A second grade math inquiry

At the heart of the IB Primary Years Programme is the belief that learners learn best through inquiry and finding out for themselves rather than being told, and that learning is deepest when learners have a personal connection to the learning and share in the decision making about what they learn and how. In class we have been talking a lot about inquiry -what it means and what it looks like:

  • It’s when you are discovering and finding things out.
  • It looks like you are playing but you are learning at the same time.
  • If you have an idea that you want to try and you do it again to see if it works, that’s inquiry.
  • Sometimes it’s noisy!

This week the children have had opportunities for “free” mathematical inquiry. We talk about how this is not a free play time, but a time to explore a mathematical interest or idea of their own choosing, with a view to finding out more. The children know that they will be held accountable and that at the end of the session they will be asked to share their learning with the group.

To help the children get started, we begin by brainstorming together to come up with some possible lines of inquiry. Over the last two weeks, I have noticed that several of the children have shown an interest in large numbers, often talking about millions, billions and trillions. I suggest that this might be an area they wish to pursue more. We write this idea down on the chart paper. Another child suggests an inquiry into Number of the Day. This is a daily quick mental math activity designed to develop children’s understanding of number. Yet another child left a “really tricky” math problem as a comment on the blog. Several children have risen to the challenge and want to try and find an answer.Marcus's math problem

In the classroom all our math equipment is organised into colour coded baskets and kept in one area. Someone suggests that “we could do inquiry with all of the math in these baskets”. Several other children nod their heads enthusiastically so we add that idea to the chart. Once we have listed some possibilities the children go off to conduct their individual and small group inquiries.

DSCN0165As the children go about their inquiries, I observe to see what “big ideas” the children are exploring. I will take these ideas and interests into consideration when I plan our math engagements over the coming weeks.

DSCN0171By now, the children know they need to record any work that they believe shows their learning -a new understanding or a skill development- for their learning portfolios. The children are learning to do this independently. We have brainstormed possible ways of recording and the children have access to the necessary resources. (In this case, the student decides that a photograph is the best way to record his 3D math work.)

Marus inquiry1
We have talked about collaboration, what it isn’t and what it is: It isn’t some people doing most of the work and others doing little; it isn’t talking about things that are not related to the work at hand; it is working together with someone, building on each others ideas to create something that is better than one person could do alone. Two students come to me to explain that they both have good ideas and they think they can do “even more better” if they work together. At the end of the session, they are delighted with their work. They come and show me, proudly, and decide they want to record what they have done. It is clear that they have been on task and that the end product is more than either student could have achieved on their own.

mathchatAllowing some “free” math inquiry, where the students can choose what to work on, is key to helping them develop enthusiasm and motivation. Students who started the year as hesitant mathematicians, reluctant to take part in some of our numeracy drills, are now choosing to spend their free math inquiry time on these same drills.

DSCN0214One student is so delighted with his improvement, (“This is my best EVER!”) that he asks another student to take a photograph so he can show his parents.

DSCN0197I can see that there is an interest in the pattern blocks that could lead to an inquiry into shape, tessellation or area. I make a note of this; for the moment, I make a teaching decision to focus on developing students’ numeracy computational skills. However, the interest of this group, and of other groups around the room, get me thinking about when and how I will introduce other mathematical concepts in line with our G2 Common Core math standards

Mathchat 1When we come back together for our reflection at the end of the session the children share their work, first in detail with a partner and then a summary for the whole group. These children are learning to think, talk and act like mathematicians. I make a note of the children’s reflections so that I can consider them as I plan next steps.

Building a class learning community

For the first week of school, our primary focus is on building a sense of community amongst the children and the adults they will be working with. The quote below is from “Starting the School Year Right” by Thomas Guskey in The School Administrator, August 2011 (Vol. 7, #68, p. 44)

“The first two weeks are the most important time in the school year for all children … What happens during this critical period pretty much determines how the rest of the year will go.”

It is important that the children have time to get to know their new classmates and to explore and develop relationships. They need to feel safe in their new environment in order to learn. They need to trust and respect the members of their learning community so that they can develop as risk takers and experimenters. Throughout the year they will learn with and from each other as they conduct their individual and group inquiries. Time spent now building a strong learning community and developing a culture of collaboration will stand us all in good stead as the the year progresses.

We talk about how we are all different, with different interests, styles and strengths. The students draw self portraits of themselves, using mirrors to look closely at their own faces.

Self portraits

We read The Important Book by Margaret Wise Brown

This is a wonderful book for helping children to think about what makes them “them”. Once we have read the book, the students sit knee to knee with a partner and share some of the things that they think are important for other people to know about them.


Then the children go off to write. The Principal, Mr Dolesch, joins us for this session. The children see that he is also part of our learning community. Everyone writes for around thirty minutes, after which we all gather on the carpet to share the writing. As the children (and Mr Dolesch) share their writing, those in the audience make connections (we call these “text-to-self” connections) to their own lives.


Eric suggests that we display the writing with the self portraits that we did yesterday. Inbar and Sophie think that we could ask people outside our class to try and guess who the portraits and writing described. Our learning community is growing!

Some students are wondering about how we should decorate our classroom. So far the walls and display boards are empty. Everyone has ideas. I suggest they record their ideas so that we can revisit them over the coming weeks. The children  use a mixture of pictures, diagrams, words -even a collage-  to help explain their ideas for the classroom.

The students’ ideas open the door for mini group inquiries and authentic reasons to write. Ayden thinks we should have a fish tank, with three clown fish and three goldfish. This leads to a discussion about whether the fish would need warm or cold water, fresh or salt water. We conclude that we needed to do some research. We wonder where we could get a fish tank. Maximilian thinks we will need money to buy the tank. A small group of children are planning to write a letter to Mr Dolesch to ask him for some money. Shameer chooses to read a book on how to write a letter during reading time so he can guide the letter writing group

Sophie, Gawan, Dilara and Yunha think we should have plants in our classroom. Several children take action by bring some plants from home to decorate the space. We will develop these ideas further at our class meetings to decide on some next steps for organizing our learning space. Some children have already started a to-do list which includes photographs and special birthday calendar.

As the children get to know each other and begin putting their mark on the classroom, they are developing ownership of the space and of their learning. As they share about themselves and about their ideas for the classroom, they are taking risks and finding their place in the group. As they discuss and negotiate, as they listen to the ideas of others and refine their own ideas, as they rethink and reshape their ideas in the light of new knowledge, these children are developing relationships with each other and with the space that will be the foundation of much of the learning that happens in class this year. It is tempting to start the year with a ready made classroom, walls decorated and bulletin boards already up. There is often pressure to go over the rules, give out notebooks, and get straight down to “work”. But time spend on establishing a learning community, and the ownership, trust, acceptance and respect for ideas which that entails is likely to have a deeper impact on learning in the long run.

Goal setting for personalized learning


As part of our school-wide focus on personalised learning, each student in the elementary school sets personal learning goals. These goals are revisited, reflected upon and adjusted throughout the school year. Today, parents and students came to school for their individual student goal setting conferences. At these conferences students, teachers and parents work together to discuss how to help students achieve their personal learning goals.


Involving students in setting their own goals helps students to share responsibility for and take ownership of their own learning. Goals help students to think reflectively about their learning as they identify strengths and areas for further development. The goals give direction and focus for student effort and provide a standard against which students can measure their own progress. By revisiting and readjusting their goals regularly, students can see how they have progressed which is a key factor to developing self confidence and understanding oneself as a learner.

Love Learning with Kids

Love learning -it’s not just for students!

This year, we are exploring a new approach to teacher professional development. Teachers will be working in small inquiry groups of their own choosing to explore areas of professional interest to them. The inquiries will be framed around conceptually driven big ideas.


We began out learning journey by coming together as a large group to begin brainstorming possible directions for the inquiries by identifying concepts that they would like to explore further.


Teachers recorded their ideas under broad titles on flip chart papers.


The following morning, we met again to revisit and refine our thinking.


Over the next couple of weeks teachers met in small groups to settle on a central idea for their group inquiry and to come up with a SMART goal and action plan for their inquiry. one of the requirements was that each goal must focus on students. We now have ten inquiry groups, each with their own central idea and action plan. We have set aside a block of time approximately once a month for teachers to meet in groups to discuss and develop their inquiries. We are excited to see how these teacher inquiries unfold.

Love Learning Logo

It’s not just for students!

Teaching Now For The Future


This week we invited parents in to school to talk about our approach to teaching and learning here at AAS. We began by thinking about the shift in education over the last decade.

A shift is happening…

David Perkins, a Professor from Harvard university and co-founder of the international Project Zero has spent the last twenty years looking into the development of critical thinking skills and what we can do to develop these skills. He says that we need to think carefully about what it is we want students to know.

Parents worked in small groups to think about what attributes they thought were important for their children to possess as they went through school and beyond.


Our school wide focus this year is the central phrase in our school mission statement -love learning. George Dolesch, the ES Principal, concluded the session by explaining that our hope for students during their time with us was that they would leave AAS Elementary School with an appetite to know and a capacity to learn.

How We Organize Ourselves


Grade 4 have begun a unit of inquiry into the trans-disciplinary theme of How We Organise Ourselves.

Central idea:

  • Humans create systems to solve problems to support human endeavour and enterprise.

Lines of Inquiry:

  • What a system is
  • The purpose and function of systems (human endeavour)
  • How systems connect with each other

Before the teachers introduced the Central Idea to the students, and as the students became familiar with their new classroom, schedule and routines, teachers and students made a note of systems in their classroom, as part of the initial “settling in” process.

The following week, the teachers introduced the central idea. The inquiry began with students making connection to their prior knowledge and experiences. Teachers asked students to think about what systems they used in their lives.


Rita Ehrman, head of our school communications department, and John Bishop, one of our school librarians, came to talk to the students about the process of renovating the school library. They explained all the systems that were involved and how the systems all interacted with each other.


The students did an activity designed to demonstrate the interconnectedness of systems and to illustrate what happens when one part of a system breaks down. See the video below to see what systems were involved in our library renovations.

ES Love Systems from AAS Moscow on Vimeo.

At the end of the session, Mr Dolesch, the ES Principal, asked the students for their help in figuring out how to improve the system that is currently in place for student lunch cards. We are looking forward to hearing the students’ ideas.


Back to School

It is hard to believe that our first week is over already! Teachers began preparing last week, spending many hours setting up classrooms and planning provocations for student and teacher led inquiries.

Planning Aug 2014

On Saturday we held an orientation day to welcome new students and their families to AAS and give them an opportunity learn more about the school.

Back to school 2014

On Monday students, new and returning, came to school with their families to meet their teachers for 2014-15 school year and to see their new classrooms. On Tuesday, school started back on regular schedule. There was a wonderful calm and focused energy about the school.

During the first couple of weeks of school, the focus is on settling students in and building a class community and forging relationships.

creating a positive atmosphere

It is important that students have time to get to know their new classmates and teachers and to explore and develop relationships. Team building is an important part of the first week. The students need to feel safe in their new environment in order to learn. They need to trust and respect the members of their learning community so that they can develop as risk takers and experimenters.

team building

Routines are established so that students can work independently and share responsibility for their own learning.

establishing routines

Essential agreements and codes of collaboration are discussed and agreed upon. Throughout the year students will learn with and from each other as they conduct their individual and group inquiries. Time spent now building a strong learning community and developing a culture of collaboration will stand us all in good stead as the year progresses.

creating essential agreements

Our school-wide focus for this year is the middle phrase of our mission statement: love learning.

AAS Mission

To quote a great Irish poet, “Education is not the filling of a pail, but the lighting of a fire.” William Butler Yates 1865-1939

An inquiry into inquiry

“…inquiry is a collaborative process of connecting to and reaching beyond current understandings to explore tensions significant to learners.” ~Kathy Short

This week, Kathy Short came to AAS to work with Elementary School teachers on developing our understanding of inquiry. Kathy Short is a leading thinker in this area and we are extremely fortunate to have had this opportunity to work with her. Teaches met with Kathy in small grade level and subject area groups, to think about the inquiry what inquiry looks like in the classroom.


Inquiry as a stance on curriculum:

  • Inquiry is a way of learning that applies to all subject areas and to life -not just units of inquiry.
  • Inquiry combines uncertainty and invitation to go beyond one’s current knowledge and find out more.
  • Inquiry reaches beyond knowledge and facts.
  • Inquiry has no end point -it is never ending.
  • Inquiry requires tension a sense of being off balance. The learner is compelled to find out more.
  • Inquiry is a collaborative process.  Learners learn together and from each other.
  • Inquiry needs to start with what is important to the learner -not what is important to the teacher. Its needs to connect to the learner’s own personal experiences.
  • Inquiry is a natural way to learn. Out of school, children learn through inquiry all the time, but in school we tend to become very topic based.  As educators,  we spend time thinking about how we teach, when we should be thinking about how students learn.
  • Inquiry is conceptual
  • Inquiry is problem posing as well as problem solving. Often, adults pose problems for children to solve.  Children need to be involved in posing the problems themselves.

Teachers used a curriculum framework, Kathy Short’s authoring cycle, to help them organise their thinking. Through this framework, teachers thought about how inquiry could look in their classrooms. They reflected on the balance of personal, collaborative and teacher guided inquiryand considered ways of helping students to make personal connections to the big ideas.

Kathy Short's authoring cycle

Kathy will return in October to help us on our inquiry journey. This work is closely connected to the work we have done on personlizing learning to meed individual student’s specific learning needs.

Personalised Learning

At AAS we have a strong commitment to ensuring personalised learning for each and every student. Teachers have been reflecting on what personalised learning looks like in their classrooms and across the elementary school as a whole.


Teachers and administrators brainstormed in small groups to come up with examples of ways in which they personalise learning to meet the needs of individual students. They organised their ideas under the four headings below.

Learning outcomes are identified and clear; students have a choice in what they learning; differentiated instruction.

  • Learning outcomes translated into student friendly language in the form of “I can….” statements.
  • Student and teachers work together to set individualised personal learning goals.
  • Units of inquiry are designed to allow students to follow personal interests within the broader central idea.

Students knowing outcomes ahead of time, having multiple opportunities to demonstrate learning, to be able to show learning in different ways, specific, timely purposeful feedback integral part of this process

  • Learning outcome in the form of “I can…” statements a visible part of the assessment
  • Students have choices on summative assessment tasks
  • Report cards includes a personalised section for individual areas of strength and next steps for development
  • Student self-assessment and reflection are a central part of the assessment process

Student Teacher relationships
Teachers knowing the strengths and needs of students as learners, nurturing environment conducive to risk taking; students and teachers have relationships the exhibit mutual respect and empathy; teachers are available beyond the classroom

  • Grade level village times
  • One-to-one teacher student conferencing and goal setting
  • Teacher -student negotiated curriculum

Involving students and families
Communication between students, families and teacher is clear and happens often; parents and families are welcomed and valued in the conversations about their children’s learning.

  • Student led parent conferences
  • Class blogs and newsletters
  • Student Portfolios


What are you learning?

A next step for us is to think about how we will document each student’s individual learning journey.