Overcoming Math Phobia

A phobia is defined as an extreme fear or aversion to something. This can often be associated with mathematics both by students and teachers alike. Human nature is such that when we feel we are not good at something, we therefore can’t be successful at it and we tend to avoid that what we will fail at. This self-fulfilling prophecy is often alive and well in a teacher’s or student’s thoughts.

I will be the first to say that at an earlier stage of my career I was very uncomfortable and unsure of myself when teaching mathematics. Sure I knew how to do math, but did I know how to teach something I was not very comfortable with. I had to do something to ensure that my skills and pedagogy were improving. Thus began a voyage of self-learning or self-guided professional development. Now, twenty-five years later I am still on that journey of learning about how to best teach mathematics so that my students learn and are engaged in their world that is so filled with math.

As with anything else you must find the right tool or vehicle for learning. I attended as many workshops as I could on mathematics. The Waterloo Region District School Board offers a wealth of learning opportunities for their teachers as does ETFO and the Ontario Association for Mathematics Education (OAME) (http://www.oame.on.ca/main/index1.phplang=en&code=home).

These are several key areas where you can start your journey of learning. I would like to share three key resources that have helped me become a more efficient and knowledgeable mathematics teachers. The first is the work of Dr. Catherine Twomey Fosnot. Her work and approach to the instruction of mathematics is the number one influence I attribute to my growth in mathematical instruction. I attended several of her sessions as well as visiting her site in Harlem. I would highly recommend her series ‘Young Mathematicians at Work’ as a classroom resource.

The second most useful tool I have come upon is the series entitled Super Source. There are many reasons why I like this resource. The first is the rich problem solving tasks that are in each book. There are a variety of tasks and each task is connected to an area of mathematics where it can be used like number sense or patterning. There is a book written for each type of manipulative (Base 10, Pattern Blocks, Tangrams etc…). The most valuable asset of this resource is that there is a section where the mathematics behind each task is explained to the educator (the big ideas) as well as suggestions on how to bring out the math in your students. As with any resource this provides a jumping on point where a teacher can then adapt the task to meet their needs.

The final resource I would like to share with you is one of the many works of Van de Walle. I used this resource as a teaching tool for myself. It helped me understand the concepts I was teaching and how to bring out both a level of engagement as well as a deeper understanding of mathematics in my students. I hope these resources prove to be as valuable a tool to you as they are for me in my teaching of mathematics.

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Options

My grade five class is almost done their perimeter and area unit. At the close of this unit, I was having trouble deciding what the best option would be, a project or a test. I decided to present both options to the class and then let them select which one they should do.

I then had an issue with letting students who had received an “A” on their reports not do both. I wanted them to challenge themselves by trying both since they had achieved such a high mark on their report card.

Some students reacted very negatively to this thinking they wish they had received a lower mark. I on the other hand, tried to explain to them that since they had such a high mark on their report, they have proven that this unit is not a challenge to them so they should challenge themselves by trying to take on two activities.

It was interesting how many students chose to take the test over the project. I for one, HATE tests and as a child never enjoyed spending time after school studying for them. As a teacher, I dislike giving them as well because they do not offer any creative elements for the child who is writing it. So when some of my students chose the test over the project, I was rather shocked.

I am happy I gave my students the option because I loved seeing students debate over both and then finally arrive on their final choice. I think that when I was in university learning about choices for students, I never really understood the feeling over power it would give my future students. It was amazing seeing them weighing their options and I am happy I was able to give them that feeling.

Who? What? Where?

One of the anchor charts in my classroom states that Reading is… Remembering and Understanding. This is what I use to help students understand that good reading is so much more than word decoding. In my classroom I am often faced with trying to help students who have difficulty in their reading comprehension. They lack the ability to recall what they have just read or their recall is very generic and lacks specific details. I have developed a game to help improve a student’s ability to recall the specifics around characters, main events and setting. This learning task is called Who? What?  Where?

IMG_1794This is a three phase unit. The first step is to model it using a read aloud novel. After each chapter we pause and take a minute to review the characters that were a part of that chapter, what were the main events that occurred in that chapter and finally where did that part of the story take place. I do this for about two or three chapters into the novel. From there we move to a graphic organizer where they now have to answer questions I have created about a chapter after it has been finished. The questions are designed to elicit one or two word answers and thus can fit easily in the boxes on the page. The other purpose for the short answer is to focus on comprehension and not spelling or sentence structure. After each chapter I ask three questions, one of each type. As the chapters progress, the questions become more and more specific and thus a deeper recall gradually begins to occur with my students. The students earn points based on their ability to recall accurate information. For most students this is a motivator by itself.

IMG_1795The final stage of this unit is to transfer the learning that has occurred to an independent reading task they complete. This is called their Book Project. They are able to select a book that meets the following two criteria:

  • It has to be at a level that is just right or challenging for them (teacher approved)
  • It has to be a narrative (thus focusing in on the three elements of a story characters, setting and main events)

From here they now have to read their novel, decide on a way to share their understanding of the story (that best fits their learning style) with their classmates and teacher. It is here during this summative task I find out what gains have been made by students in their reading comprehension as well as finding further gaps that need to be addressed in the upcoming reading lessons. A natural progression that occurs is also the move away from just basic recall and the move to more critical literacy questioning and answering. But as many students have taught me, they need to have well grounded foundation skills prior to moving into higher level thinking skills.

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Student surveys

If you haven’t had your students use google forms, the survey creator on google drive, then you must! Students will have the chance to create online surveys and administer them to anyone they want.

We took our data management project to whole new heights when they created a survey for a certain grade to answer. We were looking at student satisfaction in regards to clubs and teams available at school. The answers were shocking as sometimes 75% of  students in the grade were unhappy with the clubs and teams available to them. My 28 students were divided up among all the grades at school and each group surveyed the grade they chose to survey. We will now look at the results and try to accommodate to add the new teams and clubs to our school.

I also was able to survey my students using the same program, google forms. I asked them about the way I ran the math program, language program and drama program. They were able to check mark all that they enjoyed about each program. Here are the results for the math section:

  1. 11 students enjoy projects
  2. 9 students enjoy group work
  3. 8 enjoy math around the class
  4. 6 enjoy tests
  5. 5 enjoy lessons on the board
  6. 2 enjoy quizzes
  7. 1 student wants to learn taxes

This way, when I do my next math unit, I can plan for maximum student enjoyment. It is important to know how your students want to learn so that you can have the best learning environment possible.

The upside of encouragement

Photo by Peter Kratochvil https://creativecommons.org/publicdomain/zero/1.0/
Photo by Peter Kratochvil https://creativecommons.org/publicdomain/zero/1.0/

It’s that time of year again. Autumn leaves have turned colour and fallen without a care to the ground. Halloween candy supplies are at seasonal lows and sugar fuelled misbehaviour incidents are subsiding.

There is a love-hate feeling attached to this time of year. A love of the beauty that nature has bestowed upon us, and a hate for the extra work it adds to the lives of many. How we see this season may define our perspectives in many areas of our lives. I will not be raking this year, but always take time to enjoy the changing colours.

Fall is also a time for appreciation and reflection. For many educators, it means time to write Progress Reports. It can also be a time of mild anxiety on both sides of classroom.

Teachers might be asking, “Have I assessed enough?”
“Did I give students enough opportunity to demonstrate their understandings?”
“Did I do everything I could to foster success?”
“Did I catch it when they were successful?”
“What will parents think of my assessment of their child?”
“What are the next steps in my class before the next reporting cycle?”

Students are probably wondering how they are doing too?
“Did my teacher notice that I am trying my best?”
“Did I do everything I could to succeed?”
“What marks will my friends get?
“Am I below, at, or above average?”
“Will my parents be happy with my marks?”
“Am I happy with my marks?”

Come to think of it, I have been thinking a lot about assessment lately. Educators assess for, as, and of learning. We use conversation, observation, and product to quantify student achievement and qualify our instructional methods. We have achievement charts, success criteria, and demonstrations of understanding all orchestrated to associate a grade, mark, or secure a checkpoint before moving forward. There is however, another key catalyst to move our students towards success. And that is encouragement.

Think of it this way. Have you ever been complimented by someone after something you did? I’m sure it was encouraging? Of course it was because you were noticed and validated for your efforts by someone else. I always value when someone takes the time share their appreciation for something I’ve done. Even when I didn’t see it myself. Each time I receive encouragement makes me want to work even harder. Our students respond this way too.
Why wouldn’t they?

When I look at what educators hold in their actions, words, and interactions with students – it is the power of encouragement that can make the biggest impact. So how can we use it to empower our students to succeed? Have you ever seen a student happy after receiving a mark, or feedback that only magnifies what was wrong with their work? How about after you complimented them after a job well done?

Students, usually, know where they stand in the classroom, whether they are budding on the tree, or withering. This could be emphasised for the better every time educators choose to acknowledge the good that is in each of their learners. Bandura shared that, “Teachers should also encourage students as a way to enhance their self-efficacies and thus improve their learning.” Some might call this Strengths Based Learning. For me encouragement is a simple, yet crucial instructional tool which promotes a positive outlook on effort, learning, and assessment.

When students are encouraged they are free to become risk takers who are safe to try, safe to make mistakes, safe to fail, safe to try again, and always safe to learn. As the marks fall on this year’s progress reports, with encouragement, students will see the beauty in their efforts instead of being raked over for their work.

Ontario Student Record Search

Wow, we are already into the second month of this school year and I am not sure I really know my students very well yet. I have a working idea of who they are as students and as people but need to gather more information to help me with my programming. That is where using their Ontario Student Record (OSR) can help you gather further data to assist me  in this process.

I typically do not complete my OSR searches until after the first month of school so that I can establish my own opinion about them as learners. The OSR is a cumulative record of them as a student since their entry into the Ontario education system. It is a legal document that travels with them from community to community and school to school in Ontario. It is a valuable tool for any educator who is working with a student.

There is a wide variety of information that exists in a student’s Ontario Student Record. First and foremost are the provincial report cards from their time at school. It is here that a teacher can gauge where a student has typically performed in the various curriculae. In addition there is often a wide variety of other sources of information specific to that student. For example, there could be documentation around outside supports such as occupational therapy, early intervention, psychological assessments, legal documentation around custody, Family & Children Services involvement, suspensions, Individual Education Plans and Safety Plans. When you look at the back of the OSR you can see a history of whether a student has had a stable education in one school or whether their circumstances show multiple schools with little or no stability. I have had one student who was entering into his 8th school and he was only in Grade 4.

There is a combination of hard data as well as data that has a subjective component and is based on the interaction and opinions of adults. It is important to differentiate between the two. I am not saying you should discount in any way or ignore that data, but rather understand that the circumstances in which that data was obtained may have been affected by many outside factors. For the student who was entering into his 8th school, his OSR showed that he had difficulty making friends. That data was accurate but was also impacted by his inability to be in a single place long enough to establish friendships or the fact he knew if he did make friends, he would probably be moving soon.

The OSR search is most valuable to me for my at risk students. Students who I know come with challenges either from an academic or behavioural standpoint are the first ones I search, as they demand my attention immediately. When I have a firm understanding of what level of achievement my students are displaying I then look at previous report cards to help me. If for example a student is obtaining a lower mark in mathematics then what has been previously reported it prompts me to further examine my assessment data to ensure my determinations are aligned with my criteria.

It is important to familiarize yourself with the proper protocol of what goes in an OSR, who can access an OSR, where that OSR can be viewed and the responsibilities a teacher has in regards to filing information in a student’s Ontario Student Record. A really rewarding aspect of doing my OSR searches is that I get to see how they have changed over the years with their annual photo. I have attached a template that I use when completing an OSR search.

 

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Report Cards – Writing the Narrative of Student Achievement

Although it seems like the school year has just begun a few weeks ago, it’s actually coming to a close next month. Yes! You read that right. School’s almost out for the summer – despite the fact that summer seems to be taking its sweet time to arrive with the weather feeling more September-like rather than spring. With all this mix bag of weather and perhaps emotions concerning the close of one school  year and the horizon of another, there is still one thing on every teacher’s mind: report cards! Gasps for fear; leaps for joy; however you reconcile this extremely important process of formally reporting student achievement, the narratives we write have the potential to impact our learners in very significant ways.

Though the Report Card tends to be written with parents/guardians in mind, it really has a wider readership that includes the students themselves as well as a host of future teachers who have access to it through the Ontario Student Records (OSR). Knowing this, how might we be more intentional when writing the report card since the contents have far reaching implications?

Firstly, the report card is meant to be meaningful. As teachers with teaching degrees and constantly immersed in “edubabble” (terms that are usually commonplace for educators), it is important that the things we say in the report card are communicated in the most effective way so that our message comes through with intention. Keeping the use of educational terminology to a minimum will ensure that the audience can arrive to its intended message with ease. This might mean rewording the curricula using reader-friendly terms. Remember this revised versions of K.I.S.S. – Keep It Simple […and Significant]. Report comments should serve as a window to student achievement in ways that demonstrates both the scope of learning that took place as well as the degree of success students experienced within it. Teacher jargon can inhibit this very clear message which can be then deemed irrelevant to parents/guardians and students.

Next, embrace a positive tone. The rhyme, “Sticks and stone may break my bones but words may never harm me,” proves false as words have the power to either build one up or tear them down. When writing the narrative of student achievement with a focus on both their strength and next steps, it is important to frame students’ areas of need from an asset-based approach rather than solely iterating deficits. “Karly constantly talks during independent work time” tells a very different story than “Karly is beginning to regulate his behaviour during independent work time.” Mere semantics? Maybe. But the impact of one semantic can birth a positive outlook or reinforce a negative one.

Finally include feedback that will matter. This is particularly true for the final report card of the year as that the content that will be learned in the new grade will differ from the grade-specific content that the student is graduating from. In this case, next steps should serve as feedforward  as opposed to feedback. What might be the skills or habits of mind that will be salient in future learning opportunities? What concepts will form the foundation for future understanding? These are the next steps that will prove useful if articulated well. Including student voice in this aspect of report card writing is a great way to value the person who is set to internalize the feedback given. Imagine the partnership that can be developed when students remain accountable to themselves as well as previous teachers for their commitment to improving their outcomes.

So my few suggestions, though not revolutionary, can alter the ways in which the report card serves out its function. Families are notified of students progress and achievement, students are empowered with meaningful next steps and future teachers read the narrative of a student from an asset-based approach. Happy writing!

More Than Right or Wrong

“Did I get it right teacher, did I get it right?”. This I am sure you have heard over and over again when it is time for students to take up their work. I can go back to my elementary school years (way too long ago to provide a date for you) and remembering sitting there anticipating getting my paper back so that I could look at the top of the page and see my grade. Red on your paper was not a good thing. Either a smile or a sad expression immediately came across my face and I would be asked to get it signed by my parents, return it to my teacher and move on to my next unit of study.

Good assessment pedagogy now has taught us that the opportunity for learning is in examining the mistakes, looking at what strategies were being used and providing timely feedback that allows a student to learn from their own work. This approach helps facilitate their growth toward those target outcomes.

I have an anchor chart in my room that is used by both my students and by myself when we are looking at the work we have completed. On that chart are three defined types of mistakes that can be made. The first is referred to as ‘Careless Mistakes’ which are characterized by minor mistakes that are made as a result of miscalculations, rushing through work or more typically a student not looking back and checking their work prior to handling it in. When I am conferencing with a student about their work and find these types of mistakes it indicates to me that the student has grasped the key concepts and need feedback/strategies on how to avoid making those types of errors.

The second type of mistake that can be made are ‘Misconceptions’. These are characterized by a student’s understanding of a concept being inaccurate and thus as the student moves forward with his/her thinking, that student is immediately going down a wrong thinking pass that will result in his/her work being wrong. This will lead me to create a mini lesson for that student or a group of students that will help adjust their thinking by clarifying the necessary content to eliminate the misconception(s).

The final type of error is due to a ‘Lack of Knowledge’. In this scenario the student does not have the necessary background knowledge or sub-skills in order to accomplish the task at hand. This immediately indicates the need for me to assess where the student knowledge base lies and backtrack to that point in order to provide him/her with the necessary next step in his/her learning. I find this often is below grade level and thus requires me to modify the content to help that individual gain the necessary knowledge to move his/her learning forward. This scenario occurred just last week in my class as we moved into a unit on fractions. In my diagnostic task it became very clear to me that my students had little or no understanding of what fractions were despite being comfortable with using the word fraction. They could take an apple and split it into two pieces, describe each piece as a half but not quantify what that meant.

By sharing this understanding with my students, it facilitates their participation and role in the learning process. They now have more ownership over their work, over their effort and over their plan on moving forward with their own learning.

Tracking Students’ Progress

If there’s one thing I’m constantly reflecting on, changing, and rethinking, it’s my assessment practices in the classroom. I’m not sure I’ll ever feel like I’ve found a way to track my students’ progress that works for me 100%, but I’m getting close! I’ve spent some time recently chatting with colleagues about how I assess my students, and based on the feedback I’ve gotten from them, I decided I would share my general assessment practices here in case anyone might find them helpful.

My assessment binder has a variety of components: class lists with a bunch of little checkboxes where I track completed work, marks, and so on; class lists with a comment box after each student where I write anecdotal notes about specific tasks; a large table where I keep sticky notes with anecdotal observations throughout the week; other pages I find helpful along the way. I’ll try to address these all specifically in this blog post.

Daily/Ongoing Assessment

I start every day with a discussion or a small task designed to reinforce something my students learned the day before. Discussion questions provide my students with the opportunity to practice their language skills in a relaxed way. Questions range from silly what-if situations to more serious topics like bullying. While my students are discussing the topic, I make notes about their speaking and listening skills on small post-it notes (one per student). These notes not only record students’ strengths and areas of need, but also inform my teaching in the sense that I can target my lessons to common areas of need or errors being made by many students. I try to focus on different students each day so that by the end of the week, I’ve noted something about every student in the class. When I have a moment, the post-its go on a laminated table I have.

The table has a box for each student in my class. Throughout the week, as I write down notes about students, I keep the post-its on the table in my assessment binder. At the end of the week, I transfer those notes into an electronic document for each student. I have one document for each student, which allows me to look back over the year and see my observations for that student all in one place. After I’ve transferred the notes to my computer, I usually shred the post-its. Sometimes the post-its are about specific subjects rather than learning skills or behaviours, and in those cases I may choose to keep them elsewhere rather than my computer files. I have an area of my binder for each subject, so it’s easy to keep the post-its in the appropriate part of the binder when necessary.

Sometimes I have a question or two on the board which I ask students to answer in writing rather than having a discussion. For example, this past week I have been teaching my students about light, so occasionally when they come into the room in the morning I have asked them to answer questions about what we’ve learned. This shows me who is understanding the material, who needs a bit more guidance, who is totally off-base, etc.

Task-Specific Assessment

When I want to keep notes about students’ achievement relating to a specific task, such as a project or presentation, I use a class list with a comment box next to each student’s name. I keep notes on feedback I provide to students, collaboration with peers, etc. in those boxes. This way, when I provide feedback to students, I still have a copy of what I said to them on-hand and can see the whole class at a glance. I keep those sheets divided by subject/strand in my assessment binder. They’re used for reporting and evaluation of student progress in specific subject areas.

Reading Assessment

I do GB+ evaluations (the French equivalent of PM Benchmarks) every two months with my students. These running records get placed in alphabetical order in a section of my assessment binder specifically for them. I like to keep all of the running records from the beginning of the year to the end.

 

Those are the three primary ways in which I track student progress. It works reasonably well, though there are definitely improvements I could make to my system. I find it easy to find information when I need it, which is handy when meeting with students’ families or trying to look back on the feedback I’ve provided to a specific student over the past few months.

One last piece of advice, regardless of what system you use to track student progress: back everything up. Whether you use a paper system, an electronic system, or a combination thereof, make sure you have a copy of your notes somewhere. You never know when something might go awry with your binder, your computer, your files… speaking as someone who has lost a term’s worth of data unexpectedly? Don’t be that person who has to scramble to figure out student marks and comments at the last minute when your hard drive fails!

Field Trip to the Toronto Symphony

Last month, all of my grade four classes went on a field trip to Roy Thompson Hall to see the Toronto Symphony Orchestra play their annual concert for students. I love going on this field trip. For most of my students, this is the first time that they have ever seen an orchestra live and for many of them it is a rare occasion that they visit downtown Toronto. They ooohhhed and aaahhhhed as we passed by the CN tower and marveled over the fancy seats at Roy Thompson Hall.

Before, during and after the field trip there were many details to organize to ensure a safe, fun learning experience for everyone involved.

Before the Trip

Logistical Planning (A couple of months before the trip)

  1. My first stop before planning the field trip was to ask my administrator for permission to go. I was asked to fill out some forms with information about costing, busing requirements and date of attendance. After my administrator gave the green light to plan, I made contact with the coordinator for student field trips and decided on a date.
  2. (Note: In my very first year of teaching I inadvertently booked my school on a field trip. I was calling two different locations and trying to enquire about dates for both. I had not booked or signed any contracts with either place but one of the locations turned around and sent me a bill for around $500 dollars for not showing up to the field trip day that we had spoken about on the phone months before. Through lengthy discussions with the location the situation was resolved. So learn from my errors and be VERY explicit when discussing dates with potential locations.)
  3. After the date was selected and my administration approved the forms I added the date to the master calendar of my school so that nothing else got booked on that day.
  4. Once I booked the trip, I approached my office staff for a cheque to pay the deposit.
  5. I followed my school’s protocol for ordering the buses and kept the confirmation in a safe place.
  6. The next step was to prepare a parent letter for field trip. (Here is the letter….Toronto Symphony letter 2016)

Logistics (The final couple of weeks leading up to the trip)

  1. I put a plan in place for students who did not be attend the field trip. For my school, this was all the grade 3 and 5 students in split classes. The teacher of the grade 4/5 class stayed back and taught all the grade 3 and 5 students during the day.
  2. Also, I ensured that there was a plan in place for students with special needs. I was the extra support person for the class that required assistance. I stayed with a group of high need students the whole trip.
  3. I spent a lot of time preparing students for the assignment that they were required to complete post field trip.
  4. In class we reviewed expectations on a field trip. I was very explicit. We all did role plays of good audience behaviour at the symphony. What would audience behaviour look like at a symphony versus a rock concert. It was a lot of fun.
  5. With so many details to remember, I sent an e-mail to my administration and all the teachers attending the field trip one week before the trip to review all of the information required for a successful day. Hopefully this list will help remind you of a few items for the day.

Hello everyone,

 Here are some final pieces of information/reminders about our trip on Thursday and a schedule of the day.

  1. Our office staff has provided me with a master list of all emergency contacts for every student in grade four.
  2. Just a reminder that all grade four students will be having pizza day this Wednesday not Thursday.
  3. Remind your students to eat a big breakfast on Thursday. Lunch will be slightly later than normal on Thursday so remind them to fuel up before we leave. I have told your students not to bring their backpacks or lunch bags with them on the trip as their will be no space for them. However, I have told them a small purse or a small string bag would be fine.
  4. Remind students that there are no devices on this trip and students do not need to bring money.
  5. Remind students that there will be time to visit the bathroom before the concert and after the concert at Roy Thompson Hall. Please encourage them to use the bathrooms at those times so that they are making every effort to watch the one hour show.
  6. Please ensure that all students with medical needs bring their epi pens and puffers on the field trip.
  7. My cell phone number is ———-.
  8. This year the organization of the TSO student concerts have changed slightly.  “Ushers will meet you at the main doors of Roy Thomson Hall to guide you and your class to your assigned seats.  Please note: there are no hard tickets for this concert; ushers will be working from a seating plan. I have the busing and seating information package and will be bringing an extra copy for both buses on Thursday.
  9. I have attached the schedule for all students not attending the trip.
  10. Finally, remind your students to look awesome on Thursday as we are having a fancy dress up contest!”

 

During the Field Trip

Before we left I handed in the attendance of students on the trip, the bus number and an emergency number to the office staff. I then helped students find their seats on the bus and at Roy Thompson Hall. I was very careful about who my students were sitting beside and worked hard to ensure that the students were making good choices all day long.

After the Trip

Follow up activities

Besides having an amazing, awesome fun day with the students, all five of my grade four classes had an assignment to complete in the last hour of school when we returned from the trip. Leading up to the trip, I spent a lot of time prepping the students for what they were going to hear and see at the symphony. We spent a lot of time analyzing pieces of classical music and using word banks that they would be using for this assignment. In addition to analyzing music, I also showed the students the actual assignment and wrote examples of a level 4, 3, 2 and 1 answer. Every student also received a paper with a word bank that I have from Musicplay’s Listening Resources and a list of the songs played by the orchestra.

Here are the Anchor charts for grade 4 assignment and Grade 4 symphony assignment for your use. Hope you and your students have an amazing, wonderful, excellent, awesome time on your next field trip!!!