Accessing Deep Learning in Math through the Design Thinking Framework

Accessing Deep Learning in Math through the Design Thinking Framework

In this paper, Design Thinking will be examined as an effective pedagogical
practice in math. As with any pedagogical practice, it should not be used in isolation,
and is meant as part of an effective math program. It should be used with other
Pedagogical practices, such as Number talks, Station rotations, explicit teaching,
small group guided math and independent practice. As part of a balanced math
program however, it has the potential to lead to Deep Learning in math at the same
time as developing students’ Global Competencies and the
Catholic Graduate Expectations to produce students who are caring, well balanced, empathetic
graduates who live up to their God given potential.

Design Thinking is a framework used in businesses, innovative companies, as well as the

education sphere. It is an innovative framework that allows for problem solving to take place

through prototyping solutions to authentic problems and real world issues. It is sometimes called

user centered design, as it originated as a way for companies to think about how to better

design products and services with the end user in mind. The process starts with empathy and

perspective taking in order to design something to solve an issue or address a problem.

There are many models of design thinking, and many frameworks that can be followed.
My favourite one, and the one that will be the focus of this blog, is the d.School of Design
Thinking from Stanford University. A graphic of the model can be seen below.

This model begins with empathy, and is thus connects beautifully with our Catholic Graduate
Expectations. Developing empathetic, caring Catholic Graduates is the aim of our entire system,
and engaging in design thinking can certainly be one approach to help foster this.  

An inquiry using this framework begins by students developing empathy towards a person,
group of people, or animal. This could be through researching a complex issue or problem, or it
could be through observation that leads to the identification of a problem. Once the issue or
problem is identified, the next stage is to clearly define the issue or problem. This phase
involves research and asking lots of questions. Next students engage in ideating. This phase
involves thinking of as many divergent potential solutions as possible. There are many protocols
which can be employed at this stage to help students brainstorm as many ideas as possible.
Next students choose a solution and begin prototyping it. Once they have a prototype, they then
test the solution out to see what works, and what doesn’t work. This leads back to more
research, idea generating to problem solve and prototyping.

At the OCSB, we have adopted the Deep Learning as a framework, based on New
Pedagogies for Deep Learning, to guide, plan, inform and wrap around all that we do. So how
does Design Thinking relate to Deep Learning? Let’s first break down the process and look at
some examples to see the connections.

As mentioned, the idea of empathy connects meaningfully with our goals as a Catholic
organization, and connects to our moral imperative to develop caring citizens as our Catholic
Graduates. It also supports the Global Competencies, specifically Citizenship. The definition of
Citizenship on our OCSB Deep Learning site is “Giving witness to Catholic social teaching by
promoting peace, justice and the sacredness of human life, considering global issues based on
a deep understanding of diverse values and worldviews, and with a genuine interest and ability
to solve ambiguous and complex real‐world problems that impact human and environmental
sustainability.” With Design Thinking, students start by developing empathy and taking the
perspective of people to understand issues. This can be on a small, local scale, or it can involve
a global scale initiative. An example of a small, local scale issue comes from Our Lady of Peace
school, in which a school wide design challenge was launched, and students identified
backpacks sliding off little backs of Kindergarten and primary students as being an issue. They
discovered this through observation, and in the next phase refined their understanding through
interviewing students who were experiencing this issue. See picture below of the clip students
designed on Tinkercad to be 3D printed to help students keep their backpacks in place.

An example of a large scale issue comes from Holy Trinity student who designed a reflective
backpack with LED signal lights which are solar powered to solve the issue of bikers being
injured and killed in collisions with cars, particularly in the dark. Click on the image below to see
a video about the project.

In the definition stage, students engage in research to define their issue, and learn many
perspectives and reasons for the problem. This ties in well with Critical Thinking, as students
must research, and critically evaluate information. This can further the development of deep
understanding of complex and ambiguous issues, as students dig into what the problem really
is, and contributing factors to the problem. For instance, consider the backpack example from
Our Lady of Peace. Upon further researching the issue, students discovered that more
expensive backpacks had a clip built in to help keep the straps in place. They then discovered
that many families may not be able to afford the more expensive backpacks. This then leads to
deep discussions of equity, poverty, and related complex social issues.

The ideation phase dovetails perfectly with Creativity as a Global Competency, as students
develop an “‘entrepreneurial eye’ for economic and social opportunities, asking the right inquiry
questions to create and adapt novel ideas” (OCSB Deep Learning site). The idea of an
“entrepreneurial eye” means students are looking for ways to positively impact the issue of
problem they are trying to address in a creative way. This could be raising funds through
something they create for an organization, or it could be developing an object that addresses an
issue.

Prototyping encourages students to develop the Global Competency of Character, as they
persevere through multiple iterations and designs. It can also be seen as a non-threatening way
to integrate hands on learning. We know that as students get into the higher grades, even in
elementary, they sometimes resit using physical models and manipulatives in math, either from
a fear of stigmatization or ridicule from peers, or from teacher attitudes towards math
manipulatives for the older grades. Prototyping leads to the use of physical representations and
manipulation of objects as students create, design and improve on designs they have made.

The entire process of Design Thinking is predicated on good communication and
collaboration throughout. Students often work together on designs, or on ideating or throughout
the process. They must communicate in each phase of this process, from conducting empathy
interviews, to ideating, through to working together on designs and giving feedback to each
other.

Although this framework is applicable to any content area, for the purposes of this paper, math
will be the focus curricular area. When doing a Design Thinking inquiry, math skills are explicitly
taught, but in context, and when needed at the appropriate point in the inquiry. A great example
of this comes from Holy Trinity High School, where grade 7 math classes decided to create bird
houses, which they then sold to raise funds for the Wild Bird Care Centre.

In this example, concepts from Geometry, Measurement and Number Sense were explicitly
taught and embedded into the inquiry as necessary skills students needed in order to complete
their projects. Students were invested in the project, and were engaged in learning the math so
that they could be successful in the process. Bush et al. (2018) describe an inquiry in math undertaken by a middle school class in which
students develop empathy for a younger student in the elementary school that feeds into their
school who had lost a hand. The student had difficulty pressing the ctrl+Alt+Del combination on
her laptop to log into the computer. So students decide to design, prototype and eventually 3D
print a prosthetic for the child that would allow for pressing those three keys at the same time.
Focusing explicitly on math concepts must be done intentionally while engaging in an inquiry
such as this while, but the benefit is that it can lead to math that is learned in context. The
important concepts that students needed to understand in math were explicitly taught and were
carefully considered throughout the inquiry. As the authors highlight “Keeping the mathematics
tightly woven into the stages of the Design Thinking Framework was part of what made solving
this authentic problem in their home community both of great significance to students but also
high leverage in terms of engaging students with key mathematics content” (Bush et al, 2018,
p. 5). Students develop their conceptual understanding of math concepts when they are
developed in context, rather then as skills in isolation to be memorized.
In terms of the mathematical process skills, many can be mindfully embedded and developed
through the Design Thinking process. Consider the process skills of connecting and
representing for example. Through Design Thinking, students represent their mathematical
thinking through prototyping. This could be using a software program such as Tinkercad to
model a 3D object which they can scale and manipulate in space. It could be creating a
cardboard model of something they are creating to solve an issue. They may need to size and
scale their design, or may need to precisely measure it to fit within certain parameters. Problem
solving is at the very core of the Design Thinking process, and when embedded in the math
class, students are invited to problem solve rich, real world problems. The design thinking
process lends itself very well to communicating as a mathematical process. Students must
communicate their mathematical thinking effectively together while they collaborate, and during
the final stage of the process when they share their designs. The teacher plays an important
role here in ensuring that students use their mathematical vocabulary and explain their
mathematical understandings effectively. The connecting process works here as well, as
students are learning the mathematical concepts in context, and are connecting these concepts
to other mathematical knowledge and content that they must master in order to be successful
with the current challenge. Since the learning is cross curricular, they are also connecting
important mathematical content and developing conceptual understanding in math in context,
and seeing how math operates in the real world.
Spiralling of the curriculum in math also fits in very well with Design Thinking. Research
clearly indicates that spralling the curriculum leads to greater retention and deeper learning in
Mathematics (see for example this video clip explaining what spiralling is).  In spiralling,
students revisit math concepts throughout the year, instead of learning topics in longer chunks
such as chapters or units that they engage in once a year. This idea can be worked into Design
Thinking as mathematical concepts are revisited throughout inquiries as needed to move the
inquiry forward. Key mathematical concepts can be intentionally woven into the inquiry and
engaged in throughout the year, leading to greater retention and deeper, conceptual
understanding then teaching the concept in bigger chunks in isolation.
Design Thinking is an effective pedagogical approach that can lead to deep learning in math.
Considering the research indicating the importance of wellbeing in math (see for example the
recent monograph from the Ministry of Education in Ontario), and mindset in math, an approach
like Design Thinking that leads to greater engagement, excitement, and feelings of self efficacy
for students is a welcome addition to any math program. Design Thinking is an effective way to
develop both students’ Global Competencies and their Catholic Graduate Expectations to
prepare students to be contributing citizens who are able to approach complex issues in the real
world as caring, Catholic graduates.

References

Bush, S. B., Karp K. S., Cox, R., Cook K. J, Albanese, J. &  Karp, M. (2018).

Mathematics Teaching in the Middle School, Vol. 23, No. 4 (January/February

2018), pp. E1-e5.

Ontario Ministry of Education (2018). Yes, I can! Paying Attention to Well-Being in the

Mathematics Classroom, Capacity Building Series, Special Edition 48.  

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/math-classroom2018.pdf

Ottawa Catholic School Board (2018).  Deep learning site. https://deeplearning.ocsb.ca/

Stanford d.School of Design Thinking https://dschool.stanford.edu/

Reflections on PQP Part 2 10 Day Challenge

Over the course of the ten day challenge I have learned and reflected on both my current role and my future role as a Catholic Leader in a school. I enjoyed the articles and activities that have both consolidated and pushed my thinking about the role of technology in our schools, and how a leader might leverage technology to be a connected lead learner and encourage staff to leverage technology to support students’ development of global competencies and engagement. In our current reality, leaders no longer have an excuse to not be connected. The digital world offers endless possibilities to learn, connect, share ideas, and seek help.

This quote from Pope Francis really resonates with me:

The digital world can be an environment rich inhumanity; a network not of wires but of people. Let us boldly become citizens of the digital world.”

Pope Francis, 2014

When I reflect on becoming a Catholic leader, I am struck by how our Holy Father is so supportive of innovation and has such a deep understanding of the potential to use technology in a positive way. When I think of Catholic leadership, I really believe that we have the potential, and in fact the moral imperative, to use digital tools to promote empathy, compassion, innovation and our Catholic values. Catholic leaders today have a responsibility to ensure that everyone in their school sees the potential to use technology for good and positive impact in the world. They also have a responsibility to ensure that everyone in the building understands the role of technology in accelerating student learning and the development of global competencies. This recent blog post by George Couros reminds me that the best way to have effective classroom management is through excellent and engaging teaching. Curos points put that this same principal applies to all learners, including adult learners. When I think of being a leader in a Catholic school, I think about the importance of building relationships with the people in the building, and creating the opportunities to focus on what can be improved through exciting and innovative ways. Empowering the staff in the building to learn, innovate and improve through providing opportunities for engaging PD, highlighting amazing work that is happening, and empowering all educators and support staff to pursue new learning that is of interest to them is one way to continually focus innovating within the school. Allowing educators opportunities to see me model the importance of being a connected leader, and encouraging them to be connected leaders is key to building the culture that I want to foster in the school. I truly believe one of the most important roles of the principal is to be the lead learner, always in an open learning stance.

My next step as a potential future leader in a Catholic school is to continue to consider how to build relationships, and focus on empowering the students and educators I will serve. When everyone is invested and engaged in the learning, and focused on what is best for students, we will develop cultures that are innovative, connected and focused on care, empathy and academic rigour.

Reflections on the PQP 10 Day Challenge

I started this challenge thinking there was not a ton I would learn through it since I am already an active twitter user, and work with educational technology a lot in my current role. Through digging into the various challenges, I am pleased to reflect on some new learnings and reflections I have had. I think sometimes we need to slow down and think about what we are learning and how we are using tools, such as digital tools, in our practice, and engaging in the 10 day challenge certainly gave me opportunities to reflect on this. It was also great to learn some new things, such as how to use the Twitter extension for Docs and how to use Pivot tables in Google sheets from forms.

What I really gained out of this 10 Day challenge was time to reflect on my practices, and what I want them to look like as I move forward. When I think of effective digital leaders, I notice they are active on their chosen platforms, be it a blog or a Twitter account. They carefully curate information before sharing, and they reflect through their digital presence. I hope to continue to cultivate my own digital skills by continuing to be active on my Twitter account, and by blogging more consistently.  I also reflect that this 10 Day challenge was a great opportunity to connect and follow many more of my colleagues and educational leaders throughout the world. I hope to continue to build my digital network and use the digital platforms to connect, share and learn.

Blog Post for PQP Part 1 "Why Blog?"

I really enjoyed reading the “Why I Blog, a A Principal’s 13 reasons”. There are many compelling reasons to Blog. I really like the idea of blogging to develop vision. Blogs, as the author states, are not static, but rather real time thinking in action. As a potential future leader, I think blogging would be a great way to continue to refine and develop this vision as a leader.  

I think the most compelling is to blog as a tool for reflection on my own learning. Blogging is a great way to really pause and think about what I have read or what I have been learning. I also find blogging tough. It is hard to find the time. It is hard to think of what to write. I feel like it won’t be of interest to anyone, or that I don’t have anything new to contribute. I read some blogs about blogging, and this one from one of my favourite bloggers AJ Juliani spoke to many of my hesitations about blogging: http://ajjuliani.com/blogs-still-matter-2017/

He writes about why blogs still matter in 2017. I think about how many Blogs I read, and certainly I read a lot of different Blogs and look forward to them coming out so I can continue my learning.

So I hope to continue writing, and continue blogging. These readings have really inspired me to continue working away at this!

What is a Makerspace?

What is a Makerspace?

I am excited about the idea of makerspace and maker education. As with any concept in education though, there are many definitions and thoughts about what exactly a makerspace in education is, and what purpose it serves. After much reading, reflecting and considering, I have developed my own working definition of what a makerspace is:

One important aspect of Makerspace education in schools is the idea that it gives students authentic opportunities to develop the Global Competencies, while increasing engagement and student agency. An important part of my definition is that Makerspace activities can be leveraged to specifically address curriculum expectations. I am a true believer that students need many opportunities to explore freely, and create based on their interest and ideas. However, I also am also passionate about leveraging these engaging activities to authentically address specific curriculum areas and expectations. I think the key is balance and gradual release. Click here to read a blog post on one of my favourite blogs by Diana Rendina about the value of guided projects in Makerspaces.

When introducing a new tool or piece of equipment or activity, it is important to build in time for students to freely explore and engage. Once students are comfortable, introducing specific challenges that are directly related to specific curriculum expectations can lead to deep learning for students.

I have visited a number of schools to talk about Makespaces, and the first question is often, what about the curriculum? This comes down to accountability. Can I give students real world, authentic, engaging hands on experiences and still be accountable to the Ontario Curriculum? Absolutely!

I have been working on curriculum linked activities for makerspaces, stay tuned for more info!  

I would love to hear your thoughts about what a Makerspace is!!

Learning Environments

With our board wide focus on Deep Learning, September seems like the perfect time to begin the discussion with a focus on Learning Environments!

First, what is a learning environment, and why should it matter? Much educational discussion right now focuses on learning environments like flexible seating, 21st century spaces, student choice. Just Google Flexible Seating, and you will pull up more articles and pictures then you can look at about these great new learning spaces!

I am a firm believer that these spaces do have a great impact on student learning, and that the environment is key to success for many students. Research supports the important impact an environment can have on learning (see for example: http://www.emilyanthes.com/data/uploads/neuroarchitecture.pdf http://www.cmu.edu/homepage/society/2014/spring/disruptive-decorations.shtml ). Studies have looked at many important aspects of the learning environment, including those environments are are visually overstimulating and cluttered, to the amount of natural light and green space that can be seen, to the importance of temperature and comfort in the room.

However, the idea of Learning Environments goes far beyond the physical setup of the room. You do not need to be an interior designer or an avid Pinterest fan to create an effective learning environment. Learning environments start first and foremost with the community of the classroom. Students must be made to feel safe, feel that they are valued and are members of an inclusive community, and can take risks with their learning. In the Deep Learning Framework, Learning Environments are one of the four elements that are mobilized for the development of the Global Competencies. The conception of Learning Environments goes beyond the physical space, and takes into account the climate and culture for students, student centred and accessible environments for students.

I think the idea of designing a learning environment in a purposeful way should start with a careful consideration of philosophical issues in education. How do you want your students to feel in the room? Whose room is it? What kinds of word do you want students to be able to do? What are the student needs in the room?

Once those questions have been answered, you may want to consider what kinds of zones you want to have. I have seen some teachers think of it like a home, and designate areas as a living room, dining room, breakfast bar etc. Other classrooms have created a fire pit (not a real fire, but a cozy area for students to gather around). Others have designated some areas as loud for active collaboration and others for more quiet work. Many schools are also designing outdoor learning spaces, which can extend the classroom beyond the four walls. Flexibility is an important concept in today’s learning environment-both flexibility of furniture to accommodate different learning activities and styles, and flexibility for students to exercise agency in deciding what they need for their learning. By focusing on the learning environment, we can foster student voice and choice, and give students important opportunities to continue developing their self regulation skills.

If you are looking for a place to get started, a Twitter search of the #ocsbfirstday shows many amazing learning environments right here in the Ottawa Catholic School Board! #flexiblesseating shows many interesting ideas for flexible seating in classrooms. There are many online resources and books about learning environments as well.

Welcome to my Blog!

I decided to write this blog as a reflective tool for my own learning, as I begin another journey through the school year. Since I finished my Doctor of Education in July, there has been a lot of lighthearted talk about what I might do with all my free time! So I thought this was as good a place as any!

I have many areas of interest and read a lot of amazing things from other educators and academics, and I thought this blog would give me a place to pull together some of my thoughts and consolidate what I have been learning.

I thought a lot about what the focus for this blog should be. Should I focus on Deep Learning? Should I focus on MakerSpaces? Should I focus on inclusion? So many areas I am passionate about! So I decided instead of having a specific focus area, I will make my blog a general place for thoughts and reflections. I called it Making Meaning in the OCSB to reflect the core purpose of this blog and really of all learning, making meaning. I thought about what many of my interest areas have in common, and I realized it is really about making meaning-be it through MakerSpace activities, Maker Mindset, Deep Learning, or inclusion, making meaning is a common thread.

So I hope if you chose to read my posts you will engage in discussion, suggest other resources and articles and books, and mostly, reflect on the meaning they make for you!