Am I to Be or Not to Be a “Math Person”, That is the Question
The last few weeks, we have explored how our views in math can hinder us from succeeding. By adopting a growth mindset, we can overcome our struggles and learn from our mistakes. But what if you don’t struggle? We discussed phrases such as “I’m not a math person”, and “I’m just not good at math” and challenged it saying that “everyone can be a math person with the right attitude”. But what if you are a natural “math person” and math comes easily to you innately? Does talent exist or are “math people” just work harder than the rest of us? I believe that some people are naturally better at math than others. This does not mean that if you are not born with natural talent you cannot be a “math person”. It just means that more work is involved to get to the same level.
Being someone who has struggled with math, growth mindset and learning from mistakes is an applicable strategy that I can embrace. I want to improve, and I know that I will succeed if I persevere through my mistakes and learn from them. I am growing my brain and learning valuable skills through my effort. But how does talent benefit a “math person”? Is it better to be talented or to work hard?
Level: Minimal Effort
This idea of talent verses hard work reminds me of my musical experiences growing up. I was always told I have a talent for singing, and my experiences reinforced this idea. I barely practiced, yet I succeeded through each lesson. Each year in competitions, I received high marks and often placed in first and second place. In my teens, I represented my city in provincials five years in a row. And I did all this with minimal practice. I breezed by on talent and little effort. I still learned new techniques to improve, but I didn’t have to work very hard to apply the techniques like others in my studio. Even when I went to university for singing, and was rudely awakened to the concept that talent only gets you so far, I was still able to learn songs the night before a lesson and be praised for the “hard work you clearly put in this week”.
I’m not trying to brag. It was just my reality. And I’m not sure having this talent was a good thing. I struggled a lot through university when my talent didn’t cut it, and I think I hit walls harder than those who might not have had it so “easy”.
Does Talent Only Get You So Far?
A study conducted by David Hambrick and Elizabeth Meinz explores if talent or hard work ultimately fares better in the real world. Their findings conclude that while talent initially fares better, hard work almost always wins out. This is because people who are talented are often LAZY.
Yes, I’ll admit it, I am! Why should I work hard if I can naturally get away with minimal effort and still succeed?
Except my talent only got me so far. When techniques and repertoire being challenging, I didn’t have the growth mindset skills to persevere and work hard. I just despaired and struggled and resisted. I was too lazy to try to work hard. And it killed me that I wasn’t “good” anymore, and I suffered with mental health issues in my final year. Those in my program who might not have been at the same level I was at when I first arrived at school were now surpassing me. Those rare gems who were talented AND knew how to work hard were superstars. But it was the people who knew how to work hard that really understood the craft. They embraced their struggles, learned from the mistakes, took the time to develop their skills. This allowed them to gain a deeper understanding of how to sing.
Mistakes? What Mistakes?
In our math classrooms, we need to emphasise the importance of making mistakes to learn. We also need to make sure we challenge our students enough to allow them to make those mistakes. We focus a lot on the students who struggle with math. But we also need to remember that maybe those students are better off than those who don’t struggle with math. They will know how to persevere, how to develop a plan to improve, and the many components of a concept. Those with talent might miss out on all those valuable lessons, and become content with a shallow understanding of math.
Creating Hard Working and Talented Superstars
How can we differentiate our instruction to allow all students to develop perseverance and hard work, even if they are “talented”?
One solution suggested is the use of open ended math problems. These allow all students to explore a variety of solutions to a problem that might not have a definitive answer. Focusing on the HOW they solved the problem rather than only their final answer will teach students how to break down their problem-solving skills and gain an understanding on a deeper level.
Hello, internet! You might have noticed my hiatus from blogging for the last few months. I promise it was not wasted time. I began my internship in my teaching placement, which was quickly followed by my first teaching block. With the help of my lovely associate teacher, I gained rich experience teaching primarily math and music throughout the many weeks of my block. Who would have thought the girl recovering from a bad relationship with math for most of her adolescent life would end up teaching it every single day in her first block? Talk about break away from your comfort zone!
After successfully completing my teaching block, I went back to classes for a semester. After that, I got a fantastic summer job working at the St. Catharines Museum and Welland Canals Centre as a Program Assistant. I spent the summer organizing tours for little kids, designing and facilitating activities for events, and most importantly, I created a huge teacher resource! My partner and I redeveloped the museum’s Education Kits. These are rented out by teachers for 12 days, complete with lessons and materials. The kit was less than ideal when we got out hands on it. Activities were loosely connected to the curriculum, if at all, and provided little education background. The materials were old or needed to be expanded to be properly used. By the end of the summer, we created 64 new lesson plans for grades 1-8, covering an 8-day unit plan. We also designed, made, and coded all the materials! The documents look official and I’m very excited to see what it looks like when it comes back from the printers. The process of unit planning for multiple grades, and creating all the corresponding materials is going to be so beneficial when I begin unit planning for this year’s classes and teaching blocks.
Year Two: Building Bridges
Classes began last week and boy, are we hitting the ground running this year! And yes, I am once again thrown into the gladiator ring with my old nemesis, Mathematics. As I’ve stated above, last year we began to build the broken bridge brick by brick. Each brick contained a base of Growth Mindset, with additives of New Experiences, Research, Determination, and a dash of Fun. The bridge is basic but solid. I can cross it easily with little to fear. But it isn’t anything grand or expansive. I shouldn’t get ahead of myself though. It will take many years to build a masterpiece with Math. This year, I will just work to make some upgrades to further support this bridge with Math.
I was a little unsure on how to approach these upgrades during the first Mathematics class this semester. I came in with the ingredients that had worked last year, prepped and ready to go. My professor started the class with a card trick and tasked us to figure out why it works, and alternative solutions to continue to make it work. My group struggled to figure out the basic mechanics of the trick, forfeiting and asking for help from another group. Now we had to find the next number that would also allow the trick to work. This is where all my ingredients went stale, and it all started with the deterioration of Growth Mindset.
The professor had stated at the beginning of the trick that it was the “simplest card trick”. Yet, we couldn’t even figure out how to do the trick on our own, never mind how to break down the patterning. Already, I felt like Math was beginning its old tricks again, working me up with an overwhelming challenge that I was just too stupid to understand, yet it was supposed to be “simple”. I barely understood what the next step was supposed to be. "Find the next number that would work." I began to rack my brain for mathematical formulas or solutions to find the number. Would fractions work? No, the deck wasn’t confirmed to be accurately divided during the trick, so it wasn’t a case of fractions. Addition and subtraction would also need to be determined by an equally divided deck. What about multiples of 3? Did it have to do with prime numbers? It became more and more overwhelming as the options flooded my mind with to only hit a wall and crash together in a confusing whirlpool. Once that happened, I just gave up. Someone would tell us the answer in a minute. But we didn’t. The worst part is I still don’t know the answer because we never discussed the problem. I don’t know how to problem solve for next time!
And thus, the Growth Mindset I honed all last year disappeared in a flash. The bridge with Math began to crack and crumble. It’s still intact, but it is not as strong as it was when I walked into the classroom. How could my efforts give way so quickly?
Too Good to be True…
This experience is something I want to remember when teaching my future students. I want to remember the confidence I thought was strongly assembled from the year before yielded so easily at the first sign of a challenge. I want to remember how the idea that a task was “simple” made me feel like I was stupid because I didn’t understand it. I want to remember how I gave up on myself and my determination to keep trying because it was just “too hard”. I was never good at math anyway. Why bother trying again? Clearly, I hadn’t learned as much as I thought I did last year.
It was that easy to lose my growth mindset and confidence. Math and I were fighting again after we had worked so hair to repair our relationship. It was easier for me to fall back into my belief that I was not a “math person”, a myth I have internalized for a very long time. And when we didn’t discuss the solution, I was left with the feeling that everyone else had gotten the answer, so it wasn’t taken up. I felt ostracized by math! I want to remember this will happen to my students too.
The Fine Art of Criticism….
We work with students to build their confidence, giving them opportunities for positive learning experiences and encouraging them to foster a growth mindset. But it’s just like criticism, you need three to five positive comments to outweigh one negative comment. One negative experience with math is going to take at least twice if not three times as many positive experiences to reaffirm confidence and secure a strong growth mindset. Positive experiences don’t need to mean that there is no challenge and the student understands the concept easily. Positive experiences mean the student is given the support they need to find the solution. They need to feel safe enough to explore their options. It will give them an opportunity to learn from their mistakes, and do better in a similar situation.
To provide positive learning experiences for our students, we need to be careful how we phrase our questions, avoiding stating something is “simple”. We need to model the tools students might need to solve similar problems. We need to provide encouragement during mistakes and during each step in the problem-solving process. We need to be transparent in discussing the solution and emphasize the strategy of learning from mistakes.
My goal for this year is to find more positive experiences with math to outweigh the negative experiences. I want to upgrade the bridging relationship I have worked so hard to mend over the last year. My goal is to build a bridge strong enough to support my students who might be struggling to build their own crumbling bridge with math too.
How will you encourage your students to continuously foster a growth mindset when the struggle becomes too real?
Q: Think about how you will use the Assessment page of your Digital Portfolio during your first teaching block.
I will use my assessment page to remind myself my growth from what I though assessment in school was, and how it is actually more similar to my experience through singing lessons than I thought it would be. I will also use it as inspiration to motivate me to implement for, as and of learning strategies in not only my placement class, but also in extracurricular opportunities, like privately teaching in my home.
I will also use my assessment page, specifically the AER form, to use as reference to any questions or strategies I can use to help with assessment or planning ideas. I found some very comprehensive strategy guide on Assessment As Learning, as well as working with the Achievement Chart that I would like to really get to know more thoroughly.
Q: Choose 1 professional learning goal from your AER Strategy Form that you would want to emphasize during a job interview.
I would talk about using the achievement chart to guide my lessons in an interview. I found an interesting resource that explained how to use the chart effectively, and it provided examples of how to implement each category in multiple facets. This is a key component and ability for differentiation, and to provide students with many different opportunities to demonstrate learning. Often, this is assumed in the end product, but I found it interesting that this resource suggested differentiating for each achievement chart category with performance, conversation and written strategies to assess knowledge, thinking, communication and application.
Singing is so much more than saying words to changing pitches over rhythmic duration.Singing is technical. You must control your breathing. You must listen to your voice, and the other voices and instruments around you. You must be aware of your body, and manipulate it the correct way to produce a proper sound. Singing is intellectual. You must read poetry from the lyrics, make connections to historical, cultural and narrative allusions and influences in and of the music. Singing is emotional. You need to determine meaning, feelings, and over encompassing ideas, and ultimately decide the best path to convey those emotions and ideas through the vocal and performance choices you make. Singing is reflective. It makes you reflect on your own feelings about an idea or meaning. It also makes you reflect on your strengths, your areas of improvement and the next steps to achieve your goals.
So much goes into performing a song!
Communicating orally is much the same. You have to be able to have control of your voice, be able to manipulate your body to convey meaning, understand what you are saying and reflect on your successes and where you still need to go to get better.
There are a lot of resources and information on the benefits of singing and language development in young children. Children use singing to help them develop articulation skills when they begin to learn how sounds shape words, and the meaning of multiple words together. It helps them learn the construction of languages. Singing can be used to model the rhythmic patterns and tones in speech to better improve a child’s deeper understanding the structure of words and sentences. Studies have found that singing unfamiliar texts to familiar tunes can improve reading fluency.
With all this information about the benefits of music and singing to teach young students the basics of language construction, I assumed when I began to research a way to connect music and oral communication for a lesson plan for the middle grades, I would be overwhelmed with activities and rich content to choose from. I was highly mistaken. While there are many a blog or article touting the benefits of music/singing to communication skills, it is generalized into a surface statement without any accreditation or supporting findings. It was even harder to find any lesson plans, activities, or a direct explanation of the reasoning behind the connection of oral communication and music, specifically singing.
Reading through the specific expectations in the Ontario Language Curriculum under the Oral Communication strand, I immediately saw a correlation of required skills and my experience with singing instruction. Curious, I explored the Music strand of the Ontario Arts Curriculum. I found some expectations that could easily match with the oral communication expectations. Since I have 18 years of singing experience, and my teachable is vocal music, I wanted to create a lesson combining these two curriculums of oral communication and singing.
I choose to focus on the use of musical elements and vocal effects to infer meaning and mood, accompanied by facial expressions and gestures. I created a lesson plan that allowed students to compose an arrangement of a familiar holiday carol to convey a new mood, by changing elements such as pitch (tone), tempo (pace), accents (inflection), dynamics (volume) etc., and requiring them to perform the arrangement using facial expression and gestures to help communicate their mood. The students watching their peers perform were expected to actively listen to their peers, identifying the elements and expressions used and determining the mood from what they heard.
Cross Curricular Lesson Plan
In that single lesson, I used more expectations from both strands than I could assess. For music, the lesson provides opportunity to sing and/or play, in tune (C1.1), apply the elements of music to create a specific effect (C1.2), create musical compositions for a specific purpose (C1.3), identify the elements of music in the repertoire they perform, listen to, and create, and describe how they are used (C2.2). In the language strand, this activity asks students to actively listen to their peers’ arrangements, determine and communicate the inferences made from listening and watching their peers and identify the purpose of the performance. It requires students to create and present an idea with purpose (convey a specific mood), by using appropriate vocal and non verbal elements in a clear manner. That is roughly covering 5 music expectations, and over 10 oral communication expectations!
The above image shows the many connections between the Grade 6 oral communication curriculum and the music curriculum. Can you find anymore?
Singing can be an engaging way to teach and practice almost all of the oral communication expectations in the Ontario curriculum. There are 3 overall areas listed as skills students should learn in middle school oral communication: listening, speaking, and reflection. Music and singing can easily be incorporated into each of these sections.
Listening
Music has the uncanny power to elicit powerful emotions, as well as convey a variety of intentional and unintentional messages with or without words. Music is complex, consisting of many layers and elements to be absorbed, identified and interpreted. Part of good listening skills consist of being able to isolate and identify all the elements of what you are hearing, direct or in direct. Music provides a rich combination of sounds to practice deep listening skills in order to gain information and make connections. This translates to oral communication because when listening to someone speak, you do not just hear the words someone speaks. Yes, you hear the words. But you also hear the tone or quality they use. You hear their stresses and pauses on certain words. You hear where they breathe. You hear the speed in which they speak. You hear the volume of their voice. All these elements give you information about what the words mean and you make inferences based on this information. It might have nothing to do with what the actual words said mean.
“I got promoted.” If someone says this in a higher tone, you might infer that they are excited, or if there is a quiver in their voice, you might interpret that they are nervousness or uneasy about the news. The words are still the same, but the implications are different. You can gain information by listening to the accents on the words. A stress on “promoted” might mean something very different to a stress on “I”, as if they were surprised they got the promotion. Volume might indicate angry, happiness, fear, sadness etc., speed might indicate the same emotions.
These elements go hand in hand with watching skills as well. Communication is more than just sounds, but also consists of observing and interpreting body language and how certain facial expressions, posture or gestures can alter the meaning of a certain phrase.
Singing teaches all of these skills. When you watch a professional singer, you will notice not only the lyrics they sing, but facial expressions they use, movements they make, accents or timbre of the words/notes, and the dynamics they use. These elements help the singer “tell the story” or present the meaning of the song on a deeper level than just text. One way to help students practice this listening skill of gaining information from elements beyond the text is by watching singers perform a song in a different language. They will learn to pick up information without the lyrics to help them. This allows them to isolate the cues needed to infer information. The music helps engage students more readily than simply listening to a speaker, as well as easier to hear and see the subtle indicators of non-text oral information.
Lyrics are the text of singing, and along with the elements discussed above, provide even more opportunity for students to practice analyzing meaning, point of view and overall comprehension of the song. They then are able to reflect on the influence or affect the elements had on their understanding, and the effectiveness of the performance/presentation. From there, connections to other musical or non-musical media or ideas can be made to further extend their knowledge.
Students need to practice actively listening to all elements of communicate to learn and apply what they see and hear into their own oral communications.
Speaking
The above non-text elements that provide information to the audience of a singer obviously are important to put into practice when singing yourself in order to communicate effectively. By learning to listen and watch for these tools of communication and how it can be used to convey different meanings, students should then be able to understand and be able to implement them into the own singing.
While taking private singing lessons, and eventually when I privately taught vocal lessons, one of the biggest things I was told, and emphasized, was to “tell the story” of my song. Yes, technique was important too, but if I didn’t tell the story, what was the point of singing the song? So I would create a song map. I would interpret the poem of the lyrics, and figure out what I was trying to say as a character, and what I was feeling in each phrase. What was the most important thing in this phrase that I wanted my audience to understand? Would changing the stress on a word change the meaning I wanted my audience to understand? If I sang this part soft, what did that mean? If I sang it loud, it would often change the feeling entirely. For example, one song I love to sing is “I’m not afraid of anything” from Songs for New World (unfortunately I don't have a recording of me performing it) and the final phrases claim that the character won’t let anything or anyone stop her because she is not afraid. Now, I could sing the entire ending in full belt, loud and confident, and convey the same meaning as the word imply. However, I like the sing the final “I’m not afraid” softly, implying a contrasting idea to the text that perhaps I am not so unafraid and confident. Unfortunately I don't have a recording of me performing it yet, so I can't demonstrate what I mean.
As a performer, facial expressions and gesture can reinforce or contrast with the literal implications of the text. Students need to practice the manipulation and understanding of body language’s ability to provide more information than just the text.
This video is from recital I had about 7 years ago, and is one of my favourite songs for expression and body language. I had fun playing 3 different "characters", living on 3 different levels, which I used my body language to help represent timidness, formality, and looseness. I played around with excitement, sarcasm and self discovery in my facial expressions. I used dynamics to convey and contrast certain ideas. Overall, a fun experience to practice communicating all this characters feelings!
By singing, students can play with interpreting lyrics, experiment with vocal effects, create a character with distinct expressions, similar to drama, but with unique musical constraints and freedoms. Singing also develops students’ projection, posture and breathing regulation in a more controlled manner over drama.
Reflection
Singing is a very vulnerable and intimate physical endeavor. It is unique to you, and is purely an instrument of your body. Because of this, there is a deep connection to our singing voice. It is you close companion and can carry a lot of weight of self-confidence, and provide you with rich opportunities to reflect on your abilities, but also reflect on your emotional and physical well being. This dissertation explores the areas of reflection that can be gained from singing. The first is our Self-Reflective Vocal Experiences. Not only do you reflect on your own perception on your sound, but also on your narrative self vs. experiential self. It forces you to reflect on your introspective perception of your body, which then allows you to reflect on your physical and mental well being. Singing allows you to connect with your individuality of your own unique voice. By creating awareness of interpretations when listening and performance choices made to convey certain emotions, singing opens up a reflective window into the inter-workings of the emotional self and the perceptions of the world around you. Pretty deep stuff for a 5th grader!
Because of the apparent familiarity and control we have over our voice, we can use it as a flashlight, to explore its origin, history, mental and physical and social clues and influence. In this context, the voice can be seen as an avatar of the self; they both contain this paradox of being apparently timeless and immutable while being also inherently embedded in the present and shaped by our past experiences (age, traumas, accents, intonation, fillers, vocal posture). - Rebecca Kleinberger
Students also learn to assess themselves by listening and watching their performances and reflecting on what they might not realize they are doing, or notice improvements they didn't recognize at the time of performing. Students (and anyone, really) should be encouraged to record themselves during practice and performance in order to gain insight into their growth and provide an objective tool for perception.
More research needs to be made into explicitly connecting the use of singing instruction and how it can improve and develop oral communication skills in not just young children, but also into the middle grades. Maybe this is something I will pursue in a master program one day, who knows. However, one thing is for sure. I am grateful to my grandmother for putting me in singing lessons. I have never been more appreciative of the extra benefit I gained from learning how to sing, and definitely have a deeper understanding how it has helped me in my confidence to speak, convey, and control my emotions. Now to teach my students the same skills!
The Ontario Ministry of Education document, Growing Success, is a goldmine of information that is extremely valuable to pre-service teachers. It breaks down everything from navigating the curriculum expectations, explaining learning goals and success criteria, the types of evidence of learning, and the difference between formative and summative assessment. All this information is followed by a step by step walk-through of the report card system and what to expect when completing a class set two times a year, in addition to a progress report in the fall. In addition to the walk-through, it also provides a few chapters of strategies for assessing students with special needs, such as IEPs, ESL, or any modification/accommodations.
What Do You Want?!?
One enduring idea that I gained from reading this document was the importance of developing learning goals and success criteria in student friendly language, and making it transparent consistently throughout the lesson. I don’t remember this being something I was aware of in my elementary schooling. This leads me to believe it might have been given during some assignments, but not explicitly explained as the point of the lesson, and how I could show I understood the concept. Going into my undergrad, and even into this post grad program, I appreciate how frustrating it is when you are given an assignment, but the purpose and criteria are vague. I do not know what direction to start, or how I can make sure I cover what is expected. Often, my work might vary greatly from that of my peers’. Because of this disparity in expectations, I may be disappointed with my final assessment, or feel like my work is worth more than the person who did less than me, but got the same result. This experience is something I will remember in my own teaching when planning any lesson.
It is important to give students access to the learning goals and success criteria, and stress the importance of referring to the criteria often during the learning process. By doing this, student should develop the habit of checking guidelines as they work, and edit as needed. This will ideally help diminish the disparity between the quality of student’s work, as the habit develops.
As I said, I will be sure to make the learning goals and success criteria clear for my students in my classroom, but I will also take this approach to my teaching privately. I spoke about my learning experience in vocal lessons growing up, and how the model was mostly assessment as and for learning, with minimal summative assessment. But I did not talk about my experience teaching privately.
Outside the Classroom
I taught private voice lessons for about 15 students while covering a maternity leave. As a first time teacher with absolutely zero training in how to run a vocal lesson, I was at a loss at how to manage practicing or tracking student growth. I managed to swim with my head just above water, and my students progressed successfully, but it was not without many bumps along the way. If I had known about the strategy of providing clear learning goals and success criteria for a lesson, a span of lessons or even for a specific song or technique, not only would I have had an easier narrowing down a focus for feedback and finding strategies to help my students, but it would also have given students a clear understanding of what they needed to work towards during the lesson, and during their practice time. Students often would say they didn’t know how to practice, even if I gave them something to work on. Perhaps just saying “say these lyrics as a monologue” or “practice this exercise this week”, I should have given them attainable goals, and described how they would be successful in their practicing. I might say “recite these lyrics as a monologue using expression and natural pauses. Make sure you can put accents on certain words, experiment with gestures and facial expressions, play with dynamic changes. You should practice it 3 different ways each time you practice.” Perhaps providing a learning goal and success criteria for each step of learning a song, or what it looks like to correctly practice a technical exercise. Growing up, a similar method might have motivated me to practice singing more, and more efficiently too. I would have gone into a lesson more confident and even if I didn’t practice enough, I would have at least had an idea of what we were going to focus on during my lesson. My students would most likely have benefited the same, and I intend to implement this when I open a private studio in the (hopefully soon) future.
Being transparent with the purpose of a task and the criteria to be successful gives students the road map to their learning. They are most likely to meet you along the way if the know the path to follow.
Last week
my associate teacher was explaining a writing activity she has carried through her
classes over the past 5 years, inspired from a technical fluke of her Halloween
classroom decorations. She had an inflatable lawn ornament of a cat that she
brought into the classroom and set up the week before Halloween. The students
loved the big cat in their classroom, and gave it a name (I think Cookie was
their consensus).
One day she plugged it in, and for some reason, it inflated in
a way that legs of the cat were awkwardly up in the air. The students shuffled
into class, and started to laugh at Cookie’s position, asking the teacher what
happened to him. Inspired by her student’s questions, my associate teacher used
their engagement for her unplanned opening activity for the day. She asked the
students to take out their language journals and to write what Cookie had done
to get into that position. The students eagerly wrote creative scenarios about the cat chasing
a mouse and how the mouse had outsmarted him, or that Cookie was a secret agent
sleuthing through the students’ desks and was trying not to get caught when the
students came in. Delighted by the response, the teacher would place Cookie in
odd places or positions before the students came into the classroom and then
the students would start their day writing a short reason behind his position.
What an
exciting way to engage students to begin creative writing! By using a prop and
a guiding question, students are given a focused channel for their creativity.
Journaling gives them a space to write their ideas freely and keep track of
their ideas for later reflection or developing. My associate teacher used this
as a quick writing exercise for students to practice their creative writing,
but the activity could easily be developed into a lesson unit on the creative
writing process.
Using Props
as Prompts
Writing
prompts are key to help students inspire and focus their creative ideas onto
the blank page in front of them. Introducing a physical prop or character provides
them with a concrete item to build a foundation on, and work from that point.
In my associate teacher’s case, she introduced a cat character, Cookie, as the
focus of her students' creativity. Any character prop could work just as well.
Similar to the Elf of the Shelf idea parents practice each December, the
teacher could manipulate the character into different positions or places
around the classroom or in the school. Once the class has all seen the new change
in the character, students should be given time to creatively write how the
said character got into that there. I personally would do this activity as a
quick write, where the grammar and spelling didn’t matter, but shift the focus
towards creative thinking. This could be done in a language journal, google
document or on a digital classroom forum. Students could include pictures, or create
audio files, depending on their preferred style of learning or differentiation
needed, as long as the creative ideas are recorded.
Quick
Writes to Short Story
Writers
rarely just sit and write from a blank screen at a Starbucks for hours,
producing page after page of a story. Usually writers plan out their characters,
their settings, and their plot long before the actual writing begins. Teachers
can easily use a Character Prop, as well as quick write stories to cultivate
these development skills. After a determined period of time, students should
have a nice collection of creative ideas in which to create a story. Students
should be encouraged to review their ideas and to develop a plot for a short
story based on one or more ideas they had. At this point, mini lessons discussing
plot diagrams and features of a good short story could be introduced. To help
students develop a plot, a graphic organizer or digital tool could be used. BBC
has a really awesome tool called PinBall in which the user can manipulate
ideas, images or words, either generated by the program and imputed by the
user, in various ways. There is the option of a mind map, a timeline, an idea
sorter, and an image manipulator. For an fun extra activity, this MadLibs-style story generator would be an interesting prompting tool.
This method
could then be transitioned towards the details of a story, like character and
setting development. After the plot outline is complete or even during the
quick write period, give students a graphic organizer in which to determine the
details about the prop character. Discuss character traits, descriptions, likes
and dislikes, relationships and goals. Ask them to draw a picture of the character
on the graphic organizer, or could be included as a task for Visual Art class. Once
students have their plot outlined, students could create a character profile
for each main character. Students could be tasked to do the same for certain settings
in their story.
Writing the
Story
Now that
they have the plot outline, the characters developed, and the settings
organized, students are ready to start writing their first draft. This can be
done again by using a graphic organizer for each plot point, or students can be
given free range to write. Students should be able to write on paper or on a word
processing software. Provide time for students to write in class, as well as
give them checkpoints for each draft. 2-3 drafts should be submitted before the
final product is complete. No grade should be assigned to any of the drafts,
but should be covered with lots of descriptive feedback.
In order to
avoid overwhelming students with negative feedback, find an editing focus for each
draft.
For the
first draft… Focus on the organization of the story, the descriptions and if
things need to be clarified. Provide suggestions or questions to prompt
expansion of an idea or an alternative solution. Only edit major formatting or
phrasing errors.
For the
second draft… Focus on the finer details, like formatting or grammar. Correct glaring
spelling mistakes. Avoid over correcting, keeping the focus primarily on plot
and formatting details.
For the
third draft… Now is the time to focus on all the spelling and grammatical errors.
They should be ready to publish their story, and this should be more of a proof
reading stage. This can also be done through peer editing or on Grammerly.
Publishing
Now the fun
part! There are lots of ways students can publish their stories. Teachers can assign
one specific way of publishing or offer a few options students can choose from.
They could be published in a hard copy or digitally.
"Tyla's Spell",
4 chapter short story, circa 2003
by 12 year old Mrs. Day
Long ago, in my Grade
Seven class, (yikes, 13 years ago!), I wrote a short story about a fairy who needed help
by some children during Halloween. I drew pictures above my text and created a picture
book by putting the pages into a small binder. We later read our stories to our
reading buddies in a Grade One class. Technology would have been an interesting
way to publish my story though, and maybe the graphics would have been better
than my poor illustration skills. Maybe I'll upload the story here using one of the options below.
Some digital
publishing options include:
GoogleSlides, PowerPoint orSlide Story- Each slide could be a section of the story
with images. Students could also record their voices reading out the story on
each slide.
StorytoporStoryJumper – create a scene by scene story, by adding text to backgrounds and
images
PowToons –
create an animated video with sounds, images and text
Final
Consolidation
Students
should then share their creations with the class, other classes in their
division, to younger grades, or create a digital portfolio of all their hard
work. Students could create a blog, Prezi, or RealTime Board showing off their
creative writing process. They could post a few of their quick write samples,
or their character and setting outlines. A video trailer for the plot outline could
be created. At the end, the final project should be presented. Students could
also post a reflective paragraph, audio or video file explaining their process.
There are
so many cross curricular and unit expansions that could develop from a simple
prop placed in an interesting position in the classroom. The activity could be
modified towards a small journal entry, or to an entire unit lasting a few
weeks. Students have lots of ideas. They sometimes just need some unique
inspiration.
Seriously though, geometry has the best puns, especially for angles. Not only are they funny, but they can help students remember key features about types of triangles and angles. I particularly like the last three jokes, as they really enforce the idea of a right angle being 90 degrees, and an obtuse angle is more than 90 degrees. Such an important concept and yet, such a simple way to engage students.
In my placement class, certain students are still struggling to grasp the concept of benchmark angles. Benchmark angles are the main angles that one can use to eyeball approximate angles. They are the starting points of angle estimation.
Benchmark angles also help students develop an understanding of angle size. At first, students describe angles qualitatively (less than a right angle, greater than a straight angle); eventually they use a numerical value (“The angle is a little smaller than a right angle, so it’s about 80°”). - Geometry and Spatial Sense, pg 41
The first and most important benchmark is a right angle, or a 90° angle. It looks like an L. Some non-standard tools to help students recognize a right angle is the corner of a piece of paper, the corner of a book, the placement of the hour and minute hand on a clock at 3 pm. An easy tool they always have with them is their hands. If they make an L shape with their thumb and pointer finger, this creates a right angle.
Once they understand the what a right angle looks like, and that it is 90°, they can begin to learn the other benchmarks (45°, 135°, 180°). An simple activity to help students understand the relationship between recognizing benchmark angles and the types of angles is to practice identifying obtuse and acute angles without the use of a protractor. Obtuse angles extend more than 90°, and Acute angles are smaller than a 90°. It was surprising how many students in my placement struggled with this.
An activity that my associate teacher did with her class was to take the students outside, and they recorded and investigated angles and polygons. They looked for right angles, found acute angles on leaves and identified obtuse angles on rocks. Students were engaged and actively looking for different types of angles and shapes around the yard. Some brought back some leaves, and they measured the exact angles with protractors, without being prompted!
Benchmarks are important for students to recognize, especially right angles, so when they start learning about perpendicular lines, they are able to identify the right angle quickly. My grade seven students who hadn’t quite grasped the concept then ran into problems when trying to identify a perpendicular line segment.
This week I found something really, really cool that I would like to share with you. I have already mentioned in my first post about how math always confused me, and even though I am musically inclined, I struggled with music theory as well. But what if you could learn them together and explicitly see the relationship between them without having to do a lot of inference? Maybe that would have helped me make the connections I somehow missed.
In practicum yesterday, I observed an awesome grade 4/5 music lesson. As part of it, we were singing a song that was very similar to the Christmas carol, “Angels We Have Heard on High”. The music book pointed out in a footnote to notice the translated pattern in the melody of “gloria”.
As you probably know, the word “gloria” is sung to a melisma comprised of a series of notes repeated 3 times, each time one whole tone lower. Okay, not everyone understands it in those terms, but you probably realize there is a repeated pattern in notes and rhythm. The idea of patterning in music stayed with me when I started to think of what to blog about this week, so it was a natural inclination to decide to research how to teach patterns and algebra with music.
However, I was disappointed. I spend almost 6 hours researching, and while I found countless articles and studies alluding and supporting a link to music and algebra, I found little actual lesson plans or activities to actually teach the link. I found a few activities for patterning and music, but much of it was suited for primary curriculum. Anything else I found was for high school algebra or really complicated university level math. Why couldn’t I find anything for middle school algebra that was comprehensive yet easy to teach? I almost gave up to write a boring blog post on a text book activity. They always say it looks darkest before dawn, and today I rung true. I finally struck gold and came across an innovative program that is quickly becoming a prevalent method of teaching algebra and music.
Mathematician and pianist Marcus Blackwell Jr. discovered how he had learnt to play the piano by ear by constructing the pitch relationships in mathematical terms. Using this euphony, he has created an entire curriculum using algebra to teach musical pitches and chords to current pop songs by artists like Justin Timberlake and Taylor Swift. He likens a scale on piano keys to a number line. After explaining the relationship between a semitone and whole tone, students practice figuring out the relationship of note a to note b. For example, a whole tone is 1 step in pitch. So D natural is 1 step/whole tone away from E, and one whole tone away from C. To figure this out, students are encouraged to use the piano scale/number line to find the related pitch. This can be put into an equation such as D + 1 = E, or D – 1 = C. Once this is concept is established, students can then find out the new note that is 2 or 3 whole tones away from D. Then comes the algebra. In order to find the first chord to a selected song, the student has to figure out the whole tone amount (the variable) towards each pitch. To do this, students are given x = 2. They must substitute the variable to find the note in the chord. Once they have figured this out, they have the chord. After doing this 3-5 times, they have the basic chords for a full pop song (honestly, you can play so many pop songs with a limited amount of basic chord progressions it’s laughable).
By reading articles, watching videos, and combing the website, all I can really pull out concretely without reading the actual workbooks is using the musical scale to represent and describe relationships between numbers, which can be useful to explain adding and subtraction, but also as a tool to introduce functions. In Making Math Meaningful, Small defines a function as “a relationship that leads to a particular output for a particular input”. In the Make Music Count program, the function would be +/- (# of whole tones) = (Pitch). The input would be the number of whole tones, labeled x, and the output with be the note/pitch. From the demos I have found, students practice substituting a given number into the input variable to find the pitches.
I have asked for these work books for Christmas and am extremely excited to get to the details and extensions this program offers. Looking at their store, they also have a book on graphing and one on fractions. Needless to say, it’s a creative and exciting way to math, and as a reward for using math, students learn music. Can’t get much better than that!
Stay tuned for after Christmas for another post describing this program in detail. Has anyone used this program in their school? Can you explain how it works a little more deeply? Let us know in the comments!
