Category: concept based learning

When is Inquiry not “Best Practice”?

When is Inquiry not “Best Practice”?

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My co-teaching partner leaned across her desk and asked, “So at what point do we stop ‘inquiry into this’ and start teaching them something?”. I responded with nervous laughter because her question sounded like blasphemy. It was an absolutely valid question though and has lingered in my mind for ages, particularly since I am aware of Professor John Hattie’s meta-analysis on high vs. low impact influences on student learning. According to Hattie’s Visible Learning Rankings, inquiry-based learning has a low ranking on its impact scales. I do recognize that inquiry-based learning comes in a variety of flavors, which is well represented by Sarah Plews’ breakdown in her Concept-based Inquiry Mini-PD course:

So I have often felt skeptical of Hattie’s findings because I think generalizing inquiry-based learning is doing this approach a disservice. However, I have come to accept that some content lends itself better to inquiry than others, and some concepts must be developed in a more structured way. I think the reason why inquiry-based learning falls flat on Hattie’s Impact Scales is that many practitioners aren’t sure when and why we might use different approaches.

So, are there moments in our PYP classrooms when we need to put inquiry-based teaching methods on the back burner and provide explicit and direct instruction? Yes, yes there are! And that doesn’t mean we are tossing out all the other PYP practices. This is not a “either/or” situation–either we teach through inquiry OR we are NOT a PYP school. Having a strong PYP program means that practitioners know what content and skills would be best taught through a variety of methodologies.

Ok……so what content and skills might those be, you wonder? Well, here’s the thing, it’s not just the WHAT but it is also the WHO. We have to consider the needs of our students before we decide HOW best to teach them. So what students benefit the most from direct instruction? I think the guidance below is helpful:

Students who learn and think differently. Without explicit instruction, students who struggle with attention or working memory may not focus on the most crucial ideas in a lesson. With explicit instruction, you cue students in to the most essential information.

English language learners. When you use consistent and clear language in each step of instruction, English language learners (ELLs) aren’t overwhelmed with new language demands. Research has shown that explicit instruction can lead to achievement gains among ELLs.

From Understood.Org

When we consider our students with learning needs, it seems obvious that we might alleviate the cognitive load by providing direct instruction. Consider this-When students have a clear understanding of what they are learning about, they are not using their brain power for meaning-making; instead, they are using their working memory to process this information and store it for later use.  This actually helps them, later on, to engage in an inquiry because they have the knowledge to draw upon during a more open-ended lesson. It’s a support, not a deterrent to more inquiry-based approaches.

Explicit and Direct Instruction for the Key Conceptual Lens of Form and Function

One of the filters I use for deciding when we need to explicitly teach something is considering if this is going to be new knowledge to students. Typically it is more efficient to teach the key concepts of What is it? (form) and How does it Work? (function) through a more direct instruction approach when students are acquiring new understandings of concepts or skills. Students need to know the definitions of things and procedural knowledge. Let’s not leave them guessing or feeling confused.

Think about it- can we just send kids with a stack of books and have them generate theories about how language works and then teach themselves to read? No, that would be professional malpractice! We have to explain foundational concepts to students.

Image from https://www.evidencebasedteaching.org.au

Let’s think about the words “explicit” and “direct”, another synonym is clarity. You might also think of this as “scaffolding”, in which the teacher is explaining and demonstrating a concept or procedure, and then giving students the opportunity to have guided practice. Educational research shows that when we “show and tell” how something works, it has a greater impact on learning.

Students require more explicit instruction with some of the following content and skills:

  • phonics and decoding skills
  • research skills
  • collaboration skills
  • using mathematical tools and strategies
  • safety skills
  • spelling and grammar
  • understanding time and chronology

So what might this look like or sound like in a PYP classroom?

Sounds like: Today we will be unlocking our thinking through the concept of Form and answering the question, “What is a closed syllable?” . We will be successful at becoming knowledgeable of this syllable type when we can:

  • Define what a closed syllable is.
  • Identify what words contain closed syllables and which ones do not.
  • Read at least 5 words with closed syllables in them.

So you may be wondering, What is a closed syllable? A closed syllable is when a vowel is followed by (or closed in by) one or more consonants.  The vowel sound is ‘short’.  This pattern is often referred to as the CVC pattern (consonant – vowel – consonant), although a closed syllable does not always begin with a consonant. Let’s take a look at some examples……

Now it’s your turn, can you sort these 10 words into the categories of Closed syllables and Not Closed syllables? When you are done sorting, read your words aloud, do you hear the short vowel sound in the word? When you think you have sorted the words correctly, you can compare your answers with a partner…..

Okay, before we go today, I want you to whisper to a friend what a closed syllable is and write at least one new word that contains a closed syllable on this sticky note. You can put your sticky on our Definition Chart for closed syllables. And, if you find any other new words when you are reading, grab a sticky note and write it down with your name on it, and put it on our chart.

Looks like:

  • teacher-selected materials and examples
  • the teacher talks more than the students
  • the students are engaged in a specific task, with little agency over how it is done.
  • there is an explicit “right answer” based on attaining the learning goal.

A closing thought

Teaching is complex, especially in the PYP. Although I have made a stark generalization in what Key Concepts might demand a teacher-directed approach, I ask you to think carefully about your unique learners and consider how best they acquire the knowledge, concepts, and skills they need to be successful. There are moments when we are not actively soliciting curiosity, asking students to problem-solve, or generating theories in our PYP classrooms. And if you choose to develop a lesson that isn’t inquiry-based, it doesn’t mean that you are desecrating the PYP principles.

We want to emphasize that being ‘an inquiry teacher’ does not necessarily mean using an inquiry approach for EVERY lesson.

-Carla Marschall and Rachael French, from Concept-Based Inquiry in Action

So, let’s be thoughtful and skillful in our pedagogical decisions, taking a more teacher-centered approach and providing direct instruction when the moment calls for it. Perhaps if we are more mindful of the merit of the precision of explicit teaching, then our inquiry moments will be more profound.

When Numbers Divide and then Multiply

When Numbers Divide and then Multiply

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When I think about Who I Am as an educator at this moment, you could say that I’m 40% teacher, 40% student, 20% teacher-leader, but I am always 100% parent. Everything I think and care about in education is definitely shaded by my perspective as a parent and my hope for my daughter’s future. In fact, my love for her is the fuel which creates an urgency for changes in education and can blind my decision-making.

Although I am not a proponent of homework for young children, I do spend an evening a week “doing math” with my 3rd-grade daughter because, during our transition to Laos, her academics have dipped. We usually sit together to play Math For Love games but after her MAP test, we’ve been doing some lessons on Khan Academy to supplement her classroom learning. My husband and I have been trying to investigate other more “fun” options for self-directed learning since she is getting older and desiring independence. Since my daughter just recently stopped counting on her fingers, we’ve decided to explore the math website Reflex Math that was recommended by a colleague:

Full of games that students love, Reflex takes students at every level and helps them quickly gain math fact fluency and confidence. And educators and parents love the powerful reporting that allows them to monitor progress and celebrate success.

Sounds like its worth a try, right? We felt that if she could become more proficient in her math facts, she’d feel more assured when engaged in math. So for the last few days, she’s been “playing the game”, and the report we got made us gasp:

Screen Shot 2019-04-11 at 4.51.27 AM

So then we asked her to do this game daily, while she found fun in its novelty, excited to do it independently, eventually, it became a drag on her motivation for math learning. Last night, when I came in and asked her why she was staring at the screen, it brought her to tears. Perhaps it wasn’t one of my “good parenting” moments when I asked her that, but I was afraid that she was just allowing time to elapse until the “store” opened, and she could take her avatar shopping-something that a lot of kids might do to”play the game”.  I really felt awful that my words stung her heart. When I inquired further behind her emotion, she told me that she didn’t have enough “think” time to solve the unknown facts. Oh man, I really had misunderstood her blank stare!

And I, like many parents, had fallen into the trap of thinking that fast=fluent. Instead of creating confidence, I had crushed her esteem. Darn it! As an educator, I know better, so why didn’t I do better?

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After dinner, I decided to give her a little quiz and any math facts that she needed more than 5 seconds to solve, went on a flash card. On the flash card, along with the answer, we’d create a strategy to help her remember it better. We only focused on addition and subtraction.

Now all of a sudden, what had become a drudgery of math practice had suddenly become strangely exciting. Whenever she could quickly give me an answer, she started dancing around the room and laughing. And the ones she got “wrong” (aka, not quick)?-well, when she shared her strategy for solving it, she had solid mental math strategies such as using derived facts. I started giving her harder ones like 17+17 and, as she exclaimed “34”, I wanted to get up and dance around the room with her. Suddenly a “bad parent moment” had turned into a “good teaching moment”, for both her and I.

So what did I learn? Technology isn’t a teacher. I am. Conflict can help develop a deeper understanding of one another. Time may be relative, but conceptual thinking is not.

And most importantly, when I think about homework/home learning–it’s never the worksheet or activity that improves the performance of a student, instead, it is the parent relationship that builds understanding through compassionate attention and love of learning–it’s the US, not the IT.

 

“The Standards” Aren’t a Race: The Importance of Assessment in Getting to a Finish Line

“The Standards” Aren’t a Race: The Importance of Assessment in Getting to a Finish Line

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I didn’t enjoy Math until I was in high school. Trigonometry was the first time that I remember gazing up in amazement and wonder. Sin and Cosine. Identities, theorems, and proofs. Parabolas and Ellipses.  It suddenly became interesting even if it was hard. I loved using the nifty functions on the calculator as well. But why did it take me so long to appreciate the beauty of math? I wonder where and who I might be if I had learned less about standard algorithms and more about number concepts and reasoning at an earlier age.

I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide. ……. to create a profound simple beauty out of nothing, and change myself in the process. Isn’t that what art is all about?

From A Mathematician’s Lament by Paul Lockart-

For me, if I can invoke wonder and surprise, then the beauty of communicating in numbers becomes self-evident and a student’s heart awakens to the joy of an interesting problem or question. Creating this experience is a passion of mine. After spending a week with Lana Fleiszig, it’s hard NOT to be more inspired to create a love of math in our classroom. Her enthusiasm is contagious, and her advice about inquiry is clear–know your destination, but don’t worry about how you get there. Don’t be afraid to throw students into the “pit of learning” and allow them the experience of confusion. As I have come to appreciate her point of view, I recognize that when students climb out of their “pit”, that’s where beauty lies.

So here we are, in another stand-alone unit, which might be considered the “place value” unit, which is not typically the most exciting math concept. It’s a ho-hum inquiry into base-10 blocks in how we express large numbers and use it to develop strategies for addition and subtraction. But what if we threw them into the learning pit and took our time to really develop number sense. How might we approach our planning and execution of the unit if this wasn’t a race to tick off a curriculum math standard?

The Standalone

Let me break down the basics of the unit for you:

Central Idea: Numbers tell us How Many and How Much

  • The amount of a number determines its position in a numeral.
  • How we know when to regroup.
  • How grouping numbers into parts can help us find solutions

(All lines of inquiry and Central Idea from conceptual understanding in the PYP Math scope and sequence and subsequent learning outcomes in  Phase 2)

Knowledge and Understandings, aka, “The Standards”

I’m going to cross-reference 2 commonly used national curriculum, Australian and American Common Core, because our team needed clarity into exactly WHERE our destination needs to be in this unit of inquiry:

Australian:

Count collections to 100 by partitioning numbers using place value (ACMNA014 – Scootle )
  • understanding partitioning of numbers and the importance of grouping in tens
  • understanding two-digit numbers as comprised of tens and ones/units
Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015 – Scootle )
  • developing a range of mental strategies for addition and subtraction problems

The Common Core:

Understand place value.

CCSS.MATH.CONTENT.1.NBT.B.2
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
CCSS.MATH.CONTENT.1.NBT.B.2.A
10 can be thought of as a bundle of ten ones — called a “ten.”
CCSS.MATH.CONTENT.1.NBT.B.2.B
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
CCSS.MATH.CONTENT.1.NBT.B.2.C
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
CCSS.MATH.CONTENT.1.NBT.B.3
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Use place value understanding and properties of operations to add and subtract.

CCSS.MATH.CONTENT.1.NBT.C.4
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
CCSS.MATH.CONTENT.1.NBT.C.5
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
CCSS.MATH.CONTENT.1.NBT.C.6
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

 

Planning the Unit

If you “peel” back these standards, what (math) concepts and skills seem evident to you? What are the “big ideas” that students need to walk away with?

  • Collection or Group
  • Place Value
  • Position
  • Partitioning: composition and decomposition
  • Reasoning

Since I teach 1st grade, we would be exploring the key concept of Form and Function, mainly, throughout this unit. But we would also look at the Connection between using groups of 10s and developing mental strategies for problem-solving in which we can Change addends/subtrahends around to make friendly numbers. Students would also need to consider the Perspective of other mathematicians in our class when it came to solving a problem in different ways.

With this in mind, we looked at these standards and identified 5 main guiding questions  that will be the basis of our inquiry and the purpose of every provocation that we create:

  1. How does the place value system work?
  2. How does the position of a digit in a number affect its value?
  3. In what way can numbers be composed and decomposed?
  4. In what ways can items be grouped to make exchanges?
  5. How can we use place value patterns for computation?

Provocations to Explore and Reveal Math Thinking

Once we had clarity around the big ideas in our unit and created our guiding questions, it became easy to start planning provocations.  Using a guide like this one, Task Identification Tool_Identifying High-Quality Tasks (1),  from the work of John J. SanGiovanni in his book series on how to Mine the Gap for Mathematical Understanding really helps teams like ours to create a high ceiling, low-threshold activity for inquiry-based maths.

We knew from a previous provocation, (14 or 41–the position of a numeral doesn’t matter. Agree or Disagree. Prove it.), that students still were developing an understanding of what a written number means. We needed to further explore it. So we began with place value.

Guiding Question #1: How does the place value system work?

We decided to launch the unit with an emphasis on language since we noticed that a lot of students were mixing up their teen numbers when explaining their ideas. So we started with Teen vs. Ty, is there a pattern or a rule about these numbers?

  1. Sixteen and Sixty, What do you notice about these numbers?
  2. Seventeen and Seventy? How are they different, how are they the same?
  3. What do you think “teen” means? What do you think “ty” means?

We then began exploring expanded notation with showing the tens in a number. Students were introduced to how expanded notation is related to the place value mat, which can be represented as:

43=40 + 3 or 4 tens and 3 ones. 

The students played a partner game called “guess my number” in which they had to express a number in tens and ones and have the student create it with base-10 blocks and numerals.  They did really well. We thought we were smashing it and ready to move on to using it for addition and subtraction.

But how could we be sure they “got it”? ……….

Assessment

We decided to assess if they got the idea of base-ten and how we use the place value mat as a structure to show the parts of numbers. We used this SeeSaw prompt to assess if they truly understood:

How we know when to regroup – Using a collection of objects – how do you find out how many items you have?

We decided to use unifix cubes because the “tens” weren’t prepackaged, sort of speaking, as they are with base-10 blocks. In this assessment, we had them grab a handful of unifix cubes and organize them on the place value mat, explaining to us what number they thought they had. What we observed stopped us dead in our tracks and ask what misconceptions do we see? Here is an example of a common surprising result:

As you can see, this student didn’t connect the quantity he had in their collection at all. These students would need some additional support with connecting the amount of a number to how it is written and presented.  We felt we needed to go deeper into how we “bundle” tens to count things efficiently. In fact, we felt we needed to do an inquiry into 10, so they could appreciate how this is the basis of base-10.

Back to the Starting Line?

We are in Week 4 of this unit, and we are going back to the starting line. Based on our observations, it seems that the students don’t quite have the idea of ten yet, and, we have a group of students who just need to work on skip counting by tens. It would be easy to move ahead and push through so we can tick off our standards, but we’d rather spend more time immersed in context and play that develops their number sense than to push them along. We understand our future impact. Moving ahead hoping that they “get it” later on would seem like a disservice, as they’d lose the interest and motivation to do more complicated mathematics and have half-baked conceptual understandings.

Since have a free flow of student groups, in which children choose what Must Dos and May Dos they want to participate in. However, ideally, we have 3 primary activities that we want the students to work through in small teacher groups throughout our math learning time:

The Big Idea of our teacher-directed groups: 10 can be thought of as a bundle of ten ones — called a “ten.”

  • The Base-10 Bank

Students will pick a numeral and build numbers using “ones” which they can exchange for tens. As partners, one person will be the “bank”, which the other partner can trade in their ones for 10. No place value mats, only the base-10 blocks.

  • Race to 100

Using dice, a hundred’s chart and a place value mat, students have to roll and add their way to 100. As they roll their way up to 100, they have to build the new number, using the place value mat to show how the quantity that is ever-increasing, as well as giving a context for exchanging units.

Making Bundles: In this activity, students are given a collection of objects and they have to bundle them up into tens, so that they have an appreciation of the value of a number.

Additional Games and activities that they can do independently, when not working with a teacher. The May-Dos:

Traffic light (Partner Game): One partner comes up with a “mystery” number and, using a place value mat, has to try to guess what digit is in what position.

Big 4 (Independent or Small Group): In this game, we use a hundred chart to try to get to the biggest number in just 4 moves. A child rolls a die and moves that many spaces, moving in any direction, forwards, backward, diagonally, upwards or downwards. This game gives them practice at thinking about number patterns as they move around the hundreds chart.

Ready or Not?

After all that exploration, we hope that these games will prepare them for the following formative assessment:

4+4 = 44. Agree or Disagree? Show how you know. (This actually is inspired by a misconception that we observed) Students can use 10-frames, the Hundreds Chart, Math Racks or Base-10 blocks to provide evidence of their reasoning. (We determined that these sorts of materials would help them to “see” patterns and make connections, rather than loose parts alone)

If they can articulate and demonstrate a firm understanding of place value in this provocation, then we feel that we can move into applying our understanding of using the base-10 for addition and subtraction, examining the guiding question:

How can we use place value patterns for computation?

This is the ultimate reason why place value is such a critical understanding after all. However, it is the journey into number sense that makes this a beautiful experience. We are not quick to move them onto pencil and paper. We want them to experience numbers and segue them into contextual situations.

The Summative

We are still in process with determining the actual prompt, but we feel that we need to give them choices with the task. Choosing a task that shows how they apply grouping strategies to solve addition and subtraction problems will ultimately be our goal.

For our low-level readers, we will give them an oral word problem and then hand them a collection of objects that need to be counted. We want them to observe if they create groups of tens to determine the number. No place value mats offered, but they can request one. For our stronger readers, we will give them a word problem, and, again, offer them concrete materials, but other tools to solve the problem are upon request.

At the end of this task, we can identify the skills and understandings they have acquired. Although we have “mapped out” where we think this unit will go, we can be flexible and stop to address misconceptions along the way. Will they arrive and “meet the standard”? That is entirely up to us, and how effectively we observe, challenge and question our students’ thinking as they playfully and joyfully experience numbers. At the end of the day, that goal–to appreciate and be fascinated with numbers--that is the true destination of math inquiry.

 

Into the “Pit” or upon the “Clouds”: Kensho and Satori Moments in the Development of Number Concept

Into the “Pit” or upon the “Clouds”: Kensho and Satori Moments in the Development of Number Concept

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It’s Sunday morning and as I soap up greasy dishes, I hear Susan Engel say on the Heinemann Podcast: 

One of the things that I think that our schools have unwittingly done is ignored all the processes that kids use at home and try to replace those with a set of formal procedures that aren’t always as effective…. But it’s a shame because while we are busy trying to sort of force these somewhat formal kinds of learning beacause we think they are more “efficent” or “high powered”, we waste a lot of the natural learning skills that students have. And often a lot of the natural teaching skills that grown-ups have.

Huh, I think I know what she is talking about. Whether we are teaching a genre or the scientific process, teachers are constantly “telling” kids what to pay attention to and to think about. When I start examining my current practice and reflecting on Who I am as a teacher, I have come to see my role as a provocateur and coach. I am always considering who is REALLY doing the learning in our classrooms?–is it me, or is it the students?

egg
I think of this quote often, reminding myself that if I  tell students, then I’m “breaking their egg” and killed the opportunity for their learning.

So I am constantly asking myself that question because I know that “the person who does the work, does the learning“. But when I say “work”, I mean thinking, and there are so many of these micro-moments in our classroom in which I have a chance to tell kids what to do or to ask them what they think they should do to approach a situation or problem.  Sometimes these moments of learning are Kensho, growth through pain, and other times it is Satori, growth through inspiration. I first encountered this term when I read this blog and Kensho immediately reminded me of our teacher-term, the learning pit. You need determination and resilience to get out of that pit and your reward is Kensho. However, we rarely talk about it’s opposite, Satori. Up until this morning, I didn’t think we had a name for Satori in education. It Kensho is the “learning pit” than Satori must be up in the “clouds”, having a clear view and understanding. But Susan Engel articulated best in the podcast:

There are certain kinds of development that children undergo that are internal and very complex and they don’t happen bit by bit. They happen in what seem to be moments of great transformation of the whole system. ……

At that point, I stopped and turned toward my device. I recognized exactly what she was talking about it. I observed it the other day. My ears perked up some more as I moved closer to listen:

When children are little, their idea of number is very tied up with the appearance of things. So, this is a famous example from Jean-Pierre, a line of 10 pebbles to them is a different quantity than a circle of 10 pebbles, because lines and circles look so different.

The idea that it’s 10, whether it’s a circle or it’s straight, is not accessible to them. At a certain point, virtually every typically developing child, no matter where they’re growing up, acquires this sense that the absolute number of something stays the same no matter what it looks like. Whether it’s a heap or a straight line or a circle, that may sound like a tiny discovery, but it’s the beginning of a whole new way of experiencing the abstract characteristics of the number world.

You can’t teach that through a series of lessons. That’s an internal, qualitative transformation that children go through. Once they’ve gone through that, there are all kinds of specific things that you can teach them about the nature of counting and number and quantity.

Yes! I totally know what she is explaining. I was a witness to it. And perhaps, when you reflect on these Zen philosophical terms as development milestones, you may make a connection to your own classroom learning.

Here’s a snapshot from a recent example in our Grade 1.

Some context

There’s a math coach that I love, Christina Tondevold. She always says that “number sense isn’t taught, it’s caught”.  I’m always thinking to myself, how can I get them to “catch” it. This past week, we did just that using the Visible Thinking Routine, Claim, Support, Question making the claim:

The order of the numbers don’t matter–12 or 21, it’s the same number.

The students took a stand, literally, in the corners next to the words and image for Agree or Disagree, with  I Don’t Know, in the middle. This was great formative data! Then we provided the students with a variety of “math tools” to Support or prove their thinking is correct. They had to “build” the numbers and show us that they were actually different. It was neat how the students who stood in the I Don’t Know and Disagree areas were developing an understanding of what a written number truly “looks like”. We didn’t jump in and save them at any point, but some of them were experiencing Kensho. It was painful because they didn’t know how to organize their tiles or counters or shapes or beads in such a way that they could “see” the difference between the 2 numbers. Meanwhile, the students who chose the unifix cubes were experiencing Satori- and it became very obvious to them that these were different numbers. 

In our next lesson, we introduced the ten frames as a tool to help them organize their thinking and develop a sense of pattern when it comes to number concept. We did the same two numbers: 12 and 21, and they could work this time with a partner. Oh man, was there a lot of great discussions that came out as they talked about how the numbers looked visually different. The concept of Base 10 started to emerge. As observers, documenting their thinking, it was exciting to see the connections they were making. But the best part was yet to come.

We then brought in the Question part of the thinking routine. We asked them “if the order of 1 and 2 matters to 12 and 21, then what other numbers matter?” They told us:

“13 and 31, 14 and 41, 24 and 42, 46 and 64, 19 and 91, 103 and 310.”

A Hot Mess of Learning

Once unleashed, the kids grouped up and flocked to resources. There was a buzz. Giving students choices allowed the opportunity to choose whether they wanted to stay with smaller numbers or shoot for the BIG numbers even if they had no idea how they might construct a number past 100. They could use any math tool they wanted: cubes, blocks, 10 frames, Base 10 blocks, number lines, counters, peg boards–anything they wanted. Those choices, of itself, really provided some great data.

Here is an example of one of the groups who went with lower numbers:

But the ones who went for the BIG numbers, were the most interesting to watch because they were Kensho. Most of them grabbed unifix cubes, thinking that the same strategy they used before with 12 and 21 would work with 103 and 310. big numbersOh man, they persisted, they tried, but it took a lot of questioning and patience on our part to help guide them out of the pain that their learning was experiencing. Only one group naturally gravitated toward the Base-10 blocks, and when they realized how the units worked, it was a moment of Satori. They moved on from 103 and 310 quickly; they tried other numbers and invented new combinations. And interestingly enough, those groups, at no point, looked over to the ones engaged in the struggle to suggest that they might try another math tool. It was as if they knew that when one is in Kensho, best to leave them alone to make meaning on their own.

And there we were, in the midst of this math inquiry, and we felt like exhausted sherpas but satisfied that we were able to let them choose their own path of learning and made it to their “summit”.

As I consider how the role of the teacher is evolving in education, I think it is recognizing these moments of pain and insight in learning, and guiding them towards the next understanding in their learning progression. I absolutely agree with Susan Engel that when we see children fumbling around, we should be asking if they are within reach, developmentally, to even acquire the knowledge of skill that we are working on. For me, inquiry-based learning is the BEST way in which we can observe, engage assess our learners to truly discover their perceptions and capabilities. It is through capturing the student conversations and ideas that emerge as they give birth to a new understanding that is the most exciting to watch and inspires me in our planning of provocations that lead to their next steps.

How about you?

 

 

The PYP Planner: A Shift in Our Approach to Planning Inquiry (#enhancedPYP )

The PYP Planner: A Shift in Our Approach to Planning Inquiry (#enhancedPYP )

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Quick Quiz: What is the first “box” in the PYP planner? Did these things come to mind?:

What is our purpose?   To inquire into the following:

  • Transdisciplinary theme:    
  • Central idea :  

summative assessment task(s):

What are the possible ways of assessing students’ understanding of the central idea? What evidence, including student-initiated actions, will we look for?

Now with the enhancements in the Primary Years Programme (PYP), we can redesign our planner which has to lead to an overhaul of our collaborative planning. If you notice in the Box #1, aside from clarifying our theme and central idea, we would start planning our summative. However, we haven’t done any assessment of student’s prior knowledge, and I often found that determining the summative assessment before we have even launched a unit of inquiry (UOI) has always led to more teacher direction in our units, as if we are nudging and, sometimes pushing the students toward our end goal–The Summative Task. Think about it, when we plan in this way, we are already dictating the terms of what we want the students to Know, Understand, and Do (aka: KUD) before we have even gotten them to SHOW US what they already know, understand and do. A bit presumptive of us, really, eh?

Needless to say, since the reigns are off, and schools get to design PYP planners in the Enhanced PYP, there’s been a shift in how we approach planning. And the new “Box 1” (figuratively) is about planning our provocation FIRST so we can let the students reveal to us what they know and lead the direction of the UOI, rather then us marching them towards the summative. It may seem trivial, but when you consider how AGENCY is the new core of our curriculum, we need to be approaching our units in different ways.

Let me provide a context, looking at our Math Stand Alone:

Patterns and sequences occur in everyday situations.
-Patterns can be found in numbers.
-Types of number patterns
-Patterns can be created and extended.

Key concepts: Connection, Form, Reflection

Related concepts: pattern, sequences, collections/groups

As a team, including our Math Leader of Learning (Olwen Millgate), we sat down and discussed the many different ways that we could plan a provocation around this central idea. At the end of the day, we determined that the most open-ended, the better, so that students could exercise as much creativity and skills as possible. We would just be the “researchers” in the classroom, observing and noting what the students came up with when given the challenge–Create as many patterns using one or more of the materials provided. 

As teacher researchers, we divided up the students so that we could take notes, making sure that all students were given the time and attention to “show what they know” about patterns. Here is the simple observational sheet that was created for this provocation: (Free to use)

We gave the students a variety of math tools to work with:

  1. counters
  2. ten frames
  3. unifix cubes
  4. Cuisenaire Rods
  5. beads
  6. pattern blocks
  7. peg boards
  8. tanagrams
  9. popsickle sticks
  10. white board and markers
  11. stampers and paper
  12. dominos
  13. magnetic letters and boards

As you can see, they had a plethora of options, and the students engaged freely, making their own choices and creations. Some students preferred to work by themselves while other collaborated–another aspect that we noted along with capturing their conversations. Here are just a few of those creations:

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There was a very loud and animated group at the Unifix cube station–which surprised us all by how excited they got about building “tall patterns”, with a lot of debate about whether they were just snapping cubes together or generating a true pattern. Although to outsiders, it may have felt chaotic, there were fantastic conjectures going on, which we saved a few examples to use for future provocations. (The Guiding Question: Is this a pattern? Why or Why Not?)

Later, our team met to discuss what we observed and we were able to sift through our documentation. We unpacked the provocation, and shared our photos and notes, describing some of the interactions that we had with them. Then we went to our curriculum and examined the phase the students might be achieving at in their conceptual understandings. Our central idea comes from the PYP Maths Scope and Sequence in Phase 1, so we needed to challenge it —is this the phase they are actually in or are we seeing evidence of Phase 2 understanding? We decided to stick with our central idea and lines of inquiry because we felt like we saw and heard evidence that most of our learners were on the tail end of this phase, applying their understanding of pattern.

After this conversation, we went on to determine what our next steps could be. Most of the patterns were ABABAB–do we encourage them to make ABCABCABC or other more sophisticated patterns? At the end of our deliberations, we decided that rushing them might create conceptual gaps so we wanted to stick with their ABABAB, but create a series of opportunities to look at how we could manipulate only 2 variables to generate a variety of patterns. What can we do with only 2 attributes?–This became the guiding question for our upcoming provocations.

So here we are, in Week 2 of this unit and we still haven’t nailed down our summative task. Gasp, right? But, on Friday, after this week’s follow up provocations, we can safely appreciate our learners, where they are and where we can take them during the remaining weeks of the unit. I find that thrilling. We will create our conceptual math rubric, using this generic one as our guide:

math standalone 2

Hopefully, you can see that we are thinking about planning not as boxes but phases in our inquiry. We are using this “tuning in” period to dictate the terms of our how we will ultimately assess students. And we are spending more time researching and planning our provocations so that they can make the children’s thinking visible and expose their understanding of the math concepts. I believe that as this approach to planning evolves, our attitudes toward our students also evolve when we are observing how they are competent and creative when expressing their ideas.

I’m wondering how other schools have begun to consider the impact of planning on agency and how it will look in the Enhanced PYP. The planner has always been a tool for us to shape our collaboration and thinking about how best to meet our students’ needs in the inquiry. I think it will be fun to see how schools begin to shift as they reflect deeply on the importance of it–it’s more than just an exercise in paperwork, it is an artifact of learning.

So what’s your “Box #1”?

#InquiryMaths: Planning for Play as a Stance for Math in the #PYP ?

#InquiryMaths: Planning for Play as a Stance for Math in the #PYP ?

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I’ve been binge learning through the online conference on The Pedagogy of Play. It’s been really inspiring for me. Last year, I felt like I was moving away from play-based learning and into more formally academic structures when I began teaching first grade. This has been a challenge for me because I miss the discoveries (theirs and mine!) and creativity that are natural by-products of a play-based approach. So as I embark on this school year, I have two questions that I am holding in my mind: How do I make math more fun and authentic? and How do I provide rich open-ended tasks that allow for multiple approaches with low threshold, high ceiling tasks?

These questions come from this quote from Jo Boaler, a math educator hero of mine.

Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it—which is the essence of real mathematics—they become more deeply engaged and perform at higher levels.
― Jo Boaler, Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching

loris malaguzziAs I reflect on that research, I believe the answer to my questions is to play. Not just because it develops curiosity and self-expression, but it cultivates self-motivation and an appreciation for the pleasant surprises that our mistakes bring us in our learning process. Moreover, from Boaler’s academic point of view, “they become more deeply engaged and perform at higher levels”. Um…so why on Earth wouldn’t we connect play and math?

What is play?  Play is the ultimate What If question in my mind because it allows us to explore with possibilities. Most Primary Years Programme (PYP) Early Years educators feel that the word “play” is synonymous with the word “inquiry”. As teachers, we can be intentional about marrying the joy of learning through play with our learning outcomes. I don’t think we have to suck the fun out of everything to make it “learning”; in fact, I think it has to be injected back into the process, especially when I consider that real * (think Albert Einstein and Euclid and Leonardo Pisano aka Fibonacci) mathematicians are exceptionally creative and playful with their ideas. (*Actually, I think ALL of us are REAL mathematicians, but not all of us embrace and delight in this aspect of ourselves).

So then if I approach inquiry maths through the lens of play, I need to consider ….

What tools can we use for play?

  • Loose parts?
  • Technology?
  • Each other?
  • Math resources (traditional, like geometric shapes, Unifix cubes, hundreds chart etc.?)
  • Math resources (non-traditional materials that allow students to create. ie: a bridge)

What mathematical ideas can be developed and deepened through play?

I actually believe that most of the time, when we are authentically engaging in math decisions, we are not doing “number” and then “measurement” and then “data handling”–it’s not that discrete in real life and often time these strands are happening simultaneously and overlapping. Play expresses this transdisciplinary nature.

What language can I use to invite “playfulness” with math?

I think our teacher talk is actually a critical component of shaping our mathematical identities. Also, the enthusiasm I communicate, either through my speech or through non-verbal cues is something that I want to be mindful of. My favorite book that addresses this is still Mathematical Mindsets  but I also love the simplicity of Peter Johnson’s ideas on language and I recently read In Other Words: Phrases for Growth Mindset: A Teacher’s Guide to Empowering Students through Effective Praise and Feedback which had a lot of gems in there that can be applied to developing our language around math learning.  I’ve been ruminating over how I can embed more sophisticated math language in our classroom vernacular, especially with our English Language Learners (ELLs). I really want students to talk like mathematicians, explaining their algorithms and debating approaches to problem-solving in a way that is light and spirited as if we are having a cool conversation. I know that deepening my ability to express the “fun of math” is going to be an area of growth for me because I have been brainwashed into thinking (like many of us were) that math is serious and hard. I STILL have to unlearn this when working with older children.

How can I document their learning decisions so I can create more opportunities to engage, process and reinforce key concepts while also expanding their cognitive boundaries? Right now I am reading A Guide to Documenting Learning: Making Thinking Visible, Meaningful, Shareable, and Amplified by Silvia Rosenthal Tolisano and Janet A. Hale in the hopes of deepening my knowledge and finding answers to this complex question. I also find that this Math Mindsets Teaching Guide from YouCubed will be incredibly helpful in my professional learning journey.

So as I think about our first unit of inquiry in our stand-alone Programme of Inquiry (POI), I find this a wonderful opportunity to develop play as a stance to inquiry maths. Here’s the unit:

Central Idea: Exploring patterns and solving problems empowers us to think mathematically

An inquiry into how mathematicians . . .

1.Construct meaning based on their previous experiences and understandings
Make meaning from what they understand

2. Transfer meaning to connect and deepen their knowledge and understanding
Make connections to deepen their knowledge and understanding

3. Apply their understanding of mathematical concepts as well as mathematical skills and knowledge to real life situations
Use what they understand to solve problems

CONCEPTS – Connection Reflection
ATTITUDES – Independence Confidence
LEARNER PROFILE: Knowledgeable Communicator

 

I am considering what provocations would allow the students to “to show what they know”–which is really the essence of our first unit.

Before I do any provocations though, I have to survey and collect data. Nothing fancy, but I need to know their answers to the following questions and then analyze their answers to make informed choices on how we can create invitations to play in mathematics. Also, it helps me to assess the Key Concept of Reflection. aflThese are the open-ended statements that can help me understand where the students are now:

  1. Math is……
  2. Math makes me feel…..
  3. Math is fun when….
  4. I do math by…
  5. Math is everywhere (agree or disagree) because…..

Here is some of the brainstorming that I am considering for “provocations” to begin to shape our awareness in our daily lives and help create an authentic invitation to play. (By the way, this is my first thinking–I haven’t collaborated or researched with peers–so this is raw and rough ideas, happening in real time on this blog):

  • The ole’ suitcase: Place inside a seemingly odd collection of items from everyday life  that represent mathematical strands* like a pair of pants (measurement), a bottle of water (shape and space), a license plate (number and pattern), a bag of candy (data handling), a clock (number), a map (shape and space), some rocks or shells (data handling/number and pattern), some tape (measurement). Then have students pair up, select an item, and discuss the guiding questions. Record their thinking onto SeeSaw.

(*May I just say that I know that selecting those items and arbitrarily labeling them in particular strands is a bit comical because I know that the students will come up with more interesting ideas and connections than I ever will. But this is just an “accounting task” to ensure that, in my adult mind, I’ve covered all possible topics.)

The Guiding Question(s): If math is everywhere, then how are these things related to math? What math might someone have used to create these things?–What ideas were people thinking about when they made these items? (Key Concepts: Connection, Perspective)

The next day, we would need to share those survey results with the class so that students can start developing their identities as mathematicians. We’d probably come up with a display and have the students do a gallery walk and discuss what they noticed. Then I would set out these items and ask a follow-up question: If you were to sort these items, which things would you put together and why? (This is just to further identify the connections they’ve made)

Up until this point, I am just trying to kill two birds with one stone: plant a seed that math can be everywhere and collect data about their thinking. But now I have set up the opportunity to have purposeful math discussions through invitations to play.  Of course, the types of tools and learning situations that can be engaged through play will obviously vary based on the survey and the data collected from the provocation.

But I think we could set up a variety of “challenges” or authentic contexts that can be steeped in play-based situations.

Example: The Challenge: Your mission should you accept it……

  • Fill the cup: using a straw and this bowl of water, how might we fill the cup to the line?

Possible Tools: drinking straw, spoon, soap pump, timer, popsickle sticks, paper, pencils

Because I didn’t ask for a particular tool to be used, then this becomes a more open-ended task, allowing more choice and helps me to get data on the student’s thinking. This amps up the play quotient and math possibilities.

Possible teacher questions: What if you used a spoon (or straw, or soap dispenser, etc..), how might this change your results? How do you know that you have completed this challenge? How might you do this challenge faster? How do you think we could record your success?

This forward planning for a provocation and “play-storm” is really just the beginning. In less than 2 weeks, the doors will officially open and learning will officially commence for the 2018-2019. I couldn’t be more eager to approach this year’s learning with a dedication to play, taking their ideas and imaginings and connecting them to math learning that matters to them is going to be important and fun work. As I consider the possibilities with play, it gets me really excited. I hope, no matter what age we teach, educators see the value and need for play in developing mathematical thinking.

 

Surprising Reasons Why You Should Moo and Not Oink

Surprising Reasons Why You Should Moo and Not Oink

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“Why do we even bother educating children in the first place?” This question posed by Tom Hobson (aka, Teacher Tom)  really made me pause and reflect on the value of an education during the recent Pedagogy of Play conference. He suggested that treating school as if it was preparing children for the unknown jobs of tomorrow as rather silly when vocational training is really the domain of corporations and businesses and instead we should prepare students to be involved and caring citizens. In fact, he reminds us that our youngest learners today will be the creators of “those jobs of tomorrow”, so we should be dedicating our learning time to problem-solving and making informed decisions in order to develop sound critical thinking skills and creativity.

My favorite antidote he shared is how he takes out his box of toy farm animals on the 1st day of school, grabs a pig, and says to a 2-year old, “A pig says Mooooo!” just to get a reaction and get the kids thinking.  pig as cow.jpgHe wants to provoke them into questioning this information and seeing if it adds up to the experience and knowledge that they have about their world around them. I just loved that! I love it for so many reasons because this seemingly small moment opens up the possibility to learn that…

  • We need to really listen to what people are saying.
  • We can challenge information that seems “off”.
  • We have a responsibility to debate and deliberate information so that we come to a greater understanding of each other’s perspective and understanding of “the truth”.
  • We build intimacy with others by having difficult conversations with friends and family rather than destroying it by allowing misunderstandings to linger.

As I reflect more deeply on this idea, I find it imperative to have these “safe” opportunities for students to question authority so that they can learn how to express ideas with kindness and courtesy. We need children to look at us in the eye and say, “Hey silly, pigs go oink, not moo.” And we can lean back and laugh, acknowledging that the correction of information came from a need to develop connection and trust between us. Providing these sorts of opportunities to have them question the “truth” of information is really a critical need, particularly as we reflect on how technology is shaping our society. We need for them to get a sense of confusion and wonder so we can express our knowledge and debate our understanding–even if it doesn’t change peoples minds–the essential outcome is that they are thinking and challenging why they believe the way they do.  This habit begins in our earliest years of life and we have, I believe, an obligation to nurture it throughout their lifespan in our educational systems.

I’m a believer!-Provoking thinking and offering up opportunities for debate should be on our “schedule” of learning every day. As I think forward to this school year, I’m wondering how I can instigate and give more space to these small moments for arguing issues that matter to them. Honestly, I think opportunities will present themselves and it just becomes a matter of allowing the discussion to take place, honoring their need to feel heard and engaging in dialogue. Because these moments are so vital to developing the brain along with the heart, I will put “challenging the moo” on my list of learning objectives for this year.

 

#Inquiry in the #PYP: From Paper to Practice: 5 Approaches for Provocations (that “Stick”)

#Inquiry in the #PYP: From Paper to Practice: 5 Approaches for Provocations (that “Stick”)

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Even though we all use ‘the framework’, we have all sorts of curriculums in our schools.  Some schools use the PYP Scope and Sequences, others use their national curriculums and yet others look at curriculum like a buffet- take a bit of AERO Standards, some of this from the Common Core and a portion of  NGSS (Next Generation Science Standards). (Nevermind that most schools don’t even acknowledge any Technology Standards) Whatever approach you take to the “Written Curriculum”, you have to bridge what you put on paper with what is the “Taught Curriculum” is going to look like and how on Earth are you going to let student agency influence it.

This sort of tension is what I am really thinking about and concerned with–how are we going to shift our thinking about the “Written Curriculum” being the driver into it being the “map” that we can use to go on divergent paths created by student’s interests. And I think solid provocations are the “starting line” from which are learning journey begins. Although I have written about provocations before, I wanted to come at from a different angle from the ideas presented from the book, Made to Stick. (I am a huge fan of the writing of Dan and Chip Heath). Because at the heart of a provocation, we want it to leave an indelible mark and make a real impact on students’ thinking in order to create action and authentic agency.  They would call this type of learning “sticky”. (Don’t you love that?)

But the challenge of creating a provocation is that you know too much. The Heath brothers term this, the Curse of Knowledge. Here’s what they mean:

It’s a hard problem to avoid—every year, you walk into class with another year’s worth of mental refinement under your belt. You’ve taught the same concepts every year, and every year your understanding gets sharper, your sophistication gets deeper. If you’re a biology teacher, you simply can’t imagine anymore what it’s like to hear the word “mitosis” for the first time, or to lack the knowledge that the body is composed of cells. You can’t unlearn what you already know. There are, in fact, only two ways to beat the Curse of Knowledge reliably. The first is not to learn anything. The second is to take your ideas and transform them.

Stickiness is a second language. When you open your mouth and communicate, without thinking about what’s coming out of your mouth, you’re speaking your native language: Expertese. But students don’t speak Expertese. They do speak Sticky, though. Everyone speaks Sticky. In some sense, it’s the universal language. The grammar of stickiness—simplicity, storytelling, learning through the senses—enables anyone to understand the ideas being communicated.

(From Teaching, Made to Stick, by Dan and Chip Heath)

I can really relate to this, especially when I taught older students because I thought they already “knew stuff”. With that in mind, provocations can really reveal what students are thinking and feeling.  So now that you have the context of why provocations can be so powerful and transformative for student learning, I’d like to share with you 5 approaches for provocations (that “stick”):

1.Unexpected: Create curiosity and pique interest with unexpected ideas and experiences that open a knowledge gap and call to mind something that needs to be discovered but doesn’t necessarily tell you how to get there.

Example-Central Idea: The use of resources affects society and other living things.

Take out all the classroom resources that are made from petroleum products after school one day. The next day,  have the students come in and be shocked?-where did all those resources go? Then have them consider what these resources have in common. And then have them consider the impact on society if these non-renewable resources went away.

2. Concrete: Ground an idea in a sensory reality to make the unknown obvious.

Central Idea: Economic activity relies on systems of production, exchange, and consumption of goods and services.

Create a classroom economy by “printing” money and having students create businesses. Turn all of your classroom resources into “commodities” or by providing services (like sharpening pencils) to illustrate the conceptual understandings. This provocation goes on for weeks, by the way, so that they can experience the related concepts of scarcity and marketing.

3. Credible: Demonstrate ideas and show relationships to “prove” a point.

Central Idea: Informed global citizens enhance their communities.

CRAAPgraphicGo through news articles either on a social media news feed or through an internet search on a topic that is relevant and interesting to your students or controversial (ex: climate change). Have the students examine at least 3 websites or sources of information and put them through the filter of the CRAAP test.

4. Emotional: Powerful images, moving music, role-play–anything that incites either strongly positive or negative feelings.

Central Idea: Homes reflect local conditions and family’s culture and values.

Using images from photos of children’s bedrooms from around the world have the children try to match the picture of a child with a picture of a bedroom. Why do they think those images go together? What evidence in the photo might suggest the values and culture of that child’s family?

5. Story: Use a story, whether from a book, a video or from your own life, to illustrate a challenge or provide a context worth exploring.

Central Idea: Our actions can make a difference to the environment we share.

Share the story of One Plastic Bag and have students reflect on the impact her small action had made in her community. What would you do with a plastic bag? (During our  1st-grade classes’ personal inquiry time, students were invited to take some plastic bags and play around with those materials. It is interesting to see who and how they took action.)

So there you go. These are just 5 approaches to 5 central ideas. Crafting provocations are probably one of the best things I love about the PYP and when we share insight into how we can approach these central ideas, I think it elevates everyone’s schools because of the insights gained.  I’d love if others could share and post ideas for provocations to further illustrate the importance that they play in deepening our students learning and inspiring authentic connections and action.
#ChangeInEducation: Setting a Match to the Report Card? A Couple of Questions on #Assessment in the #PYP

#ChangeInEducation: Setting a Match to the Report Card? A Couple of Questions on #Assessment in the #PYP

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I hate report cards. Hate is a strong word, but I think they are an outdated form of educational technology and we need to set a match to it. 31479586_199389720679114_1677575111550435328_nI can’t believe they haven’t gone by the waste side yet, like horse-drawn carriages or 8-tracks. It doesn’t serve where we are in education and what we know about learning and teaching. And, as a parent, the letter A (approaching), M( meets) and E (exceeds) next to a subject area with a couple of sentences that explains the justification of those letters really doesn’t help me figure out how I can support my child. And, as a writer of those comments, knowing that parents are intended audience for these report cards, you end up summarizing the skills gained vs. the conceptual understandings–because at the end of the day, parents just want to know if their kids can read and do math up to the “standard” of their peers. So really, the report cards provide late feedback that schools may feel “report” the learning but ultimately doesn’t serve any of the stakeholders involved, students included.

Let me elaborate a bit more. I am risking embarrassment here for the sake of all of us to reflect and consider how messy and difficult it is to create “reports”.

Here is an example from our school of how we are to create continuums of learning of our conceptual understandings.

vis template continuum

This is a template, an exemplar, if you wish, so how does THIS match our report cards? Well, I have to comment on the subject areas and the learning outcomes of the unit and this model really haven’t helped me decide how to grade them in Reading, Writing, Speaking and Listening, let alone Transdisciplinary Maths, Social Studies or Science. So in our current How We Express Ourselves, we changed the headings a bit and tried to offer more specifics into assessing their conceptual understandings.  I still feel like this is an epic fail.

express oursleves

So now that I shared with you the pseudo-continuum for students,  would you like to see what a typical report card is on this unit?

Here are the outcomes that I have to grade:

manageBac
Parents don’t actually see the learning outcomes that we are grading against. They just see those letters next to the strands.

Now here is a comment, written for the parent’s interest, as it related to the Strands that they will see. (Math comments were made in the Math Stand Alone section of the report)

Strengths

Student X is a wonderful communicator so this has been great unit for him to expand and improve his skills. In particular, he has learned how he can interact and provide constructive feedback on other’s work, as well as reflecting on the comments other’s have made on his.

Learning Target

Although Student X has grown a lot with recognizing and writing words, he has a challenge with staying focused on longer texts. This impacts his ability to read fluently at higher levels.  As a writer, he is developing his ability to expand upon and give details in his writing so that a reader can “see” the setting and conflict within a story.

Now I warned you that this is an epic fail!–Can you see my point??? What would you do if you were in my situation, short of writing pages of commentary?

My school encourages us to come up with conceptual continuums but then want us to write concise and helpful comments that provide suggestions for next steps that parents could use for supporting learning at home. Total mismatch. And this isn’t a bad reflection on my school–this discrepancy is in nearly EVERY school! I believe this isn’t a one-off derelict example–this is a normal challenge that I reckon PYP schools have. We use a concept-based curriculum and yet we have these report cards focused on skills and knowledge. What are we to do?

I’d really like to challenge our schools to think a bit more deeply about how this communication tool, the report card, could look as we think about how our PYP schools share this philosophy around life-long learning.

What would it mean if we were to think about this through the lens of constructing meaning over time?

Do we need to have “reporting” due dates? What if our communication with parents was more detailed and frequent? Would this thing called the “report card” even be relevant?

And another question that pops into my head, as I think more about this is:

How might we co-construct meaning when we include The Learning Community?

So instead of report cards talking about the student, what if they included student voice, choice, and ownership? And what if families could chime in with evidence of learning? Again, would report cards even be relevant?

I just keep thinking about how assessment is going to look with our transition in thinking of data to inform learning and teaching with a collection of evidence vs summative tasks that help us mark those boxes in our report cards. Jan Mills refers to this as creating a “tapestry” of the children’s learning.

I have strong feelings about this–if you couldn’t tell. And I’d like to set a challenge for myself to really push my thinking about what could and SHOULD replace the report card. Yes, digital portfolios like SeeSaw help to bridge our next steps, but this institutional tool needs to evolve. Badly! I really want to do some deep thinking around this. Anyone else with me on this quest?

 

#PYP: Sticky Learning: Moving from a Topic to a Conceptually based Central Idea

#PYP: Sticky Learning: Moving from a Topic to a Conceptually based Central Idea

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As an early years teacher, it’s not hard to notice that so many national curriculums are “pushing down” learning skills and content knowledge. So a common traditional approach in preschools and kindergartens has been teaching the literacy and numeracy skills through topics. You teach an “Animals” unit, a “Farm” unit or a “Weather” themed unit.  So when I was recently asked if I could help write a Central Idea for a unit on “sound” for nursery age students, it harkened back to those days for me. Since I know how difficult it can be to break those habits of thinking about teaching those skills through a topic, I thought there might be others out there who’d like to figure out how to take a topic and have it evolve into a conceptually-based unit and I decided to disentangle this approach in a blog post.
First of all, what is all the hubbub between a topic and a concept anyhow? Let’s just get that squared away before we go further. made-to-stick_quoteA classic definition of a concept is an enduring understanding that is broad enough that you can transfer it across disciplines and time. But I’d like to add that a concept is something that makes you think, makes you wonder, gets those neurons firing. A topic fades from your mind, just like a rainbow after a shower–it seemed lovely at the moment, but quickly disappears from your memory. You see that quote from Chip and Dan Heath–our goal whenever we write a Central Idea is nearly the same–an idea so profound that an individual could spend a lifetime learning about it. This is why the PYP makes such a fuss about developing conceptual knowledge and skills. Learning facts and skills without a context is a waste of time and often evaporates unless we make units that are “sticky”.  Concepts are like a bad rash that won’t go away. Concepts get under our skin and stick with us and reappear in new contexts that broaden our perspectives.
I’d just like to say that writing a central idea is easier than you think, but first, it’s important to ask Why is this worth knowing and How does it connect to other learning? –This is especially true for younger students since they have limited life experience to draw upon. No matter what ideas you bring forward in the learning, this is where we start. In a previous post, #PYP: 3 Things to Consider when Evaluating a Programme of Inquiry, I reiterate the driving force behind the Written Curriculum, in which Central Ideas are developed to be engaging, relevant, challenging and significant.  Here is how the IB defines them:
Engaging: Of interest to the students, and involving them actively in their own learning.
Relevant: Linked to the students’ prior knowledge and experience, and current circumstances, and therefore placing learning in a context connected to the lives of the students.
Challenging: Extending the prior knowledge and experience of the students to increase their competencies and understanding.
Significant: Contributing to an understanding of the transdisciplinary nature of the theme, and therefore to an understanding of commonality of human experiences.
So when writing a UOI, I start with related concepts. “Sound” is typically considered a topic all by itself and it would really narrow the learning experiences of students. However, if you add the related concepts, then it makes the unit more conceptually based. Taryn Bond Clegg shared a helpful list of these related concepts.
So, let’s have a think about concepts that sound is connected to…..
The concept of Pattern can examine sound relationships such as rhyme, rhythm, tone, and pitch. It’s also a great math link.
The concept of Properties can make a connection to materials and how it impacts the quality of sounds. This also makes a great math link for attributes and data.
The concept of Imagination is another one that could make for an engaging unit, as the students in this year group can interpret sounds and make images related to sounds they hear  (Interpretation is another concept that might be relatable.)
So, looking at those related concepts, now it’s a matter of determining what’s relevant and worth knowing for your students. I’d choose one of those concepts and write a simple central idea–especially if they are 3-5 year-olds. Anything longer and more sophisticated is just “blah-blah language” (a term described by a 4-year-old to me once. Bless his heart.) The younger ones are constructing meaning, so let’s honor that’s where they are at developmentally.
Examples of UOIs that reframe this topic into a conceptually based learning unit might be:
Discovering patterns help us make sense of our world.
The properties of a material determine how it is used.
The interpretation of sounds can spark our imagination.
The intention is for students to construct the meaning of these concepts and we can embed the topic of “sound” in our lines of inquiry.
For example: Discovering patterns help us make sense of our world.
  • what is a pattern (form)–thinking about beat and rhythm
  • how we use sound to make patterns (function)
  • patterns in language (connection)–rhymes and poems
  • different ways we can change a pattern (change)–tone and pitch
  • patterns in our world (reflection)–sounds can be a learning lens for this
 (I bet if I had a music or performing arts teacher sitting next to me, they’d be nudging me with more examples.)
For older students, we can expand this Central Idea:
Discovering patterns help us make sense of our world and spark our creativity.
*the and in that Central Idea invites students to move from exploration to creation of the concept of patterns because we would expect older students to be applying knowledge since they’ve probably already constructed a basic understanding of this concept.
However, I wouldn’t say that Central Ideas have to be lengthier or all about applying knowledge in upper-grade levels. They will likely come across concepts are entirely new, and there would be a danger of “overpacking” a Central Idea. More complex concepts might be biodiversity, government, and networks. We’d want central ideas to go deep, not wide, and yet provide for a multitude of student inquiries. Consider the challenges in teaching the following Central Idea:
The well-being of an ecosystem can be determined by its biodiversity.
If this is the first time that students are exposed to the concept of an ecosystem, then this will make for a challenging unit because the teacher will have to ensure that the students have that understanding of food webs before they can build upon it to get the concept of biodiversity. Make sure it has been explored in previous units or rewrite the Central Idea so that it’s simplified:
The growth of living things determines the well-being of an ecosystem.
The “blah-blah language” has been diluted and now the focus is developing a strong foundation. Hey, I heard you in the back of the room-Can you write biodiversity into a line of inquiry? No, I would caution it simply because you are adding another level of complexity and decreasing the chances that students feel confident to drive their learning.
I’m not sure if this helps in clarifying how to write concept-based Central Ideas but at least these ideas should get you started in writing units and hopefully empowers your approach to writing a central idea and a unit of inquiry. Remember: If a central idea “sticks” in your mind, then it’s probably worth spending time inquiring into.

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