Math & Identity

I just read this great piece by Karin Brodie:

Entitled: Yes, mathematics can be decolonised. Here’s how to begin

 

When we think about math, we often think about the content – but what about the way we think about it, the way it is taught? If think about math in these ways, we are able to consider how identity plays a role in how we teach, understand, and apply math.

What is identity? It is connected to the groups that we affiliate with, the language we use, and who we learned the language from. I believe that we all have different identities depending upon the different groups that we belong to, and that this has implications in terms of the languages and discourses we use.

What is important is that I recognize the intersection of my identity with identities embodied within the Ontario Public School system, my school board, schools, and students that I will be working with next year. In identifying this intersection, can I truly facilitate math learning, and promote higher achievement for students? Especially if my identity is stark compared to the identities that exist within classrooms across Ontario schools?

But this is not comfortable. One of the ways we as educators try to deal with this discomfort is to think of math as a ‘purist’ subject. This is but one way that we can strive to reconcile the dissonance we can feel about dealing with multiple identities in math.

But it is important to hear the identities and cultures of our students, in order to ask better questions about how math can be learned, versus merely finding the ‘right’ answer.

What can we do?

I think that Culturally Responsive Pedagogy (CRP) is one way to begin to address this question and forge a path forward. Inherent in CRP is the idea that I as an educator would continue to use student culture to transcend the negative effects of dominant culture. It becomes a tool to explain the ways in which I will develop deeper cultural knowledge of students, and thus use cultural referents to increase opportunities for student learning.

Here is a great piece to learn more about CRP: Framework for a Culturally Responsive and Relevant Pedagogy:

I do have many questions however.

How do I know that I am actively supporting a safe school environment, and not just thinking that I am because it fits with my own identity and dominant culture in society?

How can teachers situate their own privilege and oppression of themselves, and that of others? It is through this that we can start to understand identity, and understand how diverse our experiences surrounding math can actually be.

When we consider the multiple identities of teachers and students, we can understand that a standardized test is just one type of outcome for student learning. There are so many additional ways that we can capitalize on to enhance student achievement in math, to help us move beyond the spaces where we simply consume knowledge, into spaces where we can critically examine mathematical knowledge and how it plays out in our lives, and with our own identities.

This is especially important with Indigenous students. Canada has a history of experience with colonizing Indigenous communities. Because Indigenous peoples were on this land first, it stands to reason that the diverse cultures of Indigenous peoples are allowed to be welcomed and understood in our classrooms, as a way to promote and enhance the identities of Indigenous individuals, cultures, and incorporate their diverse experiences with math.

It causes me to ponder the importance and power of language. Language is part of our identity, it forms how we know the world – thus how we understand and know math. We need to learn the languages and narratives of our student identities, and check out our own, in order to co-create the necessary mathematical experiences that will lead toward higher math achievement.

Perhaps it is important to use CRP to help co-create new languages of math in our unique environments of unique identities and cultures – that can help us shape our understandings of different cultures, contexts and sensitive issues. It will be important to have agreed upon norms, and exercise them in ways that help us to foster truth and respect. It will also be important for me to frame this as discourses of education, and not discourses of the individual.

It is also important to facilitate the creation of math opportunities that allow students to discuss their own aspirations for the future.  Noting how students solve problems, and sharing the different ways that problems are solved. I can strive to move away from relying on my own identity and personal experiences to make sense of how math should be solved in the classroom. In this way, I recognize that math is culturally defined, and that I can change the narrative that I learned from dominant culture that math is a pure subject that has the correct answers, and is culturally neutral.

It is time to get really uncomfortable with math.

 

Deborah McCallum

Language, Culture & Math

I just spent the last 3 days at a Summer Academy for Purposeful Math Planning. I was very intrigued when we were discussing number sense and the need to become more flexible with numbers and how we use them in our world. Only one person brought up the issue of culture and how numbers are perceived. It really gave me pause to deeply consider the impact our culture has on how we perceive math as well. Particularly in the areas of spatial sense.

In the article ‘Does Your Language Shape How You Think’ by Guy Deutscher, I was really drawn in when I read that speakers of geographic languages appear to have almost superhuman senses of orientation, and simply ‘feel’ where the directions are. I couldn’t help but consider how language has deep connections to visual and spatial sense and how we ultimately perform – especially with English when used in our Eurocentric, settler based curriculum.

As the article said:

The convention of communicating with geographic coordiates compels speakers from the youngest age to pay attention to the clues from the physical environment (the position of the sun, wind and so on) every second of their lives, and to develop an accurate memory of their own changing orientations at any given moment”.

The language we use compels our students to pay attention to different cues in the environment. Our language thus shapes our habits in ways that make our spatial understandings feel like second nature.

I was struck by the fact that different languages lend themselves to different languages of space. Some languages explore directions from a more egocentric point of view – ie., directions given in relation to ourselves, whereas others are more geographically oriented. This may not sound like a big deal, until you consider how deeply language shapes our realities and how we perceive and learn about the world around us depending upon the language we have learned.

More questions I have include:

What ‘habits of mind’ form due to the spatial language that we use?

How is our ability to succeed in math class affected by our language?

What if the instructions we give in say a math class is what is preventing a student from understanding instructions?

What about our English Language Learners who may be confused based on instructions that are more egocentric or more geographic?

Do we assume that the student has learning difficulties?

Also, what happens when we are trained via language to ignore directional rotations when we commit information to memory?

 

This is another example in the article that was very powerful to me – basically, if I walked into an adjoining hotel room that is opposite of mine, I might see an exact replica of my own room. However, if my friend who spoke a more geographical language walked into my room, they would not see an exact replica – rather they really would see that everything is reversed, and would have the language to describe that. This has big implications therefore in how we commit events to memory, recall them, solve problems, and critically think about the world around us.

The language we use compels our students to pay attention to different cues in the environment Our language thus shapes our habits in ways that make our spatial understandings feel like second nature.  It therefore will compel our students to think differently about math.

We make so many decisions each and every day about the world around us – so much of this is spatial. We just simply don’t know our language and habits impact our ability to succeed in math.

We really are at the center of our own worlds. If we determine that subjects like math are linear and one-dimensional, with set algorithms and languages to describe, know and understand, then we are absolutely missing the worlds of many of our students. To dismiss language, culture and our identities of our students could very well mean the difference of success and achievement vs failure.

 

Deborah McCallum

D

Spatial Reasoning and Student Success

 

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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: http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf

 

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

References:
http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf
http://tmerc.ca/research/
http://www.pme38.com/wp-content/uploads/2014/05/RF-Sinclair-et-al.pdf
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

https://www.tes.com/lessons/sGvLjtLFbRRUZA/math-and-makerspaces?feature=embed

Math Mindsets

 

 

Originally Shared on:

http://ontariomathresources.blogspot.ca/2016/10/the-importance-of-growth-mindset-and.html

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:

Math Assessment, Home Connections

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?

Strategies

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

2016