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.


Emotions, Context and the Reluctant Writer

One of the biggest challenges I face is getting my students to enjoy and take risks with writing. Too often they get bogged down with the fear of not knowing what to write or nervous about experimenting with vocabulary they do not know how to spell. There are two critical approaches I take in helping my very reluctant writers to engage in the writing process. The first is to help them understand the stages of writing (Idea, Plan, Draft, Edit/Revise, Publish and Share). Each stage is explored and its purpose discussed and demonstrated in multiple ways. Once a student understands that the edit/revise stage occurs after you are able to get your ideas, thoughts and/or feelings into print form they become more likely to take risks in getting their ideas out. When they give themselves permission to let their ideas free flow without word-by-word critiquing, the quantity and quality of their work improves. A completed draft version allows them to separate I have good ideas and can write from I need help in making sure my writing is correct and ready to share with others. I also experience a huge drop off in the question “How do you spell _____________”.  That focus typically grinds the creative process to a complete halt.

The second element that greatly assists me in helping my reluctant writers is to as often as possible design a writing focus around an event relevant to their life. This may be something going on in their school community like writing a persuasive writing piece on allowing students to wear hats in school. It may be a news event from their community or a global situation that will help connect my students to a bigger audience.

Several years ago when the Chilean mining catastrophe occurred we had taken time to have it as a part of our morning circle conversation. That lead to a brainstorming session on what might we do to help out. The final decision was that we could write letters of support to them.  I found the address to the Chilean Embassy in Ottawa and we mailed our letters to them. The power of the contextual relevance automatically tapped into their emotions. When emotions are involved in the learning process the lesson, the message, the focus becomes more consolidated in their cognitive realm. A magical bonus on this project was that my class received a letter from the Chilean Embassy acknowledging our letters and honouring the efforts of my students. Our next writing unit was accepted with little or no resistance.

Anchoring Learning

Anchor charts have long been identified as a high-yield learning tool. What exactly is an anchor chart? Why use them? How do you determine what should be on an anchor chart? These are common questions faced by teachers as they try to establish optimum learning environments for their students.

I have heard anchor charts best described as the ‘third teacher’. The following is a quote from Scholastic’s Literacy Place – For The Early Years, 2010. “ To promote literacy skills and encourage independence, you will want to make strategic and purposeful use of print resources such as posters, signs, lists, charts, and student/teacher writing samples in your classroom. One tool in particular, the anchor chart, is very effective in promoting student success. An anchor chart outlines or describes procedures, processes, and strategies on a particular theme or topic and is posted in the classroom for reference by students. Examples of anchor charts include: what to do in an interview, tips on using commas, what readers need to do when they infer, how to choose just right’ books, or how to write a literature response.

This of course aligns perfectly with the visual learner. Visual learners learn through seeing, observing and anchor charts allow them perpetual access to critical information and not just when instruction by a teacher is occurring. They can return to the key ideas or concepts when they need to and as often as they need to.

One lesson that I have learned is that not everything can be an anchor chart even though it is all so valuable. If the visual scene in your classroom becomes cluttered the benefits of this tool diminish as they just become part of the scenery and no longer a tool for the students. In my class we have a large variety of anchor charts positioned around the classroom with different colours, fonts, sizes, shapes and almost any other way I can make them unique and stick out. I did an experiment with my students one day where I gave them post it notes and asked them to go around and put them on the anchor charts they used most often and felt were most helpful to them. Prior to that I had made my prediction of what might occur. Needless to say, what I thought was most important did not align with their view. Sooooo from that point on, my anchor charts became a mutual task created by my students and myself. I still do all of the finish work, but the content and positioning in the room is a shared decision. One final change in my practice as a result of that data collection was that I am constantly changing the visual cues so that they stay fresh as learning tools and not just become a regular site in the room.

Another feature of this great tool is that I also have personal anchor charts around my desk that help me as I learn new pedagogy to add to my practice. I am able to return to them throughout the day to evaluate my growth and development progress. IMG_1799 IMG_1803 IMG_1804 IMG_1797 IMG_1806 IMG_1798 IMG_1800 IMG_1801

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.



Painting with the same brush.

PublicDomainPictures / 18043 images CCO 1.0

An artist was preparing to paint one day. First, she stretched and secured her canvas over its wooden frame. The artist continued by arranging her brushes, planning a colour scheme, and then by setting up her supplies. Finally, it was time to ponder her subject forever to be captured in a moment of time and occupied space – where her vision would be on display in pigment, oil or acrylic for evermore for all to enjoy.

The artist could already see her finished masterpiece. As if the picture had miraculously painted itself. Without anything left to imagine, conjure, or deliberate she began.

Un-(der) inpired
It was all right there in living, er um, cold dead colour. All she had to do was slather it onto the wintery whitewashed space in waiting. She pulled out the widest brush in her kit, dipped it into the first colour, white, and painted a perfectly straight line across the top of the canvas. She dipped her brush again and repeated, the same thing over and over, with the precision of her first strokes until she has covered the entire canvas. She felt satisfied, but did not have time to admire her work for long. There were 29 more canvases to cover just like the first one. She smiled, sighed, dipped her brush, and started on the next one.  Yet, with a pallet of colours and brushes at the ready, the artist only knew how to paint with a single brush and to use white paint to do her work.

http://kaboompics.com/one_foto/880/brush-painting-the-white-wall CCO License

Under pressure
Does teaching ever seem like this to you? Do educators feel they are asked to paint blank canvases everyday, but are only given one wide brush and a single colour to work with? I wonder whether that is how some teachers have come to feel when a learning system is imposed on them which expects students to be taught to the test?

Teachers plan and prepare their materials to deliver a lesson much like the artist in the story above and in the end are expected to use the broadest brush and one shade of paint. What may be more disappointing, is that many only have time to paint one coat before feeling they have to move on.

I am not a huge fan of the traditional textbook. In fact I have called them “knowledge coffins” in the past. When traditional textbooks are at the centre of the instructional day, there is little option for learners to explore beyond its pages.  Yes, it’s all in there, but at what cost are other things and ideas being left out?

First, consider the cost of purchasing texts/licenses per class. Math books alone can range upwards of $1500 to $2000 for a class set per subject. What happens when the curriculum gets revamped like what has recently happened in Ontario with the French(2013), Health/Physical Education(2015), and Social Studies(2013). Could the money schools, boards, and government pour into photocopies and textbooks be used to provide Chromebooks for every student instead? Imagine the cost savings in paper alone. If we did this, every learner from K to 12 could be equipped with a productivity and research tool for the classroom at their fingertips? And, at home too if WiFi is available.

I am a fan of adaptive and hands on learning environments. In the classroom, I want students to have a voice in how and what they are being taught so we can democratize education. I believe all educators possess the means/ability to transform and tailor their instruction to suit their students. What they need now is a safe place to do so and that’s an issue of system and school leadership.

JFK Paint by Numbers
JFK Paint by Numbers

To paint a portrait of the future, educators need to use the prescribed curriculum as a pallet filled with colours that is not limited to a paint-by-number task. However, many are afraid to use other, less traditional brushes and materials to paint their masterpieces because the outcomes might not look resemble or match work gathering dust on the walls.

Yes, there are things to be taken from the past, but the world outside our classrooms has not remained fixed in space and time. Neither should it remain static inside. The classroom must become a vibrant and connected place where students have access to, and be able to contribute to a world of knowledge.

This requires courage to happen. It requires time for others to understand, accept, and embrace. It doesn’t have to look perfect. The mess is an important part of the process.

Ask yourself what or who inspires you to take chances as a learner? What new idea(s) would you try in your classroom if you knew you couldn’t fail? Start by giving yourself permission to change things up in one subject area, and then go from there.

I’ll be here to chat if you want to talk more about how we can change the portrait of education to a landscape of creativity, differentiation, and encouragement.

In the meantime I have some brushes to clean.

Movers and shakers

I might catch a little fire for this title.
And thank you in advance for reading.

Every classroom has them- fidgety student(s). You know the ones who cannot get comfortable to sit still, are unable to focus for longer than 8 seconds (there are statistics for that), and are constantly in motion. Some days you see your classroom is more like a garden filled with hummingbirds flitting, buzzing, and appearing to faff about even when totally engrossed in a task.

Are they learning? Can students learn when their distractedness is a distraction? You’re thinking about your students right now(past and present) aren’t you? I am, and yes like yours are incredible capable learners, each of whom possess a curiosity and creativity that we allow to flourish.

So, how do(did) we manage to harness a student’s abundance of energy without blowing a fuse or short circuiting the individual? For me, working with* a ‘busy’ student, whether officially identified with ADHD or not, requires a deft balance of patience, structure, and at the same time flexibility. Inside of this is an expectation of great things that is mapped out and shared with the help of the individual learner. It is not my agenda that gets carried out. Student voice is crucial in this process. Negotiation skills training is included in the deal.

Do you allow students to doodle? This simple artistic expression allows students a place to focus the fidgety moments onto the paper while freeing their attention to concentrate on the lesson. How about a soft foam squeeze toy? In my class we have several available that are specifically dedicated to any students who might feel a bit of stress or the need to keep their hands occupied. Plus they’re fun to throw around the class as a kinaesthetic activity and to practice Math facts or French verb conjugation.IMG_0164

Doodling and fidget toys seem counter-intuitive to many teachers who were educated annually in the art of rote in row after boring row, but can be great ways to support your busy students. Sadly, the education from the good old days doesn’t always honour the progress of humanity in the 21st Century. Especially, when it keeps referring to what worked or is rooted(stuck) in the last one as the only path to knowledge. In my opinion this is antithetical to the needs of modern learners who, as a result of innovation, technology, and pedagogy find themselves barely coping in some classes while thriving in others. 

My teachers had a kid like that, me. My mom shared, that after some tests and upon the school’s urging our family doctor prescribed some meds which were intended to help channel my “energetic” demeanour. My parents refused. Thanks mom and dad!

Although some of my colleagues might volunteer to renew the prescription for me, I am glad my parents decided not to take the pharmaceutical option. Instead they chose to work with my teachers on implementing strategies which would keep me busy, moving, and engaged.

Do you know how many notes I delivered around the school, erasers I cleaned, or how many times I helped the caretaker sweep? And that was during instructional time. Every recess(2 x 15 mins + 60 mins lunch) was spent running, jumping, climbing, and playing. It was the time outside, in motion, that made the time inside learning tolerable. So it makes me wonder how many others went through, or are going through the same thing as I did?

Without apologies I wish to proclaim and thus forever own my ADHD. In fact I wear it like a badge knowing it was a blessing in my life as a learner and is a gift in my life as an educator. The challenge for learners and educators comes in finding that Goldilocks Zone between perpetual motion and learning progress each year that is just right.

As the researchers note, “in the school setting, the challenge becomes how to create an environment in which creativity is emphasized as a pathway to learning as well as an outcome of learning.” from The Creative Gifts of ADHD by Scott Barry Kaufman in Scientific American

And therein lies one of many Catch-22s in our profession. We have some who have blessed their classrooms for  35 years or more, and others who are just being hired. The gap between youth and experience is not going anywhere? How do we re-invigorate mindsets, open ourselves to greater collaboration, and sharing the wisdom gathered from experience. There is much to gain from having both. Now the challenge is preparing, pairing, and finding some playtime between the two sides.

* I had originally considered using the word ‘handle’ instead of ‘work with’ as I wrote this post. Upon reflection it was wiser to be considerate of the fact that handling a student conjures negative thoughts, whereas working with a student evokes a working opportunity.

Modifications and Accommodations in the Music Room

Modifications and accommodations happen daily in every classroom in Ontario. Teachers strive hard to make sure that their students have the necessary tools and supports to help them achieve the expectations of the Ontario Curriculum or modified goals. The following are some of the accommodations and/or modifications that I have used this year with a focus on the most common tool used in music…instruments!

When you ask my students what their favorite part of music is, many of them would answer quickly that they like using the instruments. I agree, instruments are AWESOME, but they can also be very challenging for students with impairments in fine motor skills, breath control, impulse control or visual acuity. To help these students, try a few of the following tricks…

  1. Xylophones- Most xylophones have removable bars for students who are overwhelmed with all of the notes laid out before them. I take the bars off that the students don’t need to play a particular song. I also rearrange the bars to make sections of the music more playable for some students. For example, I will move the E and F bars away from the G and A bars so that the student can more easily see the space between the two and identify them as separate. Selecting only part of the melody or accompaniment can also give students with processing difficulties a chance to keep up with the pace of the music. For my students with impulse control challenges, I give them a heads up that while I am giving the instructions I will be holding their mallets and as soon as we start playing I will return them. Furthermore, improvisation can be your student’s best friend on the xylophone as it takes the pressure off of playing specific notes. Finally, metallophones have much better contrast for students with visual impairments than regular xylophones.
  2. Recorders- To help students match their fingers to the right holes on the recorder, I have used small pieces of coloured electrical tape. I put a small piece of blue on the first hole of the recorder and put a small piece of blue on their pointer finger of their left hand. I add one finger at a time and work towards removing the tape when the student is ready. I have also matched a colour coded system to the music that they are reading. For students who have large challenges in fine motor skills, I have also taped the back hole for the first section of the year to let them focus on the front holes.
  3. Drums and Percussion Instruments- When it comes to the percussion family, instrument choice becomes very important. Maracas, bells and guiros are some of the more difficult instruments to use to produce clear rhythms. Rhythm sticks and bucket drums are a much better choice as the sound is more easily produced and controlled. Another helpful tool is to use words to learn rhythms. Using words to help students learn rhythms is great for all students but is especially important for students who need extra support. From the tabla in India to the taiko drum in Japan, there are so many countries that use words to share rhythms. Simple or repetitive words are much more accessible than musical notation for many students.


Waiting is worth its weight.

I wanted to share a post about the joys of waiting.

No it is not Health curriculum based so uncover your eyes and read on.
It might be worth the…time spent before something happens.
Ha! You thought I was going to write the word ‘wait’ there.
Dang it! I just did.

In the Tom Petty and the Heartbreaker’s song The Waiting the chorus goes, “the waiting is the hardest part” and in the classroom it is no different for teachers.

There are a lot concepts to cover. There are a lot of assessments (for, as, and of learning) to record. And yes, there are a lot of students to teach. One thing there does not seem to be enough of is time. So in an average, active modern learning environment, there is little time left to permit students to engage in anything but what Daniel Kahneman refers to as System 1 Thinking. Yet, what we need to be doing, more than ever, is allowing our students and ourselves to engage in System 2 Thinking.

Here’s a graphic comparing the two. Click to enlarge.


Understanding and implementing think or wait time in my classroom has changed the dynamics of learning for my students. It is no longer a contest to see whose hands can defy gravity the fastest or longest. It has increased the number of participants and ideas shared. It has deepened our discussions in many subject areas such as Science, Social Studies, and Literacy.

For my part, questions are crafted, whenever possible, that require the awkward silences achieved while learning and thinking beyond automatic or immediate responses. Letting students know before they respond that no hands will be acknowledged until think time has happened for the entire class has helped transition my instruction.

What about Math? Yes, even Math. Here’s an example to support think/wait time in Math from Kahneman’s book Thinking Fast and Slow that I share with students and adults alike:

A ball and a bat cost $1.10.
The bat costs $1 more than the ball.
How much does ball cost?

According to the book most people get this question wrong because they are engaging the wrong system of thinking. I did. So how can we as educators afford more think/wait time in all of our classrooms?

My suggestion is to slowly integrate it into your daily instructional routines. Be intentional with a few questions in specific subject areas to start. Be patient. The silence can be deafening at the start, but is worth it.

Want to know the answer to the bat and ball question?
Take your time. You’ll get it. It’s worth the wait.


Tortoise Brained Learning and Students

In my last post I focussed on the philosophical belief that quality vs quantity of professional learning is a more effective way of enhancing pedagogical practice. What does that mean for my classroom instruction? As I grow to understand the presence of different learning styles in my class, the presence of multiple intelligences and the wide variety of learning rates it forces me to re-examine both the long term and short term planning that I set up.

In the earlier part of my career my long-range plans were reflective of an efficient way to ensure that all of the curricula was covered. This I now refer to as curriculum planning and not student centred planning. As my understanding of differentiated learning and assessment grew, so did the need to adjust the way my planning unfolded. What I had experienced was a short-term understanding of content and when that topic was revisited months later there seemed to be a regression in the level of understanding of my students. That forced me to ask myself as to how well they had really learned the content in the first place.

Through years of experimenting with both my long range planning and unit design there arose two aha moments for me. The first was the need to revisit big ideas (overall expectations) through a spiralling curriculum. This means that I would chunk the content into more manageable pieces and revisit the content several times over the course of the year (quality vs quantity).

The second profound understanding was in time management and how do I accomplish the ability to revisit overall expectations with so many demands on the school day. Thus came the desire to increase my skill set in integrating learning across a variety of curricula. The following is a direct reference from the 2006 Ontario Language Curriculum:

In cross-curricular learning, students are provided with opportunities to learn and use related content and/or skills in two or more subjects. For example, teachers can use social studies reading material in their language lessons, and incorporate instruction in how to read non-fiction materials into their social studies lessons. In mathematics, students learn to identify the relevant information in a word problem in order to clarify what is being asked. In science and technology, they build subject-specific vocabulary, interpret diagrams and charts, and read instructions relating to investigations and procedures. All subjects require that students communicate what they have learned, orally and in writing. Their studies in the different subject areas help students develop their language skills, providing them with authentic purposes for reading, writing, listening, speaking, viewing, and representing.

Needless to say, this is a spiralling learning experience for me as I continue to help my students consolidate the learning that they are a part of each and every day.

Assessment for Inquiry Projects

Alison_BoardTeachers are encouraged to use inquiry in all subject areas. Using inquiry is not necessarily a set of steps to follow or instruct, but an approach to guide student learning. It usually results in greater engagement and can easily be differentiated to individuals and groups. What is often the biggest challenge for teachers is the assessment piece.

Here are a few ways to support your assessment:

  • determine check-ins with students as they complete specific stages of the process, such as planning, research/recording observations, interpreting and communicating (use rubrics for these stages as provided in curriculum document – Continuum for Scientific Inquiry)
  • use mini-lessons to teach skills and content to the whole class that support the Inquiry subject area
  • use whole-class discussions or small group discussions to make observations about student knowledge and understanding (this also builds knowledge among the larger group)
  • provide access to a computer for each group or a notebook to record their questions and plans and stay accountable. Communicate with them to further their thinking and provide next steps (Google Docs works well for this)
  • Keep observations sheets handy to make notes and take photos
  • Inquiry work provides an excellent opportunity to demonstrate the learning skills
  • Provide students with a checklist to ensure specific learning, such as “Show impact on environment” or “Determine best solution for power generation at our school” – when assessing effectiveness of final task/project that students may present in a variety of ways (poster, video, website, etc.)

There are some great project based learning guidelines and assessment tips/strategies on the website http://www.edutopia.org/ or follow edutopia on Twitter.