more likely to modify their own preconceptions of math.

b) My Mathematics Creed

1) I believe mathematics is a universal language. All human beings have a shared/collective understanding of mathematical ideas and concepts.

2) I believe mathematics is a discipline. The study of relationships, measurements, properties, shapes, and space,  using symbols, numbers, patterns and formulas as a tool.

3) I believe mathematics is a human endeavour.  “Develop an understanding of mathematics as a way of knowing the world that all humans are capable of with respect to their personal experiences and needs” (Saskatchewan Curriculum).

4) I believe mathematics is a science. Both areas of study focus/deal with understanding the world around us; uses similar problem-solving approaches and tools.

5) I believe mathematics is a social activity. Mathematical teaching practices that encourage student-to-student discourse (group work) can increase student knowledge, and even promotes deeper and prolonged learning.

Entry #1: My Mathematical Autobiography

 

Throughout my academic career, I have always had a great interest and enthusiasm for mathematics. It has always been one of my strongest subject areas, one which I have consistently excelled at.

Looking back at my early elementary school years, I was never very fond of math. I found the countless assignments and worksheets to be repetitive and purposeless; I believed they were not relevant or a true indication of a student’s knowledge. In addition, I struggled with the material because the classes were more focused on memorization and regurgitation than about true understanding, application and logical thinking. It wasn’t until I entered high school that my experiences and feelings towards math shifted to a more positive place. I believe that this change in attitude was, in part, influenced by my fellow classmates  and excellent teachers. Not only was the material presented in a more relatable and stimulating  way, but the strong quality of instruction enabled me to comprehend and succeed at the subject. Furthermore, my teachers’ support and positive encouragement added to my success and understanding. Needless to say, very quickly, I developed a passion for math.

Once I approached grade twelve, math became second nature to me. However, I still enjoyed, and valued, the challenge of the subject matter. Overall, the combination of encouragement, positivity, and sense of accomplishment was the verification I needed to pursue a career in mathematics.

Math, to me, is a human endeavour, discipline, and multidisciplinary or collaborative language and tool. More specifically, it is an methodical/organized area of study that encompasses the logical thinking of structures, patterns, shapes and quantities that can not only be integrated within two or more academic fields, but also applied to real-world situations enabling us to understand the world around us. Thus, math is all around us, making it an important subject to study. In my opinion, mathematics provides several fundamental, or rather necessary, skills. Specifically, these skills include: the ability to see relationships (between content and authenticity), logic and critical thinking skills, problem solving skills, and the ability to identify, explore and consider patterns. Everybody uses or applies math whether they realize it or not.

My minor is dance education. Many people are surprised that I have chosen different areas of study to focus on because they see little connection between them. However, consider the following…

A dance performance is visually appealing because of its artistically composed structure. However, this structure can be described mathematically in sequences, numbers, patterns and relationships. Thus, by understanding the structure of a dance, by simply taking it apart and analyzing it, you are doing math without even realizing it. (My EDAN prof, Ann Kipling Brown, would always make such correlations and connections, I credit her for this example).

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