Artifact #7: Math trail.

The seventh artifact that I am including in the portfolio is the math trail assignment. In

this assignment we were instructed to go on a walk somewhere and take pictures of the various

forms of math that we saw, connecting them back to the five strands of math- Number Sense and

Numeration, Measurement, Geometry and Spatial Sense, Patterning and Algebra, and Data

Management and Probability. Through the completion of this assignment I got a different

perspective of the world around me, when looking at it through a math lens. This type of

assignment can be done with students of any grade level and not necessarily just with math, I

think any subject could be used as a lens for students to look through. This kind of teaching

shows students that what they are learning is relevant to their daily lives and it will make it so

much more fun and engaging for them.

Connection to standards.

InTASC standards.

Standard #3: Learning Environments. The teacher works with others to create

environments that support individual and collaborative learning, and that encourage positive

social interaction, active engagement in learning, and self motivation.

Standard #4: Content Knowledge. The teacher understands the central concepts, tools of

inquiry, and structures of the discipline(s) he or she teaches and creates learning experiences that

make the discipline accessible and meaningful for learners to assure mastery of the content.

Standard #5: Application of Content. The teacher understands how to connect concepts

and use differing perspectives to engage learners in critical thinking, creativity, and collaborative

problem solving related to authentic local and global issues.

assessment to engage learners in their own growth, to monitor learner progress, and to guide the

teacher’s and learner’s decision making.

Standard #7: Planning for Instruction. The teacher plans instruction that supports every

student in meeting rigorous learning goals by drawing upon knowledge of content areas,

curriculum, cross-disciplinary skills, and pedagogy, as well as knowledge of learners and the

community context.

Standard #8: Instructional Strategies. The teacher understands and uses a variety of

instructional strategies to encourage learners to develop deep understanding of content areas and

their connections, and to build skills to apply knowledge in meaningful ways

NYS Code of Ethics for Educators standards.

Principle 2: Educators create, support, and maintain challenging learning environments

for all. Educators apply their professional knowledge to promote student learning. They know

the curriculum and utilize a range of strategies and assessments to address differences. Educators

develop and implement programs based upon a strong understanding of human development and

learning theory. They support a challenging learning environment. They advocate for necessary

resources to teach to higher levels of learning. They establish and maintain clear standards of

behavior and civility. Educators are role models, displaying the habits of mind and work

necessary to develop and apply knowledge while simultaneously displaying a curiosity and

enthusiasm for learning. They invite students to become active, inquisitive, and discerning

individuals who reflect upon and monitor their own learning.

Ontario Ethical Teacher standards.

developing students' potential. Members express their commitment to students' well-being and

learning through positive influence, professional judgment and empathy in practice.

DOE claims.

Claim 1: Medaille College graduates know the subject matter in their certification area(s)

Claim 2: Medaille College graduates meet the needs of diverse learners through

effective pedagogy and best teaching practices.

Anna Dobrucki

EDU 502

Zuhra Abawi

June 23, 2020

Picture 4 Picture 5

Picture 6 Picture 7
Picture 8 Picture 9

Picture 10 Picture 11
Picture 12 Picture 13
 For my Math Trail I went on a walk through my neighbourhood, a suburb in Courtice,

Ontario. In picture 1 you can see a walkway leading up to a house that is located on a corner lot,

the walkway goes up diagonally at a 90 degree angle, or a graph growing exponentially, between

the two sidewalks and shows algebra. Picture 2 shows a house number, which are present all

throughout the neighbourhood and shows number sense, it helps people to find a specific house

knowing that the numbers will follow each other in order down the street. Picture 3 shows four

parallel lines stamped into the concrete of the sidewalk, as well as one perpendicular line which

all four parallel lines will eventually cross- this shows geometry. Picture 4 shows a curve of

bricks along a driveway, this curve can be calculated using an algebraic formula, the bricks also

follow a pattern. Pictures 5 and 7 show mailboxes, each individual mailbox is a square and is

labelled with a number- these pictures show number sense and numeration, geometry, and

special sense. In pictures 6 and 8 you can see bricks laid in a pattern in the sidewalk as well as in

a driveway, which show patterning, geometry, and measurement. Picture 9 shows symmetry very

well, except for the house number, a line could be drawn down the middle of the picture from the

peak of the roof to the driveway and the left and right sides would be mirror images of each

other- which goes under geometry and special sense. The fence that is shown in picture 10

displays measurement and patterning. Pictures 11 and 13 show two shapes that I saw during my

math trail, the circle of the manhole cover and the perfect square that someone made around the

base of the tree- geometry. In picture 12 I wanted to focus on the stairs, they show measurement

and they also would look like a graph if looked at from the side so algebra is present. There are

also square patio stones used in front of the stairs laid in a square pattern to show geometry and

measurement.
Reflection

I actually really enjoyed math in elementary school, however while doing the math trail it

put a fun spin on traditional math for me. I definitely never had this sort of math experience

when I was in school. We learned math very traditionally- lecture style, in a classroom, using a

textbook, and completing worksheets. While this worked fine for me, I know that other students

in my classes struggled with that traditional, rigid style of teaching, if our teacher had tried to

make math more engaging and fun, probably all the students would have benefited. I remember

that all of the subjects were very split up, we learned math during math class, but I think mixing

the subjects up and integrating them with one another would have been much more effective to

our learning. I will definitely incorporate math trails into my teaching some day. When we are

able to show students that you can learn in many different ways, not just by sitting at a desk and

reading a textbook, we make learning so much more fun for them and they will want to learn

more and more. Just like when you are driving on a highway and specifically look for blue cars,

you will see so many more of them compared to if you aren’t thinking about blue cars. When

you go on a walk specifically looking for and thinking about math, you will see it everywhere. I

think this could also be incorporated into other subject areas- going for literacy trails, science

trails, art trails! All of these would lead to valuable learning experiences for students, and the

more we get them to change their perspectives, they will start going on and noticing these trails

all on their own.