Saturday Morning Reflections from Twitter

My colleagues often hear that one of my best sources for professional learning is Twitter. Well it’s true. Here are some Saturday morning reflections.

When I read this I had an ‘ah ha’ moment about where we have come from and where we are going in education and online learning. Here is a quote from this article, Constructionism vs. Instructionism.  The subject in the quote is mathematics but we could be talking about any subject, the point is the distinction between teaching and learning.

“What I was going to talk about if I had been there, is about how technology can change the way that children learn mathematics. I said how children can learn mathematics differently, not so much how we can teach mathematics differently. This is an important distinction.” Seymour Papert

I think this explains something that’s very helpful.

Many online programs were developed because technology enabled us to teach differently. The focus was on teachers doing things in new ways.  It was exciting and innovative. How do we put ‘curriculum’ online?  It is, was, a lot of work, there is no doubt about that. I recall reading news articles on how technology will change the way we teach.

As teachers we know that our work is really about student learning and we certainly have integrated many effective practices into online courses with that focus. Yet, I think we could reflect on the work we do and see where we got stuck on,  ‘technology changes how we teach’.  We need to ask ourselves have we taken full advantage of how technology changes how students learn?

Technology enables kids to learn differently and that’s the direction we need to go or educators will be left behind by students who are already learning in new ways. Take a look at this TEDxWestVancouverED talk.

There are several articles here  Constructionism vs. Instructionism. All well worth reading.  I also liked this”

So, in a way, the computer becomes invisible. The computer becomes just an instrument. I said if you asked that child making the picture, “What are you doing?” she would have said, “Making a picture, making a bird.” It’s interesting to compare this — imagine going to a poet and saying, “What are you doing?” You’d be very surprised if the poet said, “I’m using a pencil”. The poet would have said, “I’m writing a poem,” or, maybe, “Just leave me alone, I’m busy.” Of course the poet was using a pencil, but that’s not worth mentioning, and the same should be true of computers.” Seymour Papert

That Moment

Jo Boaler’s course titled: How to Learn Math,  inspired me as a math teacher and learner.  This course challenged me to think of ways to include  Number Talks as part of my online course for grade three students.  One way I have done this, is by developing Three Act Math lessons* in the form of videos to promote discussion between my students and their parents.  As I developed these math conversations in my online course, parents have shared the joys and challenges of participating in this new way of thinking.

Yet I wanted to do more. I wanted to get kids talking and showing what they could do with mathematical ideas, and I wanted kids to see and respond to the thinking of their peers.

There’s even more.  I feel strongly about the power of writing and drawing, as a way to explain math thinking, and so I have students use math journals. However enabling students to respond meaningfully in a math journal is a challenge. Students struggle to reveal understanding when writing skills limit the explanation of their math thinking.

 

Student created math videos is an option I’ve long considered.  And so I started to explore options for easy screen screencasting tools for kids.  I started asking students to recored their math thinking using one of three iPad applications:

  1. ScreenChomp
  2. ShowMe
  3. Explain Everything

My students also have the option of using the video recording tool in Moodle, the Learning Management System I use.  Moodle has a video recording plugin called, PoodLL, (Ha ha of course, you say, what better name could there be?) Happily all of these tools were easy to teach my students to use.

I started by creating my own math video as a model for students.  I used ScreenChomp. Mine, was not polished production but a recording of my thinking and drawing.  My purpose was to get students to focus on the math, and enjoy using new tools. We started with the the following math journal questions from our unit of study at the time:

How can you multiply two numbers?

When so you multiply?

How does an array show multiplication?

Do you ever have that moment when you see or experience something and your skin just tingles with excitement? Well that was my experience as I started viewing the videos my students created.  Not only were they revealing their thinking, the whole process of creating a video powerfully strengthened their learning.  It was evident that creating a math video required my students to communicate mathematical ideas as they explained and supported their reasoning.

As we’ve progressed my students are contributing to a bank of wonderful student explanations of math concepts.  Which in turn, is becoming a rich resource for learning.  I am beginning to think of new and creative ways to use these same videos to develop more math conversations. That’s more to tell in a future post.

Let me know what you have tried to do with students screen casting.

*For many of these ideas I am  indebted to Graham Fletcher who shares 3 act math resources. Find him here: Twitter: @gfletchy  and here: 3-Acts Lessons.

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

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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.

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December 2014, Travels to India.

The bridge was a parade of life in Haridwar, Hindu pilgrims, who came to wash in the holy water of the Ganges, priests, holy men, families, and school children. School boys flew kites from the bridge in the cool breezes. They skillfully competed to send the other’s kites into the fast flowing Ganges. Their laughter and enthusiasm filled the air. Younger kids, likely five years old, made their way across the bridge wearing tidy school uniforms, red sweaters, navy pants or skirts with enormous backpacks hanging low on their backs.

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We were not the only observers on the bridge that December afternoon.  We were carefully scrutinized by this little person.

Child on bridge

We wandered the streets for awhile, surprised that the stalls which had been open and busy the night before were closed now. We were pleased at our ability to find our hotel once again, a 100 year old home once owned by a wealthy Indian. His portraits line the walls. The central courtyard has a temple and each morning and afternoon a Hindu priest comes to conduct payers to Vishnu. This hotel also has a Private Ghat or bathing area where anyone can go to bathe in the river Ganges. Haridwar means the footprint of God, or heavens gate. And this will explain the sacred ceremonies performed each day at dusk.  There is more to tell….

View from Haridwar bridge.

View from the Haridwar bridge. December 2014

 

 

 

 

 

 

Mathematical Curiosity

Curiosity –  Can you think of a time when you or your kids were mathematically curious?  When it comes to math it seems that we focus on knowledge not on curiosity.

Jo Boaler’s course interviewed several speakers who have a passion for math, people who have what she calls an ‘inquiry relationship’ with math.

Computer scientist, educator and robotics designer, Sebastian Thrun, spoke about having an intuition. I marvelled when Sebastian Thrun explained how he looks at a math problem and develops an intuitive understanding of the solution. In fact he states that we should not move further with the problem until we have an intuitive understanding.  Then he takes a further two weeks to fully solve the problem mathematically. I marvelled because the intuitive understanding of the solution comes first.

Take a look at the qualities identified in an inquiry relationship:

Screen Shot 2014-09-24 at 9.00.48 PMImage from How to Learn Math by Jo Boaler.
  • being curious
  • making connections
  • not worrying about uncertainty or making mistakes
  • using intuition
  • exciting inquiry – you can solve any problem

As an educator I can only say:  “Help me develop these qualities in the young learners in my classroom!”  In fact help me live my life that way.  It would be ever engaging.

My question is: “How do I give students who do not have the inquiry relationship  – this curiosity,  sense of intuition, and connection that makes math come alive?”

Today my online grade 3 students shared their solutions and processes for solving a math question related to patterns. Afterwards we talked about the things that we do as mathematicians to solve a problem. As a collaborative group, I was pleased with the ideas these grade threes identified. However I need to go further to guide my students to as they make the inquiry relationship their own.

At first they may not see how all this happens but as parents and teachers, model and talk about curiosity, courage, intuition and connections  – students will see what an inquiry relationship looks like.  By identifying attitudes, thought process, a willingness to take risks, and communicating that math is an engaging challenge and fun, I think we can guide students to develop this passion and connection.

There is more.  Intuition and curiosity are linked to understanding and confidence. Jo Boaler describes these qualities as a double helix.

  Understanding and Intuition

Confidence and Curiosity

These attributes are iterative, a child must develop the understanding to gain intuition and intuition carries understanding further.  Confidence grows as curiosity is satisfied and curiosity depends on the confidence to explore.

 Cultivating those qualities in a math classroom means that as a teacher I  promote, model and identify those qualities as we engage in a mathematical world.

Teacher Language Matters

As I listened to examples of number talks in the math classroom, this stands out, teacher language matters.

“I think I heard you say.”

“How did you know you should have…..”

“Where do you think your mistake came from?”

“So you are saying…”

“How did you figure that out?”

“Do we see it another way?”

“How do we see this one?”

The teacher’s language conveys that effort, thinking processes  and grappling with the ideas are what matters. Students have the freedom to explore the ideas.  Relational equity develops as each student’s contribution is valued and analysed in an effort to come to a common conclusion.

And there is more … students see that math is a beautiful, creative and connected subject.

 

 

 

My Mother and ‘The Number Talk’

My brother nodded in agreement and chuckled, “Yes our mother was great with numbers.”  She had the ability to use numbers fluently, a skill we we both easily acknowledged.

How well I remember standing next to my mother in a grocery store or bank as she quickly and easily calculated totals.  I would line up the digits mentally in my head, carry or borrow if needed, and try to remember the numbers as I worked.  What a cumbersome procedure!  She, on the other hand, already had the answer and cheerfully let the clerk know the amount required.  I recognized her skill and longed to have it.  It wasn’t speed I wanted, it was the ease with which she worked. Why couldn’t I do that?

Was it the education my mother received during the 1920’s in the Netherlands?  Or was it as a young, single woman when she worked for Unilever that she developed proficient number sense? It was not until later in my mathematical life that I learned her secret. Perhaps I would have benefited from a motherly ‘Number Talk‘.

A Number Talk?   Yes, the kind of talks I plan to use with students this year.  Parents certainly can engage their children in number talks. They’re fun!  And teachers of math will find them a best practice for developing number sense in students.

I observed a number talk as part of my summer math course. Here are my observations.

How Number Talks Work

The instructor sets the students up for the number talk telling them they are to figure out a math question.

1.The question is written on the board and students are asked to solve it. No pencils, no paper, they are to calculate their answers mentally. No comment is given on how to approach the problem.

2. Students are given lots of thinking time and respond with a thumbs up once they have the solution. A low key way to respond so that everyone can take the time they need.

3. Students then share their answers and explain how they arrived at the solution.

4. Through the discussion students are led to see the interesting variety of approaches used to solve the question.

Open ended questions such as these spur the discussion on.

“Anyone try something different?”, “Anyone else do that?” These questions give everyone a chance to explain their process.

“I think I heard you say.” or “How did you know you should have…..” These statements give the student opportunity to clarify thinking and communication. The teacher does not add to the student’s explanation she only repeats what she hears. The onus is on the student to ensure that the explanation is clear.

“Where do you think your mistake came from?” Helps the student clarify logic and identify the error. Mistakes are part of the solution process both acceptable and interesting as part of the learning.

 5. The process students use to solve the problem is written on the board so that it is easy for everyone to follow. This is important. Everyone needs to understand how the numbers are manipulated.

6. All solutions are represented on the board and students are asked to draw a picture of their solution and someone else’s solution. Another important step as it makes the learning more concrete and helps students see how they can work flexibly with numbers.

Screen shot from XEDUC115N How to Learn Math

Screen shot from XEDUC115N How to Learn Math

Number talks are one way to help students develop insight, ability and willingness to to break numbers apart and regroup them as they observe and discuss different ways to solve math problems.

Yes, the answer is important but it is not the most interesting part of a mathematical question.  As we show students that problems can be solved in different ways we teach them the very, very important building block of number sense, a skill that is foundational for the rest of math.

Ahhh yes,  a number talk would  have given me insight into the skillful mind of my mathematician mother but I think I am on to her secret now.

 

 

Creating Safe Places to Take Risks for Learning

What messages will you give your students about the value of mistakes as we learn?

Mistakes, fertile ground for growth.

Live on the learning edge – don’t be afraid to make a mistake.

The path of learning is littered with mistakes – thank goodness!

Mistakes are the stepping stones to learning.

If you can’t make a mistake you can’t make anything. 

How to grow new pathways in your brain:  

1. Take on a tricky problem.

2. Never fear mistakes.

3. Share your thinking.

4. Persist till you meet success.  

Parents and teachers, what messages do you give your kids to encourage risk taking as they learn?

 

Taking on the Challenge

And the moral of the story is….

Ugh!  A didactic tale can fall flat. With little meaningful connection to the story the message is seldom remembered or lost to the reader.  You may identify with this.  I for one, recognize this didactic interaction not only in books but in my classroom.

Lesson 4  of How to Learn Math with Jo Boaler  describes the didactic contract in the classroom.  See if you recognize it.

The Didactic Contract  identified by by Guy Brouseau, states that there are certain expectations for both the student and the teacher in a learning setting.  Teachers are to demonstrate and guide their pupils, and students are to learn with ease.

Here is how it happens in my classroom.  During a math class I quickly step in to clarify, add to a student’s math explanation, or demonstrate the next step. Students on the other hand, are quick to ask for help  when faced with uncertainty because they do not necessarily believe that learning involves struggles or challenges. Together we fall into this unspoken contract. This way of interacting in the classroom becomes a barrier to learning.

Jo Boaler describes it well: We empty the interaction of learning and reduce the cognitive demand for the student.

As a teacher responsible for student learning, it is too easy to take ownership of something that belongs to the learners. Instead of this didactic interaction I need to allow mistakes, reflection, redirection, and meaning making, as students develop math skills.  My goal as a teacher is to have an engaging classroom where students  pursue questions and discuss their thinking about mathematical processes.  This dynamic interaction would promote deeper thinking and meaningful problem solving.

It is critical in this setting to ask the kinds of questions that promote meaningful engagement.  What is a good math question? Here is a challenge I love!  I am building on what I know and will share more with you in a future post.