Growing As A Mathematics Teacher

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

a) Which one was your ‘favorite’ entry and why?

My favorite blog post this semester was when I had the opportunity to share and discuss different assessment strategies that can successfully be incorporate into mathematics. Entry #4 – Assessment Strategies provided the opportunity for me to make connections and reflections; How did my high school teacher assess our math classes? Which assessments did I learn about in EMTH350? Which ones were used similarly in my high school experience and which ones would I like to try and implement in my future teaching experiences? This post was based off of a previous class where each of my colleagues and myself researched a type of assessment and presented it within our small groups. I appreciated this assignment as I felt it to be the most hands-on and realistic entry I made as I can look back on it to implement these strategies during my internship and teaching career.

b) Which entry would you most like to ‘do over’ and why?

Entry #5 – Letter To A Friend would probably be the entry that I would like to have the opportunity to do over again. I do not feel that my information is incorrect or unsatisfactory, but I would love to have the opportunity to look deeper into the Annenberg Learner website and go through more of the videos to share with my friend. This particular blog prompt had asked that we watch one specific video and then one of our choice and discuss it in a letter to a friend. If I had the chance to redo this entry I would have gone through more of the high school math videos, watched at least a handful of them then chose from there which ones were most applicable to me, make connections between various videos and gain a better understanding of the different assessment strategies put into practice in the classroom.

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

When reviewing my blog posts, I noticed there were a few different entries that allowed me to learn a lot about myself as a learner and becoming a teacher. First, I chose Entry #2 – The Importance of Mathematics Teachers’ Beliefs because it challenged me to truly sit down and decide on five detailed creeds on what I believe mathematics is all about. Not to say I had no idea at all, but it is difficult to place your ideas and beliefs into open statements. Through this particular entry I feel I grew as a future teacher, identifying my beliefs for myself and others to see. The other entries that I learned about myself through were both a) and b) of Entry #6 – Role of Teacher Education as it allowed me to reflect on my experiences in university classes, previous field experiences, and how I felt my Education program is facilitating my growth as a student teacher. In entry a) I shared my initial feelings to the impact the program has on my experiences, how the field experiences aid in my preparation to become a teacher, as well as my mathematical beliefs that I felt would never change. Entry b) then allowed me to make any necessary changes to these feelings after I had a chance to experience them during my pre-intership placement in March/April. Through these three specific blog posts I learned a substantial amount about what I truly believe about the importance of mathematics in general, as well as what I believe is important while teaching this subject.

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

What were difficulties you came across creating your inquiry lessons? Were there any unexpected struggles executing this teaching strategy? Did you have the opportunity to use inquiry lessons (previous or new) during pre-internship?

The most common difficulty I had while creating my inquiry lessons in class was being able to determine how long a task would take, if students would be able to complete it in one period and reach a sensible conclusion, but also how to assess students during this. I find ‘right’ or ‘wrong’ distinctions during inquiry to be redundant as this is an opportunity for experimentation and freedom for students to use their own ideas and approaches. Should assessment simply be how well they answer open-ended questions or if they do indeed reach an ideal outcome? These questions were prominent throughout all lessons that my partner and I created in this class.

One major difficulty I came across implementing inquiry towards our colleagues was that we are on too much of a friendship level, so trying to view them as students and expect them to treat us like their teacher was almost impossible to enforce. They were talking over one another, visiting with other groups, and it was tough for us to take each other seriously as it would normally pan out in a classroom situation. Inquiry is also challenging how to plan, as we are unaware of what questions students will ask. Sometimes we can assume, and try to predict where the activity will lead students and who will come up with what question, but each one of our students learns differently and at different rates so it is hard to accurately execute that preparedness.

Yes, I was able to use my WA 10 – Design a Hockey Rink inquiry lesson with my Grade 10’s at Miller Comp. I had to make some alterations to the lesson, ended up making it a speed skating rink instead, and created more activity pages for them to submit throughout, but the general inquiry outline was the same. I also had the students explore around the class at the beginning of the unit, visiting different stations I had set up and have them measure various objects with different tools. This allowed them to connect what objects represent roughly 6 inches for example. Overall, using inquiry in my pre-internship turned out to be a success.

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

Throughout this course one topic I wish would have had more emphasis on would be the actual creation of inquiry lessons. During the class times we participated in various examples of inquiry and read about the importance of this teaching approach in our assigned readings, but speaking for myself and I know many of my classmates, we were lost as to how to successfully approach planning one. Is there a process or outline that would be helpful to follow? We tried using a basic, traditional lesson plan, which worked as far as we know, but altering how our minds work while planning a day-to-day lecture towards an inquiry lesson was extremely difficult and I felt as though I lacked some sort of ‘helpful hint’ or guidance as to how to make it easier.

Lastly, a topic that could have been extremely interesting and beneficial to be incorporated would have been Treaty Education. This whole semester the topic of Treaty Ed was preached to us in our many ECS classes, but as everyone knows it is a difficult topic to properly cover through mathematics. Now, since all third year Education students had an orientation seminar for our internship coming up in the fall, it was brought to our attention that there is a Treaty Ed component that our cooperating teacher is observing that we incorporate during our four months. I have little to no experience planning math lessons for Treaty Education, but I have also had zero math education professors provide us with lesson examples, or suggest topics that we could cover that accurately incorporate First Nations and Treaties. I think incorporating and at least touching base with both of these topics would be most beneficial for future students.

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

My first, most paramount goal I have already set for myself during internship this fall is to get involved with as much as I can outside of the classroom. My cooperating teacher coaches the Jr. Girls Volleyball team which I am hoping to help out in, I have talked to the music teachers who put on a musical every fall and want to help throughout that, just to name a few. I am determined to work with even more extra curricular activities as long as I am able to successfully balance everything. The reason I feel so strongly about doing so is because it allows you to build a much more respected relationship with students outside of their math class. Once we are aware of the hobbies, talents, and skills our students have we can incorporate those into the content we teach to make our lessons more relatable, and even as simple as congratulating them on a win or medal in front of the class will show them that we do care about them outside of the math classroom walls.

My second goal is to make certain that I stay organized. I only fear losing assignments, or having to replay a lesson because I have too many loose papers in my books. This shouldn’t be the case as I am a very organized person, but I belief that if I set a deadline for the students to meet for submitting their assignments, I should be returning that favor and handing them back with necessary feedback and grading promptly. Not only does that avoid frustrating students/parents not knowing how they did on an exam, but it also prevents me from losing any of their work when I collect it all in an organized manner, mark them, then return them punctually as well.

Deep down there are definitely more goals I will set for myself during my upcoming internship experience, but I would definitely say those are my top two and I anticipate the opportunity for me to implement them successfully this fall!

Entry #6(b) – Professional Development Journal Response

(i) Now that I have successfully completed my pre-internship experience I have had the ability to reflect on my beliefs and expectations of a math teacher. Prior to my three-week blog I spoke highly of student interaction and involving inquiry as much as possible. None of this has significantly changed so much that I disagree with it, in fact I feel the need to stress student involvement even more now that I have experience teaching in a high school setting. Realistically, teenagers do not love attending school all day, and for the most part they do not look forward to sitting in math class for over an hour. That being said, these classes are only as fun as we teachers make them to be. Yes, we can get up, stand in front of the class and dictate notes, power points and examples. But to students, this is extremely boring. My very first day with my Workplace and Apprenticeship 10 class we were starting the systems of measurement unit, which I happened to create an inquiry unit on! So  right away when the bell rings, I split my class up into assigned partners, send them to designated stations and had them measure all sorts of objects, using various tools around the room. To keep them on task and in line I created questions including myself and their names, incorporated situations occurring at Miller to make this activity as relatable as I could. There was about five minutes remaining when a few groups could not believe class was almost over. Their exact words, “Miss. Stein, is the clock broken?” No, why? “Because math class normally drags on forever, and it has flown by! By the way, come look at what we found when we measured these Olympic Rings!”. It took extra effort and planning on my end to incorporate inquiry, have them work with systems of measurement before I explain them to them, as well as getting them up out of their desks and working together. However, a few of my classes from there on out required traditional lectures where we would go over examples together then assign some individual work as well. But most of my students grasped the concepts much easier when I brought in real objects, or had them come up and explain an example to the class. Student involvement is crucial and I was so grateful that this experience confirmed and strengthen this belief. I was also able to assign and mark the Skating Rink project with my WA10 class. They were able to create their own, deciding their own dimensions and reasonings for so, automatically allowing them to take responsibility and leadership for their own learning. They were due the last Thursday of my three-week block, so I ensured I finished marking them that evening so that I could go over my feedback with them on the last day. Again, emphasizing the importance of returning assignments/feedback in a timely manner as their assignments are asked to be submitted on a specified date. None of my prior beliefs were seen to be incorrect and change drastically, however, they were justified and strengthened, showing the importance of each one of them.

ii) Freese mentions that during internship students are “students at the same time that they are learning to be teachers..” which I completely agree with. Yes, we are in the schools teaching our own students, but we that is our practice time to learn, grow, and improve as preservice teachers and must receive necessary feedback and suggestions from our cooperating teachers. During the field experiences and internship placements we are provided with throughout the education program, it is the role of the school and teachers to challenge our beliefs, introduce us to a variety of teaching strategies, and ensure that we preservice teachers take responsibility for our actions and choose to improve from our mistakes.

I appreciate the suggestion Freese provides about being a consistent reflector while we are preservice teachers, but I also argue that this process should be ongoing throughout our career. It is essential to think about, look back on, and reflect on how our daily teaching goes. Which aspects of our lesson worked well and what could use improvement? Which lessons engaged my students the most, which assignments were unclear or too difficult? Since we are still new with noticing weak areas and knowing how to adjust to make improvements we must be openminded during our internships and allow our cooperating teachers to point out necessary alterations. It is important we take all suggestions as constructive criticism and take all feedback with a grain of salt; decide what we think is useful and what is not useful then go from there. Preservice teachers need to be responsible for their learning while they are teachers; communicate with colleagues for extra assistance, ask our coops for help or resources, and make sure to ask for as much feedback as possible to continue growth and improvement. In conclusion, all teachers, both preservice and current, must be openminded and accepting of suggestions to change. Being open to new ideas and various perspectives of how to teach will help us improve our teaching as we can pick and choose specific criteria of what we observe works best in the classroom, either from experience or observation.

Entry #6 (a) – Role of Teacher Education

I strongly believe in the importance of pre-internship, field experiences, and internship placements. They provide a true, living experience of the career and expectations we are about to take on. In my first semester of Education, ECS 100 to be exact, I was already placed in a school for half a day, once a week, to dip my toes into what it will be like to be a teacher. There are very few programs available out there that allow for hands-on-experience at such  primary stage in the degree. From this experience, I believe one of the main reasons for field experiences is for student teachers to identify whether or not this profession is made for them or not, instead of waiting until fourth year internship when they find out they absolutely hate it. Fortunately, the field experiences have confirmed my passion for teaching, and I love it more and more every time I enter a new classroom. Another purposes these placements represent is the ability for student teachers to learn from other educators; whether it be teaching strategies, classroom management techniques, copies of resources, and so on. I was able to learn so much from my previous cooperating teacher, and anticipate the experiences I am about to have with my pre-internship and internship co-ops. A huge reminder when discussing what we learn from other teachers is to remember that we can also observe what not to do. Not one teacher plans, teaches, or marks the same way, so we take all suggestions and criticism with a grain of salt and have the opportunity to choose what ideas we want to take into our own teaching. Most importantly, I appreciate the interactions and additions to our professional learning networks we are able to make by getting to know many other educators around Regina and Saskatchewan.  Nothing is more comforting than knowing you have colleagues you can fall back on if you ever need any support or guidance during our internship and first few years of teaching.

Teacher education programs are useful in the sense of hearing about different teaching strategies, how to deal with racism and bullying, practice making lesson plans, teaching to our peers, and providing those field experiences for us to practice these approaches. I find the actual lectures to be very repetitive in the sense of always discussing the same controversial topics, realizing they are important, but I wish we were taught how to go about confronting these issues opposed to realizing they exist. I also wish some courses would provide resources or opportunities to explore various grade levels in the curriculum as I have generally only been able to work in the Grade 10 Mathematics area. For the most part the textbook resources are beneficial and are something we can take with us in the future. But I definitely feel I learn the most about teaching once I am exposed to the real life experience through field placements.

There are a few commitments and beliefs that I have about becoming a mathematics teacher that I look forward to implementing during my pre-internship/internship experiences and do not feel they will change. I believe there is a need to incorporate as much student involvement as possible; no child will be engaged in any subject where the teacher stands at the front of the room, dictates notes and examples, then they go to work. I have recently been introduced to inquiry based teaching, which is difficulty and timely to plan, but the learning experience is extremely authentic and engaging. If this is overwhelming still, even as far as ensuring to call upon all students while doing examples on the board can maintain their attention longer, knowing that the teacher values their ideas too. A commitment I want to maintain is returning assignments and exams the next period, just as I expect their work to be completed on time. There is nothing worse than a teacher who takes off late marks for each day an assignment is late, but will then take weeks to return it to them with their feedback. Lastly, I believe math should not be kept as a memorize-regurgitate-repeat type course. I want to keep math fresh, relatable, and continually available for students to make their own personal connections with. There are an endless amount of transferable skills in mathematics that relate to the world around us, so why not ignite this prior knowledge in our students and allow them to be successful in their own way? Building strong, responsible relationships with our students is essential as well, and I am confident to say that none of these beliefs or commitments about being a mathematics teacher will change during my field experiences.

Entry #5 – Letter To A Friend

Dear Jess,

In one of my Math Education classes I am enrolled in this semester we were asked to watch two short videos that dealt with different assessment strategies used in mathematics. Since we always had each other to learn from and grow off of during our high school math with Mr. T I wanted to share these with you too! I’ll share my short write up of them both, highlighting what I learned from them and why I felt they were so important to pass onto you.

The first video was called Teacher Insights 9-12 – program 10, where different teachers shared the assessment strategies they use frequently in their classrooms and providing justification for such. The main proposal of this video began by stating that we need our students to go beyond memorization in mathematics and become critical thinkers. Well, realistically they are not going to switch gears on their own, they are depending on us to bring that attribute out in them, thus our job is to evolve our evaluations and assessments to meet these needs. Different assessments mentioned throughout ranged from group work, oral reports, class response/participation, tool kits, self-assessment, peer-evaluation, presentations, and portfolios. I’m sure you can recall as well as I do that we rarely experience any other assessment in class aside from homework checks, quizzes, or exams. Could you imagine how much more engaging and interesting our classes could have been if we were allowed to create different projects, reports, tool kits, or portfolio collections of how we improved? I’d love for you to take a look at this and let me know of anything else you could pick out that we did not experience and how much more interesting our classes could have been if it were incorporated. A few specifics that show how beneficial these assessments are for students are reflected in their comments. For instance, group work allows students to collaborate with each other and share ideas, the marking scheme chosen for this was a rubric and allowed students to conclude with what “we earned..”, taking responsibility for their own learning. Oral reports had students decide and gather “what makes a good group work [well]” and self-assess based on how well they think their contributions were. Presentations let students share “this is what I know”, and provided the opportunity to the remainder of the class to provide peer feedback. Lastly, my favorite, portfolios; students are able to choose a goal that they want to reach, submit assignments based on that goal into the portfolio to show their growth and improvement.

In the second video, Beyond Testing – program 11, discussed how we want our students to make meaning of what they are learning opposed to simply acquiring more information. Adapting necessary assessments and evaluations so we don’t have to wonder “what sense are they making”. This video explores how teachers must incorporate more problem solving and reasoning, and since these expectations are changing assessment must change. Do you remember doing problem solving all the time? Yes, me too, but our assessments were very traditional math exams to test our problem solving skills still. Beyond Testing makes an excellent point that students learn in different ways, therefore teachers have the responsibility to assess us in different ways. Think back to our class, all of us possessed many different skills, talents, and learning abilities. Even when Mr. T altered Calculus to represent Survivor it hit our multiple intelligences in many more intriguing ways than simples note taking and homework assignments. More specifically geared towards my EMTH 350 Inquiry class, we also were not exposed to this exceptional way of learning, and the video touched base with the fact that students should do less paper/pencil work and more hands on. I wish we could have done that! As well as being assessed on-going based on learning improvement instead of emphasis on what grades we should be getting.

I personally feel that most, if not all, of these suggestions were incorporated into our math classes throughout our years we would have enjoyed that class that much more. I invite you to give both of these videos a look and let me know what you think. Did you agree with the traditional paper/pencil, notes, homework, exams assessment we were used to, or do you think having teachers alter the assessment for the needs of their individual students should be taken more seriously?

I anticipate hearing back from you so we can continue our conversation reflecting on our previous math classes. Man, do I miss those days. Hope all is well, we will stay in touch!

-Rebecca.

Entry #4 – Assessment Strategies

My most memorable assessment experience in high school was in my Calculus 30 class when my teacher turned our entire course into a “Survivor” challenge. It all began the first day of classes, we chose our teams at random, picked our ‘tribe’ names, and went over the rules that are required in order to survive. He had the team’s marks working together to see which tribe could vote off a member; only the team with either the highest average on an exam, the most homework check completions  or most quizzes passed could vote a member off of their own team or choose a member from the other team. At the end of the semester the team with the highest overall average won, and generally we would choose to vote off the stronger students from the other team opposed to weaker students on our own team, which helped those students continue to participate and motivate them to try and improve their grades to not let their tribe down. His quizzes he incorporated into the day to day classes consisted of two or three questions on the content we learned the previous week, plus one bonus question about the content we were about to learn next. This bonus question did not penalize those students who were not ahead of the group but they still had the opportunity to give it a try, as well as allow the higher 1/3 of the class to succeed and provided him with pre-assessment of who already had an understanding about the new topic.

Various assessment strategies have been explored throughout this course, and interviews was a specific type that I dealt with personally. I gained a new understanding and appreciation for the use of interviews in mathematics, where initially I thought they would be irrelevant, simply because I had no experience or awareness of this assessment while being a student. Fortunately, I now realize conducting interviews with our students is very beneficial as we can communicate with them one on one, in pairs, groups, or by a whole class, to get an idea of where our students understanding level is at. Interviews allow students to explain concepts or ideas to teachers when they may struggle with writing or performing calculations but do understand the process. They also provide teachers with the opportunity to pull students aside to give group evaluations, this is where the most truth on member participation/behavior will come out, and they are welcome to share their strengths and weaknesses on the topic. On the other hand, interviews have a time and a place to when they would be most suitable. It is not always convenient for teachers to send his/her students off on their own to work on assignments and continually pull students aside for discussion; this is where a general class interview would be most useful.

Two other assessments I learned about, which I felt had a strong connection to inquiry through mathematics, were peer assessment and journal writing. Again, I did not personally experience these in my high school experience, my assessments were almost always strictly homework assignments, quizzes, and exams, so I automatically did not think either related to mathematics. Throughout sharing of these assessments I gained more valuable understanding of the two, making connections and realizations of how they can be implemented into a mathematics classroom. Peer assessment, for instance, provides feedback to other classmates, which can often ‘hit home’ or be more relatable to students than the feedback from teachers. Peer assessment also allows students to identify each other’s and their own strengths and weaknesses, plan their learning and how they can be successful, as well as giving students the chance to be responsible for their own assessment and learning to see past their grade. Journal writing provides students with the chance to express their knowledge in written language if they struggle with completing mathematical steps, as well as privately asking questions or stating areas they may struggle in to avoid exposing their weaknesses. I was only introduced to journal writing in my English Language Arts classes, however, keeping this personal conversation (provided we take the responsibility to respond promptly) will instill a safe, welcoming environment for our students to learn. Journal writing is an assessment that can be taken for either formative or summative reasons, which is also beneficial to have the flexibility as teachers.

One considerable value these performance-based assessments can have is embedded in the variety that teachers use. It is essential to avoid choosing one that you have had success with and never incorporating these new strategies into our classrooms. Students benefit from assessment strategies as much as teachers do, they provide opportunities for them to express their knowledge in different formats, and allow teachers to look at their skill/understanding from multiple angles. I strongly believe that, regardless of the assessment strategy chosen, assessment for learning should be present in each and everyone of our lessons. Assessment of learning is necessary to for grading purposes, to let the students, parents and school know where that particular students is at in the course, but all of these strategies could be altered to be successful in either.

Relating specifically to interviews, peer-assessment and journal writing, I would personally use interviews as assessment FOR learning, peer-assessment would be assessment OF learning, and journal writing could be equally both. Within my memorable assessment experience in high school that I shared above, the assessment strategies were generally assessment of learning, and usually homework, quizzes, or exams. That being said, it was so memorable and enjoyable for my class and myself because it was relatable to our everyday lives, connecting the reality TV show into our Calculus 30 class. We were able to ‘play’ the course as a game, yet encouraged each other to reach their greatest potential and succeed together.

Entry #3 – Teacher Transformation

1) Throughout this course I have been learning about teaching mathematics through inquiry from a variety of resources. Our weekly readings have provided many useful examples on how teachers are learning how to teach inquiry, as well as successful methods of how students learn best through inquiry. I have found in-class activities to be the utmost beneficial strategy to understand inquiry as we have now acquired the knowledge from both the view points of the teacher and the student. At the beginning of EMTH 350 I was aware that inquiry learning existed, but I had little to no exposure to this in my high school math experiences; I was lost when it came to knowing how to teach this way. The first inquiry activity we did, exploring radians using tape, caught my attention right away on how useful and essential teaching through inquiry is for our students. I would have never thought about radians in that way as I am so used to math being simple, straight forward formulas and definitions to regurgitate (similar to Brea’s initial experience). Being assigned this small inquiry unit has been challenging, more so due to my unfamiliarity with this strategy in my past, but I am confident to say this is finally a beneficial assignment in my university experience! Another appreciative factor involved in our lesson planning is the opportunity to be paired with a colleague for collaboration reasons. Working alone would have made this experience more difficult, whereas feeding off each others’ ideas and learning from one another is an excellent opportunity during our pre-service years.

2) My university ed math courses have challenged my beliefs as a mathematics teacher many times, but so far always for the best. I have come to acquire a much more open mind, have learned an endless amount of different teaching strategies, and continuing to further my knowledge and understanding of high school math content and curriculum. After being introduced to teaching through inquiry specifically I feel the article has affirmed my beliefs about mathematics teaching and how import self-reflection is in order to notice necessary changes that should be made. Connecting specifically to one creed I stated in my last blog, “I believe mathematics offers an opportunity to further understand the world around us by connecting concepts to real life situations”, Brea mentioned this as well, in how her students were digging deeper as she allowed for an open minded classroom. They were coming to class with their own connections they had made to the material opposed to her traditionally lecturing, having them take exams and no further exploration. Inquiry, whether guided or not, fits into another one of my creeds, “I believe teachers have the responsibility to take the necessary extra steps of making lessons interactive and engaging for all students”. Brea first realized the need to change when her position as a mathematics teacher became dull and unenjoyable for her, this doesn’t even go to mention how the students were feeling about it if the teacher did not even feel passionate about the lessons. This article affirmed my belief that teachers have the responsibility and choice to take that step, improve the lessons, make them more engaging, and if we feel unprepared to do so we can attend these extra conferences or courses for professional development.

Therefore, these changes in beliefs and experiences will continue to exist throughout my teaching profession, especially as I am just starting out. Fortunately, the article is another useful resource to affirm my current beliefs, and throughout this EMTH 350 course I will continue to be exposed to inquiry lessons to experience professional development with my colleagues now before we enter the field. Our university program has so much to offer our pre-service teachers and we would be hindering ourselves and our future students if we do not explore these opportunities deeper.

Entry #2 – The Importance of Mathematics Teachers’ Beliefs

a) From reflecting on the readings assigned, I now have a much clearer understanding about what my own beliefs are towards mathematics as well as the awareness of the endless strategies, expectations and practices teachers have for themselves. Reading the variety of categories mentioned in Goos’ ‘Why Teachers Matter‘ I found my beliefs to fit into many of them opposed to being fully defined in one. I strongly agree with the concept that teacher’s beliefs reflect how they portray themselves in the classroom throughout their practice. Mathematics is constantly around us, some of us may not always be aware of it. Whether it is dealing with numbers in school, measuring supplies to build a house, providing change at the grocery store or bank, or simply figuring out how much flour to put in your cookie recipe, we are continually using math skills. Therefore mathematics is an essential subject that we must offer our students so they can learn and improve these transferable, significant skills. 

Another excellent point made in these readings was how powerfully our interests and beliefs of the subject matter are reflected onto our students. I have easily had a handful of high school teachers and some professors who made the class and content extremely distasteful because it was not something they truthfully enjoyed. If we enter our classrooms (the environment that we have the ability to create) and simply write the facts on the board, have them copy it down, practice endless worksheets, then regurgitate the formula-based processes back to me in a few weeks on an exam is not going to interest my students, or myself quite frankly. Teachers need to have that passion to change the predisposition many students have about the importance of math. As mentioned above, I truly believe math is important for the reason of relevance and daily existence in our lives that if I continually use a textbook from 10 years ago, blasting questions at my students to solve oppose to understand, I am completely missing out on the opportunities for them to build on their existing knowledge, explore their world around them and to gain a full understanding of mathematics rather than memorizing it.

b)

– I believe mathematics is applicable, relatable and can be successful for all individuals

– I believe mathematics offers an opportunity to further understand the world around us by connecting concepts to real life situations

– I believe students should have the freedom to try different approaches to reach their solutions and expand their learning at their desired pace

– I believe teachers have the responsibility to take the necessary extra steps of making lessons interactive and engaging for all students

– I believe mathematics allows students to successfully take abstract concepts and break them down to concrete tasks that they can accomplish