Making Meaning

Several years ago, Jo Boloar’s course ‘How to Learn Math’, included a video clip, of Sebastian Thrun speaking about his approach to problem solving and math. I felt a spark of recognition and a sighed with relief to hear him say that we should not move ahead with a problem until we understand it intuitively; that we need to take time to understand and internalize the meaning and context of the problem. Time to think and develop a meaningful context changes everything for learners. Problem solvers become more emotionally vested in a solution when they make connections and link concepts. Every teacher loves the ‘ah ha’ moment when a student thinks, ‘There is sense here!’ and learners who have time to explore, question, and play with the ideas, develop that intuition and agency over their own learning.

Peter Johnston in his excellent book: Choice Words, states:

“There are hidden costs in telling people things.  If a student can figure something out for him-or-herself, explicitly providing the information preempts the student’s opportunity to build a sense of agency and independence.” p.8

And this I love too: ” … most accomplished teachers do not spend a lot of time in telling mode.” p.8

And so, I work to cultivate courage and curiosity in my classroom. Courage to tackle something that is hard, knowing that it is OK to make a mistake, and the curiosity to question what we see and think as we work together. This means that I promote, model and identify those qualities for any challenge we face as learners in my classroom.

I highly recommend, Choice Words by Peter Johnson. I love this book! Can you tell? Perhaps it’s because these ideas fit with my own reflective personal style, but more than that, Peter Johnson excels at demonstrating the power of well chosen words.

There will be more posts to come on this engaging and thoughtful book.

Reflections on, ‘Creating a Passionate Literacy Classroom’

Today I had the opportunity to hear Pernille Ripp, a Wisconsin 7th grade teacher, who started The Global Read Aloud in 2010.  Check her blog: Blogging Through the Fourth Dimension to learn more about her passion for students, learning and literacy. The session, Creating a Passionate Literacy Classroom, was organized by the Edmonton Regional Learning Consortium.

It was inspiring to hear Pernille speak and while I have lots to share and think about, for now, I want to identify some of the resource gems she provided in her presentation.

The Human Digital Library:   The website states: ‘The Digital Human Library (dHL) is a nonprofit organization that connects Canadian teachers and students with hundreds of organizations and experts around the world who are delivering interactive curriculum-based opportunities for learning using technology – for free.’  I like this, for free. Take note, dHL is spotlighting A Kid’s Guide to Canada ‘a national teacher-led initiative organized by elementary teachers from across the country.’ I’ve registered on this site and now I’m thinking about the ways my students will be involved.  If you are planning a project contact me, maybe we can share ideas.

Pernille spoke about the value of global projects as a way to create connections and promote empathy. Here is a link to a Padlet (online bulletin board) with a variety of global projects. Take a look, in what way might your students get involved?

As a book lover I was curious to hear about her favourite books.  Pernille shared a number of picture books, middle school books, and young adult books. Of course like all readers, she explained that her book lists are ever evolving, as you will see if you check her blog. Each book she described had appeal.  Here is a sample of a few that I appreciated because of the connections to history and social issues.

Picture Books:

When We Were Alone – David Alexander Robertson, an author from Manitoba, The story of a mother and her grandmother.  Sharing the memories of the native boarding school.

This House Once by Deborah Freedman out next week – different pieces of the house as the house is built is shows where all the parts came from.

Stepping Stones –  A Refugee Family’s Story by Margriet Ruurs and Nizar Badr Canadian Author in English and Arabic.

She challenged all of us:  How would you describe your reading/writing identity as a teacher?  Who are you as an adult reader? As an adult  writer?  And… Who are the literate role models for our students?

This was a keen reminder to me. While I occasionally share my own experiences as a writer with students, her questions prompted  me to try write more often, and to be that role model of writing that kids need to see.  And as for reading?  I am an avid reader and so I loved her advice, the best planning for instruction that a teacher can do, is read.

Question, Interest, Intention

Is it true that those who teach learn twice? If so teachers are the most fortunate of all.

My question for this year: “Is there a way I can shift more agency to the learner?” A question inspired by, Invent to Learn by Sylvia Libow Martinez and Gary Stager.

My interest and goal: Strive to remain current with research about learning.  Apply this understanding to my work with young learners in my online and blended learning classroom.

My intention: Never confuse the pencil, the poet, or the poem. In other words integrate best practices for learning with technology in such a way that the technology becomes invisible, enabling both the learner and the learning to be the focus of all that happens.


The Girl on the Bus

12967961_0e4a21df7f_mOnce upon a time a small girl sat on a city bus staring out the window. It was a regular day, cars and trucks drove alongside the bus, mothers with babies were out shopping for their families, and the sun shone down on it all.  The little girl looked out the bus window and felt sad. She thought to herself, “Everything in the world that we need to know has been discovered. There is nothing left to learn.” Such a sad thought for a young girl!  Well that little girl was me and I vividly remember the day and the feeling.

My thoughts may have been realistic about school and learning at that time in my young life. Then, we believed that education consisted of pouring knowledge into student’s heads to prepare them for the real world. A set amount of knowledge was all that was needed. No wonder my little girl self felt discouraged!

Preparing students for the real world was discussed during YouTube Live 1 as part of immooc .  It is safe to say that we are beginning to understand that preparing students for the real world means bringing the real world right into our classrooms.

The little girl I was, would be excited about the potential for change and innovation that we have in education today.  We understand so much more about how people learn; we have tools to create and to collaborate; and we are rethinking what ‘schooling’, means.

I’d deeply hopeful and enthusiastic about the new horizons that are opening up before us. I love the opportunities I have as a teacher to be a continual learner, explorer and risk taker. Last year my exploration led to teaching Scratch Coding to a group of grade 4, 5 and 6 students. This naturally evolved into developing a Maker Space in our school this year. This spring I was inspired by Sylvia Martinez and Gary Stager’s book and two day session in Edmonton called  Invent to Learn and this fall I am anticipating great things from  blendED2016 as well as the community of learners who are part of immooc.

Thankfully the girl on the bus grew up to discover that there are always new things to learn. I can’t think of a more exciting time to be a teacher.

One Common Thread

What a week this has been!  So much to think about.

On Monday Martin Brokenleg engaged us all as he spoke about the Circle of Courage: The spirit of Belonging: I am loved, The spirit of Mastery: I can succeed, The Spirit of Independence: I have the power to make decisions, and the Spirit of Generosity: I have a purpose in my life.  Martin’s words of wisdom, stories and insights as a gave us a deeper understanding of how to connect with youth at risk. Not only youth at risk, but every child that comes into a classroom. He reminded me again of how all of us thrive when we have healthy relationships, the ability to succeed, opportunity to make decisions about things that matter to us and a sense of purpose in all we do.

Later in the week there were conversations with colleagues about, Teaching at the Pace of Learning. This phrase is food for thought.  How is it possible to teach beyond or outside of the pace of learning?  Imagine if a student is not yet ready for the new learning or if a student has mastered the concepts we are teaching? Is it really a teaching and learning relationship then? Or are we both filling in time.

Still, I know it is a challenge, how do we enable teaching at the pace of learning?  So many good ideas were shared in our conversation. Ideas put forward included, refreshers for students at any point in a course, ‘Blue Pencil Cafe’ – a meeting where students mentor each other, providing pace support for students, identifying the critical learning so that a student is ready to tackle the next level successfully, and, identifying the real needs of an individual student, which comes back full circle to Martin Brokenleg’s session on Monday.

One last conversation was about assessment.  Of course, what teacher conversation would be complete without a discussion on assessment? Think the words we use. Whenever I am working away at giving students feedback on assignments I consider that what I am doing is this, ‘supporting student success‘.  My colleague uses the following words which resonated with me, ‘assessment embedded instruction’. Yes! instruction is guided by student needs.  And somehow I feel like this brings us back full circle once again.





Thoughts on Student Assessment


Will this assessment help me to identify student’s needs as learners? Will it help me to guide next steps?  These questions swirl around my brain.  See that determined orange tabby climbing higher to to new levels?  That’s what I want for my students.

Recently this phrase, caught my attention, actionable feedback. Feedback kids know they must act upon, as apposed to feedback that sounds like advice or a mere suggestion. Actionable feedback gives a clear message about the next step or goal.  An example might be asking a student to revise a piece of writing by adding lively action words. It could also be just the right question to push a student’s thinking forward. How will I do this? Specifically identify what was done well, then drive the learning forward with a clear next step or insightful question. This requires mindfulness on my part as I guide students to next steps.

 What about exemplars and rubrics? We have all used exemplars when assessing student work. I have to admit that I sometimes look at a piece of student writing and compare it to exemplars at each level.  Hmmm… is it most like the limited, adequate, proficient or excellent example? I use the exemplars to determine the achievement level.  Now turn this thinking around, the exemplars also clarify the rubric when I assess student work. For example what does ‘descriptive language is simple‘ really mean?  Looking at an exemplar to see how ‘descriptive language is simple‘, is demonstrated, gives me better idea of what that descriptor on the rubric means.  An exemplar should make the meaning of each descriptor on the rubric clear to me and reveal the next step for actionable feedback.

Imagine what this would be like for a student.  How does a rubric and exemplar help a student to self assess? For a student, what does ‘descriptive language is simple’ really mean?  Maybe nothing at all! Exemplars can make next steps clearer for students too; by helping them see what their learning looks like and what is missing in order to move it forward. When a student says my work is like the ‘3’ exemplar, I can ask them why it is not like the’4′ exemplar; this may prompt them to identify a next step and they will be on their way. Actionable feedback once again.

It is about helping students internalize this reflective and iterative process.


Shout it from the Roof Tops!

Current research helps us understand what high achieving math students do and it is most interesting, in fact Jo Boaler tells us it is worth shouting from the rooftops so here it is:

High achieving math students use flexible thinking,  are able to easily decompose and recompose numbers and naturally compress ideas to move on to harder concepts.

What does all this mean? Let’s look her explanation.

Consider a simple computation such as this:

 5 + 14




There are several possible strategies to use.

Counting all: First count all the blue counters to 5.  Next, count the purple counters to confirm that there are indeed 14.  Lastly, proceed to count all the counters from 1 to 19.

Counting on: Count the first set of blue counters to 5 and count on to 19.

Known facts: A student may simply know that 5 + 14 equals 19.

Derived facts: Students use what is known about numbers and facts to complete the computation.  Fourteen is also 10 + 4 so, since 4 + 5 equals 9, add 10 and solve the problem to get 19.  Although this may seem obvious to an adult reader it is important to note the process of decomposing and recomposing the number to make the problem easier.

People who are good at mathematics decompose and recompose numbers all the time.” Jo Baoler What’s Math Got to Do with It? p.148

Interestingly enough students who are low achieving at math use approaches that are more difficult.  For example, imagine using a counting back strategy for subtraction.

25 – 14 = ___.

There are many steps involved in counting back from 25.  This is a complex task and one where a student can easily become confused.  Students who find math difficult often apply a ‘follow the rules’,  problem solving process, lacking the understanding to make sense of numbers in flexible ways.   How much easier this very problem would be, if the student worked flexibly with numbers as was done in the earlier example. Fourteen becomes ten and four. Now the problem becomes  25 – 10 = 15 and step two,  15-4 = 11.

Open Cones or Long Ladders? 

High achieving students compress mathematical ideas.  What does this mean?  Think about learning multiplication. Initially students struggle, work through the process and practice examples.  Once students understand what multiplication is, and how to use it, the concept is compressed and easily used in new settings.


Jo Boaler  uses an image of an inverted cone to show what is meant by compression and how it helps students as they learn.   Learning is compressed as students begin to apply understanding efficiently. New learning is built on compressed ideas and  understanding grows.

Low achieving students who work at trying to remember rules, methods and procedures have a different view of mathematics, much like an endless ladder to be climbed and a long series of steps to be remembered. These students need to be guided to develop the skills of working flexibly with numbers, and to develop a deeper understanding of number sense.

This post is a summary of the information presented in Jo Boaler’s book: What’s Math Got To Do With It?  Key Strategies and Ways of Working Chapter 7.  Also available at the St. Albert Library.


Your Brain is Amazing!

All I can say is, “Thankfully we are developing a deeper understanding of how we learn.”

Once upon  a time I lived in a world of the fixed mindset¹ and likely you did too. Some students were smart and others were not.  Intelligence was viewed as fixed at birth and one of the roles of education was to sort students and direct each one to the correct vocation.   And,  if you think about it, too often we still organize learning in this way.

Let’s identify the qualities this fixed mindset promotes and you will recognize it right away.

Students working under a fixed mindset:

  • Are afraid to make mistakes
  • Avoid challenges
  • Give up more easily
  • Fear of constructive criticism
  • Feel threatened by the success of others

Think what this does to learning. Consider what happens when students see themselves in this way.

Contrast this with a growth mindset¹, a term which on its own sounds encouraging. A growth mindset states that intelligence can be developed and our true potential is unknown.

Students with a growth mindset are:

  • Persistent
  • Not afraid of mistakes
  • Willing to take on a challenge
  • Resilient
  • Inspired by the success of others

How can these ideas change instruction?

It is not the student who ‘knows’, that we should recognize rather the student who says, ‘hmmm I am trying to figure this out and I have not got it yet. It is this student who demonstrates a growth mindset. As educators we need to communicate that everyone can get better if they work on it, which means that persistence becomes a  key quality to encourage.

And for this reason our view of mistakes plays a critical role in our mindset. How do mistakes impact learning? The student who makes a mistake has multiple opportunities to learn.  First from recognizing the mistake, and then from working through the process to correct it.  All this creates more opportunities for brain synapses to fire and grow. Working through mistakes causes our brains change and develop.

What message shall we give to students?

 Mistakes are fertile ground for learning.

As an educator with a growth mindset, I am motivated to create an environment where risk taking is safe and encouraged, and where  learners at all levels are recognized for their effort.


¹Carol Dweck – Mindset: The New Psychology of Success Random House Publishing Group December 26, 2007

It’s a scary mathematical world out there! Hmm… really?

Math, math, math, what are your thoughts on this subject?

Is it true that math is portrayed as a hard subject? As a student have you ever received the message that  some people are math people and others are not?

Do we hold stereotypical messages about gender or race and ability to do math?

When you were in school what did you think about your own ability to do math?

You might be surprised to hear:

“All students can achieve at the highest levels in maths at all levels of school right up to the end of high school.”

Yes, there are countries in the world where this is the expected norm.

This summer I am using this blog to reflect on my learning in the course: How To Learn Math by Jo Boaler. This course is intended for teachers and parents and presents new research ideas on learning, the brain, and math that can change the way you think about math and how we learn.

The ideas on this blog will be a combination of my reflections and notes from the course.  My hope is that along the way I’ll add clarity, and a deeper understanding to what I already know about math instruction and gain new ideas on how enlarge and enrich the world of math for my students. I hope you’ll join me in this adventure.




An Online Math Course verses Summer Reading

This summer I am taking an online math course from Jo Boaler, Professor of Mathematics Education, Stanford University.

It is fitting I think, that an online math teacher should take an online math course and it is logical then, that one of my interests is the very structure and organization of the course. How do I as a student interact with the course and with other students?  In what way is this course engaging? How do I assess my progress?  Does the course provide resources for further learning? And how on earth can an online course compete with summer in Alberta?

Summer reads verses online math courses, its a tough competition.

Summer reads verses online math courses, its a tough competition.

It must be engaging, and you may be happy to know it is, both in content and structure, because for a period of time each day I am passing up on warm sunshine and relaxing beach reading, to sit in front of my computer.

What are the features of this course that make it work for me? Each lesson consists of a series of  short videos with accompanying text.  I can view the videos several times if I wish and stop at any point to jot notes. The videos are short, from less then a minute to about 12 minutes and each video ends with a question that asks a response from me. In addition each video includes a forum where participants can reflect and comment on content. As a whole the course is easy to navigate, I can see my progress and understand what is next.

Already I can see these strengths:

– short chunks for learning

– immediate opportunity for response to the content

–  interaction with other students

– flexibility to work through the material in any order.

– easy to navigate

– learn when I want ( and enjoy the sunshine too!)

Have you ever taken an online course?  How was it structured? Did the course format work for you? What worked well?  What would have improved the course for you?  I would like to hear about it.