Be an Inquirer

Teacher leaders embrace an inquiry stance to focus on learning while not stopping forward progress.

As a former Primary Years Programme Teacher and Coordinator, I know that taking an inquiry-approach to classroom instruction is fundamental. However, inquiry shouldn't just happen in front of students. It's about taking an inquiry stance all the time, which means being a curious learner as a teacher leader, with oneself and with one's students.

As a leader, if you notice something happening in a mathematics classroom that confuses, angers, frustrates, or saddens you, your first steps should be to ask questions to understand. Avoid blaming, shaming, sharing your anger, belittling, or accusing. Instead, ask simple, open-ended, non-confrontational prompts like "Can you help me understand?" As a teacher leader, your goal is to ask questions not to challenge, but because you're curious.

This inquiry stance should also be applied to your own classroom. When something doesn't go quite right, ask yourself, "What can I learn from this experience?" Instead of getting bogged down in shame and embarrassment, focus on what you can do to improve.

To model this inquiry stance with students, start by showing them how to be curious and how to ask questions. You can also model how to solve a problem and the questions you ask yourself as you tackle it. When asking students questions, try to understand their thinking instead of trying to fix it.

You’ll also want to keep in mind the balance of confusion and understanding in your classroom. As MaryAnn from the Making Meaning of Operations case book said, "This situation made me wonder about the wisdom of leaving students in the middle of a misunderstanding," (Case 14, p. 52). We need to find a balance between acknowledging when students' lines of thinking are incorrect with not stopping their forward progress. And as case 18 and case 9 from the same book illustrate, we can find fascination and value in discussing different ways to approach a problem and different perspectives. By embracing an inquiry stance, we can create a more collaborative and engaging learning environment for ourselves and our students.

Concepts in the PYP

In January 2018, the elementary teachers in our district's two PYP schools set out to explore the enhanced PYP content that make up the document "PYP: From principles into practice." Many thanks to fifth grade teacher and guest blogger, Lauren Ryan, for authoring this post on concepts in the PYP.

As an educator in the fast-paced, digital era of the 2000s I feel fortunate to be a teacher at a PYP school where inquiry, curiosity and student-centered learning is celebrated. I remember seeing a meme on the Internet a few years back about how readily information is available to people in today’s world. It depicted a math teacher from decades ago saying to his class of students who were sitting in well defined, compliant rows, “Now you better memorize this because it’s not like you’re going to be carrying a calculator around with you in your pocket every day.” Enter a picture of a pocket-sized smartphone.

People today have access to endless amounts of facts and information at the click of a button, on a device that is regularly not more than a few feet from us at any given point. It makes me wonder what a teacher can provide to her students in today’s world that they can’t receive from a quick Internet search. The answer- a conceptually-based, inquiry driven curriculum.

The Primary Years Program says that “concept-based inquiry is a powerful vehicle for learning that promotes meaning and understanding, and challenges students to engage with significant ideas.” It is a way for learning to be built around big ideas that transfer across subject areas and can be applied to new situations. The seven Key Concepts defined by the PYP are form, function, causation, change, connection, perspective and responsibility. Teaching through these concepts allows me to help students construct mental models of how things work and connect throughout the world. It is a way to connect new, abstract, or complicated learning with things that students already know and to extend their learning to new ideas and topics.

An example of this is when I taught first graders about addition through the concepts of change and balance. While addition can feel complicated and abstract for students, I was able to help students explore the idea that an addition sign will change a number by adding more to it or making it bigger. We also explored the idea of balance when thinking about the function of an equal sign. The equal sign is often thought of by kids as meaning “the answer”, which is a narrow way of thinking and has implications for future learning when it comes to more complex math topics, such as algebra. Additionally, we looked at the concept of balance so that students understood the idea that both sides of an equal sign had to be the same. Looking at addition through the lens of balance helped our students make the connection to the idea of “same as” instead of just “equal to”. For example, we read basic addition as 2 + 2 is the same as 4 rather and just 2 + 2 = 4. Now, as an intermediate teacher I value conceptual teaching even more as I see how much more successful a student can be when he or she is able to make connections to previous learning and transfer past knowledge to new situations.

In general, concepts help guide the way I construct learning experiences in the classroom and they help my students think critically about big ideas. They are a launching point for questions around a topic and help students develop their curiosity and understanding. When key concepts are too broad, related concepts act as way to explore concepts in more detail or to add depth to an area of study. Related concepts are narrower and more focused, often addressing content specific information, or standards that must be addressed on a more local level.

Knowledge is accessible nearly everywhere in today’s world, but true understanding of the world is the heart of what a PYP teacher’s role is in preparing students for success in school and beyond. Key and related concepts allow teachers in today’s age to root essential learning of skills, facts and knowledge in concepts that are deep, transferable, broad, abstract and not locked in place or time, so that students are able keep pace with a fast-moving world, full of complex systems and relationships.

As a PYP teacher I feel I get to address the evolving needs of students in an environment that encourages me to think about the enduring understanding I want my students to walk away with. An area of action for me is to be more intentional about teaching conceptually in stand-alone units or in content areas that do not align directly with a unit of inquiry. This might look like writing concepts on my “Learning Targets” bulletin board, or leading a lesson with questions about a topic that are concept driven. It might also look like backwards planning an ELA or math unit thinking about the long term concepts or deep understanding I want my students to understand and creating lesson content that will drive towards deeper conceptual understanding of a topic.

As a school, PYP buildings have a unique opportunity to provide students with common language that develops the skill of conceptual learning. All teachers, from kindergarten through intermediate grades, can teach students to recognize patterns in learning and talk about content in terms of key concepts. This can be supported through collaborative time for team teachers to plan units and lessons that align with concepts that will provide students with common and rigorous learning experiences and through vertical alignment of content so that conceptual understanding begins at a young age and is carried on through a child’s PYP experience. Furthermore, PYP coordinators can work with their teachers to develop skill as writers of curriculum and help craft lessons and units that are conceptually driven and be provided with support for developing inquiry opportunities that support students’ ability to access curriculum in a way that connects to their natural interest and prior knowledge.

Source:
The PYP Curriculum Framework. International Baccalaureate Organization, 2005-2018, <https://resources.ibo.org/pyp/works/pyp_11162-51681?c=2972d4b6>

KNOW THY IMPACT: Using Hattie's Math to Determine Your Impact

John Hattie is an invaluable researcher in the field of education. His way of looking at the impact of particular influences on student achievement helps educators around the world shift the conversation from what works to what works best.

http://www.education.vic.gov.au/Documents/about/research/ravisiblelearning.pdf

Despite this, Hattie's research can sometimes seem removed from life in the classroom as the effect sizes that he presents in his books are based on very large research studies. Teachers may lament that it is hard to know if the large effect sizes of some the most impactful influences can be replicated in their classrooms, with their unique students.

Until now.

In his book Visible Learning for Literacy (2016) that he co-authored with Fisher & Frey, Hattie encourages teachers to reflect on the impact of their own instruction and presents a formula for calculating effect size in their classrooms.

Being able to calculate impact in this way gives teachers the mathematical ability to quantitatively see if instruction is having an impact on their students' achievement and who is not being impacted too. Armed with this information, teachers are able to adapt their teaching as to maximize their effectiveness for the benefit of all students in their classrooms.

In order to calculate effect size, Hattie suggests that:

• Lessons have clear learning intentions.
• Lessons have clear success criteria.
• The success criteria indicate what quality looks like.
• Students know where they stand in relation to the criteria for success (p. 136).

With this in place, teachers only need a pre-assessment and a post-assessment score to be able to calculate effect size.

Below, I demonstrate how to calculate effect size by analyzing students' thinking from an inquiry lesson I recently taught with third graders. The lesson is fully described here: Inquiry into Moon Phases.

What did I want students to learn?

During the lesson, our goal was to answer this essential question:

What would success look like?

A successful response will ...

• Contain academic science vocabulary related to the lesson (1 pt awarded for inclusion of each of the following:
• observe, Earth, Moon, change, orbit, shadow, light, new moon, crescent moon, full moon, phases*, Sun*, reflecting*, darker*, lighter*
• *Not introduced during the lesson, but still important scientific terms that came out during the post-assessment.
• Contain different ideas (1 pt awarded for each complete idea)
• examples of complete ideas are: the moon orbits the earth, the moon reflects the sun's light, the shadow gets bigger as the light gets smaller, the full moon is when the moon is all it up).
• Be accurate
• 4 pts awarded for accurate statements with details/evidence,
• 2 pts awarded for semi-accurate statements with little details/evidence and some misconceptions
• 0 pts awarded for inaccurate statements with no details/evidence and many misconceptions

How do I know they've learned?

Assessment task: The task for the pre-assessment (measure of what students initially understood, knew and could do) was the same as the post-assessment (measure of what they learned). For both, I prompted:

• "Write what you think the answer to our essential question is. Make sure to include scientific vocabulary in your response."

To calculate effect size (p 138)

1. Analyze the pre- and post-assessments.

This step was a snap, thanks to the pre-established success criteria. I recorded these results in a Google Sheet:

	Total pre	Total post
Student A	9	13
Student B	8	12
Student C	5	11
Student D	3	6
Student E	6	14
Student F	2	12
Student G	3	13
Student H	7	13
Student I	7	10
Student J	6	10
Student K	3	16
Student L	3	12
Student M	2	13
Student N	3	13
Student O	2	11
Student P	6	4
Student Q	2	14
Student R	4	11

2. Find the average of the pre- and post-assessments

Using the average formula (=AVERAGE) this step was easy too!

• Average pre: 4.50
• Average post: 11.56

3. Calculate the standard deviation for the pre- and post-assessment and then find the average of the two standard deviations.

This step was super simple too, as the Standard Deviation formula is just (=STDEV).

• Standard Deviation pre: 2.28
• Standard Deviation post: 2.83
• Average Standard Deviation: 2.56

4. Determine effect size

Using Hattie's formula: (Average Post - Average Pre) / Average Standard Deviation

• Effect size: 2.76

This effect size is quite sizable and is most definitely off the scale of the Barometer of Influence that Hattie presents in his work. Some things to consider:

• Whereas this is a large effect size, it is just a number. With this quantitative data, a teacher should also reflect qualitatively:
• In what ways did the students grow the most?
• What about the lesson was successful that should be replicated?
• What wasn't successful that can be eliminated?
• This was just one lesson and the sample size is minute, compared to the studies Hattie typically meta-analyzes. Therefore, little relative importance should be placed on this effect size. After several weeks of working on making scientific observations using scientific language, another assessment could be administered to see if students have continued to show growth with this skill.

5. Determine individual effect sizes

Although the impact of this lesson was quite high on average, that is not necessarily the case for all students. By calculating individual effect sizes using individual assessment scores and the average Standard Deviation, you can see for whom this lesson was successful and for whom it was not.

	Individual Effect Sizes
Student A	1.56
Student B	1.56
Student C	2.35
Student D	1.17
Student E	3.13
Student F	3.91
Student G	3.91
Student H	2.35
Student I	1.17
Student J	1.56
Student K	5.08
Student L	3.52
Student M	4.30
Student N	3.91
Student O	3.52
Student P	-0.78
Student Q	4.69
Student R	2.74

The effect sizes of these individual students is also beyond the scale of Hattie's Barometer of Influence presented in his work. I don't believe that is important though. What is important is to look at the individual effect sizes in relation to one another along with looking at students' thinking and reflect:

• What causes one student (student F, for instance) to make sizable gains, whilst another student (like A or B) just grew marginally?
• What kinds of thinking are these students demonstrating?
• What about the teaching made such an impact on these students that could be replicated in the future?
• What about the teaching caused other students to not gain as much that should be avoided or adapted in the future?
• What do these students need next in their learning?

Below, I've included some samples of students' thinking:

Student F Pre:

Student F Post:

Student N Pre:

Student N Post:

Student O Pre:

Student O Post:

Although most students showed they learned a great deal during this lesson, Student P did not do as well on the post-assessment as he did on the pre. Using this quantitative data, a teacher must look more deeply at the student's response and reflect:

• What kinds of thinking is this student demonstrating?
• What about the teaching had a negative effect on this student's learning that should be avoided in the future?
• What does this student need next in their learning?

Student P Pre:

Student P Post:

Being able to calculate effect size to determine what works best for individual students is powerful and has the potential to transform the ways which we respond to students. How could you use Hattie's math to determine the impact of your instruction on individual students' achievement?

Helping Students be Successful by using the Gradual Release of Responsibility Model

I recently had the opportunity to teach an inquiry lesson to third graders, during which we explored how the moon appears to change during the month. (The lesson is fully described here: Inquiry into Moon Phases). The essential question that we were seeking to answer during the lesson was:

One of the goals of the lesson was that students would be able to accurately describe how the moon looks like it changes during the month and provide evidence/details about what is really happening. In order to get them to meet this goal, I used the Gradual Release of Responsibility model, as described by Doug Fisher in the article Effective Use of the Gradual Release of Responsibility Model.

Focus Lesson/Modeling (I DO IT)
After walking around a model of the moon in the dark (with a flashlight pointed at it) and observing how the moon looks like it changes, we returned to the classroom and began to draw our observations out on a Moon Calendar (we used pictures to help us remember). After week one, we paused so I could model how to make a scientific statement.

On the board, I wrote the sentence stem, "I observe ..." and modeled how I would describe how the moon looked like it changed during week #1.

I said, "I observe that the moon looks like it is changing because the shadow on the moon is getting bigger."

I asked students to notice which scientific words they heard and added those to a bank of science words on the board, by the sentence stem. I added moon, changing and shadow.

Guided Instruction (WE DO IT)

We continued to draw our observations out on the Moon Calendar. After week two, we paused to make a scientific statement together.

I asked for volunteers to describe how the moon looked like it changed during week #2. I guided the volunteers to use the sentence stem, "I observe ..." and as many scientific words as possible. When students said scientific words that weren't yet in our word bank, we added them (eventually that list grew to 9 words).

As I guided different volunteers to describe how the moon looked like it changed during week two, my responsibility as the teacher was to:

• encourage them
• celebrate their effort and successes
• give feedback on how they could improve by
• adding more scientific words
• including additional new ideas
• addressing misconceptions

Collaborative Learning (YOU DO IT TOGETHER)

We continued to draw our observations out on the Moon Calendar. After week three, we paused to so that pairs of students could make a scientific statement together.

I asked the students to think about how the moon looked like it changed during week #3. I reminded them to use the sentence stem, "I observe ..." and as many scientific words as possible. After students had a chance to think, I invited them to pair up and share their scientific sentence with a partner.

After 1-2 minutes, I signaled all the students back together and randomly chose 3 different pairs. As one partner said their scientific sentence, the other partner was in charge of counting how many scientific words they used. 

As the different pairs described how the moon looked like it changed during week three, my responsibility as the teacher was to:

• encourage them
• celebrate their effort and successes
• give feedback on how they could improve by
• adding more scientific words
• including additional new ideas
• addressing misconceptions

Independent Learning (YOU DO IT ALONE)

We continued to draw our observations out on the Moon Calendar. After week four, we paused to so that individual students could make a scientific statement.

I asked the students to think about how the moon looked like it changed during week #4. I reminded them to use the sentence stem, "I observe ..." and as many scientific words as possible. After students had a chance to think, I randomly chose 3 different students to share their scientific sentences with the class. As each student shared, the rest of the class counted how many scientific words they used.

As the different students described how the moon looked like it changed during week four, my responsibility as the teacher was to:

• encourage them
• celebrate their effort and successes
• give feedback on how they could improve by
• adding more scientific words
• including additional new ideas
• addressing misconceptions

Post-Assessment

After gradually releasing responsibility to the students to describe how the moon looked like it changed during the month, I asked them to respond to our essential question (just as I had at the onset of the lesson for a pre-assessment):

The difference between students' response to this question at the beginning of the lesson versus the ending was astonishing. Below is a sample of students' responses. It is clearly evident how much they grew during this lesson in their ability to accurately describe their scientific observations.

Student #1 PRE:

Student #1 POST:

Student #2 PRE:


Student #2 POST:


Student #3 PRE: 


Student #3 POST: 

By slowing and gradually releasing responsibility to students, they were ultimately able to independently describe how the moon changes during the month. How do you successfully use the gradual release of responsibility model in your own classroom?

Priorities, daily schedules & the PYP

The language we use and the way we spend our time are reflections of what we value.

In schools that subscribe to the International Baccalaureate's Primary Years Program (IB PYP) our language and use of time must reflect a prioritization of significant, relevant, challenging and engaging learning that is enacted by implementing the PYP Approaches to Teaching. In the PYP, among other approaches, we value:

• inquiry
• a balance between transdisciplinary and disciplinary learning
• concept-based learning
• differentiation
• collaboration

In the elementary school, teachers often post a schedule or timetable in the room, to outline for students the plan for the day. As PYP educators, it is important to ask if our daily posted schedules reflect the priorities of the PYP.

In order to guide them through this reflection, I recently had teachers with whom I work explore PYP expectations and then look at a couple of sample daily schedules.

We first started looking at how the PYP expects us to spend and organize our time:

from IB Program Standards & Practices:

• B2.10.a: The schedule or timetable allows for in-depth inquiry into the transdisciplinary and disciplinary dimensions of the curriculum.

from: Making the PYP Happen

• “To ensure the coherence of the learning from the students’ points of view, it is essential that all teachers in a PYP school see themselves as PYP teachers, and are fully committed to and engaged with the philosophy and practices of the programme. Within each school community, the approach to the implementation of the programme needs to be holistic, not fragmented by disciplinary teaching,” p. 31.

• “Please note that mathematics, language(s) of instruction, social studies and science need to be the responsibility of the classroom teacher: the teacher with whom the students spend most of their time. Single-subject teaching of these areas is not consistent with the PYP model of transdisciplinary learning— learning that transcends the confines of the subject areas, but is supported by them. Personal and social education is the responsibility of all PYP teachers,” p. 67.

• “The programme of inquiry provides an authentic context for learners to develop and use language. Wherever possible, language should be taught through the relevant, authentic context of the units of inquiry. The teacher should provide language learning opportunities that support learners’ inquiries and the sharing of their learning. Regardless of whether language is being taught within or outside the programme of inquiry, it is believed that purposeful inquiry is the way in which learners learn best. The starting point should always be learners’ prior experience and current understanding,” p. 70.

• “Wherever possible, mathematics should be taught through the relevant, realistic context of the units of inquiry. The direct teaching of mathematics in a unit of inquiry may not always be feasible but, where appropriate, introductory or follow-up activities may be useful to help students make connections between the different aspects of the curriculum. Students also need opportunities to identify and reflect on “big ideas” within and between the different strands of mathematics, the programme of inquiry and other subject areas,” p. 83.

Next, we looked at variety of schedules, continually asking:

• What do we see / notice?
• What PYP approaches to teaching do the schedules reflect?

Then, we thought about our own schedules as we asked:

• What PYP approaches to teaching does my daily schedule reflect?
• How could I adapt my daily schedule / agenda to better align with the PYP?

After I invited teachers to think about ways they could adapt their own posted daily schedules to better reflect the priorities of the PYP, several risk-taking teachers took me up on this invitation. Below are recent schedules posted in their rooms that will no doubt continue to morph as they react to the needs and understandings of their students.

What do you see and notice in these daily schedules? What PYP approaches to teaching do the schedules reflect?

Special thanks to Mrs. Liesener, Ms. Elliott, Mr. Dawson, Mrs. Lorentz, Ms. Erickson and the other teachers who shared their schedules with us!