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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Ottawa Catholic School Board (2018). Deep learning site. https://deeplearning.ocsb.ca/
Stanford d.School of Design Thinking https://dschool.stanford.edu/
