Math Report: E.L.L. Students

Hey teacher friends!

This week's math class was full of all kinds of insight! I particularly enjoyed how Rebecca gave us the opportunity to discuss strategies by which we could assist English Language Learners in mathematics. The possibility of having ELL learners is always present, and I liked how Rebecca never limits our class discussions to topics surrounding mathematics but more so how to infuse mathematics as a "support system" in other areas of education. 

In choosing to take the Teaching Internationally online course here at Brock University, teaching English Language Learners is something I have been recently exposed to in research. I have had plenty of time to reflect on how I would cultivate inclusivity with specific teaching strategies. So...prepare for lots of advice coming at ya!

Red Pepper. "Welcome Mosaic with ESL Students". Online photo. (2008, June 25). Retreived from: https://www.flickr.com/photos/27984836@N07/2610991927/

Supporting English Language Learners is our current Ontario Ministry Document that is essential at having at our disposal as it focuses on a three-pronged approach to increase our student's success: understanding our English Language Learners, working as a school community to support the English Language Learners, and the adaptation of the Ontario Curriculum to increase student academic success. This document provides heaps of insight into the importance of understanding our E.L.L students (including their needs) so that we may make appropriate accomodations to ensure individual success. Highly recommended!

When I was completing my undergraduate studies at York University, I discovered a love and fascination for linguistics. This led me to enrolling in Second Language Acquistion and Discourse Analysis Courses - probably my most favourite electives that I chose during my time at York! I can recall reading a very interesting article written by John H. Schumann, titled Social Distance as a Factor in Second Language Acquisition. 

The article explains both good and bad learning situations for groups desiring to learn and teach a second language. There are certain societal factors that can either promote social distance or proximity between the second learning group (2LL) and acquiring the language of a target language group (TL group). So, as teachers of the English language, we would be considered the target language group. We must cultivate a reciprocated positive attitude with the second learning group so that they will intend to remain in the target language area for an extensive period of time. This way, enriched learning is achieved. Schumann expresses that the greater the social distance is between the two groups, the more difficult second language learning will prove to be. Therefore, we must achieve a sense of “low enclosure” which promotes the least amount of distance and steer away from “preservation” which is the greatest form of social distance. As leaders in the target language group, we must also carry a “non-dominant” attitude and level ourselves at their current learning status. Furthermore, remaining empathetic towards their cultural patterns (involving lifestyle and values) will encourage them to slowly assimilate into ours.

Enokson. "ESL Door Hanger." Online photo. (2006, June 12). Retrieved from: https://www.flickr.com/photos/vblibrary/4396314887/

An additional resource I would love to share with you all is found on the Brown University website, features a section dedicated to Teaching Diverse Learners. This of course includes the instruction of E.L.L students. It is a great resource that we may consult for suggestions in elementary literacy, teaching and learning strategies, policies, as well as assessment strategies – which are also extremely important to consider for E.L.L students because their rate of learning varies. Culturally responsive teaching is a category on the website that provides insight into how we can synthesize a celebration of culture in order to shape their attitude of learning and indulge in equitable access of material. 

It lists the characteristics of a culturally responsive teacher, including:

• ·      Positive perspectives on parents and families
• ·      Communication of high expectations
• ·      Learning within the context of culture
• ·      Student-centered instruction
• ·      Culturally mediated instruction
• ·      Reshaping the curriculum
• :   Teacher as facilitator 

Banlon 1964. "English Time Bulletin." Online photo. (2009, September 22).  Retreived from: https://www.flickr.com/photos/banlon1964/3945638242/

The resource additionally suggests we provide support for the child outside of the classroom which I found to be interesting. One particular recommendation that I loved is to involve the parents of the E.L.L student in translation activities. For example, having the parents participate in a culminating cultural event where they can help translate certain books that are relative to their native background. This is a wonderful way to integrate communication not only between differing cultures of students, but among different generations, too.

Now, in terms of making a student feel confident and comfortable in mathematics class, I think the same technique rings true across all subject areas and classes: incporporating visual elements. Students of learning English primarily rely on seeing and listening; it is the easiest way for them to take in information before they speak, read, or write. Perhaps including culturally relevant models, such as learning fractions with pizza if E.L.L students immigrated from Italy, or modifying my Ratio and Proportion lesson using ingredients that make up tortillas so that indigenous Mexican students can better connect to the material. In making simple adjustments, E.L.L students will feel more "at home" while feeling welcomed by all in a new community.

Confident ELL student: Challenges and Strategies. Taken Friday, October 28, 2016.

Rebecca also encouraged us to reflect on teaching strategies collaboratively within groups. Given the challenges of certain levels of E.L.L students: Early Stage, Foundation, Confident, and Fluent, we were then instructed to provide strategies that would align well with them. My group was to brainstorm ideas regarding the confident students, therefore, different challenges are presented with such students: errors in writing may occur (syntax), improper use of vocabulary, checking for understanding, and having high expectations of written and spoken language. The strategies we suggested were to have students keep a dictionary as well as a hand-made dictionary (the student can add new vocabulary to their own if new words pop up), encourage students to continue verbalizing written text but also allowing sufficient processing time, and assigning tasks that need to be expressed in different ways to exercise various skills.

All in all, I am feeling more inspired than ever to teach E.L.L students, perhaps even abroad one day! I think it would be extremely rewarding to be able to teach students learning my first language. Connecting with immigrants would resemble that "international feel" I would seek by teaching internationally. The student(s) would bring forth their own culture, heritage, values, and traditions in the classroom, which is what I think I essentially crave to experience because I am an endless learner at heart.

Until next time,

Have a beau-tea-ful day!

Miss Capano

Math Maker: Fun With Recipes!

Hello teacher friends!!

Last week was "my math week". Alas, it was my turn to present a math learning activity to our class. Our attention was directed toward ratios, proportions, unit rates, and percentages, which can all be interrelated, however, my activity primarily focused on ratio and proportion. I decided it would be best, just as every lesson in math, to form a connection to real-world contexts so the class would be more intrigued when it finally came time to complete the activity. In doing so, I chose to connect proportionate reasoning to recipes. This excited me!! I do think the demonstration of a recipe, and sorting through the ingredients together as a class would have been a lot more fun, but due to time constraints, I was not able to execute this idea. So I stuck to my other plan. 

Coconut Cake! Photo taken by me.

Each teacher candidate was announced the role of a chef; given a "recipe card" and were instructed to modify the recipe that I provided to serve more people. This would challenge them to ensure all of their ingredients were proportionate. As we know, the proportional relationship between ingredients must be correct in order for the final product to have the right texture, consistency, and of course - to masterfully present a deliciously satisfying taste! For some, this may have been a new concept because I realize not every one in our class are world-class chefs. When I did ask, there were many people who do cook or bake. It would be more interesting to see what strategies the "non-bakers and non-cookers" came up with. Some people decided to increase the ingredients by sticking to the addition of fractions. For the more skilled people in the kitchen, mental math was good enough.

 I did struggle with the idea that this activity may have not been challenging enough, especially for our age group. I feel as though decreasing the amount of ingredients, to an odd number, would have been a little more difficult. Upon receiving feedback from Rebecca, she told me that ratios were not necessarily needed to figure out the answers. A more thoughtful extension, she suggested, would have been to provide a ratio of ingredients (3 parts liquid: 5 parts flour) and tell them that they would use a certain amount of flour. Then, the students would need to decipher the amount of the rest of the required ingredients. 

Perhaps my slight confusion in forming this activity was a direct reflection of my misunderstanding of the curriculum (specific) expectations. It seems to be something most teacher candidates are struggling with, and that is why the second half of our class time was spent matching specific math curriculum expectations to the grade level. Working in partners, we played this unique "matching game".

Photo taken by me.

 My partner and I seemed to get most correct, although we noticed the very close similarities between some expectations. We really appreciated Rebecca encouraging us all to analyze the curriculum more closely in an interactive activity, as I am sure this will benefit us in future lesson planning.

I think the other girls who presented their activities on unit rates and percents did an awesome job, and these activities are surely something I look forward to every week. Especially when I know these are games I could implement into my own math classes one day. Thanks for your wonderful tips, every one!

Until next time,

Have a beau-tea-ful day! :)

Miss Capano

Math Madness

Hello friends and future educators!

You guessed it...back for more! Two math blog posts in two days. Who am I?! This is truly math madness. But I did mention I would try to become more consistent with this! (alright, really I'm just playing catch up...woops!)

Now to get to the nitty gritty. Last week's math class before the start of reading week was rather insightful, but I would expect nothing less from Rebecca's class. She consistently offers teacher candidates the most helpful advice in order to guide us on our journey in the pre-service teacher education program and ease our minds about the difficulties. A main topic of discussion during this class was the use of manipulatives - often a necessary (and of course beneficial) addition to lessons in mathematics. Manipulatives can consist of anything from blocks, wheels, coins, lego, geoboards, counters, bead strings, cards, and measuring tapes. They typically aid a student's comprehension and are thus not a main source of learning, nor should they be. They simply add variety and depth in helping children connect mathematical theories to real-life examples. That is, forming a relationship between abstract and concrete notions.

What strategies can a teacher use to ensure students do not become dependent on manipulatives? 

Well, for starters, I think a basic way to avoid dependence is to have manipulatives made available for only certain activities, and not the entire lesson. Have your students address a math problem first without the manipulative, and then introduce the manipulative if they are struggling to grasp the concept or to present a new challenge in solving the same question. Have them understand why the use of the adjunct is helpful, and not aimlessly use the items as "toys". Just as we wouldn't want our students to become dependent on using a calculator, we also wouldn't want them to become dependent on any manipulative of choice. They are used to support a child's learning experience, not as an isolated teaching technique, and therefore should not be treated as such. What if we rewarded our students to use manipulatives after demonstrating good behaviour? Perhaps we could associate it with a points-rewards system. This could get them excited and soon enhance their enjoyment around the subject. Or maybe we could even reserve our use of these tools for the end of the week, on a Friday. Whatever we decide, it is still important to realize the validity in having three-dimensional models that are visually stimulating for some learners. Manipulatives are definitely significant in having symbolic representations and promoting interaction within the classroom.

Now it's time for me to begin preparing my math activity presentation for next week! 

See you all then, but until then,

Have a beaut-tea-ful evening and enjoy the rest of your reading week!

Miss Capano

Let's Talk Math!

Hello friends and future educators!

So, it is no surprise I have put my Math blogging on the back burner. Turns out I haven't completely stopped that bullying behaviour toward the subject, have I? Haha. But I promise to be more consistent with it, especially with all of the fascinating learning techniques we are introduced to with each passing week!

Two weeks ago, our class was challenged with a very interesting math problem called a tarsia puzzle. It is a type of jigsaw puzzle that requires you to solve various problems on triangle pieces in order to create a hexagon as a final product. Working in pairs, we arranged the triangle expressions so that the equivalent expressions were matched. It is a great puzzle for practicing algebra questions, however I feel that this activity can be used with almost any topic or subject! It makes for a great "setting the stage" activity, just how Rebecca introduced the task to us. Although, it did catch us all off guard and took longer to complete than expected, so perhaps this may be an excellent core learning activity instead. The students will definitely become immersed in trying to form the hexagon itself, therefore the timing of this activity is a factor that must be considered. Regardless of how you may choose to implement it, the tarsia puzzle is beneficial for visual learners while also encouraging cooperation and teamwork for learners all across the board. There are various free downloadable tarsia puzzles found online which is incredibly convenient for us educators!

Tyler, Paul. "Tarsia Floor Puzzle". (23, Jan, 2007) Retrieved from: https://www.flickr.com/photos/glazgow/1535224849

As a class, we also discussed the differences between conceptual knowledge and procedural knowledge and their importance in relation to mathematics. Procedural knowledge is the "toolbox" of problem solving: the equations, formulas and algorithms that assist students in reaching solutions. But do the students truly understand their use of these tools? This is what conceptual knowledge touches upon. Most of us agreed that a balance of both procedural and conceptual knowledge is required in order for students to fully grasp concepts. Procedural knowledge is easily attainable by strict memorization, but conceptual knowledge is what takes learning a step further in understanding the why or how of the procedural steps. Students may then carry that conceptualization into future learning situations; not heavily dependent on memorized facts but rather on connections they have made with the content. As a future teacher of J/I mathematics, I will be mindful in creating meaningful, relevant questions pertaining to the subject. This way, students may formulate a deeper relationship with math and better communicate their understanding of subject matter in assessments, as well as in real life situations.

"..if the curriculum we use to teach our children does not connect in positive ways to the culture that young people bring to school or prepare them for the future they are building towards, it is doomed for failure." (Delpit, L. D.)

Until next time,

Have a beau-tea-ful day!

Miss Capano  

References:

Delpit, L. D. (2012). "Multiplication is for white people." Raising expectations for other people's children. New York: NEW Press.

Math Education

Hello fellow bloggers and educators,

As my first week at Brock University draws to a close, more technology has seeped its way into the Teacher Education program. It is no surprise that technology is a prime area of focus during this day and age where advancements are so frequent and prevalent. It's almost hard to keep up! However, we must try to align teaching strategies with recent developments, because when one aspect of teaching evolves, the others follow suit. And so do the learning expectations of students.

Originally, I had never considered technology becoming a huge component in math education. When I think of my own experiences in math classes, I envision the traditional textbook-paper approach, with the odd manipulative of a visual demonstration (i.e. blocks, lego, graphs, etc). Today proved otherwise. Our math class was shown a very thought-provoking TED Talk which highlighted quite a contradicting methodology: to abandon the textbook approach and lead a more "hands-on" process of teaching mathematical material. The speaker also proposed to be less helpful and let the students build the problems themselves. I found this the most interesting. Taking away all necessary information to solve a problem (i.e. the measurements of a three dimensional shape in a geometry problem), adds a new element to the challenge. This may work in favour for students who already enjoy the subject, or it may instill fear having "too much freedom" to solve the question for other students. Some may not even know where to begin, while others may show excitement being provided with this sense of autonomy. 

I did agree, however, with the proposal of integrating real-life examples, often understated in the subject of math. How many times does a teacher hear "When will I ever need to use this equation in real life?". Well, the TED Talk video really took the whole "real-life example" to the next level. To physically move a math class outdoors adds a completely different dimension, and reinforces the idea that yes, math is found in situations we may not initially consider, so yes, math is in fact important in the real world. At times it may take visual proof and practical demonstrations to accept this notion. In this sense, I do aspire to make math more fun and engaging while including various multi-media.

In case any of you would like to watch the insightful TED Talk by Dan Meyer, here it is:

http://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en

I hope you all can take away something from it just as I did.

Until next time,

Have a beau-tea-ful day!

Miss Capano

Welcome!

Hello friends, and welcome to my blog!

I will start by introducing myself. I am a 24 year old Woodbridge Native who recently moved to Niagara Falls to live with my Nonna (grandmother in Italian), while I attend Brock University. After completing my BA Honours in French Studies at York University, I continue to be passionate about learning languages and education and hope to integrate the two within my own classroom. Pursuing a career in the field of education is the only dream I have ever envisioned. From an earlier age, I believe it stemmed from a love of learning. I have always enjoyed learning new things, even if it meant tirelessly treading through the "mud" and rising to new challenges before arriving at the final destination - the big, fatty, at times indigestible, LESSON. Enriching my life with more wisdom and knowledge is worth being fond of. This is why I refer to myself as an "Eternal Student of Life", as there are simply always new things to discover in this big, beautiful world. 

Fun fact: I survive all challenges and life lessons without a single drop of coffee. That's right. I love tea more than any other hot beverage on planet earth, and quite enjoy a good tea pun every once in a while. (Hence the name of my blog- TEAcher.) I mean, the word tea is within the word 'teacher' itself - it's as if I was meant for this field all along. ;) Tea makes me feel weirdly philosophical each time I drink it...I wouldn't be surprised if I am sipping on tea with each blog post I compose. Currently it is a lavender tulsi tea - yum! Anyways, enough rambling about tea. I am here to create a space where I can share - you got it - what I have learnt and continue to learn during my journey, here in the Teacher Education program at Brock University. 

As a Teacher Candidate, I am just now dipping my toes into the vast ocean of what educating the younger minds entails. I expect to learn valuable things each day while being introduced to new philosophies, innovative ideas, and methodologies from various professionals. Today has been especially eye-opening for me in my Teach Digital Learners in the Digital Age class. I am not the most tech-savvy person in the world, despite owning a Macbook and an iPhone. This happens to be my VERY first blog post. Not bad, huh? An accomplishment of mine for this class already!

Today, we learned about a concept called 'Genius Hour'. This refers to the allotted time (at least 20% of the school day), given to students so that they may have the opportunity to express their passions and deepest desires. David began the class with an interesting video and exercise - creating a drawing in only 10 seconds. We then attempted the same exercise but were given a few extra minutes. The result - both in the video we watched and in our own classroom - was a more detailed, creative approach to the exercise, knowing we had more time. This is the exact concept Genius Hour promotes: allowing more time for students to express creatively and authentically, because that is when the real magic happens. Students then feel more inclined to share ideas with their peers because they have created something on their own terms, about something they feel particularly excited for, as it will derive from their personal interests. Productivity levels will also increase when a student has so much freedom to feel inspired. This self-manifested sense of purpose is definitely a student-centred approach I aspire to implement in my own classroom some day. 

Our instructor, Dave, presented an additional `Genius Hour` inspired activity for us to complete. We were introduced to a digital resource called ``Google Draw``, where we designed a Passion Heart Map. Individualized to what we love, we had fun brainstorming and releasing the energies conjured up during this expression and momentum of freedom. Surrounding the heart (or whatever shape(s) we preferred), were words representing people, places, or things of deep significance to us. It was wonderful to see what every one had created.

This diagram accurately depicts the aspects of Genius Hour that were put into practice today:

I hope this post inspires you all to get out of your comfort zone and expand your digital identity, or your perception on teaching methods, in the same way I was challenged to do so. I am confident in knowing the course Teach Digital Learners in A Digital Age will benefit my future career.

Until next time,

Have a beau-tea-ful evening!

Miss Capano