Becoming a maths inquirer

I have decided to write about something that is close to my heart for my final blog and that is maths inquiry.

As a student I found maths incredibly difficult and was often frustrated and defeated by the maths that we did in class. I would often find that while I was able to complete an exercise in class I could not apply it in an exam. This is because I was unable to apply my mathematical understanding, because I didn’t really have it and because I never understood any real purpose to what I was learning.



Thankfully for students today attitudes have changed to a certain extent and we realise the importance of students seeing the relevance of what they are learning and being able to apply their understanding. This does not mean skills should not be taught but they can often be taught in the context of a student inquiry.

As Jo Boaler, a professor of maths at Stanford University says:

My research on math learners suggests that when students think they’re in class to learn — to explore ideas and think freely — they understand more and achieve at higher levels than when they think the point is to get questions right.

Students need the opportunity to explore maths concepts and to be driven by their own curiosity. One great blog that I follow is by an Australian primary teacher working in Switzerland Graeme Anshaw . His blog Enquiry-based maths is a fantastic source for teachers who want to bring maths inquiry into their classroom. Like our school he uses the PYP Maths planners to plan and teach mathematics. Rather than working through a textbook which for most kids is pretty boring and is really only aimed at the middle achievers of the class.

Mathematical Freedom


By using the planners we can develop a central idea, get the students tuned in, give them opportunities to develop their understanding further and to explore their understanding and ideas in greater depth.

We begin the unit with a Central Idea and then use the PYP Concepts to develop questions that they might have to help drive their inquiry later on. Here is an example from our data handling unit:

The students are given tuning in activities that help them to understand the skills and concepts needed. They will generally work in differentiated groups that have been created from the information I have gained from pre and formative assessments. They are given opportunties to explore one or more of the concept questions or any other questions that may have come up through the inquiry. Often the work will be integrated with our unit of inquiry.

Other great sites and blogs that I follow to improve my maths teaching:

Bruce Farrington’s Authentic Inquiry Maths

Taylor Boyd’s Inquiring naturally thru maths

Andrew Blair’s Inquiry Maths

Jo Boaler’s Youcubed

As teachers we have to change both our mindset and the students mindset so that all students can be mathematicians and realsie that they can do mathematical thinking. Jo Boaler’s work on maths and mindsets is changing the way that we view mathematics.

Technology means that as teachers we can keep up to date with new ideas, share ideas and find many different ways of improving our teaching. Just like COETAIL!

Overcoming the fear!

“There is no illusion greater than fear.” 
― Lao Tzu

This is the post that I have been dreading. I am very good at sharing ideas and collaborating with others when I am in the room with them but I have found the whole idea of a PLN very difficult as I feel slightly fearful when it comes to sharing my thoughts and ideas online, where they are out there for everyone to see and comment on – forever!!

COETAIL has helped me to see the benefits of developing a PLN and I intend to make this a goal for life after COETAIL. In the meantime I am trying to develop a PLN but I have to admit I am still lurking more than I should be.

I’ll be honest Twitter just doesn’t seem to work for me. I find it difficult to relate to and am more comfortable having a ‘conversation’ with someone than I am finding Tweets and commenting on them or retweeting. I do try to do this but my following and followers are growing at a slow rate.

The place where I am most comfortable is on Facebook and I have become a lot more active with some of the groups that I am in on FB. Groups such as:

Seesaw Teachers Grade 5,

PYP online Collaboration and

PYP Teachers – let’s share some ideas

Here are a couple of examples:

These groups can be a lot of resource sharing but there are also often posts that get you thinking, sharing ideas to enhance the students learning and developing strategies that work to improve inquiry teaching. The way that I see it is that this is where my greatest interest lies in ways to develop inquiry and to improve my teaching and the students learning opportunities so by linking in with like minded teachers I will get the best for my class.

While I was thinking about what my PLN looks like and how to stop lurking I came across this blog from Teacher Challenges: Using Webinars to build your PLN. This really appealed to me as a way of developing a PLN. I have started using the webinars from both YouCubed and Seesaw as ways of developing my teaching in maths and digital portfolios. The only drawback is that being in Eastern Europe means that they are often held in the middle of the night so making immediate interaction difficult. But you can still make comments and take part to a certain effect after the webinar so I will continue to work on this.

My Action Plan:

  1. Overcome the fear and use Twitter. Setting aside some time each day would help it to become a routine rather than something to worry about.
  2. Continue to post in the PYP groups I have joined. I genuinely enjoy this and have learned a lot from other PYP teachers through these spaces.
  3. Keep writing in my blog. Getting my thoughts down and sharing my ideas is another way of overcoming my fears of my printed words being out there in cyberspace.
  4. Continue to take part in webinars and to join in the conversation.


Making the changes- Final Project.

This final project has helped to make a huge difference to the quality of the How The World Works unit. We had tried making adjustments to the unit in the past but they had been small and at times misguided and had not really added any depth to the unit. For the first time in 4 years both my teaching partner and I have felt really positive about the teaching and learning that has taken place in this unit.

The goals that I set out at the beginning of the unit have mainly been met:


  • Students develop an understanding of physical and chemical change and give examples of them in real life
  • Students develop an understanding of how to use the scientific method
  • Students learn how to use Cornell Notes for research
  • Students are able to use Seesaw as a digital portfolio
  • Students make constructive, positive comments on each other’s work.


Unfortunately due to time constraints and my not realising how long it would take to role out Seesaw we have not yet used that platform for comment making. The students did mark a rubric and give feedback on the presentations verbally following the comment rubric that we had been looking at. We will move on to putting these comments on to Seesaw next week and will also be inviting the parents to comment as well. I will be sending them a copy of the rubric along with an explanation and examples.

On reviewing the ISTE Standards I feel that the students have been knowledge constructors in the way that they have carried out their research and it definitely gave them the opportunity to explore real life problems. I was really pleased with how many students chose to take action, building on the knowledge they had gained from their inquiries. They have developed their Creative Communication skills by using a variety of different tools that allowed them to be creative and to try and communicate their message in different ways.

Using Tinkercad to design a 3D model


They were global collaborators in the ways they worked together in teams and I was incredibly pleased at how organised and collaborative they were in their thinking. We now need to move beyond the class and grade and to try to make those global connections with other schools.

Whilst I feel that much of the technology used is still really at the Augmentation stage of the SAMR model there are certainly some aspects that have reached the Modification stage. A much greater use of flipping the classroom gave us greater conversations in class and I believe more depth when applying their understanding to the inquiry. The collaborative work that went into the inquiry which included the use of Book Creator and share docs as well as creating their own scientific investigations. In the latter several groups had to email and make appointments with the secondary teachers so that they could access the secondary science labs and equipment. Two groups booked sessions with science teachers so that they could develop their investigations further.

Water sample testing with Mr Lamb, Chemistry teacher.

As with everything on this course it is the process that is important. My students have developed their skills with a variety of technology tools, my partner teacher and myself have also become more confident and willing to take the risk to try new ideas in a more creative way, the students have developed their collaborative skills and I feel that all of this will help us move forward into greater use of Redefinition in the remaining units of the year.

Seesaw  means that the students can have everything in one place, in a variety of forms and the parents as well as other students can see and comment on it throughout the year. I believe this will be an excellent digital portfolio tool that we will be able to use effectively as a great way of communicating their learning to their parents and others. I will be sharing with the rest of the staff my experience with Seesaw in the new year and hopefully the pilot that I am doing will be extended to other grades so that we can make a decision about it at the end of the year.

One particular challenge for me was making an iMovie. I have not had much experience of doing this and it has taken many hours to get my head round it all. I am not overly thrilled with the end result but I now have something to build on and I will continue to work on these skills as I have to admit I really enjoyed pulling it altogether.

I have learned a lot over the past 18 months in my Coetail journey and I know that journey will continue.

Here is the updated planner:

Course 5 lift off!

After far too much procrastination I am at last ready to write my first post for Course 5!

Image credit:

I am focusing on the unit How the World Works. The Central Idea for this unit is:

Physical and chemical changes can have an impact on people and the environment.

I chose this unit because it has always been one that we have found challenging to teach and we are never completely satisfied with how it has gone.

The last couple of years we have tried to build inquiry into the unit and to give the students more ownership but there has been a lack of depth to their understanding of the concepts and even by the end of the unit although they have understood some aspects such as what physical and chemical change is and how it impacts the environment the understanding seems shallow.

It is also one of the few opportunities in the elementary school to look at the scientific method as science, particularly investigative science, is not done as much as it probably should be. So I wanted to be more focused in the teaching of certain skills and understandings such as the scientific method, the vocabulary and how this can be applied to real life problems.

Last year we gave the students discovery boxes that we had created and let them explore these to develop their understanding of physical and chemical change but there were too many experiments, not enough time and it ended up being more fun than learning. Though they had some understanding they were unable to apply it and their understanding of the scientific method was not strong.

This year we will begin with teacher demonstrations that look at the science and the process, as well as using books that explain the scientific method and create posters that show their understanding of those concepts before beginning the student experiments. We will then get the students to plan their own experiments in small groups that focus on physical and chemical change. They will use the scientific method to do the experiment and then share the question, method and materials with other groups to do.

Once the students have a good understanding of the first part of the central idea we will look at the second part and how it applies in real life. The students will look at Chernobyl as part of their understanding of the impacts of pollution; there is a great museum here in Kiev on Chernobyl and some great videos on Youtube.

They will then focus on either air, water or land pollution for their inquiry. This is where I intend to try and make the switch from project based to challenge based learning with some of the students.

I looked through the planner that I wrote last term at the end of Course 4 and realised that I was taking on too much with my ideas for technology and that in a 6 week unit I was unlikely to be able to introduce as much as I wanted to and still teach the content of the unit and give students time for inquiry. My original plan was to introduce Seesaw as a blog/ digital portfolio, teach the students how to use Book Creator and also look at video skills and commenting.

It has taken a lot longer than I hoped to get started with Seesaw as the school were looking at other possibilities and we had completely new Admin this year, so they had other priorities. But as we were about ready to start with this unit I got the go ahead to trial Seesaw, albeit only the free version. So I have begun to work with Seesaw with my students and it is a fairly slow process as I am learning alongside them how we can use this tool.

I have to say the Seesaw help desk are excellent and I have joined various Facebook groups for Seesaw that offer lots of ideas and advice. They also have webinairs to help you get started and to learn about how to use the app. I have chosen to not include the parents at this point as there are lots of blips along the way and I want to be sure that everything is working properly before introducing them. I have also had the comments turned off for the students as I want to make sure that they know what is appropriate and constructive before letting them do this. So learning how to comment constructively will be part of the unit.

The students will have the opportunity to use video as part of their learning if they chose to do so and they will be supported on a ‘just in time’ basis where they skills they need can be individually taught.

Throughout the unit we will flip the classroom, the students will have opportunities as part of their homework to learn new information and to bring it into the classroom so that we can develop their ideas and apply their learning.

So here we go and here is my updated planner:

Course 5 Final Project


I have decided to use our science unit on chemical and physical change for the Course 5 final Project. This seems like a good choice for the final project because it is a unit that we are planning on revamping anyway as we feel there are areas that are not strong enough and that we can enhance the teaching and learning process so that it is a stronger unit of work. It is also a unit we will be working on whilst doing the course so it will be easier to see how it works in real life

One of the challenges will be introducing Seesaw to the students as a blogging tool. My students have no previous experience of blogging and I have not used Seesaw myself as yet. But during this course I have seen that many of my fellow COETAILers are using it and very successfully so I am in the process of getting permission for Grade 5 to trial it. We are hoping to use Seesaw as both a blogging tool and as an electronic portfolio so I intend to have the students posting reflections as well as some of the activities that they do. I very much want them to understand the process of their learning throughout this unit.

This unit has always been project based learning but now we would like to make it more challenge based by linking it more firmly to real life problems. One part that I still need to think through is how to make those real life links authentic and that will be a focus for me during Course 5. As an inquiry teacher I know that those links need to come from my students to give them real ownership and to make the inquiry worthwhile.

What are some of your concerns about this unit?

The main concerns would be:

  • Time. Is there time to include all the new ideas and ensure that the students get enough depth in their understanding of the unit?
  • Resources. Being sure that I have a good understanding of the technology tools that we will be using.

What shifts in pedagogy will this new unit require from you?

I don’t think there will be a big shift in pedagogy as I think of myself as an inquiry teacher and that is the basis for this unit. It is more a case of trying to get the students to go a little deeper in their inquiry and to make it more challenge based than previously.

What skills and/or attitudes will this new unit require from your students?

They will need to learn several new technology applications; Seesaw, Book Creator and possibly some additional video skills. This is a lot of new learning in a short period of time. There is still another 3 weeks before we begin this unit so I will try to introduce some of these skills prior to the unit.

Learning, collaborating and creating with technology.

Giving students a computer in class does not automatically make them succeed. Does having a 1:1 programme ensure that students do better in class? Should every student have a computer in class in order to be able to meet 21st Century demands? Is a 1:1 class better than a 1:2 or 1:3 class? What age should a 1:1 programme begin? Laptops or iPads?   All these questions are being asked by many stakeholders in education. There is research that supports a 1:1 programme and research that says it makes no difference to student success.


i think a lot depends on the way in which a 1:1 programme is introduced, implemented and monitored. Most of the articles that I read saying it made little difference to student attainment were studies of American public schools where students may be following a fairly traditional curriculum with regular testing, teacher led activities and a very grade driven environment. In this type of classroom the activities that the students are doing may mainly be substitute or augmentation activities (SAMR) Consequently the tools that they are using, in this case a computer or tablet rather than pen and paper, makes little difference to the learning outcomes.

In a learner centred classroom there is a greater likelihood of seeing modified or redefined  tasks. The students will have more control over the content and skills that they are using to accomplish the task.



Sir Ken Robinson said that we needed an education revolution to transform the way children learn. There is a need to move away from the linear model of education to a personalised learning model   Having a 1:1 laptop or tablet programme isn’t going to give us that on its own but by using technology in a way that allows students to do their own personal inquiry we give them opportunities to develop the learning skills that they will need in the future.

Students need a lot of different learning experiences and technology can help to make those experiences valid. In my classroom we have 1:1 Chrome Books and the students will often work independently on them using a variety of different programmes. They use them to research, publish, correspond with others and to present their work. They can choose how they present their work from a wide range of different media such as Google Presentations, video, podcasts, Book Creator etc.

But a lot of the time they need to collaborate and to produce work through shared projects. At times I will say that they only need one computer between 3-4 of them as it is only being used to record their ideas and it is better to just have one scribe so that they can focus on the thinking and the shared ideas.

We use technology to learn more about the world, to connect with others, to present our ideas and to create new ideas. As we move forward I am hoping that my students will be able to spend more time creating their own content and using the programmes that are being developed for use on Chrome Books to share their ideas with a wider, more global audience.


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