EDBE- 8P39 🧮🔢

 

Teaching Mathematics at the Primary Junior Grades in Ontario 

Hello, And Welcome to My Teaching Mathematics At the Primary and Junior Grades. My Name Is Ms. Cara, I am a teacher Candidate at Brock University. 

The purpose of this Math Reflective Journal, is to document my Journey as a Teacher Candidate At Brock University around the subject of Math.  My Math Course is about developing an  initial awareness, knowledge, capability and confidence about Mathematics and Mathematical Knowledge for Teaching. In this course we use the High Impact and Effective Instructional Practices, Ministry of education of Math Curriculum and Making Math Meaningful. 

We learn about understanding the development, profession, trajectory and connection, network of importance through the mathematical across the curriculum. Learn how to support student learning through careful consideration of conversation, observation and product, and how to give appropriate feedback, while also accessing high quality mathematics learning resources, with manipulators that are tactile, and digital, and understanding how to incorporate socio-emotional learning skills in mathematics. 
I feel very honoured to be apart of such a wonderful learning community and team at the Faculty of Education at Brock University. 

A little about my self,  I received an Undergraduate Bachelors Degree in Visual Arts and Art History from York University and a Diploma in Early Childhood Education from Seneca College. I grew up in Richmond Hill Ontario and relocated for Brock University teacher college programs to downtown Hamilton. I have worked in various childcare programs, Montessori classrooms. I've experienced building schools abroad in Kenya, and India with Free The Children  and I've taught art and English in Peru. Last year I worked as an Emergency Supply Teacher at a elementary school as a supply teacher, RECE and EA in York Region. Outside teaching I enjoy traveling, being outside in nature and painting and cooking

In my First Year of Teachers College, I have become more aware that my default way of functioning as a teacher/ student was closely aligned to what I experienced in my time as a student. This Reflective journal will allow me to document my journey, as a teacher candidate. My reflective journal and portfolio will incorporate concepts of learning and teaching mathematics, learning moments, and connections to my prior learning experiences and future teachings and philosophy.  I will attach digital photographs and screen captures of my work, and some external resources that I find along the way, to support my reflection and understanding. 

Welcome to Session 1 EDBE- 8P39!! 😄

Today we looked into the Expectations of the course. We were Responsible to Read The textbook Making Math Meaningful to Canadian Students, K-8.  Chapter 1 How Students Learn Math and What Math we Want them to Learn, and Read  Chapter 6: A focus on Communication and Discourse. 

Today's reading illustrates the following: 

1. Research on Mathematical Learning, Teaching, Classroom Environment 

2. Conceptual Understanding 

3. A constructive Approach 

4. Using Manipulative 

5. Mindset 

6. What Mathematics We Want Students to Learn 

7. Differing Perspectives on What Mathematics is and what it is not, is valued & what Grade levels 

9. NCTM "National Council of Teachers of Mathematics, Principles and Standards 

10. Teaching Developmentally 

11. Importance of a Teacher's Pedagogical Content Knowledge 

Extension Activity:

(P.12) Interact with a K-8 Student:

📁Ask a student about a recently explored mathematical topic. Ask the student how he or she knows that he or she really did or did not understand the math learned. Observe whether students focus on their ability to use procedures or their ability to solve problem 

(P.12) Interact with a K-8 Teacher:

📖Ask a teacher how the changes in approach to mathematics in the past  10 to 15 years have made it easier (or harder) than expected for him or her to effectively teach mathematics 

How to Prompt Students: [ in a oral setting, teachers can use property questions such as theses mathematical thinking]

~ Why do you think that?

~ Would it also be true if...?

~ Could there be a different answer?

~ How did you figure that out?
~ What was the easiest part of...? Hardest part of...?
~ What strategies did you use to...?

~ What did you decide to...?

On the first day of Class, we engaged in many different learning activities before starting the lesson. 

Before our first activity we talked about Notice Wonder Routine  The routine supports students in becoming successful, perseverant problem solvers by leveraging multiple competencies and drawing on multiple sources of knowledge. Asking students what do you notice? what do you wonder?  which allows students the opportunity to see problems in big- picture ways and discover multiple strategies for tackling a problem.  When we focus on the notice-wonder routine, we focus on kinds of observations of patterns (missing/does not fit), opinions, let children wonder without giving the answers.

(Notice Wonder Routine: By: Annie Fetter)

Mathematical Practice:  The specific task used may expand Mathematical Practice possibilities, but in general, this routine will encourage students to use

🌎💻 Resource: Notice and Wonder Implementation in class 

[This is a really good resource for implementing Notice and Wonder, with Video]

In our 1st activity we played a game called "Magic Keys" which a treasure is hidden behind six doors, and we must use a pentomino key to unlock the doors. 

Which of theses Key Below (using 3 squares) follow the rule 

🌎💻Resource: To complete this activity  ; we used Mathigon, 

this link, contains activities/ rescues for the ENTIRE mathematics curriculum and are FREE.

Our 2nd Activity, we practiced the Routine of Wondering and Noticing. 

( Mathigon Resources For Teachers) 

During class, we worked on a  online google document to complete our magic keys activity with our group. you can access the google document here.  Our group created six different keys, where each unit and key contained five squares edge to edge. we than answered the question of what we noticed and wonder about this activity 

I notice: Each worm has a arrow on either end, worm is made of triangles, they end with triangles, each day the worm gets longer, add two tri's to each worm each day, 

I wonder: why triangles? if triangles are re-arranged, make a different shape? Why middle triangles rather than squares? are Middle triangles half days? how do they grow each day?

Our third activity,  we used a program called Desmos, this program is a math software tool, using cutting-edge technology, with free digital classroom activities. All the guided activities are guided by pedagogical philosophy, which  open up a world of possibilities for students to explore concepts more deeply, collaborate with their peers on problem- solving and apply knowledge creativity as mathematics.  

This activity we were presented with dots, where we had to draw how we courted, and then write an equation for how we courted. before the activity we discussed the wonder and notice routine. 

We completed another example of grouping with a few other images. 

"Which one Doesn't Belong?" Routine:                                      Our fourth activity involved the "WODB" , a website dedicated to providing thought- provoking puzzles for math teachers and students alike. This changes the conversation from 'correctness' to 'justification' [ Am i right -> This is true because...] , this changes the conversation from 'correctness' to 'justification'

- Learners have to make use of properties/ attributes:  visual, conceptual or both. 

they have to think of critical features and how things belong together and do not belong together (sorting and clarifying)

-They are provided an opportunity to reason and justify and engage in rich mathematical communication (discourse) in classroom. 

- The routine extends the habits of mind developed with noticing and wondering as there is a specific enabling constraint- justifying why each one could "not" belong. Notice, wonder, compare, contrast, communicate, argue (justify). 

-Opportunity for interleaving/Spiralling (spaced practice) which improves connections and retention 

A Video was shown in our first class, that corresponding to understanding Math. In the video they ask mathematicians, teacher and student a very simple question. Their answers may surprise you. 

( Youtube: The Global Math Project: Math Is _______.) 

After we watched the video, our professor shared What Learning Mathematics means to him. 

This gave me a chance to really reflect on  what Learning Mathematics means to myself also as a beginning teacher, and learner.  I was presented with some Prompt Questions [Questions that help promote mathematical thinking]

1. What is Mathematics for you? What does learning Mathematics mean to you?

I could never understand mathematics because I was never supported as a student with Learning Exceptionality, I am dyslexic. During my experience as a learner, teachers have forced me to see and solve problems their way.  In 2001, the teachers taught math in an unusual way, where the only way to be successful in math class, was to follow directly how the teacher taught us,  'copying what they do and how they do it".

2. What is your prior/. current mindset with respect to teaching mathematics?

I have been very nervous  about learning and teaching mathematics, as I did not have a positive and solid foundation around the subject of Mathematics. What I did have was two supportive parents, one highschool and elementary school teacher and the other a college professor. With the support of my parents I was able to succeed, in a way that was towards my own learning style.  Which is a more visual and hands on, with the use of manipulators, I am able to aid directly in the cognitive process.  There is a lot of research that is supportive of the use of manipulators, The  Learning Theory of Piaget and Bruner, which support the regular use of manipulative in a classroom Manipulators are a powerful tool for supporting classroom assessment, and implementing formative assessment.  Although I did not have a solid foundation around the subject of Mathematics, I am hoping to enrich own understanding  around Mathematics and be able to support learners and my future students.

3. How do the math routines and activities we looked at today encourage all students are developed as a mathematical communicator/skill in mathematical communication [Chapter 6]

Reflecting back on today's session I have realized that the Math lesson uses the creative mind of an artist. To see and create and then understand what you have created. This can be additive thinking, multiplication and arithmetic thinking and WODB (which one does not belong) What I have learned the most is that its more important what's happening in the curious minds of the students and not that of a teacher. When we get to know our students, we need to be able to adopt to our learners and create ways for them to learn and be successful. 

        (C) Sonia Cara Notes on Session 1 EDBE- 8P39)

Welcome Back to Session 2!!

Hello 😄and welcome back to Math Session 2, where our class took a closer look at the Ontario Curriculum, and Contexts Process and Strands.   Here is some work that I did to complete a focus on Problem Solving, Planning Instruction, and Focusing on the Big Ideas and Mathematics Processes. 

This Class we were responsible for: 

🗓Date:  September 2nd, 2021

💡Ontario Curriculum 2020, Curriculum Contexts Process and Strands 

📚HIIP Document 

📚Making Math Meaningful To Canadian Students, K-8 

📖Chapter  2 : Focusing Instruction Big Ideas and Mathematics Processes

📖Chapter 4 : Planning Instruction

📖Chapter 5 : A Focus on Problem Solving

Here is the Evidence of What I did...

           (C) Sonia Cara Notes on Session 2 EDBE- 8P39)

These photos below is the Process of work, that I did to complete our 1st Activity, called Tables and Stools and also called Carpenter Problem. 

I first used manipulators pink and green cubes to correspond to the legs and stools of the tables and stools.  The use of manipulators helped me figure out a strategy that corresponded to the question. When I was completing this activity, I wondered and noticed many things about the use of manipulators, it gave me a chance to work hands on to visually identity what the mathematic question is asking me to do and find,  I used concrete manipulators to count all and using a standard configuration to represent each number. this is equivalent to writing out all 3 Stools and 4 table tops. 

In this photo I recorded with concrete cubes and  used chunking each piece. 

During our class we used a chart for Anticipating Student Response, Monitoring and Selecting and Sequencing Students for Discussion Phase  where you can find here. 

Welcome Back to EDBE-8P39 Week 3.  Today we take a closer look at Strand E- Spatial Sense referring to 3D/2D shapes, location and movement. While also Reading the Text "Making Math Meaningful to Canadian Students, K-8.  This strand combines the areas of geometry and measurement in order to emphasize the relationship between the two areas and to highlight the role of spatial reasoning in underpinning the development of both.

💡 Strand E- Spatial Sense 

📚Making Math Meaningful To Canadian Students, K-8 

📖Chapter  17: 3D and 2D Shapes 

📖Chapter 18: Location and Movement 

The study in this strand provides students with the language and tools to analyze, compare, describe and navigate the world around them. It's the gateway to professions in other STEM (science, technology, engineering and mathematics)  

-Students analyse the properties of shapes, the elements that define a shape and make it unique, and use theses properties to define, compare and construct shapes and objects as well as to explore relationships among properties. 

Overtime students develop an increasingly sophisticated understanding of size, shape, location, movement and change 2D + 3D 

-They choose appropriate units measure and compare attributes and they understand the relationship between shape, and measurement to develop formulas to calculate length, area, volume and more. 

Students will use spatial relationship and shapes to help young children prepare to learn later math. Across all grades, students will understand basic number concepts, patterning and geometric concepts. 

Let's first talk about Resources for a second!!

Didax, program was introduced to us, today! It allows you to have FREE virtual manipulators, its a great way to practice and enhance at-home learning, and classroom learning. Simply drag the manipulators into position to see math concepts come alive!

This Program alspatternss you to create pattens.

After Discussing the importance of spatial reasoning, we moved into our first activity called "See it, Build it, Check it" In this activity we identified three-dimensional objects and dimensional shapes within different shapes. We were presented a 2D and 3D shape on the screen, we had to look at it, before it was taken down and make an exact replica of what we saw. I decided to complete this activity using the Didax manipulators, but you can also present this using physical manipulators. During this activity I had to determine a strategies to help myself memorize the design, but also memorize which block corresponded with the shape.

( EDBE- 8P39- Brock University) 

"It is not about the task, it is about the intention of the learning"

Pattern Block Symmetry Quick Image,

'

- challenging students, depending on the level, 

See it build it check it- Interlocking Cube 

Briefly present a 3D structure made of interlocking cubes. They must then recreate from memory. Encourage use of chunking and subtilizing strategies.
After sufficient time, reveal and have them compare.
Discussion about strategies. More complex structures over time. 

( Brock University- EDBE-8P39)

( Curious Minds) 

Good Resource that I found: To Help Understand. 

(The Robertson Program) 

What do you see? 👀🧐

-Students are counting, either the number of the blocks or the colour.  

-Some students see the shape of the blocks (different perspective) 

- Talking about what they are developing too, rotating and physically using the use of the material, 

-Help a student learn through theses manipulates 

✅Another Resource:

(Taking Space) 

 

We watched this incredible video:

Activities to Develop Geometric and Spatial Thinking

Activity:- Youtube- Mother bird story:

(integrating, literacy, math and a puppet, to tell the story) 

Look down like Mother bird did on your own structure

-> how does it show the top view?

-> What do we know? With a partner you will build it together

-> What did you do in your mind?

- 'notice to give children the opportunity to use their perception and imagination. 

- the problem had so many solutions, but all the groups did different perspectives, ex. property of the cube, some some took them apart.

- the story, and puppet, using a more child-centred way of learning 

-Observing students and ask questions 

- Teacher promoted the students with guided questions, 

students are leaning to ask the questions themselves. 

-diversity of perspective, not only one answer

(Brock University- EDBE- 8P39) 

Resource: ✅  NCTM isometric Drawing Tools 

- rotate image, 

- build structure 

- getting from one place to another 

Learning Goals: (Inspiration) ✨✨🧞‍♂️

Below I have attached  some notes, that I completed for my week three class, to better understand the context and learning. I am gathering the information and willing to share for some feedback, and changes on what I learned.  

Learning is like a science experiment. 

Notes: From Class: 

( GeoBoard,: activity, NO Pegs Allowed)  problem solving, to make sure that the dots are not connecting, work systematically, and represent thinking,  its how to get to that place (process, experiences they have, matching, drawing, angels, that create foundational building tools) 

Today's Journal Prompt asked us to upload a photograph or a drawing at least one 2D shape and at least one 3D object that we encountered regularly or that is part of our cultural heritage. The connection that I had with this prompt, was my 2D image. The key is to deconstruct the design and isolate each line and shape on its own.  Geometric Design is a branch of computational geometry, that deals with the construction and representation of free-form curves, surfaces, and volumes, that are closely related to geometric designs. The geometry in visual design is very different, I can get lost in the predictable symmetry and refreshing minimalism. 

Reflection💡🧐

This class was about Spatial 3D/2D shapes and location and movement.  

By participating during class, I have been able to problem solve, and show my work. 

2D  Image: ( Henna, Mend-hi, that I created, one on paper, and one my cousins arm)

3D  Image: (A cross, made up of a palm Branch) 

Instructions: Series of crosses, overlapping, with palm branches)

Youtube ( How to Do it, Find it Below)

By relating it 

😓🤔Overcome the fear of participating, and share your work 

-self evaluate 

- pedagogy

What I have realized during this class was that I am a very visual learner. When it comes to mathematics or patterns I have a way to do things for myself, where I fully understand the concepts. For example this week we had to do a concepts with an air balloon, I drew out the chart, with the balloons following every measurements.  By preparing and repetition, i am better to enhance my own success to visual representation in math 

Hello Welcome Back to EDBE- 8P39 Week 5!! This week we were responsible for Reading Making Math Meaningful to Canadian Students, K-8 AND taking a deeper look into Strand C: Algebra, Patterning and Coding.  

📖We also were responsible for Reading Chapter 16, Pattern and Algebra

We started our participating in Rhythmic Pattern Desk drumming idea, to create movement and pattern. 

Today is also the day that I facilitated a Small Group Problem Solving Activity  also known as PSA. 

Each Teacher Candidate was assigned a problem, we have to plan, adapt and lead a teaching -learning experience with a small group in the classroom. Each person will have at least one opportunity to lead the problem solving activity. In 15-20 minutes for facilitating the learning activity.  

Purpose of the Problem Solving Activity: provide an opportunity to solve a mathematical problem which will lead into a 3 part problem solving lesson and reflect on the overall lesson 

[ The Problem of the Day I was provided with]

We first watched this video, during our class:

(Cardio Desk Drumming- Believer) 

Questions to consider: What is the Movement Pattern? and What is similar or different from the musical pattern in the actual song. 

Another video we watched illustrated Math ON the Move 

(How I teach math and Dance at the same time) 

Talking about Math, "Movement Variable" which are pattern attribution, 

transfer the dance moves into patterns. the amount of physical, cognitive and research of embodiment of participation, working creativity within dance, will help students to help understand math. combining dance and math, embedded within a dance making activity. 

What does Movement Variable Look like: [Definition here]

" To Boost Learning. Just ADD movement"

- Students and people in general learn better when information is presented in more than one way, if we take in information through more than one sense, we are more likely to encode it in a long term memory. This would include visual, verbal and kinesthetics modes of learning [ Process Of Learning [ Article by UBC] ]] 

-Study shows that physical activity activates the brain, improves cognitive function and is correlated with improved academic performances. 

During the class we did a activity online but this time using 

GOOGLE SONG MAKER , Chrome Music lab is a website that makes learning music more accessible through fun, hands on experiments. Many teachers use Chrome Music lab as a tool in their classrooms to explore music and its connections to Science, Math, Art and more. The song maker experiment lets you make and share your own songs. 

Now do you know this song (click here) 

During class we look a deeper look into the Ministry Documents,  of Mathematics Curriculum Strand C: Algebra.

(You can access the Math curriculum Strand C, Algebra here) 

According to the Ministry of Education Strand C- Algebra, students develop algebraic reasoning through working with patterns, variables, expression, equations, inequalities, coding and the process of mathematical modelling . 

Process of Mathematical Modelling: 4 key components that are interconnected and applied in an interactive way, where students may move between and across as well as return to, each of the four components a they change conditions to observe new outcomes until the model is ready to be shared and acted upon. While moving through these components, social-emotional learning skills and mathematical process are applied as needed.....

1. Understand the problem  

[ what questions need answering? What information is needed?]

2. Analyze the situation 

[what assumptions do I make about the situation?, What changes, what remains the same?]

3.  Create a mathematical model?

[ what representations, tools, technologies, and strategies will help build the model?, what mathematical knowledge, concepts and skill might be involved?]

4. Analyze and assess the model?  

[ Can this model provides a solution?, what are alternative models?]

Journal Prompts:   The FIRST TASK was to complete the Verbs/ Nouns table and to describe the insights that we gained about this strnad, and how it connects to other strands we have studied so far in Teachers College. 

The insights I gained was learning what verbs and nouns are in algebraic expression and how to point them out in a text. By making a visual representation of which points fall under which element.  This strand is related to analyzing, comparing, explaining the properties of shapes.  I enjoyed creating this chart, to really illustrate the verbs, and the nouns. 

When  I was working towards creating this table, I remembered prior knowledge about learning  about unpacking expectations using colors, to identify Verbs, Nouns and Context, in my Assessment and Literacy class.  We were introduced to this concept when creating our Learning Goals and Success Criteria. Learning goals are brief statements that describe for students, what they should know, understand and be able to do by the end of the period of instruction (e.g. A lesson or a cycle of learning, unit or course). They can also be representing a subset of knowledge and skills that students must master in order to successfully achieve the overall expectation. 

Verbs are illustrated in RED    Nouns are illustrated in BLUE                                 Context are illustrated in GREEN 

The Second task, we had to upload a personally meaningful repeating or growing/shrinking pattern involving any modality and translate it to a symbolic representation.  I had to connect to my travels and my mothers home place. Tanzania.

In 2013  I look a trip with Free The Children, to volunteer to help build an elementary girls school and agriculture chicken coop program for the Maasai in Emojoy and Kisaruni, Maasai Mara, Kenya. I was always so fascinated with the culture and language. of my own grandparents language Swahili, and had to enrich my own understanding, with going abroad, teaching and constructing this school. In Kenya, the vibrancy of colors and fabric, and the smell of spices and traditional food, still bring me back to the moment of my trip.  I created various art projects, while I completed my undergraduate degree at York University.  This one especially illustrated my first ever trip to Kenya in  2011, where I volunteered to help build an  elementary school and water program for the Maasai in Osentio, Maasai Mara, Kenya. 

[ You can find more of my artwork, on my Instagram page [Here: sonia_art__] 

Here are my Maasai Warrior Friends, from my 2011, Trip. 

[ Kenya, 2011] 

The Maasai Identity is often defined by colorful beaded necklaces, with iron rods, becoming their weapons, and of course the red shuka cloth. this red clothe is the common color, the Maasi also used blue, striped and checkered cloth to wrap around their bodies. It's known to be durable, strong and think, protecting the Maasai from the harsh weather and terrain of the savannah. 

Here is a repeating pattern of a cultural fabric the Maasai Shuka. This cultural fabric is traditionally worn by the Maasai in East Africa, the Shuka bears a history as rich as its colours. , In the following image, you can see that I translated this pattern using Virtual Manipulatives on Didax 

Welcome Back to  EDBE-8P39 Session 6.  

Today we look deeper into Strand B: Numbers.  Read Chapter 9 Developing Fact Fluency and Representing Larger Whole Numbers, from Chapter 10.                          We  were introduced to How Numbers Work [foundational to many aspects of mathematics]

This past class, really enhanced my own knowledge on teaching mathematics through a learner lens and educator lens.  Recognizing and understanding number properties is truly a foundational when  developing  an understanding of branches that correspond to  mathematics such as arithmetic and algebra.  In the number strand, students progress through Grades 1 to 8, they learn about different types of numbers and how these numbers behave when various operations are applied to them. 

Looking Back at Math as a whole subject, something that I can personally  connect to and related to in my future teaching practice is Strand A: Social- Emotional Learning and Mathematical Process. There is a strong evidence that developing social-emotional learning skills at school contributes to all student's overall health and wellbeing and to successful academic performance. It also supports positive mental health as well as student's ability to lean, build resilience and thrive. I strongly feel that integration of Social-Emotional Learning skills throughout the school will support students in becoming healthier and more successful in their contributing lives and as contributing members of society.   The push of Daily Physical Activity in Ontario Schools. is something that is required to ensure that all elementary students have a minimum of 20 minutes of sustained moderate to vigorous physical activity each day during instructional time. 

In regards to Math, the skills that can support students in understanding mathematical concepts and in applying the Mathematical Process are the keys to learning and doing mathematics.                                                   ⚽️🥅 [Problem Solving, Reasoning and Proving, Reflecting, Connecting, Communicating, Representing, Selecting Tools  and Strategies]

In elementary school  this is built from NUMBER SENSE, where students develop the ability to flexibly relate numbers and related computations. Students will develop number sense regularity using number relationships to make sense of calculation and the ass the reasonableness of numbers used to describe situation

Students learn to count effectively and become fluent with math facts in order to perform calculations effectively and accurately, mentally or by using algorithms on paper.  THIS STRAND: is built on the belief that it is important to develop automaticity, which is the ability to use mathematical skills or perform mathematical procedure with little or no mental effort. Goal: Math Facts should enable students to engage in critical thinking and problem solving. 

Students will learn math facts, gradually over a number of years, connecting to prior knowledge, using tools and calculators. Mastry comes with practice and practice helps to build fluency and depth. Students draw on their ability to apply math facts as they manipulate algebraic expressions, inequalities and equalities. .  

BUT we need to make sure that ALL OUR STUDENTS have strong skills in number sense and a SOLD conceptual understanding of the operations.

Grade 3: Addition /Subtraction facts should be mastered by the end 

Grade 5: Multiplication / Division Facts should be mastered by the end. 

All Learners should contribute to learn about Effective Srategies and to practice and extend their proficiency in the operations throughout the grades and in the context of learning in all strands of the mathematics curriculum. 

Welcome Back , it's Session 7,

Today we focused on Strand B: Fraction decimals [ Number Sense].  We were Responsible to read Chapter 12, Fractions, and Chapter 13 Decimals. 

WHAT. IS NUMBER SENSE:

-A vital aspect of number work in elementary grades is to build what is often called "number sense", where students develop the ability to flexibly relate numbers and relate computation. 

-Students learn to count effectively and become fluent with math facts, in order to perform calculation effectively and accurately, whether mentally or by using algorithms on paper.  Drawing on their ability to apply math facts as they manipulate algebraic expression, equations, and inequalities. 

We used a resource called "Number sense and Numeration grades 4 to 6." To help take a deeper and more critical look into what Number Sense is all about. What I really enjoyed about reading this resource, it provides you will a overview of the direct volumes and a glossary that provides definitions of mathematical and pedagogical terms used throughout the six volumes of. theguide. 

Volume 1: The Big ideas
Volume 2: Addition and Subtraction 
Volume 3: Multiplication 
Volume 4: Division 
Volume 5 Fractions 
Volume 6 Decimal Numbers 

On Page 11, Learning About Fractions In the Junior Grades:

- allow students to extend their understanding of number beyond whole numbers and enables them to comprehend and work with quantities that are less than one. 

Instruction in the junior grades, should emphasize the meaning of fraction by having students represent fractional quantities in various contexts, using a variety of materials,, where they will learn to see fractions as useful and helpful numbers. 

As students use concrete materials to compare fractions, they develop an understanding of the relationship between the number of pieces that make the whole, and the size of the pieces. [ P. 20] 

You can find additional information on developing fraction concept with students Grades 4-6 Fraction. on module here [ www.eworkshop.on.ca]

Welcome Back, It's Session 8 EDBE- 8P39: 

Today we focus on Strand E, Measurements  [Spatial Sense]. we are responsible for Reading Chapter 19 and 20 on The Nature of Measurement, with a focus on Length and Area. 

WHAT IS IT?

The development of Spatial sense continues with the study of the triangle 

Students will learn the characteristics and properties of different kinds of triangles, including their Angles  and measurement. [ E2] 

Work continues with understanding and using metric system to measure Length, Area, mass and capacity and to convert from larger units to smaller ones. 

Theses are the transferable skills: [ students will have]

1. Critical Thinking and Problem Solving 
2. Global Citizenship and Sustainability 
3. Innovation, Creativity and Entrepreneurship 

Welcome to Session 9

Today we are focusing on Strand D: Data Literacy and Probability.   We were responsible to Read Chapter 21 on Data, and Chapter 22 on Probability. The related topics of statistics and probability are addressed in this strand and are highly relevant to real life.

The ONE key focuses of this strand is to support students in developing "Critical Thinking Skills", which is the process of thinking about ideas or situation in order to understand them fully, identify their implications, make a judgement and or guide decision making. 

 Throughout their development of data literacy, so that they can analyse, synthesize, understand, generate and use data both as consumers and producers. 

Critical Literacy: is a term to refer to a particular aspect of critical thinking, involves looking beyond the literal meaning of a text to determine what is present, and what is missing, in order to analyze and evaluate the texts complete meaning and the authors intent. [Points of view, context etc.]

The literacy skill of metacognition supports students ability to think critically through reflection on their own thought processes, which emerged from a powerful approach for promoting a focus on thinking skills in literacy and across all disciplines for empowering students with the skill needed to monitor their own learning. 

Hello and Welcome back to my BLOG, we are already in Week 11!

Today we took a deeper look into 💡Assessment/ Evaluation .We were  Responsible to read,

Chapter 3 and Chapter 4 Planning Instruction  In the Making Math Meaningful Canadian Students, K-8 

We were introduced to Cuisenaire Rods.  I have never used these manipulators, before, but after playing around with them, shown examples of how to use them, and reflecting with other teacher candidates about the use of them. I came out of class with a huge TAKEAWAY! 

 Re-learning Mathematics, this far in the course has really opened my mind about strategies 

We need to ENABLE ALL CHILDREN to be powerful mathematical learners!!

This week I came to terms about learning math the way that makes sense to me, with prior experience from being taught math, but also digging deeper into the "The Ontario Curriculum of Mathematics program" is designed to ensure that students build a sold foundation in mathematics and develop a positive mathematical identity by connecting and applying mathematical concept in a variety of ways. 

To SUPPORT this very process, teachers need to capitalize on student's prior knowledge, skills and experiences AND integrate concepts from across the strands, and often apply the mathematics that students are learning to types of situations that might occur outside the classroom. 

[The following chart shows the flow of the learning through the curriculum and the interrelationships among its various components]

As teachers we need to BELIEVE that all students have the potential to learn and do math,  Using culturally relevant practices and differentiated learning experiences with the focus of individual students learning needs.  AND then focusing on the development of conceptual understanding, procedural fluency, skill development, communication and problem solving skills. 

Effective instruction in all subjects is a requirement that teachers need to know their students FIRST! Teaching students about the PROCESS of PROBLEM SOLVING,  requires that students to  engage in "self talk" which they can use when faced with a problem. It also helps students to understand the overall structure of the problem, and reinforces that problems solving requires PERSERVERANCE  and that a growth mindset is very important. 

To any struggling students, each problem looks completely different, we need to support students as they generalize beyond "today's problem" 👀to see connections between problem and recognize types of problems. 

Tools and Representations supports a conceptual understanding of mathematics at all grade levels.                                                            🛑Carefully chosen tools and representation provide a way for students to think through problems and then communicate their thinking.  When paired with discussion, they hemp to demonstrate concepts and thinking. Tools and representation draw on spatial reasoning and build "beyond language bridges" they can be useful when teaching linguistically diverse students students with special education needs. They helps educators and students work together to build procedures from conceptual understanding. 

Students who can represent mathematical ideas in a variety of ways demonstrate a deeper understanding of theses concepts as each representation provides a different perspective. 

Effective Math Classroom provide multiple opportunities for students to engage in meaningful math talk. 

-Conversations about math build understanding as students listen and respond to their classmates expression of mathematical ideas. Students can share their ideas with a partner or within a small group, in the context of whole class discussions. 

-Can appear as short daily routines to support mental math and visualization strategies.  Eg. ask students to place a number on a number line, to describe how they saw a configuration of dots to compare and contrast expressions, shapes or graphs. 

-Students: can defend their thinking and their peers can add to it or respectfully disagree with it  

💡🧐 Math Prompts (start the lesson: to pose a question)

Teacher Growth Mindset Moment:  [Link to Podcast Here]

A Huge take away that I got from this podcast: is the BIGGER THEME: Working on Our Hearts!!  When we are determine to achieve a GROWTH MINDSET! 

Let's Take a look into Some Research..... 

Dr.  Dweck's Research Into Growth Mindset changed Education Forever. 

"When students believe they can get smarter, they understand that effort makes them stronger. Therefore they put in extra time and effort, and that leads to higher achievement." 

[ Take the Mindset Assessment Here] 

 8 Questions  (It has been used in many studies to show how mindsets can change, and can be used by you and your students to identify areas in which you can work toward a growth mindset. You will be delivered personalized feedback after your submit the assessment) 

To remain in a Growth Zone, we must identify and work with theses triggers, assumptions. Many managers and executives have benefited from learning. to recognize when their fixed mindset "persona" shows up and what it says to make them feel threatened or defensive. Over time they have learned to talk back to it, persuading it to collaborate with them as they pursue challenging goals. 

When we ask, we must ALWAYS REMEMBER TO stand firm, Ask and Believe, with firmness and authority.   (Ask or Answer) 

[Eg.  Your with a friend, and you are trying to figure out what to eat,  they answer with "whatever you want" and than  you ask them would you like a salad, they reply with sure. than you ask them again would you like a burger.  

When we give answers, we need to give answers with  confidence and authority. 

Our answers are something that WE thought about, mediatied, prayed on and this is what we want coming from need and love, evolve and better ourselves and  improve ourself we will be a greater serve to ourselves and other.  

MINDSET CHECK IN ✅

In regards to Our Dreams, we need to always REMIND OURSELVES like  knocking at the door, every single day, and ask ourselves. Until the door opens up. Both outcomes are a win, your consitentesity, faith and believe it worked out. What you ask for  is what you truly want.  Celebrate all our Gifts within ourselves. Be real with yourself and what you are asking and always know that it's coming from OUR HEARTS  our love and light. 

COOL BEANS MOMENT- Let's activate prior knowledge:

Prior-Knowledge Warm-Up Activities 
Your Mathematics lesson should always begin with a connection to prior knowledge. Your connection to each student's prior knowledge as they enter into the lesson for the day significantly influences what students learn in the specific situation presented by the mathematical tasks you ask students to pursue.  [connection with Language and Math]

[ This article goes through how to choose prior-knowledge of warming up activities, and the HOW TO, and WHAT TO LOOK FOR information] 

Session 12:

🗓Date:  

💡Maker-space 

💡3 Part Lesson Plan