Spatial Reasoning and Student Success



Spatial Reasoning

This year, I have had the privilege of designing a brand new makerspace for our school. In addition, I have been able to focus on visual-spatial reasoning as the thread that pulls together science, math and technology.

What is spatial reasoning?

According to the Ministry of Education, Spatial reasoning is the ability to engage in reasoning, and understand the location, rotation and movement of ourselves and other objects in space. It involves a number of processes and concepts. More information about this can be found here:


Why is Spatial Reasoning important?

There already exists a very strong body of research that spatial thinking correlates with later performance in math. In addition, research consistently demonstrates strong linkages between spatial ability and success in math and science — and those students with strong visual and spatial sense are more likely to succeed in STEAM careers.

It is absolutely clear that early exposure to visual-spatial reasoning is very important.

However, as educators, we traditionally have failed to recognize that our youngest students are actually able to perform way above the expected levels of spatial reasoning. We generally leave these tasks for older students. This has to change.

Not only is this a problem because we are neglecting our youngest students who already come to school with a high level of spatial-reasoning skills, but this also means that our youngest students are not having equal access to spatial reasoning activities that they are able to perform. This is a social justice issue. Especially when we consider that visual-spatial reasoning positively correlates with later performance in math (Mazzocco & Myers, 2003). If we know the research, and have the opportunity to employ high quality spatial reasoning activities for all students in Kindergarten, should we let older curriculum and older beliefs hold us back? Do we recognize when we are teaching in the ways that we used to be taught? What if we had the ability to ensure all of our youngest students engage in spatial reasoning? How would this impact their future?

In fact, students who experience issues with math, often have difficulties with geometry and visual spatial sense (Zhang, et al., 2012). This to me sounds like an amazing opportunity to understand mathematical achievement via spatial reasoning. The earlier we recognize this, the earlier we can respond.

Wouldn’t it be great if we gave all students the ability to access higher level learning associated with visual-spatial sense right from the get-go? Imagine the impact this could have in overall math achievement throughout our students entire school career, and beyond, in their STEAM based careers.

To me, I think this behooves us to ensure we have access to makerspaces – regardless of where they are located in our schools – to promote visual spatial reasoning skills.

What do you think?


Deborah McCallum

c 2016

Mazzocco, M. M. M., & Thompson, R. E. (2005). Kindergarten predictors of math learning disability. Learning Disablilities Research & Practice, 20(3), 142-155. doi:10.1111/j.1540-5826.2005.00129.x
Mazzocco, M. M. M., & Myers, G. F. (2003). Complexities in identifying and defining mathematics learning disability in the primary school age years. Annals of Dyslexia, 53, 218–253
Zhang, D., Ding, Y., Stegall, J., & Mo, L. (2012). The effect of Visual‐Chunking‐Representation accommodation on geometry testing for students with math disabilities. Learning Disabilities Research & Practice, 27(4), 167-177. doi:10.1111/j.1540-5826.2012.00364.x

Makerspaces & Math Links

Math Mindsets



Originally Shared on:

Big Ideas in Education

Big Ideas in Education

Growth Mindsets in Math are important for student learning. 

Our youngest students are often very excited about learning math. But then something happens. I believe that  a students diminishing excitement for math is directly related to a lack of a growth mindset.

What is a Growth Mindset? 

A Growth Mindset is a philosophy promoted by Dr. Carol Dweck. With a growth mindset, we each have the ability to achieve success beyond our innate abilities. We also have the option to move forward in the face of adversity, and become successful in our own right.

When it comes to math, there is no such thing as a ‘math person’. This is because a person’s true potential is always unknown, or unknowable.

But often, in school, we become focussed on getting the ‘correct’ answers, as fast as we can. This leads to students having fixed mindsets about their abilities in math.

In math, we want students to NOT feel shame that there are deficiencies – this is why we learn! We all have the capacity to learn through our efforts – AND through deliberate practice.

We also want students to understand that it is the process of learning that is important – not just the final product.

No matter where you are in your learning, you can always develop yourself further.

 Parents can go a long way to promote Growth Mindsets at home, Here’s How:

  • Avoid assuming that you are, or are not, a ‘math’ person. This can promote a fixed mindset in your child.
  • Have fun with math: Play math games, puzzles, cook and bake together!
  • Avoid praising speed when it comes to math
  • When a child gets an answer incorrect, instead focus on the process (logic), not the final answer (product) – try to find out what went wrong!
  • Praise your child’s ‘thinking’  rather than telling them how ‘smart’ they are. This helps students to understand that challenge is okay. Thinking that they are ‘smart’ can put pressure on them to think that struggling with math is a bad thing.
Deborah McCallum
Other Reference:

Ontario Math Resources


Here is a list of some of the best resources to support math in Ontario. Please feel free to add more to the list in the comment section. You can also check out the following blog:

Ontario Math Resources


Teaching Math for FNMI Students


The dominant ways in which math has always been taught in our Western society includes drill, rote learning, and a focus on math ‘authorities’ including the teacher.

This poses very serious problems for many of our mathematical learners, particularly for our First Nations, Metis & Inuit (FNMI) learners, whose perspectives and ways of knowing may not be included in the traditional curricular frameworks. Therefore, we are faced with very serious issues when it comes to considering who gets to learn math, and who will be included.

Math that is inclusive of different cultures and ways of knowing the world, is built on the awareness that math itself is about knowing the world. It is my view that we as teachers can do many wonderful things in the classroom to integrate basic skills with constructivist and culturally responsive ways of teaching math that will support multiple ways of knowing – particularly for students who are FNMI.

How do we use strategies and approaches that both facilitate learning in math, AND infuse FNMI ways of knowing? We start by recognizing the importance of connections, communication and contextualization of the learning of FNMI students.

What strategies help to infuse FNMI ways of knowing, perspectives and content?


The following strategies can be designed to infuse FNMI ways of knowing, perspectives and content into the Math Curriuclum.

First, recognize that students learn by attaching meaning to what they do. Students need to construct their own meaning of mathematics.

2. Integrate Inquiry Based Learning into math. Check out the following website from OISE on Inquiry in Math. 

3. Provide holistic learning experiences that include cultural and social interactions through dialogue, language and negotiations of meaning.  This would include allowing other students, community leaders, Elders, Senators and other diverse resources to teach, facilitate, share and learn in our classroom.

4. It is impossible to isolate math from culture. It is important to strive to help change mindsets about what ‘real’ math is. Ask ourselves questions including is math about making financial transactions? Is it about complex beading, knitting, or making intricate porcupine quill boxes? Are our cultural routines linked to math? Become aware of how math is linked with culture.

5. Aim to create equal opportunities for Math learning for Aboriginal students. However, exercising caution not to merely integrate holidays, artifacts, stories and more merely as a form of ‘tokenism’. Also, exercising caution not to make FNMI students solely responsible for adding culture and learning to the math classroom.

6. Engage in Culturally Responsive Teaching of mathematics. When we don’t include culture in math, we are essentially positioning people ‘outside’ of math. Serious implications thus arise as FNMI students are at a greater risk of being forced into negative math mindsets and math deficiencies. Culturally responsive teaching is about understanding surrounding communities, and making the program ‘Student-Centered’.

7. Step outside of traditional curriculum frameworks. Not Big ideas and high expectations, but the pedagogical frameworks. When we try to add culture, content, perspectives and ideas to math, we can change the traditional curriculum frameworks. Mathematical learning that incorporates FNMI perspectives, content and ways of knowing, should not be an add-on. We need to make sure that we change our traditional frameworks lest we inadvertently continue to promote the ‘othering’ and exclusion from math.

Math is about knowing the world around us. FNMI students deserve to be included in our curriculum. How will you strive to equally include FNMI students in your curriculum?


Deborah McCallum



Math Communication

Math Communication.


Podcast describing key differences between 3 amazing communication strategies for math: BANSHO, Gallery Walk & Math Congress.

StoryBird: Math Strategies used by Students

Storybird – Math Strategies for Students

Math Communication: Brief Podcast