Mathematics & My Teaching Philosophy

Mathematics in the Teacher Education program has shaped and informed my teaching practice and philosophy in a number of ways. I began this course with a somewhat strong background in Mathematics, stemming from my family that pushed me towards advanced Mathematics involving memorization of formulas to then apply to problems. I learned a great deal from this course, including and not limited to: encouraging exploration, problem-solving through group work, integrating technology, as well as resources to make math meaningful and engaging for students. The following reflection will address these key contributors to my learning and development as a future Mathematics educator.

            Although I have a strong background in Mathematics knowledge, I entered this course intimidated by the thought of teaching the subject through a student-centred approach; I now leave this course with a new-found confidence in teaching the Ontario Mathematics Curriculum effectively and on a cross-curricular level. This course has taught me that students learn best when they are given the creative freedom to explore problems and brainstorm strategies, without being exposed to a formula at the forefront. Also, through Smalls (2013), I learned a number of strategies, such as hands-on learning through the use of manipulatives, to help students avoid possible misconceptions related to various Mathematics topics. Furthermore, the SAMR (Substitution, Augmentation, Modification, Redefinition) and BUDS (Buddy Solve, Understanding Numbers, Deconstructing the Problem, and Strategy Identifier) models allowed for a deeper understanding of best practices for integrating technology and providing the best opportunities for learning in the classroom. Moreover, our progression through the unit and lesson planning assignments of this course has also better prepared me to cater my teaching practice to diverse learning needs, abilities, and interests, as well as effective spiraling of student knowledge.

            With regards to activities we participated in, I found each lesson to be packed with engaging and fun methods for teaching Mathematics, adaptable for any subject. For example, after conducting research during class about the ways Makerspace, specifically Ozobots, can positively impact student engagement, I found myself drawn towards integrating them in my microteaching lesson. I taught my students about regular and irregular shapes using the Ozobots as incentive to construct their own regular shapes, addressing Ontario Curriculum expectations. This course provided me with the confidence to step out of my comfort zone and take risks. Another example I am enthusiastic about integrating in the classroom is the Math Olympics. I found this strategy impactful at all stages of learning, a creative form of assessment that promotes team-building and critical thinking. Furthermore, the Escape Room and Scavenger Hunt activities got us out of our seats and promoted connections to real-world problems. Through these activities, we were exposed to a variety of applications and pieces of technology useful as further methods of differentiation; I specifically enjoyed working with QR codes and learning about applications such as Explain Everything, tools I hope to use in practicum and my future teaching career. 

Although my teaching philosophy is a work in progress, I am an advocate for Dewey’s theory that students learn best by doing. This course has taught me that students learn best when they understand the importance of the material they are learning, as well as participate in problem-solving and discussion with their peers. I hope to inspire lifelong learning and transference of skills through discovery both inside and outside of the classroom. I plan to provide students with opportunities to explore and support them to the best of my abilities. I also believe that human connection and relationships are just as important in the classroom as they are outside of the classroom. I want my students to know that I believe in them and care about their wellbeing. I believe that students deserve to learn in a space where they feel safe, respected, and are inspired to grow as lifelong learners.

Edugains in the Mathematics Classroom

What are the benefits of the Edugains site?

The Edugains site provides a number of fantastic resources for teachers that are beneficial for both preparation and in-classroom lessons. For example, the website includes ease of access to curriculum documents as well as the scope and sequence for various grades alongside activities to allow for teachers to build direct connections during the planning process. There are also countless resources available for supporting classroom practices, including unit videos to promote blended learning.

How might you use this site in your classroom?

The Edugains site provides teachers with opportunities to transform the classroom to that of the 21st century. Edugains allows access to digital tools for ease of integrating technology into Mathematics lessons. The website also provides lessons that promote financial literacy in the classroom, as well as tip sheets for using manipulatives with sample activities. Overall, the resources on the site promote the closing of gaps in Mathematics learning.

Top 3 Take-Aways

1. Opportunities for spiraling Mathematics lessons
2. Readily available three-part lesson plans
3. Home support resources allow for individual growth at home and extra practice if students require (i.e. TVO Mathify) 

Math Olympics in the Classroom

The Math Olympics activity allows for the development of critical thinking, collaboration, and creativity skills as students participate in a number of Mathematics-related exercises. This learning strategy is beneficial at all stages of learning - beginning, middle, and end of the unit. 

Beginning

The Math Olympics strategy is beneficial as a diagnostic form of assessment. Teachers can utilize this activity to understand what students know about a topic from the previous year in order to cater to students' learning needs in upcoming lessons. 

Middle

The Math Olympics strategy is useful for formative assessment as teachers can utilize this activity to see what topics require further review before moving forward and provide feedback. 

End

The Math Olympics activity is also beneficial as review prior to conducting summative assessment. Students may find this activity beneficial as they can practice components of the unit they struggle with in collaboration with their peers. 

Ozobots & Math

What are Ozobots?

Ozobots are small robots that allow students to learn about programming, blending the physical and digital worlds. Ozobots can be programmed to follow patterns on a piece of paper or technology, identifying lines, colours, and codes to perform tasks. The Ozobot website provides teachers with resources including lesson ideas for implementing Ozobots in various subjects. I will be reflecting on resources I found on incorporating Ozobots in Mathematics.

Ozobots & Geometry

For lessons on geometry, Ozobots can be used to engage students in creating maps for the Ozobot that pertain to various geometric concepts. For example, a task for students in grade 5 may be to create a a map that includes two rays that are parallel, while implementing some of the Ozobot coding features (i.e. tornado, spin, slow down). Another group may be required to create a map that include two perpendicular line segments. In this activity, Ozobots motivate students to apply their learning using coding and robotics. For my micro-teaching this semester, I was advised to incorporate geometry in my lesson to provide students with review to prepare them for EQAO testing. I am considereing using Ozobots as a fun and engaging component of my lesson; I hope the Ozobots will be a memorable method of conceptual understanding for these students.

Ozobots & Measurement

For lessons on measurement, Ozobots can be used to engage students in creating shapes for the Ozobot that pertain to measurement concepts such as area and perimeter. The Ozobots website suggests a challenge for students involving the creation of a rectangle that the Ozobot can complete the fastest, specifically with an area of 36 units-squared. The students would be required to determine the dimensions of their shape to obtain the correct area, as well as calculate the perimeter of their figures. They could then use the Ozobots to determine which figure they should present to the class based on the length of time it takes the Ozobot to complete the perimeter of the shape. In this lesson, Ozobots are engaging for students to apply their learning because students are motivated to determine a shape that the Ozobot moves around fastest while investigating possible shapes with an area of 36 units-squared.

Math with Connections & Kinesthetic Learning

Connection-Making Lesson Ideas

During our class this week, we were treated to donuts and muffins from Tim Horton's and were asked "Where is the Math?". This activity was fun for our class because we utilized collaboration, mathematical thinking, and creativity to come up with many possible methods of using the treats in Mathematics. Some examples we came up with include:

1. Algebra: 
• Are there enough donuts/muffins for the number of students in the classroom?
2. Fractions:
• Sharing the donuts by cutting into fractions
• Recipe cards (also implemented in measurement)
3. Geometry:
• Surface area of the sprinkles
4. Patterning:
• Rearranging the food into growing, shrinking, and repeated patterns

Using real life examples was fun because we were challenged to think about the ways we could later challenge students to make connections between Mathematics and their lives. This activity would also be fun to integrate on a cross-curricular level. For example, setting the stage in the classroom as though the classroom has been robbed. Students would then be encouraged to write a story about what may have happened in the classroom and then encourage the students to act out their scenarios - making reference to both the Language Arts and Drama curriculum. Another example may be of an Indigenous artifact placed on a desk at the front of the classroom and students are expected to write a story about it based on their knowledge of Indigenous history - making reference to Social Studies and Language Arts. There are many ways this activity may be incorporated and I am excited to implement it in my placement classroom.  

Kinesthetic Teaching Techniques

I had a lot of fun in class today as we learned about kinesthetic ways of teaching memorable pieces of information. The following are chants and dances we participated in to master the Metric Staircase and the Place Value System:

Metric Staircase: 🎶 Mickey Mouse can do many dangerous, heroic kicks 🎶 (mm, cm, dm, m, dam, ham, km)
Place Value System: 🎶 To the right, getting bigger; to the left, getting smaller 🎶

Not only is this a great activity for kinestethic learners, but for all students in general as they are encouraged to get out of their seats for an energizer that is memorable and will aid in their Math skills and knowledge. I am excited to incorporate these chants and dances in my classroom as my first block is with a grade 6 class and we will be preparing them to complete their EQAO testing.

Scavenger Hunt & Explain Everything

What?


In math class this week, we participated in a Scavenger Hunt and were expected to wander around the Brock University campus, explore various patterns (i.e. shape, colour, size, texture, direction), and document our findings with iPads. We utilized the Explain Everything software to share what we found with our classmates. Explain Everything is easily accessible on a number of platforms and involves various tools including: voice-to-text recording, pointers, text-boxes, picture and video modifications, and dropbox for submission.




So What?

The Scavenger Hunt was a great way to get us out of our seats and encouraged us to look for real-world examples of what we are learning in the class - patterning. The opportunity to learn about new pieces of technology and applications was also important for us as teacher candidates are always looking for new resources to implement in the classroom. This activity also enabled us to develop our teamwork skills as my fellow teacher candidates and I used our abilities to collaborate, communicate, and think critically while exploring our surroundings and completing the tasks assigned to us. The Explain Everything application was also interesting to explore. We found that the application was beneficial for collaboration as multiple people could use it at the same time while allowing us to express our information in methods we felt most comfortable with.

Now What?

The Scavenger Hunt is a great activity to motivate students to consider learning as not limited to the classroom. This activity encourages participants to explore the world around them in order to find real-world examples of the topic discussed. I plan to utilize the Scavenger Hunt activity on a cross-curricular level as it is a fun way to promote student collaboration, communication, creativity, and critical thinking! An example of such implementation would be in Science whereby students are given the task of exploring their school and documenting various resources on environmental issues, or even issues they would like to address. I would then encourage the students to consider the impacts such issues have on various Canadian regions which would involve both Science and Social Studies. A step further would be to ask students to critique the literature they encounter to then incorporate curricular expectations of Language Arts. As we did in our class, the Explain Everything application would benefit as both a method of presenting their learning and as a method of assessment of their findings for myself. Students would have the freedom to present their findings in a creative manner that best suits their interests. For example, auditory learners may prefer to incorporate the sound option on the application and visual learners may prefer to present their findings primarily with videos and pictures. Overall, students thrive from inquiry- and problem-based learning and such activities enable them to develop and thrive in these areas of 21st century thinking.

The following are some of the pictures my fellow teacher candidates and I captured during this activity:

Growing & Repeated Pattern

Shrinking Pattern

Growing Pattern

The "Turn-it-Around" Technique

What?

The "turn-it-around" method involves providing students with the answer, asking them to explore various problem-solving strategies, and encouraging them to brainstorm possible problems that may result in the answer provided. Through this activity, students are encouraged to construct their own knowledge while developing their conceptual understanding and mathematical thinking.

So What?

The readings this week emphasized the importance of problem-solving and this classroom activity allowed for us to see such problem-solving techniques in action. My educational experience generally involved the traditional approach to mathematics whereby I would be presented with a formula and a problem to apply it to. I thoroughly enjoyed collaborating with my peers as we worked backwards and attempted to create a word problem that emphasized real-world applications.

Now What?

I am interested in applying such a technique in the classroom because it encourages students to think outside of the box, utilize their prior knowledge of problem-solving strategies, and promotes collaboration. This activity also encourages students to explore problem-solving strategies that meet their individual needs and interests. For example, a students who is a visual learner may prefer that I provide manipulatives for them to utilize in this activity. Overall, I am enthusiastic about learning about the various problem-solving techniques mathematics has to offer. I hope to aid in the development of my students' problem-solving skills that they will use throughout their lives.

The following images are of the answer provided for my group alongside the word problem we created: