My New Perspective on Teaching Mathematics

            Prior to taking this course, 3940 - Teaching Mathematics in the Primary/Elementary Classroom, I perceived Mathematics as an intimidating subject area, one that would be extremely difficult to teach because of the many negative connotations that are often associated with it. I was nervous to teach mathematics, for I was not sure how to make mathematics engaging for students at the primary/ elementary level. However, this course has taught me that mathematics does not have to be an intimidating subject area, but rather a subject area that students can be excited about and look forward to. I believe that this course has prepared me for teaching mathematics in the future, for it has provided me with a whole new perspective concerning the teaching of mathematics. This course has shown me that mathematics can be made fun through an interactive and inquiry-based approach to learning. As a future teacher, I hope to engage my students in learning ‘through’ mathematics rather than ‘about mathematics.” In other words, I plan to apply a constructivist approach to teaching mathematics. I feel as though many teachers settle for teaching mathematics through drill and practice and before taking this course I would have probably deemed this as acceptable, for the majority of my teachers relied on this very approach. However, through this course I have learned that active involvement, collaborative group work, as well as student justification concerning strategies and solutions, are much more effective in terms of promoting student learning and understanding.

           This course, as well as my own experiences with mathematics, has also taught me that many students fear mathematics or doubt their mathematical abilities. Many students often believe that they cannot do mathematics and simply give up on trying to learn mathematics because they are not provided  sufficient support. I believe that this is an injustice. Teachers must make mathematics class inviting for all students and provide motivation and scaffolding when necessary. I am grateful that I have had the opportunity to take this course, for I believe that it has increased my own confidence in terms of my mathematical abilities, for I now understand that it is okay to take risks and make mistakes when doing mathematics since there is no ‘right’ way to do mathematics. I look forward to assisting my future students in achieving this realization.

            This course has also introduced me to a number of resources that I was not familiar with, but that can be used to assist me in my teaching of mathematics. I take comfort in the fact that the NCTM is available to offer support and assistance in my teaching of mathematics, as well as an abundance of teaching resources such as manipulatives, teacher guides, workbooks, etc.  I am very appreciative that these resources have been brought to my attention throughout the duration of this course.

 

            As a future teacher of mathematics, I hope to promote an inviting learning environment, one where all students, feel welcome. I also hope to provide my students with meaningful learning experiences that have real life application. I want my students to take pride in their mathematical abilities and I hope to teach them that mistakes are not to be feared, but rather embraced, for they provide yet another learning experience. I also hope to encourage risk taking since it allows for self-discovery, which I believe is important for students to experience. In my future mathematics learning environment, I imagine the use of a variety of manipulatives, open-ended problems and guided questioning. I envision my students learning ‘through doing mathematics’ and engaging in higher level thinking. In order to achieve this and assist all students in achieving maximum learning potential, I will provide students with problems that allow for multiple entry points and that encourage problem solving. In other words, I want to create a positive learning environment in which all students, regardless of mathematical ability and achievement can succeed.

 

Newfoundland and Labrador Mathematics Resources for Primary and Elementary

 

             In class, we had the opportunity to explore a number of resources that are available to assist educators of Mathematics in the province of Newfoundland and Labrador. I found this experience extremely beneficial, for I feel more confident in my ability to implement a lesson in Mathematics knowing that I have access to an abundance of quality resources. To be honest, I assumed that the only resources that would be available to us as future educators of Mathematics, would be grade level text books and the Newfoundland and Labrador Department of Education Curriculum Guides. Do not get me wrong, both of the resources mentioned are significant and imperative to the delivery of Mathematics instruction; it was just that I was pleasantly surprised to see that other resources were also available. These resources included teacher guides, workbooks, practice and homework books, etc.

                This experience not only introduced me to a number of resources that I had no prior exposure to, but it also gave me the opportunity to explore the resources I was already familiar with in greater detail. I was particularly impressed with the grade level textbooks for both the primary and elementary grades. While I had seen the majority of these textbooks being used in my observation days, I had never analyzed one or compared them in terms of the mathematical outcomes, highlighted as important in the Newfoundland and Labrador Curriculum Guides. I learned that in Newfoundland and Labrador there are currently two separate publishing companies responsible for the textbooks and resources used in primary and elementary Mathematics. I was not aware of this until this experience.
 

Primary Mathematics

From Kindergarten to Grade three, Math Makes Sense textbooks and resources are currently being used. 

 

 

                Each primary grade level has their own textbook and collection of teacher resources. In comparison to the resources used in the elementary grades, I noticed that the resources for primary aged students were much more vibrant in terms of colours and visuals. Personally, I was more drawn to these resources because they felt more authentic and relatable. I can see how these resources would be appealing to young children. The “textbook” for grade one and two in particular, were more like workbooks. I remember using workbooks such as these at the primary level myself. I really enjoyed having my questions, my samples and my solutions all in the one place.  Another thing that stood out to me was that the primary resources were extremely organized. They were divided according to unit of study and everything was clearly presented for both the students and the teacher.

                After becoming acquainted with each set of resources at the primary level, I also discovered that the mathematical concepts taught are consistent throughout all of the primary grades. These concepts however, increase in terms of complexity as the student moves closer towards elementary. In other words, these textbooks support the idea of a “spiral curriculum.” For example, throughout grade one, two and three, students are expected to build upon their knowledge concerning patterning, addition and subtraction, measurement, etc.

                Another thing that struck me as interesting was how different the resources for Kindergarten were. I had never seen mathematical resources for Kindergarten prior to this experience, so I was excited to discover that Mathematics instruction is provided through the use of “little books.” These “little books” are sequential in terms of content. I believe that this approach to mathematical understanding through literacy is an exciting and appropriate way to introduce young children to Mathematics.

Elementary Mathematics

 

In elementary, grades four to grade six, students are required to use a collection of resources and materials entitled Math Focus.



 

 

           The first thing that appealed to me about these resources, were how they were structured.  I found them easy to navigate and liked how each chapter was organized in the same way, each representing an individual unit with mid-chapter and end chapter reviews, as well as a chapter task. I also liked the fact that each textbook was accompanied by a master’s booklet and corresponding teacher resources. Although these resources were not as colourful or playful as the resources used in primary, I can see how they would add value to any given lesson in Mathematics.

                 Like the primary textbooks, the textbooks in elementary seemed to embrace sequential learning. Once again, I noticed that a number of concepts were taught throughout the grades, all increasing in terms of difficulty. These topics include: fractions, decimals and geometry. I believe that this spiral approach to teaching Mathematics is effective, for it allows students to build on their prior knowledge.

                Overall, I am pleased to know that there are a number of resources available to me, as a future educator of Mathematics. While I believe that the resources mentioned are great, I also believe that we as teachers must be creative and authentic in terms of the learning opportunities we provide our students with. Yes, these resources are extremely helpful, but we must not let them limit our students’ learning experiences.

Thanks for reading!



An Analysis of the "Front Matter" in Newfoundland and Labrador's Mathematics Curriculum Guides

 

In class, we were asked to familiarize ourselves with the "front matter" of the Newfoundland and Labrador Mathematics Curriculum. I chose to focus my attention on the grade two Mathematics curriculum guide, for I have a particular interest in this grade level. This particular curriculum guide can be found here.

There were a number of things that I came across in this section of the curriculum guide that interested me, surprised me and caught my attention.

First, I learned that The WNCP Common Curriculum Frameworks for Mathematics helped in the development of this curriculum guide. I also learned that this curriculum guide's main intent is to provide teachers with an overview of the outcomes, strategies and assessment tasks that they are responsible for covering in grade two.

I really liked that this curriculum document contains a section entitled, "Belief About Students and Mathematics Learning," for it provides educators with insight concerning how Mathematics should be taught in order to engage ALL students, despite the individual learning styles and intelligences they may possess. In this section, it states that "through the use of manipulatives and a variety of pedagogical approaches, teachers can address the diverse learning styles, cultural backgrounds and developmental stages of students, and enhance within them the formation of sound, transferable mathematical understandings." I believe this is important to be aware of as future teachers of mathematics.

 

Another thing that I appreciated about this curriculum guide is that it contains a section in which the Mathematical goals for students are clearly stated, as well as their expected results. This section is important to me because I believe that it is necessary that we, as future teachers have a clear understanding of what is expected of our students.

The main goals of mathematics education are to prepare students to:

• use mathematics confidently to solve problems

• communicate and reason mathematically

• appreciate and value mathematics

• make connections between mathematics and its applications

• commit themselves to lifelong learning

• become mathematically literate adults, using mathematics to contribute to society.

Students who have met these goals will:

• gain understanding and appreciation of the contributions of mathematics as a science, philosophy and art

• exhibit a positive attitude toward mathematics

• engage and persevere in mathematical tasks and projects

• contribute to mathematical discussions

• take risks in performing mathematical tasks

• exhibit curiosity.

The Mathematical processes are also effectively presented in this curriculum document and they are as follows: Communication, Connections, Mental Mathematics and Estimation, Problem Solving, Reasoning, Technology and Visualization. It is here that we can see the influence of the NCTM for these six mathematical processes mirror the six principles highlighted as important by the NCTM.

 

 

This curriculum guide also offers educators insight concerning the components that define the nature of Mathematics. An overview of the following components is provided in the document: Change, Constancy, Number Sense, Patterns, Relationships, Spatial Sense and Uncertainty.

The next section of the curriculum guide that stood out to me as important is the section on the Mathematical strands. There are four common strands for Kindergarten to Grade nine and these strands are Number, Pattern and Relations, Shape and Space, and Statistics and Probability. Once again we can see the influence of the NCTM, who also highlights a common set of content standards or strands of mathematics that appear throughout the grades. The NCTM lists, Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability as the five main content strands in Mathematics.

I was a little surprised when I read that Statistics and Probability (Data Analysis) is addressed in grade two Mathematics. For some reason I did not think that students engaged in data analysis until elementary. This curriculum document has provided me with a lot of new insights!

 

 

Outcomes and achievement indicators are also given in this curriculum guide, which is extremely beneficial for teachers.

General Outcomes are overarching statements about what students are expected to learn in each strand/sub-strand. The general outcome for each strand/sub-strand is the same throughout the grades.

Specific Outcomes are statements that identify the specific skills, understanding and knowledge that students are required to attain by the end of a given grade.

Achievement Indicators are samples of how students may demonstrate their achievement of the goals of a specific outcome. The range of samples provided is meant to reflect the scope of the specific outcome.

Lastly, one of my favourite sections found in the "front matter" of this curriculum guide is the section entitled, "Instructional Focus." This section provides educators with tips to consider when planning for instruction, ideas in terms of resources, a timeline to assist in planning, as well as a suggested schedule for instruction that includes time for completing assessment activities, reviewing and evaluating.

Overall, I am very grateful that we have access to these curriculum documents, not only for mathematics, but for all subject areas. The curriculum guides in general are extremely informative resources and I believe that they will assist me in delivering quality instruction in my future classroom.

 

 

 

 

             As a future teacher, it is extremely important that I am familiar with and understand all that The National Council of Teachers of Mathematics (NCTM) has to offer, in order to maximize my students’ learning experiences. Chapter one of our textbook, “Elementary and Middle School Mathematics,” introduces the NCTM as a U.S. based organization of teachers and mathematics educators from both the United States and Canada. Since it is probable that I will be teaching in Canada, I must take advantage of the knowledge, resources and research that the NCTM provides. The NCTM mission statement is as follows, “The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.” In order to become the best teacher I am capable of becoming, I must embrace the NCTM.

 

Content Standards, Process Standards, and Teaching Standards have been developed by the NCTM and are all fundamental to the instruction of mathematics.

 

Content Standards

 

There are currently five content standards (Number and Operations, Algebra, Geometry, Measurement and Data Analysis, and Probability). Each content standard includes goals that apply to all grade bands (the grade bands being, pre-K-2, 3-5, 6-8 and 9-12). Rather than having a different set of mathematical topics for each grade band, the NCTM have formed a common set of content standards that are taught throughout all grade levels. Instead of learning solely about one of the content standards in a particular grade and then moving on to another the following year, students are able to use their prior knowledge concerning each set of mathematical topics in order to expand on what they have already learned (spiral curriculum), which I believe is effective in producing learning that is long term.

 

Process Standards

 

There are also five process standards highlighted by the NCTM, and they are, Problem Solving, Reasoning and Proof, Communication, Connections, and Representations. As a future teacher of mathematics, it is essential that I am familiar with all five of these processes. It is our job as teachers, to promote mathematical understanding and critical thinking, and in order to do this we must encourage our students to learn mathematics through doing mathematics. We must provide our students with opportunities to engage in all five process standards, but in order to be effective facilitators, we ourselves must practice these process standards.

 

Teaching Standards

 

The teaching standards developed by the NCTM, are the standards that teachers are required to follow when teaching math education. As future teachers, we must abide by these standards if we want to enhance student learning. These teaching standards include, Knowledge of Mathematics and General Pedagogy, Knowledge of Student’s Mathematical Learning, Worthwhile Mathematical Tasks, Learning Environment, Discourse, Reflection on Student’s Learning, Reflection on Teaching Practice. I believe that all seven teaching standards are important and that it is necessary for all teachers to familiarize themselves with them before teaching mathematics at any grade level.

 

            The NCTM is designed to provide guidance and direction for teachers of mathematics education from pre-kindergarten to grade 12. The NCTM states that the “six principles fundamental to high-quality mathematics education,” that teachers should be aware of are Equity, Curriculum, Teaching, Learning, Assessment and Technology:

 

The Equity Principle: “All students must have the opportunity and adequate support to learn mathematics.” In other words teachers must have high expectations for all students. This is extremely important, for not all students learn at the same rate or in the same way. We as future teachers must treat all students fairly and continuously motivate them to reach their maximum learning potentials.

 

The Curriculum Principle: Curriculum “must be coherent, focused on important mathematics, and well articulated across the grades.” In order to effectively teach mathematics or any subject area, teachers must be experts on the curriculum.

 

The Teaching Principle: “Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.” If we want to provide our students with the best possible learning experience, we as future teachers must familiarize ourselves with the learning needs of each student and provide learning opportunities that cater to these needs, allowing for success.

 

The Learning Principle: “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” As future teachers we must recognize that all of our students come to class with different schemas, experiences and levels of knowledge. It is our job to take all of it into account when planning for and assessing student learning.  

 

The Assessment Principle: “Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.” Students should not be assessed solely on if they arrive at a particular answer or not, but rather on how they arrived at the particular answer, for mathematics encourages higher level thinking and creativity, which often results in a number of justifiable solutions and processes. We must not inhibit our student’s creative thinking when assessing mathematics.

 

The Technology Principle: “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” I believe that integrating technology (calculators, computerized games, etc.) into mathematics shows students that mathematics can, in fact have real world application.

 

            In order to be the best teacher possible, I hope to take advantage of everything offered by the NCTM. I have learned that it is necessary to approach mathematics with an open mind, for the more evident it is that you care about mathematics education, the more likely your students will deem it as important and this is essential for their future success. As future teachers, we should care about equity in mathematics, so that ALL students, regardless of their abilities, have the opportunity to learn without the fear of failure.

TEDtalks: Sir Ken Robinson - Do schools kill creativity?

 

"If you are not prepared to be wrong, you will never come up with anything original."

         In class we watched a presentation by Sir Ken Robinson entitled, "Do Schools Kill Creativity?" During this talk, Robinson states that "we are running education systems where mistakes are the worst thing you can make." He believes that this negative attitude towards taking risks, being creative or being "wrong" is negatively impacting the children in our school systems. He believes that all children have extraordinary capacities for innovation and tremendous talents that we, as educators, squander. When reflecting on this talk, I found myself strongly agreeing with everything highlighted by Robinson. I too believe that the education system as we know it, does not provide students with many opportunities for taking risks or expressing themselves creatively, because it is too concerned with academic status. I agree with Robinson when he states, "we are educating people out of their creative capacities." As future educators, I believe that it is our responsibility to create the best possible learning environment for our students, ensuring that each child has the opportunity to reach their maximum learning potential.  This means that we must nurture our students’ talents and learning styles, whatever they may be.

          Robinson strongly believes that "creativity is as important as literacy" and that the education system must recognize this. Robinson highlights that the hierarchy of subject areas are the same everywhere you go, with Mathematics and Language Arts at the top, the Humanities just below and then the Arts at the very bottom. He believes that we are educated upwards with a focus on the human mind but that this needs to change because there are many "highly talented, brilliant and creative people who think that they are not, because what they were good at school wasn`t valued, but actually stigmatized." From Howard Gardner’s work on multiple intelligences, we understand that there are many different ways in which individuals can learn and be successful. We must recognize that a learning style that fits the needs of one child, may not fit the needs of another child, and that we must allow children to experience a variety of learning styles that assess all possible intelligences, until they find one that allows them to succeed. Robinson gives an excellent example of this, when he references the story of Gillian Lynne. As a young girl, Gillian did not thrive academically in a traditional classroom setting and was considered to be disruptive because of her inability to sit still class. However, once somebody recognized that she "needed to move in order to think," she was introduced to the world of dance and went on to have a successful career as a dancer and choreographer.   

          Something that struck me as interesting when watching this presentation was when Robinson made the comment that children who are going to school this year will be retiring in 1965 and that nobody knows what the world will be like in five years, yet we are supposed to be educating them for their futures. This was something that I never really thought about until now. Education is constantly shifting and evolving and we as educators are responsible for preparing students for their futures, whatever they may be. It is troubling to know that what we teach our students now may have no relevance to life in the future. However, as educators we must stay positive and always keep an open mind. We must be flexible and willing to adapt our teaching styles at all times, in order to create the best possible learning experiences for our children, giving them their best shot at having a bright future. We must not inhibit our students’ talents and creativity, but rather encourage them if we want to produce a successful generation.

         While watching and reflecting on this presentation, I thought about ways in which it could be connected to teaching children mathematics. Mathematics is a subject area that holds a lot of prestige in the school system. Children often come to math class feeling as if they are failures because they believe mathematics to be a subject area in which there is only one answer and if you don’t have it, you are unintelligent. Since many mathematical problems often do only have one answer, teachers must emphasize different ways in which students can reach that answer and allow them to be creative in the strategies that they choose, rather than simply saying yes, you are right or no, you are wrong Teachers must make the effort to give students the opportunity to express themselves creatively and must consider the different learning styles and intelligences that each child brings to the math class and ways in which they can be utilized. I am excited to learn how to approach teaching mathematics at the primary and elementary levels through this course and hope to learn more about the ways in which I can encourage creativity and risk taking in my future classroom in terms of mathematics.

“We have to rethink the fundamental principles on which we are educating our children."

My Math Autobiography

 

 

 

          Throughout my schooling, I have had significantly different experiences with mathematics, some positive and some negative. As a primary and elementary student I enjoyed math class, primarily because I always had encouraging teachers who stressed not only the importance of learning mathematics but also the importance of having fun while doing so. I remember working in groups in order to complete simple word problems or to share manipulatives. I looked forward to math class because of its interactive nature, something I did not really experience in other subject areas. I remember using a variety of materials at both the primary and the elementary levels such as, rulers, protractors, meter sticks, flashcards and place value blocks. There were often mathematical themed posters on the walls of my classrooms, displaying different mathematic symbols or various mathematical problems. The majority of my math classes would consist of completing math problems from a math booklet, either independently or as a group. These math activities usually consisted of addition and subtraction equations, multiplication problems and word problems. In terms of assessment, I remember having to complete worksheets which were collected and marked by our teachers and then placed in a portfolio, having to complete problems at home and then participating in a homework check and completing unit quizzes which would be graded.

         As I progressed from Kindergarten to Grade 6, I became more and more confident in my mathematical abilities and this positive attitude was definitely shaped by a number of dedicated and supportive teachers. It was clear that my teachers wanted my classmates and I to succeed with mathematics and that it was a subject area that they believed to be valuable. Rather than simply handing out worksheets and asking us to complete them quietly as they sat at their desks, the majority of my teachers would circulate the classroom as we worked, providing additional instructions and praise. To be honest, math and language arts are the only two subject areas that I can clearly remember, probably because they were always given the most emphasis at my school. The constant encouragement and the positive feedback that I was given throughout primary and elementary school is what I would consider to be my overall favourite memory surrounding mathematics, in other words feeling as though I was 'good' at mathematics. I did not have any 'bad' experiences with math in primary and elementary and I believe that is why I had a positive attitude towards math in general.

          However, when I got to junior high, my attitude towards mathematics changed drastically. Since I was a Late French Immersion student, my math course in grade seven was taught in French which really threw me off course. From grade seven to grade nine I struggled with mathematics and found my teachers to be more dismissive and less encouraging. By the time I reached high school, I was ready to give up on math because I no longer thought of myself as a 'good' math student. However, it was in high school that my experiences with math became positive again. I had amazing teachers who did everything in their power to prepare my classmates and I for university level math, to change our negative views of math that had developed in junior high and to make math class an enjoyable learning experience once again. They held math tutorials every day after school and provided information classes on graphing calculators and smart boards. I believe that my positive experiences in primary and elementary, as well as in high school are why I like and value mathematics today.

           In university, I decided to take Math 1090 and 1000. Although, I found these courses to be much more difficult than my high school math courses, I felt prepared for them. I visited the Math Help Center often while I was taking both courses and found it to be extremely helpful and encouraging. Overall, I enjoyed math at Memorial and feel as though I learned a lot from both courses. However, I did not choose to do any math electives once I had my two required math courses completed.

           I do not feel as though I engage with mathematics in any major way in my life, but I do use it occasionally such as when I'm dealing with money, calculating grades or measuring something. However, as a future teacher, I know I will be using math on a daily basis and I feel prepared to do so. Overall, my experiences with math, the good and the bad, have taught me to always have a positive attitude and an open mind towards mathematics, and this is something I hope to instill in my future students, in order to assist them in reaching their maximum learning potentials.  

 

Welcome to Emily's Math Blog!

This blog will be used to highlight and reflect on a variety of topics concerning Primary/Elementary Mathematics. It will also be used to communicate with other aspiring Primary/Elementary teachers.

This blog has been created for an Education course that I am currently enrolled in at Memorial University of Newfoundland, Education 3940: Mathematics in Primary and Elementary Grades.