Noticing, naming and not allowing “ready-made knowledge” in the classroom

The first time I came across the term “ready-made knowledge” was when I read the following quote by Seymour Papert:

“The role of the teacher is to create the conditions for invention rather than provide ready-made knowledge” – Papert

Ever since reading that quote I can’t get this notion of providing students with “ready-made knowledge” out of my head. It got me reflecting on my years in the classroom and I realized that like many teachers, I am guilt of providing my students with an endless supply of ready-made knowledge… and not much else. Worksheets, workbooks, textbooks, readers…. Knowledge that has been decontextualized, oversimplified and often sterilized.

Our students deserve better.

This notion of ready-made knowledge reminds me of a picture I came across recently on Twitter.

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Like selling peeled oranges in plastic containers, I am beginning to think that pre-packaging knowledge for students is silly, time-consuming and above all else – completely unnecessary.

This year I aim to shift my search for resources away from pre-packaged, made for school, sources of knowledge. This may have you nervously wondering “Then what will students use to learn?” To answer that I ask you in return (as I have asked myself while reflecting on this idea) “What do the rest of us use to learn?” Answer – tweets, YouTube videos, TedTalks, podcasts, news articles, blog posts, research journals, interviews, documentaries… and the list goes on.

So I’ve begun to curate a list of potential learning resources that could be helpful to support our Units of Inquiry this upcoming year. I started a Google Doc and listed the main concepts for our six UOIs and anytime I come across a tweet, a video, an article, or a podcast this summer that relates to one of our concepts I added a link to the doc. I will continue to do this throughout the year. This way when it comes time for a new UOI I will have a collection of sources of knowledge  to chose from that have not been ready-made for student consumption.

Here is what it looks like so far:

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Are these sources free of bias and error? Absolutely not! But that makes them even more valuable. They provide opportunities for discussions about critical thinking, critical literacy, perspective, sourcing, citations and the like. These are essential skills to be developed because these are the types of sources of knowledge students will be encountering in their real life that they will need to be able to decode, deconstruct, analyze and make informed decisions about… not worksheets and workbooks.

I look forward to letting go of years-worth collections of school-land learning resources and instead replacing them with the same sources of knowledge that people are exposed to in their daily lives. I also look forward to sharing this Google Doc with my students so they can add resources they come across during their inquires too!

What sources of ready-made knowledge have you used in your own teaching?

How do you avoid pre-packaged knowledge in your classroom?

What questions or suggestions do you have for me to stretch my thinking further?

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Transdisciplinary Math – An epiphany and a plan!

For the past few weeks I have been helping my teams review their math scope and sequence and decide which math is transdisciplinary and fits within a Unit of Inquiry and what math is better taught in stand-alone units. This process always seems to lead to the same conclusion….

Teaching math in a transdisciplinary way is hard. 

Teachers seem to believe in the purpose and power of teaching math in a relevant and significant context and want to do it… but most seem not too sure about how to do it.

As I get ready to transition back into the classroom in the fall, this is something that has started to occupy my mind as well. How DO you do it? The last time I was a PYP teacher I can self-admit that teaching math within the context of my UOIs was not a strength of mine – in fact, I’m not sure if I did it at all. So naturally, this is an area I want to get much better at. But how? 

And then I had an idea! It hit me this weekend while I was watching BBC’s Africa series.

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Since teaching math in a transdisciplinary way was on my mind, I couldn’t help but notice that every vignette was OVERFLOWING with opportunities for math inquiries!

The average size of a giraffe’s tongue is half a meter.”

“Only one out of 1000 turtles make it to adult hood.”

One million birds migrate over the Sahara each year.”

“Each chick weighs only 20 grams.”

“The adult grows to be 5 times the size of the baby.”

“Silver ants can only survive in the sun for 1 hour.”

Every few minutes there was some piece of information about an animal or a landscape or a natural phenomenon where you needed to understand the math concept being referenced in order to fully understand what was being said. And that is when it hit me! All of the movies, books, articles, graphics etc. we use in our Units of Inquiry probably already contain opportunities for math – we just need to be looking for them and know what to do with them!

So here is my plan for next year!

Step 1- Introduce a text related to the central idea or the central concepts.

As usual, choose (or invite your students to help choose) a resources to explore the big idea in your current Unit of Inquiry. Introduce the text in an open-ended way. Allow the students to engage with the text in a natural and organic way. Read the book. Watch the movie. Listen to the song. Look at the info graphic. Allow the students to enjoy it and ask questions, make connections and offer thoughts. I’m thinking of using a back channel like Today’s Meet to allow students to communicate their thoughts, reactions and questions with their learning community while watching, listening or looking without interrupting one another. You could also provide post-its so students could record their thinking if a device is not available.

Step 2 – Revisit the text with a math focus

The next day, revisit the same text, but this time let students know that they will be looking at the text as mathematicians. Re-read the book. Re-watch the movie. Re-listen to the song. Re-look at the infographic. But this time, stop and pay specific attention to the “math moments”. If the video says “Giraffes’ tongues are half a meter long” pause the video and ask students, “What does that mean?” “How long is that?” “How can we find out?” “How can we show it?”. Any time a number, a measurement, a statistic, a pattern, or a concept is mentioned stop, point it out and explore it.

Step 3 – Follow where it takes you

When you stop to explore the math within a UOI text, be prepared to follow the inquiry. If it takes 10 minutes great. If it reveals other math concepts, skills and vocabulary that need to be explored first, back up and inquire into those. If your students need to bust out some manipulatives, look online, consult other mathematicians – do it! Allow what ever time is needed to explore and truly understand what the math means in that context.

Step 4 – Don’t stop at math! 

After the initial open-ended viewing and the math-specific viewing… keep going! You could apply the same strategy for many different purposes. Explore the same text a third time with a writer’s lens and hone in on the techniques the writer used. Explore the same text with a musician’s perspective and focus on how different segments of music contribute to the message. Explore the same text from an artist’s point of view to analyze colour, line and shape that was used. This would be a great opportunity to connect with single-subject teachers and share some of the texts with them to be looked at and deconstructed multiple times, in multiple ways, through multiple disciplinary-perspectives. Your whole week could be deconstructing one text in different ways for different purposes!

Eventually, I believe you will be able to get to the stage where instead of telling students “here is the math” when exploring a UOI text, you will be able to ask them “where is the math?”.  I also have the sneaking suspicion that if you allow students to document their thinking during the initial, unstructured exploration of the text there will be some math-related questions that are recorded about the quantities, measurements and statistics that are referenced. So you wouldn’t even need to point out the math, you could allow students’ own questions to be the driving force of the math inquiry.

So I challenge you… go back and look at some of your UOI books, videos, graphics etc and notice the opportunities for “math moments” and more!

How do you explore your UOIs through the discipline of math?

What are your best approaches to inquiring into math within the context of a UOI?

If it works for teachers… why not students?

Last week I wrote about how my work with adults will change the way I interact with students with regards to issues of classroom management. The more I thought about it, the more I realized it will also change the way I approach planning for learning experiences. After two years working with adult learners I feel pretty confident with the structure I have used for professional development sessions.

Why can’t I use that same structure with children?

I had the sneaking suspicion that I could… and lucky for me the perfect opportunity presented itself! I was asked to facilitate a one hour “bridges” session to help our transitioning Grade 5 students learn about the MYP. So I decided to approach it the way I would approach a one hour PD session with adults.

Here is how it went:

I planned Guiding Slides based on Kath Murdoch’s inquiry cycle (just like I would for teachers)

I gathered materials – pencils, markers, post-its, scrap paper. (just like I would for teachers)

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I built a Google Doc with a variety of resources. (just like I would for teachers)

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I set up groups with materials already on the tables. (just like I would for teachers)

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We played a round of “stand-up if…” to help our learning community build connections before jumping into the learning. (just like I would with teachers)

I told them I would collect their attention by simply raising my hand and waiting patiently for them to wrap up their conversations. (just like I do with teachers)

Students tuned into what they already know-or think they know. (just like teachers would)

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Students tuned into what they wondered and wanted to find out. (just like teachers would) 

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Student chose how they would find out – watch a video, read a blog post, look at a diagram, browse a Twitter hashtag. (just like teachers would)

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Students decided how best to record and organize the important information they found – write it down, type it out, take a picture of it. (just like teachers would)     

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Students reflected on how their thinking changed. (Just like teachers would)

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My reflections on the session…

It was amazing to see that when given the opportunity, students were able to take ownership over their own learning. There was no “lesson” and I didn’t “teach” them anything… but there was learning. There was thinking, curiosity, self-differentiation, risk-taking, discussion, reflection and new understandings.

What worked:

  • playing a game to build connections before starting with the learning tasks
  • individually tuning in and collectively posting initial thoughts and questions
  • raising my hand to collect their attention
  • having a collection of resource links on a Google Doc for students with devices and paper copies for students without devices
  • providing choice of how, where and with who to learn
  • having post-its, scrap paper and writing utensils on each group
  • setting time expectations, not task expectations (ex. you have 5 minutes to write as many post-its about what you know about the MYP; you have 15 minutes to explore as many resources as time allows) 
  • using familiar Visible Thinking Routines like “I used to think, now I think” and “See, Think, Wonder”
  • reflecting at the end of the session about how their thinking has changed

What I would change if I did it again:

  • time it out differently and plan to do less in one hour
  • trim down the resources to one or two per type
  • support students more in accessing and using the Google Doc
  • stick with VTRs  they are familiar with and have used before

So, can I use the same structures to facilitate student learning that I use to facilitate teacher learning?

YES! 

…perhaps just with a little extra time and support!

Assessment – Caught between two worlds

I have been an educator for 8 years and throughout those years I have learned (and tried) to be more discerning and to question educational practices. My goal – common to many 21st C educators – is to move away from “doing school” and more towards facilitating true learning.

I started my career in the Ontario system of education which provided me with a great foundation. Then I became an IB educator which really pushed and challenged my thinking about teaching and learning. The more my understanding grew and changed, the more I realized that although some of the practices I picked up as a teacher in Ontario could be transposed into my new practice as a PYP teacher, other practices no longer seemed to fit.

And then there are the practices that I’m still not sure about. Sometimes I feel caught between both worlds and have trouble figuring out which “best practices” from non-IB systems support true learning and which merely help students get better at “doing school”.

Many of these conundrums for me center around assessment specifically….

Namely success criteria, exemplars and bump it up walls. 

When I started my teaching career in Ontario I used all three of these things. They helped my students “do well” on summatives. They increased “achievement” in my class. They provided students with a clear pathway to “success” on the rubric. But now I question – were they really helping my students learn? Or were they merely helping my students get better at “doing school”?

I’m not sure, but before I move back into the classroom I sure would like to figure it out!

Should these practices be packed in our “international educator suitcases” when we leave home to be brought with us and transposed into our PYP practice?

 Do these practices truly support learning, or do they just help students “do school” really, really well? 

I’d love to hear your thoughts… 

A Model for a Year of Personalized Professional Learning – A Dream

During this past year I have blogged about our first attempt at a half day of Personalized Professional Learning, then I wrote about our second iteration of Personalized Professional Learning. Now the big question… what’s next?

I think the next step is turning this model of PPL into the basis for a year long PD plan.

This is the time of year that school teams are meeting to design professional development action plans for next year. If it were up to me, I would design the structures and systems to allow for a whole year of personalized professional learning. Usually, I blog about ideas I have tried and put into practice. This post will be the opposite. It will be about an idea – in the earliest phases of conception – that is purely hypothetical. At this stage, simply a vision. Nothing more. Yet.

So here is my vision. I’d love to know what you think!

The start of the year – tuning in:

Before a classroom teacher introduces a new unit on body systems, or fractions, or procedural writing, they (should) first tune into what their students already know and already can do. Why should planning for professional development be any different? Before any administrator or school leader even thinks about teaching/training/developing their staff in a specific area – inquiry, assessment, strategies for language development – they too should tune into what their teachers already know and can do. This is not only important diagnostic assessment data for leaders, but equally important to help teachers become explicitly aware of what they already know and can do. But how? I have a few ideas…

  1. A professional learning time capsule – Many teachers use the idea of time capsule to help students’ tune into what they already know. Why couldn’t the same diagnostic strategy be used for teachers? Administrators and leadership teams could take their school improvement plan goals and IB action plan goals and create an open-ended diagnostic assessment where teachers reflect on what they already know and can do as it relates to the prioritized topics of professional development for that year.
  2. A professional self-assessment  For each area of the time capsule, teachers could indicate on a spectrum (beginning, developing, competent, extended) where they think their professional knowledge and practice liesSlide1 Slide2
  3. Personalized professional learning objectives After completing the time capsule and assessing what they already know and can do, teachers can look for potential areas of growth in their own professional development within the context of school chosen areas of focus. These self-identified areas for growth could then be turned into personalized professional learning objectives – or what is commonly known in adult education as learning contracts.  If based on the time capsule and self-assessment, a teacher realized they have beginning understanding of inquiry-based teaching they would then create personalized professional learning objective about inquiry-based teaching.
  4. Personalized professional success criteria – Once teachers have systematically identified their own areas for professional growth – based on the areas of professional development the school has prioritized for that year – and have created a list of personalized professional learning objectives, they could then develop their own success criteria, to specifically describe what the successful attainment of each learning objective would look like.  Creation of success criteria would answer the question, “How will you know you have achieved your learning objective?”               Personalized Professional Learning Plan Template
  5. Personalized professional learning conference – If a teacher was asking a student to complete a self-assessment it would be followed up by a conference where the teacher reviews and reflects on the student’s assessment with the student. A teacher’s self-assessment should be no different. After teachers have self-assessed their learning time capsule, set their own learning objectives and developed their own success criteria they could meet with an administrator or a member of the leadership team to review their personalized professional learning plan. This is where leaders can review the time capsule and have conversations with teachers to uncover misconceptions and gaps in professional knowledge that teachers may not have identified for themselves.   For example, if a teacher has self-assessed that they have a competent understanding and skill set to support English Language Learners, but through reviewing the time capsule and having a conversation the leader thinks there is more room to grow, the leader can suggest the teacher adds it to their personalized professional learning plan.

If this seems like a long, time consuming process that’s because it is. Tuning in is not something to be rushed in order to get on with the learning. Like Kath Murdoch says, it IS the learning. Taking the time to build a diagnostic assessment tool around the school improvement plan goals and IB action plan goal, then allowing staff to self-assess against those areas and become aware of their own learning and then having teachers meet with a school leader to discuss their personalized professional learning plan are essential steps in setting the stage for the rest of the year of personalized professional learning.

Throughout the year – Finding out, Sorting out, Going further:

Once you have the personalized learning plans set, you can use those as the basis for ALL professional development times throughout the year – after school meetings, half days, full days… any time! How, you ask? I have a few ideas…

  1. Selecting a focus or two – Before a professional development day or afternoon, it would be important to help teachers select one or two areas of their professional learning that they would like to focus on. We have done this two different ways during our first iteration of PPL and our revised model of PPL and both proved to be effective. If teachers already had a list of personalized professional learning objectives, they would only need to refer to the list and choose the one or two areas they felt most passionate about.            PPL planner 1 ppl planner 2
  2. Planning in response to learning Once teachers have identified what they want to learn about it, leaders could collect data about how teachers want to learn. Personal inquiry? Collaborative inquiry? Workshops? Meeting with an instructional coach? Gathering data about how teachers want to learn can then be used to build a structure for a day or afternoon that supports personalized professional learning.                          ppl 4 image
  3. Let the learning happen – Once the day is planned and teachers know what they want to learn about and how they want to learn… get out of the way and let the learning happen!
  4. Assessing the learningOnce the day or afternoon is finished, teachers could refer back to their success criteria and reflect on whether they have met their targeted learning objectives of the day, or whether they need to continue to pursue further learning opportunities.
  5. Repeat The next time another scheduled PD day rolls around again, have teachers refer back to their personalized professional learning objectives select one or two objectives they would like to start working on (or continue working on), plan the structure of the day in response to the needs and preferences of the teachers, let the learning happen and then build in time for assessment of progress.

This process could be used every time there is the opportunity for professional development. Once the systems and structures are in place, there is minimal planning that needs to be done by the leadership team. Isn’t that the sweet spot of inquiry – low prep for “teachers”, high engagement, ownership and learning for “students”? There are also some great opportunities for formative assessment and feedback throughout the year. Bring out the time capsules half way through the year and have teachers add, change and remove things to better reflect what they know and can do now. Or have a mid-point conference with the same leader as the beginning of the year discuss progress and growth.

At the end of the year – Making conclusions:

By the end of the year, there should be so much growth and progress for each and every teacher to reflect on, celebrate and share! Wondering how? I have a few ideas…

  1. Revisit their professional learning time capsule – Provide all teachers with either a blank copy of the same time capsule you used at the beginning of the year, or the actual time capsule they filled in and let them update their time capsule to reflect all that they have learned over the year. This will be a great way to help make their learning visible.
  2. Self-assessment – For each area of the time capsule, teachers could indicate where they are now with regards to their professional knowledge and practice. Hopefully this would allow teachers to see that in certain areas they have moved themselves along the spectrum. Teachers could also reflect on their success criteria and evaluate whether or not they have met the success criteria for each of their personalized professional learning objectives. If there is criteria that is not met (yet), that could be a great starting point for the following year’s personalized professional learning plan!
  3. Share and celebrate – Provide teachers with time to consolidate their learning and decide what they want to share with their learning community. Using the RAFT format can be quite helpful to allow teachers to choose what they want to share and how they want to share it. Sounds like the potential for a mini teacher Exhibition!

I’m a firm believer that every single thing we expect from teachers in the work they do with their learners – assessment, inquiry, differentiation, personalization, learner voice and choice, reflection, ownership, action – should be purposefully modeled in the work leaders do with their learners. I think this model presents a way to allow for all of the aforementioned best practices, while at the same time working towards school-wide goals and objectives. Teachers are doing a great job helping their students reach standardized curricular goals and objectives in inquiry-based, differentiated ways. School leaders can and should be doing the same in their models of professional development.

I realize that I have referred to the learners as “teachers” throughout this blog post. I think this model could work for an entire school community. Every staff member – counselor, TA, coordinator, administrator, coach – could participate in all of these activities and develop themselves as professionals. In fact, the leadership of a school should be intentionally modelling this process for the staff and should be positioning themselves as the lead learners.

What am I missing?

Where are the gaps and weaknesses in this model of PD?

How could I refine this vision to further support teachers as learners while meeting school goals and objectives? 

 

Personalized Professional Learning – Take Two!

A few months ago, my partner in crime and I had a crazy idea to design a model of Personalized  Professional Learning that would hopefully model for our staff, what we expect to see in their classrooms. Our first attempt at PPL went really well and we received awesome feedback from our staff – but we wanted to challenge ourselves to reflect, refine and improve the model further.

Our biggest area of self-identified growth was linking everyone’s personalized learning to our School Improvement Plan goals and our PYP Action plan goals. When reflecting on our first iteration of PPL, we realized we had modelled open-inquiry. We asked our staff “What do you want to learn about” and we structured an afternoon to support those goals. However,  open-inquiry is often a luxury teachers -and we’ve come to discover – administrators do not have. Teachers have curriculum goals that students need to meet and administrators have school improvement plan and IB program action plan goals that staff need to meet. Thus bringing to light our challenge when designing the second iteration of PPL – how can we design a half day of personalized professional learning that is inquiry-based, differentiated, built on learner voice and choice… but still guides our staff towards meeting our school and program goals?

Here is how we went about it:

Step 1 – Rethinking and reorganizing topics of learning interests

Last time, our staff collectively built a learning menu that listed many different topics 21st Century teachers are learning about – maker space, play, e-portfolios, etc.

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We realized that many of those topics ALREADY contribute to our School Improvement Plan (SIP) goals and IB Action Plan (IBAP) goals – we just needed to make the connections more explicit. So our 8 person leadership team sat down and re-organized the menus by SIP goals and IBAP goals. This resulted in new learning menus that had all the same staff-selected topics of interest, but organized in a more purposeful way.

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Step 2 – Reflecting on our last afternoon of PPL 

At our school, we advocate for “no secret teacher business”, which means we also need to model “no secret leadership business”. So we were honest, vulnerable and transparent with our staff. We openly reflected on both the strengths an areas of growth of our first attempt at PPL. We admitted that we had used a model of open inquiry, and we were clear that next time we wanted to implement a model that was more guided and informed by our SIP and IBAP. To get our staff to begin to think of PPL in this way, we did an activity where everyone reflected on what they learned about during our first attempt at PPL and tried to retroactively find a connection to our School Improvement Plan or PYP Action Plan. We posted goals from our SIP and IBAP around the room and gave stickers to all staff to post based on goals that connected to what they had learned about on our last half day.

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We shared with our staff, that even though it was great that so much of our learning accidentally contributed to our SIP and IBAP, this time we wanted to ensure that our PPL purposefully contributed to our school and program goals.

Step 3 – Purposefully planning for our upcoming half day of PPL

Similar to last time, we wanted to give our staff some time to think about what they would learn, how they would learn and how they would share their learning for our upcoming half day – the difference being this time, we wanted their “what” to be linked to either a School Improvement Plan goal or PYP Action Plan goal. In order to do this, we used an after school staff meeting to give staff time with our newly organized learning menus to think about how they might to spend  their upcoming half day. Each staff member took a few small colour squares and wrote down what they wanted to learn, how they wanted to learn and how they planned to share their learning with others.

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Then, they had to post their squares on bulletin boards that we had divided up based on our School Improvement Plan and PYP Action plan.

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This allowed everyone on staff to not only be purposeful about what they wanted to learn and how it contributes to school and program goals, but it was also a great way to allow everyone to see what everyone else was interested in learning about on the upcoming half day.

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Step 4 -Planning in response to learning

Similar to last time, our leadership team wanted to plan the structure of the half day based on the learning needs and interests of the staff. In order to do this, we looked at our bulletin boards and recorded how staff wanted to learn and what specifically they wanted to learn about.

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We analyzed the data, specifically paying attention to numbers and trends in order to figure out how best to structure our half day of personalized professional learning. This approach revealed that most of our staff was interested in personal inquiry and collaborative inquiry and some of our staff was interested in workshops, mainly about math, literacy and technology. This allowed us to build a structure for our half day that was representative of our learners’ needs and interests.

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Step 5 – Let the learning happen

On our half day, we gathered as a whole staff to review the structure of the day, review our essential agreements and set personal goals.

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Then we just stepped back and let the learning unfold. It was amazing to see some staff attend workshops, some staff inquiring collaboratively and other staff pursuing  areas of personal exploration.

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OF COURSE, we kept adult recess which proved to be one of the day’s highlights again!

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And we finished the day reflecting on what we learned and how we learned.

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Step 6 – Track the learning

Always, at the end of professional development, we collect feedback from our staff about what went well and what could be improved for next time. In addition to feedback, this time we wanted to collect some data about the learning that took place as well and specifically how it contributed to our School Improvement Plan and PYP Action Plan.

We collected data on what staff learned:

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We collected data on how staff learned:

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We collected data on how staff shared their learning with others:

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We collected data on how staff’s learning contributed to our School Improvement Plan goals:

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We collected data on how staff’s leaning contributed to our PYP Action Plan goals:

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Once all the data was collected and organized, we made a display to ensure that our whole learning community could see the stats about our half day of personalized professional learning.

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All in all, I think it was a success! It felt good to find the synergy between having all learners learning towards to a standard collection of goals, but allowing them to do it in a way that was relevant, significant, challenging and engaging for each them as individual learners. Again, we received an overwhelming positive response to our half day of PPL. When learners are thanking you for letting them learn and asking for more and longer opportunities to learn, hopefully that means we’re on the right track!

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We still have lots of room to grow, so we would love to hear your thoughts and feedback on our model of Personalized Professional Learning! 

 

Inquiry Based Math Strategies

During our half day of Personalized Professional Learning, I hosted a workshop on inquiry-based math strategies, but not everyone who wanted to attend could attend… so I thought I’d recap the workshop here for those of you who could not make it – and for those of you at different schools who might be interested in this topic as well.

The structure of the workshop was very hands on, so in the absence of you being able to actually engage with the materials and manipulatives, I will provide a combination of notes, photos, questions and reflections that will hopefully allow you to engage in some of the same ideas, just in a different way.

Tuning in – What do already know?

Think about or jot down your current understanding of each of the inquiry-based math strategies listed below:

  • math time capsule
  • open ended centers
  • magic question
  • open-ended questions
  • number talks
  • math congress
  • visible thinking routines
  • inquiry cycle

If you have a thorough understanding of each of these strategies, you probably do not need to read on. If you think your current understanding has room to grow, read on!

Open-Ended Centers

I’ve already written a post about open-ended math centers and how they work in our early years classrooms. During the workshop today, each group had a bin with the three essential ingredients of an open-ended math center: manipulatives, writing utensils, and a placemat/whiteboard.

Here are some pictures of how teachers tested out a few open-ended math centers:

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The Magic Question

I’ve also written about my favourite inquiry questionWhat do you notice? In the workshop we looked at how this question can be used for math specifically.

Take a look at this multiplication chart. What do YOU notice?

Open-Ended Questions

Answer this question: Compare the following fractions using < > or =

1/4   ____  1/2

Now answer this question:

What is the same as a half?

Reflect on the difference between answering the first and second question. What are the benefits of asking open-questions in math?

Number Talk

Take a look at the following image. How many dots are there?

How did YOU figure it out? Here is a picture of all the different ways the participants of the workshop figured it out.

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Math Congress

Step 1 – Present the problem: A sports store has a number of bicycles and tricycles. There are 60 wheels in total. How many of each kind of bike could there be?

Step 2 – Work towards solving the problem. Markers and chart paper work best!

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Step 3 – Share discoveries and strategies with fellow mathematicians. Make sure fellow mathematicians are invited to ask questions, make connections, comments and conjectures!

Visible Thinking Routines:

Use the Visible Thinking Routine “Claim, Support, Question” to share some of your thinking about decimals.

CSQ

There are also many other Visible Thinking Routines that are helpful in approaching math in an inquiry based way!

Inquiry Cycle:

Kath Murdoch’s inquiry cycle is a great way to make any math more inquiry-based.

A CCSS math standard: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

What do YOU already know about this?

What do YOU need to find out about this?

How could YOU find out about this?

Math Time Capsule:

Now, think about or jot down your understanding of each of the inquiry-based math strategies listed below. A math time capsule is a great way to show growth and progress in math – whether it’s over the course of a unit, a year… or even of the course of a workshop!

  • math time capsule
  • open ended centers
  • magic question
  • open-ended questions
  • number talks
  • math congress
  • visible thinking routines
  • inquiry cycle

How did your understanding of these strategies grow and change?

In the actual workshop, after each strategy, we took some time to discuss how the strategy could be applied/adapted to different content and different age levels. Too often when we are looking at strategies we are focused on the actual strategy within to confines of the example that is used. This leads to the conclusion that “That doesn’t work for the grade/content that I teach”. Instead, I challenged the participants in the workshop – and I challenge you in the same way – to focus on the essence of each strategy and how that same approach can be used in different ways, for different ages and for different strands of math.

Here are a few examples of how the same strategy can be adapted for different content and different ages:

Math time capsules – In Grade 5 you might give students the summative task on the first day and then again on the last day to show all of the growth and progress they experienced. But in KG, you may conference with a student and voice/video record everything they know about shapes, and then record them again at the end of a unit to capture growth in their understanding.

Magic question –  In KG you might show a ten frame and ask “What do you notice?”. In Grade 2 you might show a hundreds chart and ask “What do you notice?”. In Grade 4 you might show a multiplication chart and ask “What do you notice?”.

Inquiry cycle – In Grade 1 you may use the inquiry cycle to structure a whole class inquiry into measurement. What do we know about measuring objects? What do we want to know about measuring objects? How can we find out more about measuring objects? In Grade 6 you might use the inquiry cycle to structure self-directed, personal inquiries towards calculating volume of 3-d shapes. What do I already know about finding volume of 3-D shapes? What do I still need to find out? How can go about that?

The possibilities are endless. If you focus on the “why” a strategy is effective and “how” a strategy helps foster thinking and exploration… then the “whats” become infinite! I also shared this google doc with some of my favourite inquiry-based math resources (books, blogs and Tweeters!) Feel free to have a look!

What are your favourite inquiry-based math strategies?