Non-Stop Learning in Teaching

My Learning Experience in Mathematics Primary/Junior Part 1


Many thoughts crossed my mind when I registered for Mathematics for Primary and Junior Part 1. Some of these thoughts included fear, frustration and doubt as I have never enjoyed or have been a successful student in the subject of Mathematics. I believed that we were going to look at and assess different Math concepts that appear to be the most difficult for students based on EQAO or research results. Instead, I learned about the behind scenes logistics about being a teacher teaching Mathematics. I have learned about how to develop a math community within my classroom and amongst my students, the impact of purposeful and strategic planning and assessment strategies, the development and use of learning goals and success criteria, and how we need to incorporate a variety of tools such as literature and technology into our Mathematics classes.

Creating a Math Community

Before anything academic happens in the year, educators try to create a community within the classroom amongst the students to create bonds and friendships and to assess personalities. However, it should be noted and stressed that every subject within the curriculum should have its own type of community developed for students to know how to act and what to expect within that type of community atmosphere. For this particular course, the development of a Mathematic Community is stressed for student participation and success. There are many aspects to a Math Community such as setting expectations and discussing those expectations, the teacher role and practices, student interaction, the student role of being a Mathematician, available and appropriate materials and tools, and the variety of assessment strategies. Creating a Math Community all starts with the educator and how they approach developing their learning environment. I am an advocate for the use of the Constructivist Approach in all subjects in education where “students are recognized as the ones who are actively creating their own knowledge” (Small, year, p. 3). Through the use of active learning, my future students will be provided opportunities in an environment where they are able to share ideas and work through mathematical problems in a variety of ways whether independently, as a whole class or in small groups.

As the educator and facilitator to my future students learning, it is my responsibility to provide them with quality learning experiences. Everything seems to flow together like a domino design creating a masterpiece. For my students to be successful, it all begins with the development of purposeful and meaningful lessons and tasks that emphasize problem-solving and conceptual understanding (Ministry of Education, 2011). These learning opportunities need to be rich math tasks that encourage complex thinking, have the requirement of using Math Talk, and have a range of solutions (Ministry of Education, 2011). After the planning process has come together, the need for high quality student interaction needs to occur as my teaching philosophy includes Constructivism which emphasizes learning through doing. Although it is great to see students physically involved in their learning, there is also the need for social interaction to be incorporated where students are able to talk out their problems, reasoning and concerns with fellow students. Social interaction in Mathematics is crucial for student thinking, reasoning, discussion, and questioning skills and capabilities to grow and develop with every new task or unit presented to them (Ministry of Education, unknown). These crucial elements to Mathematics learning also require students to know that it is OK to disagree with their peers as long as they can reason and explain why they don't agree (Ministry of Education, unknown). Lastly, through a Social-Constructivist approach to teaching, I can plan my lessons in order to activate student prior knowledge, incorporate tools and elements of language and technology, and discussion Think, Pair, Share processes to my lessons (Ministry of Education, 2011).

Additionally, I believe that it is also important to teach my future students how to be a Mathematician and what it means to be someone who works with numbers. The Ministry of Education (unknown) states that to be a Mathematician, students need to persevere and be open to new ideas, be collaborative, be flexible thinkers, and be able to learn from their mistakes. This is a new concept to me that I now believe should be taught, reinforced and incorporated on a daily basis as these individual skills are life skills that students need to learn and work with as they will encounter new ideas and more difficult tasks as they grow up.

Learning Goals and Success Criteria

The process of developing and using learning goals and success criteria with my students is still a new concept for me. I have had to use them during my three practicum experiences through the Faculty of Education, but I feel that I was not creating or using them appropriately, nor did I understand the actual difference between them. This course has provided me with more thorough insight and opportunity to learn about these two important concepts in a classroom. Learning goals and success criteria are important for any subject in school for students to know what they will be learning, what to expect from the content, and what they need to do in order to be successful.

As a new educator out of school, I haven’t had that much experience needing to develop lesson plans with learning goals or success criteria, but during my time at the Faculty and throughout this course, I have had the opportunity to reflect upon the areas in which I need to work on in order to improve my teaching and incorporation of learning goals and success criteria. I believe that my first immediate step is to be mindful of communicating more with my students. I have reflected upon my lesson planning and teaching approaches over the past year and realized that I have the tendency to think that everyone else knows what it is I am thinking and over plan for a lesson. I know what I want from my students, but I have a hard time expressing those expectations (i.e., looks like), goals and learning criteria to my students and keeping it simple. Therefore, I need to learn more about how to write learning goals and success criteria in brief statements in student-friendly language that describe what students should know and be able to do by the end of a period of instruction (Edugains, 2010) so that I understand what I want from them and so that they understand what I want. Overall, I need to learn how to write learning goals and success criteria. In order for my immediate next steps to occur, I need to write down the success criteria on Post-it Notes in my notes as a reminder for myself towards what I want my students to get out of this lesson and how to succeed. Moreover, I plan on incorporating the development of learning goals and success criteria with my students as anchor charts as visual referrals throughout the unit because learning goals and success criteria “are the foundation on which students base their ability to monitor their learning and determine next steps” (Edugains, 2010). Lastly, I plan on speaking with other professionals that I work with or know for guidance, reading more examples of how to write them, and practicing how to write learning goals and success criteria. By using learning goals and success criteria in my classroom, I am ensuring that students are clearly understanding learning goals because I have set the stage for students to be able to “focus on their efforts on achieving the goals, monitoring their progress, and setting their own goals” (Edugains, 2010).

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As, For, Of Learning

I am grateful that I have had more opportunity and insight provided to me for how to create the “Sandwich Assessment.” The Sandwich Assessment includes assessment of, for and as learning. Assessment of learning is the top bun of the sandwich where teachers assess what children currently understand or misconceive about a topic (Ministry of Education, 2006). Assessment for learning is everything in the middle of a sandwich where educators use a variety of lessons, assessment strategies and tools in order for students to become confident and competent self-assessors and Mathematicians in a topic and determine where teachers need to adjust their teaching approach (Ministry of Education, 2006). Lastly, assessment as learning is the bottom bun where teachers create a task that acts as a summary for each child to show and demonstrate their level of achievement in the topic (Ministry of Education, 2006).

Each section of this sandwich requires educators to always have a purpose in mind when they are providing work to their students. Although I had to create lesson plans for my practicums through the Faculty of Education, I feel that those lessons were not overly valid as I went on personal judgement all the while using the curriculum documents in order to write the lessons. My lessons, I believe, did not flow. One reason they did not flow is because I usually arrived at a school when they were in the middle of a unit and I was given the task by my teachers to simply create lessons based on what they were talking about. I did not learn anything regarding assessment for and of learning because I was never there to plan or witness the assessment of students’ prior knowledge or their new understanding and knowledge in a culminating task.

I now understand that this form of formative assessment is the most powerful tool for learning. I have learned that “learning happens when what we believe to be true is challenged with new information and can’t fit into the schema that we have tried to develop to try to explain the world around us” (Ministry of Education, 2006). When these challenging conditions are presented to students, one part of assessment of learning that needs to be constantly incorporated into assessment is the feedback to students (Ministry of Education, 2006). From reflection through my career thus far and throughout this course, I have learned that less is more when it comes to planning. I believed that when I was to be planning for my practicum classes that my lessons had to be extravagant in order for my students to be interested and learn something from them. I tried to keep this new simplistic planning approach in mind as I completed tasks for this course and as I’ve been planning for my Sunday School class that I teach every week. I have learned to keep lessons short and simple but have strong messages in them that are direct and to the point. From this change of planning strategies and approaches, I have found that my students prefer this type of teaching than the over-the-top kind I was attempting while in the Faculty. Over time with experience, my planning capabilities and strategies will only improve because I will see through my students’ work whether they are understanding the concepts I am teaching them based on the types of assessments I use.

Assessment Strategies & Tools

This portion of the course has truly been the biggest help to me for further developing my personal toolbox of assessment strategies and tools. I have learned so much from my colleagues during the entirety of the course. When I first considered teaching as a career, I perceived it to be entirely based on organization skills and being able to work with children. As I went further and further into school, I came to realize that organization is most certainly a skill required to do the job but it is not the most important thing. Out of everything I could possibly take away from any course I have registered for is the importance of deeply considering the discussions on assessment.

Assessment, for me, is going to be the hardest aspect of the job to work with.

I have been informed by many teachers I have had throughout my education that have told me that it will take about five or more years to figure everything out. With every course that I take, I realize yet again how right these educators were. There are so many considerations to take into account when you are planning your units. For example, in a general sense, I need to consider the Achievement Categories of knowledge and understanding, thinking, communication and application from the Growing Success ministry document (2010). Then, within those Achievement Categories, there are specifics as described by Small (2012) that are the following:

1. balances the measurement of both Mathematic content and processes

2. is its purpose appropriate

3. does it include a variety of assessment formats

4. does it align with student needs and expectations

5. is it fair to all students

6. is it useful in assisting students to assess their own learning

7. measures growth over time

Although the process of planning the units and the as, of, and for learning assessments are considered, seeing what the students create is what I cannot wait for in order to see their thinking put into a physical product. Small (2012) states that for students to be successful when submitting an assignment, educators must consider that it is “essential for students to have a clear understanding of what the desired product looks like. Might need to prepare examples, co-creating assessment criteria with students and involving constant use of instruction goals with students.” I have already included this practice into my teaching approach as exampled in my lesson submitted in Module 3 where students had to create a string of lights with 2 to 3 attributes of a pattern. I provided not only verbal expectations but a visual example in order for students to understand the general idea of what I was asking from them. In other situations throughout a unit, I may use other assessment tools or strategies such as mind maps (individual or in small groups), exit or entrance tickets (review of a concept to see any misconceptions or understanding), authentic assessment such as observations (i.e., anecdotal notes), providing a variety of different test formats (i.e., over a technology program such as Socrative or Pixie or multiple choice), and independent, guided or group work opportunities.

Rich Learning Tasks

Before taking this course, I had never heard of the term “rich learning tasks” and I was very lost when I was completing the readings for this module. After completing the readings, I took a look at what other individuals were submitting in the Module discussion board and kind of understood what they were. As I began to create my rich learning tasks, I slowly realized what I was doing and how I could connect these tasks to my teaching philosophy of using the Constructivist approach to learning. (2016) has a list of characteristics of rich learning tasks that made it helpful to refer to when planning these submissions. The list consists of rich learning tasks being:

- Intriguing or challenging

- Related to a key concept or big idea

- Responsive to a range of student abilities and skills

- Open to different approaches

- Solvable in more than one way

- Conducive to decision-making

- Opportunities for collaboration

Some examples of rich learning tasks that I gathered from my peers from this course include games, using real-world questions, examples and connections in order for them to take their learning into the world outside of school walls and halls, and a balloon challenge. I found the Balloon Challenge on Pinterest and it includes grouping students and providing them with a question to solve as many ways as possible on a balloon. Then, students provide the class with one way that they solved it. Whichever team has the most solutions wins a prize. I found this activity quite exciting! I would have loved to participate in something like this in Math class instead of constantly relying on a textbook and worksheets teaching me concepts which obviously didn't work. Moreover, I want to aim towards planning my lessons with a cross-curricular focus in order to make connections between the subjects for multiple "subject thinking hats" to adorn the heads of my students. I believe cross-curricular planning is beneficial for students to see how and use things in multiple ways that relate to them. Therefore, I have permanently ingrained it into my brain and teaching philosophy that I will use as many rich learning tasks as possible throughout my career. Of course, as I said earlier, the first five or more years will be a trial period of everything and anything I want to incorporate into my classroom. With everything else in this profession, it will take time for me to become accustomed to a way of teaching and to figure out what works and does not work through constant self-reflection.

Writing in Mathematics

This section of the course came to me as a surprise. I never considered that literacy can be incorporated into Mathematics further than simply stating an answer in a systematic manner. In Mathematics, just like in science or in persuasive writing, students need to learn how to justify and explain their answers. This skill, as I realized and now highly support, needs to be taught to students and constantly reinforced. When students begin to use this skill by habit, it can be used across all curricular subjects and can better support their learning. In Mathematics, it is possible to incorporate writing into assignments given to students such as using a concept and set of numbers in a story format where students write a story with characters, settings and a plot that involve a set of numbers, an algorithm, or concept provided to them. Another strategy for assessing student understanding of mathematical concepts would be to have students create their own questions to give to their peers to solve.

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The course of education and how educators are to approach teaching children in today’s classroom has changed immensely. As we are living in Generation X where children born in this period have more experience and skill with technology than their parents, we are required to incorporate that knowledge and skill set into a classroom learning environment. As supported in Small (2012), technology should be used in the classroom environment. For example, Small (2012) mentions that students are now being assessed through tweets, blogs, bitstrip comics or personally designed webpages to demonstrate understanding in unit content. It is further supported for educators to use technology as a form of assessment because students often submit richer insight into what they know and can do (Small, 2012) versus having to sit for 30 to 60 minutes in order to answer questions under pressure.

I believe that technology should be available to a child in or out of school in order to assist them, rather than rely on technology to do things in life. I believe in using technological resources such as SmartBoards, iPads and computers to aid my students in their understanding in concepts or for projects. Technology can be used in many ways. It can be used to assess students by using programs such as Pixie, Kahoot, or Socrative. Technology can be used to reinforce concepts from a variety of subjects such as Mathematics at sites like Cool Math Games, IXL Math Websites, Prodigy Math Games, Dreambox, and more. Additionally, technology like iPads can offer students with a variety of apps that can reinforce Mathematic concepts. These apps include Lightbot, Kodable or Hopsctoch. As every student is not the same in terms of the way they learn, they should be provided with a way of showing their thinking and understanding in a different way. This is where technology comes into play. If a student is behind in their writing skills but can verbally explain their reasoning, I would use a speech to text program through Google Drive or Dragon Speech. I believe in the use of technology, but not relying on it in order to teach students fully. Additionally, technology can be used to translate questions into another language for any English Language Learners in a class (Small, 2012).

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Literature in Math

Before this course I did not realize how many resources there were published for primary and junior grades having Mathematic concepts in stories. I think, especially for the primary grades, that this form of literature would be beneficial and ideal for teaching and using concepts in a variety of ways. For example, a story book such as The Grapes of Math by Greg Tang offers a fun and visual way to look at fractions while using grapes. This concept can then be implemented in class using real grapes or classroom manipulatives to further investigate the concept introduced in the book. Additionally, literature that incorporates Mathematics can be planned into cross-curricular lesson plans such as Art, Drama, Social Studies and the Language Arts. Literature with Mathematics, I have learned, can be found in cross-cultural circumstances. What I mean by this is that I did not think to investigate what books are available in the world that involves Mathematic concepts connected with other cultures. Whether in English or in a home language for an English Language Learner, having books available that show the same concept just visually shown in a different way may permit ELL students to feel a little more comfortable participating in class. Every effort helps.

Ten Little Rabbits

Final Thoughts

Although Mathematics still frustrates and scares me away from teaching it at this point in time, I feel at least more confident in the behind the scenes logistics of teaching Mathematics in primary and junior grades. From the beginning of the year to the end, it is critical to provide students with a safe learning environment where they feel that they can make mistakes and yet still thrive because a Mathematics Community has been established within the class. All the while, a variety of constant purposeful assessment is being implemented into three-part lessons which would include rich learning tasks where multiple ways of answering a single question could be the way to create a class discussion. With the aid of technology and literature assisting with introducing or reinforcing Mathematical concepts, there is nothing students in Generation X will not be able to do.


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