Mathematical Digital

PortfolioAdriana Ferlisi

Table of ContentsAbout Adriana Ferlisi . . . . . . . . . . 3Week 1 . . . . . . . . . . 4Week 2: Ontario Elementary School Mathematics Curriculum . . . . . . . . . . . 5Week 3: Number Sense and Numeration (1) . . . . . . . . . . 6Week 4: Number Sense and Numeration (2): Fractions & Decimals . . . . . . . . . . 7Week 5: Number Sense and Numeration (3): Integers. . . . . . . . . . 8Week 6: Number Sense and Numeration (4): Rate, Ratio & Proportional Thinking . . . . . . . . . . 9Week 7: Patterning and Algebra . . . . . . . . . . 10Week 8: Geometry and Spatial Sense . . . . . . . . . . 11Week 9: Measurement: Guided Inquiry . . . . . . . . . . 12 Week 10: Data Management and Probability . . . . . . . . . . 13Week 11: Formative Assessment . . . . . . . . . . 14Week 12: Final Reflections . . . . . . . . . . 16Conclusion . . . . . . . . . . 17

About Adriana FerlisiWhy am I making a Digital Mathematics Portfolio?

a) I have not had much experience in the field of Mathematics, and b) math is not only highlighted as one of my interests...yet. Well, if you should know, both of those assumptions

are wrong. I have had experience teaching simple math to students, as well as, I used to have a passion for math and it was going to be a choice of interest as a teachable, but I lead more

towards the arts.

The purpose of this digital portfolio is for me to be able to reflect on previous work, activities, lessons, and readings that I have been exposed to from weekly themes and theories of

information collected from my Mathematics course in Teacher’s college. The theme I have established for this portfolio is to build on my own personal growth of teaching mathematics

to J/I students. I want to be able to look back on this experience and reflect on my personal outlooks about the different ways that math can be taught and learned in a classroom, and

different strategies that I have used that have worked or that I have struggled with throughout the semester.

Hope you enjoy!

page 3

Week 1Entering this course was exciting, but nerve wrecking. I went into the course knowing that I would learn about teaching math. But how? How would I be able to teach mathematics? I cannot even remember how to add fractions, let alone learn how to teach students the material for the first time. I began to look through the course textbook during the first week of class, Making Math Meaningful to Canadian Students, K-8, by M. Small, and this changed my whole view about mathematics. Not only does it emphasize the importance of how to “make math meaningful,” it really takes someone like myself, who has not learned math since about grade 11, through a journey of reestablishing concepts and meanings and definitions of important topics in a lesson. This textbook really blew my mind. I was really excited to begin to read chapters because I knew from the moment I took a glance, this textbook was going to be a great guideline to help re-teach myself how to unpack and explain mathematical ideas.

But this was only the beginning...

page 4

Week 2 - Ontario Elementary School Mathematics Curriculum

One of the most significant tools to my studies this year was the Ontario Elementary School Mathematics Curriculum 2005. I remember being introduced to it during week two and being so scared and nervous to use this in the everyday

classroom and to acknowledge it in my lesson plans.However, there was a lot to learn about this curriculum document. Not only does it define what students need to know,

it unpacks knowledge and anticipates how mathematical ideas change and grow. Although there are changes through each grade, there is a connectedness of expectations, including the process expectations, which are the active

processes that students use as they work to achieve the content expectations. For example, representing, reflecting, communication (selecting tools and computational strategies), connecting and reasoning and proving. With the use of

these processes, incorporates effective practice and engages in student success.

How will this help me? This curriculum document will basically be considered my “best friend.” This particular mathematics document “recognizes the diversity that exists among students who study mathematics,” (Ontario Mathematics Curriculum 2005). The document is beneficial because all students can learn math and should be able to do so. Although all students may not learn the same way, using the same resources, and within the same time frames, this document has become an accessible tool that provides a demonstration of active participation of all students by clearly identifying the knowledge and skills that are expected at a particular grade level. As a result, it aims to challenge all students by including expectations that require thinking that goes beyond mathematics, but how it challenges them in the real world. Thus, I hope to maintain a classroom setting with these expectations and to provide consistent challenges for all students of mathematics, but that can be connected from mathematical concepts and the real world.

page 5

Week 3 - Number Sense and Operation (1)This article describes the importance of how classrooms should be placed where students are constantly interacting, collaborating, being assessed consistently, and using many ways to solve real-life problems in challenging ways. It is not a place where students feel that they cannot succeed, or can only use one way to get to an answer, or even where mistakes are not allowed. A mathematical classroom needs to be one that can help them in their lives, because of the way they are thinking and problem solving and developing an inquiry.

So why is this important to my studies?The reason this article hits everything that I would love to reflect on from the course, is because it shows that teaching math is not focused on having students get to the correct answer, but to teach math in a way that explores each students learning styles, captures the essence of real-life problems, and developing their growth in their own learning skills and work habits.

How has this article helped me grow as a mathematical teacher? As I stated, I have been very fortunate to be enrolled in this course. I learned a lot about teaching students, teaching math, but also a lot about myself. I learned that it is okay to fear the unknown and something that you may not be good at. However, in order to succeed, you must try and try again. Nothing is ever as bad as it seems. So when I first started I feared that I would be terrible at math. Learning this information has really inspired me to go even just a step deeper and hopefully take an additional course of math in the near future. It has now become

one of my favourite subjects to teach, and I cannot wait to use it in my practicum. page 6

Jo Boaler's How Students Should be Taught Mathematics: Reflections from Research and Practice.

Learning Activity Presentations

In this presentation, you become the teacher. The idea of this presentation is that one student will prepare to lead their other classmates through an 8-10 minute activity based on the theme of the week. It can be any kind of activity that interests the student, but has to follow some guidelines. During this week’s presentation, I decided to pay close attention to Matt Callaghan’s Roll to Win.

The use of fractions is unlimited!

Fractions are very important for students to learn because they help influence different methods of a situation, whether it is dividing up a workload, or planning a meal. In some instances, fractions are important for students future careers like architects, doctors, or any type of technical position because you need to have a concise answer.

Why does this game have an impact on me?

This game is simply engaging and has taught me a lot about what to prepare for when becoming a mathematical teacher. The simplicity of the lesson has taught me that it is important to keep the lesson simple, easy and fun because students stay engaged and do learn through playing a game instead of actually working.

Week 4 - Number Sense and Operation (2)Fractions & Decimals

Matthew Callaghan Roll To Win! (1 October 2015).

page 7

Week 5 - Number Sense and Operation (3)What was most significant about this lesson?

One of the most important things that I could really take away from this lesson was that I FINALLY UNDERSTAND FRACTIONS! After plenty of years being taught fractions, and plenty of years struggling to understand them, both within class and out of class situations, and after all this time I can proudly say that I understand fractions and that they are 100% relatable to life scenarios.

What are Tangrams? Tangrams are very useful within the classrooms because you can take them apart from the shape, and make different ones this

way students have a chance to figure out the fractions if they cannot identify it in a particular shape. How I can use this in classrooms is not just with fractions, but also different lessons in math like geometry too. For instance, I was able to identify that

the larger pieces would be a larger fraction because they take up majority of the space.How has this improved my personal growth as a mathematical teacher?

My experience with this lesson, is that I did need extra help with learning fractions than integers, and by spending a little more time with them and using more hands on approaches to solve for fractions, I have been more comfortable with being able to

really connect to the lesson. Math is everywhere. It is important for us as educators, and future students, to really grasp their understanding of math. If we do not teach it for ALL students to understand, there may be those students, like myself, who will

never really understand a concept until it is completely broken down for them.As a result, I hope that by gaining this mathematical knowledge about fractions, it can work for me as a future educator.

Integers

page 8

Week 6 - Number Sense and Operation (4)

A good math problem challenges a student's mind by making it wide-based where they can come up with multiple answers and solutions, but mainly something that is relatable and realistic so students can grasp the question and make it more personal. By providing a question that is realistic and relatable, students are more capable of applying what they are learning to the situation and are also being able to problem-solve with real life scenarios.

Rate, Ratio & Proportional Thinking

page 9

How do these good math problems relate to the topic of the week?The importance of having a good math problem in proportional thinking is because it is a topic that students will have a difficult time understanding. Without the questions being realistic or relatable, students may not be able to comprehend the ideas and concepts behind the lesson.

In what ways does this contribute to my personal growth? I still have a bit of a difficult time understanding portional reasoning and how to use in with realistic problems. I have been exposed to some of my own weaknesses, and I am able to use this information to strengthen my own learning. However, this particular lesson Which Has More? gives students the opportunity to break down the question to its simplest form to easily understand the question.

Laura Ionico Which Has More? 22 October 2015

Week 7 - Patterning and Algebra

What has made me grow when making this mathematical problem?What I have noticed and learned through the activity is that it is important for students to have information provided within the question, but not too much, and under a certain context. In my activity, I had been restricted to a specific time limit and therefore, felt that it would be important to give more information this way classmates would be able to understand the question and the learning goal and be able to adjust the quality for their own students with the answer they were able to find.

page 10

Reflection on this math problemwhat I can reflect on that can reflect my building knowledge for my future math

lesson plans, is to provide a question or activity that is more challenging for students. For instance, by allowing students to have many questions answered because I have identified most of what is needed to know in the question, this

limits the student's ability to be creative and think beyond what the question is looking for. By limiting resources in the questions, students can begin to think, "well do we need to use Q-TIPS?" or "how can we get to step 3, step 4, etc." (If

steps 3 and 4 were not given above).

What can I improve on?It is important that students can be presented with the question that can allow for more ideas to

flow and more questions to be asked because it creates a question that will result in multiple ways to get to the answer. I have learned this because most of my classmates got to the answer the

same way. Although it is okay that this happened, I need to keep in mind for the future that not all students will understand the one way to get to an answer, which is why it is important for me to

make the question more broad and allow the students to put their own imagination into it. Adriana FerlisiBridging Together with Q-TIPS

29 October 2015

Week 8 - Geometry and Spatial Sense One of the class learning presentation activities that was introduced in class this week

included the photo above of Super Mario's symmetrical body, where each student

would have to draw the opposite side. This particular lesson "Mario's Mirror Land,"

identified the different ways that you can introduce symmetry at a younger age group

(i.e. Grade 4).

page 11

How can I, as a teacher, engage students in geometry? Effective ways that geometry can be interesting to students is because students can make

personal connections to the understanding of shapes, especially because shapes are everywhere in our lives. For instance, many students have most likely played, at least once, or have heard about Super Mario. Therefore, the "teacher" of the lesson used this example as a way for students to be engaged and connected to the work that they were going to do.

By connecting mathematical studies to personal life, makes students more engaged in a way that teaches them, but also allows them to have fun with the learning process.

What contributions are being made to my personal growth as a mathematical teacher?Although the course has been introducing a lot of group work activity, this Mario worksheet made me realize that independent work is still just as important for students' learning. Although working in groups is great for new and creative ideas and learning from other students, it is still important to have students work on their own to be able to understand concepts and materials, and to see what their strengths and weaknesses are in math.

Eva Chu Mario’s Mirror Land

5 October 2015

Week 9 - MeasurementWhat is Guided Inquiry?The importance of guided reading is to go through the lesson or activity with the students. What I have learned about guided inquiry is that students become more comfortable with the material. For instance, working on the partner activity, it was nice to get to work as a class and have the teacher help with step by step instruction.

How will guided inquiry help in educational activities? Guided inquiry will help and be useful in educational activities because it will take a step away from student scaffolding, but allow everyone to work together. However, if there is a particular part of the students to understand, this tool will be an effective way of breaking down the material and really look at and question the material being taught.

Personal Growth In some ways, I find that because everyone is using the same materials and manipulatives for a guided inquiry lesson, and solving for equations, some students may feel that they need to figure out answers before everyone else. I do understand that there will be whole who will be faster learners in the process, but how, as a future educator, can I reassure that it is not a competition and that we will be covering all questions?

page 12

Guided Inquiry

Week 10 - Data Management and ProbabilityWhat are some disadvantages to teaching with technology?What I have been able to contribute to my knowledge about these learning activities is that there are many different ways that you can use similar sources, but also that there are a variety of different sources needed. With one of the activities, the gizmos, I have also learned that you need to reassure that time is used properly and planned well by the teacher, especially because students can get a little off track when they are using technology and getting to draw things on them. Another faulty thing about technology is if there are not enough devices to use in the classroom, or in the school at all. It makes things a little more difficult and we will have to accommodate by working with partners or deciding to use these technological apps as an introduction activity.

How can this apply to my personal growth in math?What I am learning about becoming a mathematical teacher is that I can always be exploring technology. It is important to see how different people in different schools and towns are using technological devices to incorporate their lessons in the classroom. It is also important to explore, on my own, the different sources that are available and see what ones I find I like for me, and which ones may fit the needs for all the students in my placement or classroom. I really enjoyed the opportunity to use a different technique for teaching math and seeing how we can apply problems (worksheet activities) of math, to technological links and applications like gizmos.

page 13

Week 11 - Formative Assessment

Checkbrics

These represent symbols of the achievement chart standards - so students cannot identify the level grade

they are receiving during the assessment process.

page 14

… continued

page 15

In math class we discussed the importance of assessment and were provided examples of different styles of rubrics and checklists that we could use to create correlation to improved learning in a classroom where there is a greater emphasis on evaluation or grades the students receive.

Different Types of Assessment ToolsOne of the things that I really liked was the discussion about how we could use different symbols when marking students that are in a specific level during the activity or the assignment.I really enjoy how these are simple symbols, and that students have a difficult time understanding what it stands for.

What I would use these in is a check-bric. These check-Brcs identify the student's' name, the learning goals of the lesson, the level (where you would add the symbols above), and comments that they teacher can incorporate about the student.

How has this discussion helped my understanding of assessment?Using these forms of assessment have become some of my favourite tools that I will definitely use in my classroom. I feel that assessment is a lot easier than I have been making it out to be. I have to say that this hour and a half has helped me clarify the importance of assessment, the definitions of assessment as, for, and of, and different tools to use with assessment.

Week 12 - Final ReflectionFinal ThoughtsThroughout this semester, I have been greatly inspired to succeed when teaching mathematics. I have been so great full for the opportunities and experiences, the resources, the abilities, and even the many pages of notes taken during the class. I would love to reflect each and every minute about what we discussed in class, but in reality, the ones I have chose for my portfolio highlight the most important ones to me.

With the help of these resources and all the information provided, I am now very proud to say that I am ready to become a mathematical teacher. I have a lot more confidence in myself to know that no matter the issue, it is all about student success and striving to provide the most opportunities for students to succeed. Whether it is through using manipulatives, or real-life problems, even incorporating the use of technology, I am ready and willing to do anything for my students in order to see their highest performance. I could not have felt this confident without this course and cannot wait to start teaching math in my placement block.

page 16

Conclusion I have been very fortunate to be enrolled in this course. I learned a lot about teaching students, teaching math, but also a lot about myself. I learned that it is okay to fear the unknown and something that you may not be good at. However, in order to succeed, you must try and try again. Nothing is ever as bad as it seems. So when I first started I feared that I would be terrible at math. Learning this information has really inspired me to go even just a step deeper and hopefully take an additional course of math in the near future. It has now become one of my favourite subjects to teach, and I cannot wait to use it in my practicum.

page 17