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

Joseph Boyden

This morning I read the following new article by Joseph Boyden in MacLeans. It gave me a lot to think about.

Here is the article.

http://www.macleans.ca/news/canada/my-name-is-joseph-boyden/

This article really brings into question for me about what being Indigenous really means, and what elements create your own identity. On one hand, it has really struck me that so many ‘others’ are questioning what his identity should or shouldn’t be. However, I have come to know that identity is not all about DNA or blood quantum. It is also about the ‘intimate’ conversations and language you share with the people who shape who you are. It is the language that moves through them and with them that make you who you are – perhaps more than Blood Quantum. I fear that Boyden is benefiting from claiming Indigenous identity, without belonging to an Indigenous community in this way. He states that he identifies most of his life as an anglo-white male, growing up in a mainly anglo-christian household. I am curious about which community or culture is he giving back to? Working to make better?

This is more than just about Joseph Boyden and the fact that he has some Indigenous DNA. What does his story mean for others who define their identity as Indigenous? All of the others who also do not ‘look’ Indigenous’, but are, yet continually asked about what percentage of Indigenous they are – as if there is a magic number that decides.

I am curious as well, did he ever have to live with what it feels like to ‘Live in the hyphen’? Did he experience racism by both white and Indigenous cultures? Was he questioned and rejected by both anglo and his Indigenous cultures – I would infer no, as it appears that he has not been part of such a community his whole life. It feels like he has just decided to ‘live in the hyphen’ now, but only to reap the benefits of both worlds. Not to help heal the traumas, or contribute personally – as one would do with those in our lives who helped to shape us.

After much careful thought, and more reading, I have come to the conclusion that identity is very much about belonging. Whose community do you belong to, and who belongs to you? Blood quantum cannot be looked at in isolation. If you have no community that you can truly claim, and who claims you in return, then how can you truly identify with it? How can you give it a voice? And finally, if you do have a community, how are you using your gift and fame to make your community better, and not just yourself?

This brings up a lot of questions about identity, what community is, and about whose identities deserve privileges, and whose do not. Why do we decide this? We do it without even realising as well.

If you haven’t already heard it, this is a great Podcast to listen to as well: Ep. 73: White Settler Revisionism and Making Métis Everywhere 

I will continue to think about my aporia, and my personal discomfort surrounding this situation with Joseph Boyden.

 

Deborah McCallum

Teaching and Assessment with Math Processes

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Teaching and assessment in math go hand in hand. What ties them together are the mathematical processes. Our job as teachers is to help students build mathematical knowledge and skills of the curriculum through the 7 mathematical processes. They  include:

  • problem solving
  • reasoning and proving
  • reflecting
  • selecting tools and computational strategies
  • connecting
  • representing
  • communicating

For instance, here are the math processes for Grade 4 from the Ontario Curriculum:

math_processes_II.png

In order to begin to assess what our students have learned through the expectations and processes, we must set some learning goals to help our students learn.

A Learning Goal must:

  • Have a sense of purpose
  • Build on student ideas about math
  • Engage students
  • Help students develop mathematical ideas
  • Help teachers to assess student progress
  • Connect with the classroom activities
  • Connect with math processes

 

The kinds of activities that we engage in during math class that embody math processes may include the following:

* something to ponder: can you think about what math processes can be embodied in each of the following? Are there any more we can add?

Questioning:

It is important to ask the right questions. The questions help us to facilitate the discussion that will follow. Questions are also used to raise issues and problems

 

Inquiry Based Learning.

As students solve problems, they will develop their ability to ask questions and plan investigations to answer those questions and solve related problems. The goal is to invite student entry into the math problem, and facilitate their exploration of the math.

 

Gallery Walk

The focus of a Gallery Walk is on the student work and interactive discussion shared around the classroom. Students have the ability to read different solutions and provide written and verbal feedback to each other, communicate, and solve problems together.

 

Bansho

Here, the Chalkboard becomes a record of the entire lesson. This really helps us to model effective organization to our students. It also includes cooperative learning strategies including Think-Pair-Share, Think-Talk-Write & Placemat.

 

Math Congress

Here, the purpose is to support development of mathematicians in classroom learning community vs fixing mistakes in student work. We focus the whole-class discussion on 2-3 student solutions that are selected strategically by myself, the teacher. Students also share work with one another, check answers and strategies, ask questions to provoke clarification & elaboration, and defend and support mathematical thinking.

 

Assessments we use:

Assessments will include rubrics, performance tasks, formative and summative tasks, observations, portfolios, journals, interviews and products. Assessment will be based on Learning Goals, expectations, processes and the following Achievement Categories:

Knowledge and Understanding. Subject-specific content acquired in each grade (knowledge), and the comprehension of its meaning and significance (understanding).

Thinking. The use of critical and creative thinking skills and/or processes,3 as follows: – planning skills (e.g., understanding the problem, making a plan for solving the problem) – processing skills (e.g., carrying out a plan, looking back at the solution) – critical/creative thinking processes (e.g., inquiry, problem solving)

Communication. communicating mathematical ideas and solutions in writing, using numbers and algebraic symbols, and visually, using pictures, diagrams, charts, tables, graphs, and concrete materials).

Application. The use of knowledge and skills to make connections within and between various contexts.

 

All of the instructional and assessment practices can be interconnected with the Math Processes as defined in the Ontario Math Curriculum:

math_processes

 

Makerspaces & Math Links

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

STEAM Job descriptions for Curriculum Planning

 

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Using job descriptions can facilitate program planning and student learning. A job description provides us with rich opportunities to extract content areas, learning goals, success criteria, and rich tasks for learning. It just doesn’t matter if the position is paid or not, volunteer or mandatory. The point is that you will often find key information about skills that are important in our world today, and perhaps discover more relevant ways to teach those skills.

In my quest to make learning relevant for students, I have begun to look at job postings for S.T.E.A.M. related work, and think about ways that I can apply them to the curriculum. There are a great number of possibilities that crop up when we consider how our curriculum can be interpreted through the lens of a real job.

Consider the following job description in blue. As you review it, consider the cross-curricular, and integrated learning opportunities that may present themselves. Consider the project-based learning opportunities you can use to help students gain the necessary skills to apply for this job. Where do various technologies fit into this picture?

Check it out: 

_______________________________________________________________________________

BRIDGE DESIGN TECHNICIAN

Organization: Ministry of Transportation
Division: Provincial Highways Management
City: London
Job Term: 1 Permanent
Job Code: 12682 – Engineering Services Officer 3
Salary: 
$1,122.02 – $1,410.37 Per Week*
*Indicates the salary listed as per the OPSEU Collective Agreement.
Understanding the job ad – definitions

Posting Status:

Open
Job ID:
99401
Apply Online
View Job Description
Are you looking for a new challenge? Would you like to apply your knowledge of civil engineering technology and computer abilities in a new way?
Consider this opportunity in structural design while contributing to the safety of Ontario’s transportation system.

What can I expect to do in this role?

In this role you will:
• Prepare scale drawings depicting bridge details and materials for review and approval;
• Prepare associated contract documentation according to Ministry standards using required software;
Review bridge site plans and preliminary geometry information supplied by consultants;
• Carry out quantity calculations and cost estimates;
• Provide and assist in the training of regional staff in bridge inspections, in the use of computerized bridge detailing systems and bridge management systems;
• Provide interpretation of standards, specifications and policies as required;
• Assist in bridge inspections by carrying out inspection of simple structures, and updating and maintaining related databases;
• Provide technical guidance, training and advice to junior staff on bridge drafting and contract preparations, durability and construction issues with complex structural details and innovative techniques ensuring safety and economy;
• Answer queries on technical issues from other jurisdictions as required.

How do I qualify?

(aka learning goals and success criteria, criteria for rubrics and other assessment methods)

Knowledge of Bridge Design

• You have knowledge and skills in the design, detailing and contract preparation of provincial bridge contracts.
• You have knowledge and skills to be able to inspect bridges.
• You have knowledge in bridge design and detailing principles, and ability to consider various constraints such as materials, fabrication and production techniques.
• You have practical working knowledge of the varied and complex safety issues related to the design of bridges.

Communication Skills

• You have well-developed oral and written communication and presentation skills.
• You can use consultation skills to identify needs and maintain effective working relationships with regions and other functional teams
• You are committed to customer service.

Research and Project Planning Skills

• You can understand and interpret engineering plans and profiles, technical reports and relevant codes of practice.
• You have knowledge of project planning in order to design, detail, implement, lead and manage a number of concurrent projects of varying degrees complexity, individually or within a team environment.
• You have demonstrated analytical, planning, scheduling, project management and work coordination skills.

Computer Skills

• You can use computer systems and their applications, including Computer Aided Design (CAD) systems and database systems.

_________________________________________________________________________________
Now that you have had a chance to look at this, tell me you are not inspired by the sheer opportunities to connect science, math, technology and literacy? How many skills can be extracted and channeled into balanced literacy and math activities? How many rich tasks can be created? What projects and inquiries can be facilitated? How will they culminate into an end of unit(s) assessment task that includes applying for this job?
How can we help students figure out what they need to do next in order to ‘prove’ that they have the skills to apply?
What if my students were given a small bank of job descriptions, and they need to choose one that looks interesting that they will apply for.
Here are a few steps to consider:
1. Conduct your hypothetical job search
3. Teach the feedback skills that enable all students to engage in higher quality feedback and assessment as learning processes.
4. Find the Big Ideas
5. Plan your projects, centers, and assessment protocol.
6. Reflect
7. Share
Job searching can provide key information into the skills and knowledge that are important in our world. They can even help inform our curriculum planning and instructional design. Next time you are wondering how to infuse math, science, literacy and more into your short and long range plans, consider starting with a job search.
Deborah McCallum
c 2016

Helping kids to find their Writing Superpower: by Allison Tait

The following is a guest post by Allison Tait, Author of The Mapmaker Chronicles

 

 

As an author who’s regularly asked to visit schools for talks and workshops, I have one main question for educators: Who am I talking to?

I find that the candidates for small group workshops tend to be made up of what I like to call the Keen Beans – kids who LOVE writing and simply can’t get enough of it. Most of the Keen Beans are writing their own novels by the time they’re eight.

Large group workshops, however, are a different matter. There’ll be one or two Keen Beans – answering all the questions for me – and 28 kids who simply stare at me as though I have two heads if I start talking about plots or characters or, heaven forbid, paragraphs.

This crew perks up immeasurably, however, when I mention superpowers. In particular, writing superpowers – and the fact that everyone has one.

They get even more excited when I tell them that I’m going to help them find their own writing superpower.

 

What is a writing superpower?

A writing superpower is a special strength that you bring to your writing. Everyone’s got one, but they’re not always what you might imagine. It’s not necessarily about the way that you use words, though this, of course, is part of it. It’s more about where you get your ideas from and what you do with those ideas. It’s about whether or not you can get to The End of your story, pushing through when it gets hard. Sometimes it’s about the ability to plan your story out, taking it logical step by logical step, and sometimes, for other people, it’s more about huge leaps, pushing an idea as far as it will go.

There are 10 writing superpowers

  1. X-Ray Vision: These kids are great at describing what they see. They think in pictures, and are often good at drawing as well. Encourage them to imagine a scene in their heads and simply write down what they see.

2. Supersonic hearing: This is one of my superpowers, and is a great source of not only story ideas, but natural-sounding dialogue. Lots of writers I know are eavesdroppers, and I encourage kids to look for story ideas in the daily conversations around them. Mum telling stories about the ‘olden days’ might be a story starter, as might two younger kids in the playground talking about how cool it would be to fly to the moon.

  1. The ability to leap: While it’s important that kids learn to plan a story, those Keen Beans who can start with an idea and a sentence and then follow the story to the end have a superpower. It’s a crazy way to write (I know because I do it) and can go horribly wrong, but if you have a Keen Bean who works this way, encourage them to push their idea as far as they can – as long as they finish the story.
  1. Endurance: If there’s one thing I’ve learnt about writing in the many years that I’ve been doing it, it’s this: most people are really good starters. But the ones who get really good at writing have a very special superpower – they keep going until they finish the story. Kids who finish are superheroes and should be treated as such.
  1. Analytical thinking: Kids who are good at maths often think they’re not good at writing, but that problem solving ability they have can be a writing superpower. When I talk about this superpower, I use Ironman as an example. People who are plotters and planners make up a huge proportion of published authors for one simple reason: they finish their novels. When you have a logical blueprint, you never end up with your hero stuck in a hole with no way to get out (as once happened to me).
  1. Memory: In The Mapmaker Chronicles, my hero Quinn has a photographic memory, which I think is a writing superpower. Kids who have good memories are able to recall not just the things that happened to them, but how they felt about those things. This is indispensable not only for coming up with story ideas, but for using small details to make the stories feel real. I encourage all kids to keep a journal or diary to help develop this superpower.
  1. The ability to shrink and expand at will: While Ant Man is not often associated with writing, I use him as an example of the value of editing your work. He can shrink himself when he feels like it, or be larger than life. Writers who can do that to their work have a superpower – being able to go through your words and remove the stuff that’s not necessary, or add in details that are, is a rare skill. Kids who understand the importance of editing – and are good at it – are miles ahead.
  1. Spidey senses: By the time they get to grade four, most kids have heard that they need to use all five senses when they’re writing a story. But it’s a rare kid who actually does it. If you have a kid in your class who describes the salty taste of the air at the beach, or shows you humidity by describing the sweat rolling down a character’s arms and the damp stickiness of his clothes, you have a superhero right there.
  1. Batman’s voice: this is perhaps the greatest writing superpower of all. One of the questions I’m often asked in high school workshops is this: how do I stop myself from writing like John Green/ Suzanne Collins/ Rainbow Rowell? The only way to do it is to tap into your own writing voice, which is basically the way that you put things together – the words you choose, the sentences you use, the little jokes you put in. The best writers write like they talk – only better.

What does this have to do with Batman? Everyone has their own Batman Impersonation (mine is particularly impressive now that I’ve had to do it at countless workshops). We’re all trying to sound like Christian Bale or Michael Keaton or Adam West – and yet we all still sound different.

Writing is the same. We’re all writing a story, but the thing that makes the story special is our writing voice.

A kid who has developed his or her own writing voice is a superstar.

  1. Bravery: Writers who write what they think and feel, and are willing to let other people read it, are really, really brave. The best thing about this writing superpower is that it can be developed with time and practise.

Why do writing superpowers matter?

Every kid, even the ones who don’t think that writing is for them, can find something on this list that they’re good at – or can become good at (in the case of bravery, for instance).

I encourage kids to identify one writing superpower and use it to give them the confidence to keep writing. Because when you’re confident that you’ve got at least one thing going really well, then it’s much easier to take risks with writing and to try different things.

And, as we all know, the best way to improve writing is to keep writing.

 

Allison Tait (aka A.L. Tait) is an Australian author, who has been working professionally as a writer for 20+ years. The Mapmaker Chronicles, her bestselling middle-grade trilogy, will be available in the US and Canada from 1 June 2017 through Kane/Miller Books.

Find out more about Allison at allisontait.com and more about The Mapmaker Chronicles at themapmakerchronicles.com

mapmakers3fan353

The Importance of a Growth Mindset in Math

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. 



Other Reference:




Makerspaces for All

 

 

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Over this last year, I have had the opportunity to understand what Education for All, Learning for All, differentiation and equity on deeper levels due to working in a Makerspace.

Learning is about problem solving, creating positive math mindsets, constructing and building knowledge through hands on activities, and most of all, promoting equity. No where is this more true than in a Makerspace.

However, I think that we have very deep issues pertaining to equity in our schools and classrooms. The ways that things are traditionally done simply do not facilitate success for everyone – but this is what education is all about – doing whatever we can to help students be successful.

Makerspaces (or S.T.E.A.M. Rooms – Science, Technology, Engineering, Arts and Math), are opportunities for new kinds of teaching and learning that promote equity. Based in Constructionism, Makerspaces are designed to give students the ability to build knowledge themselves with hands on tasks. Our students do not have to learn from the teachers experiences and knowledge, they can actively build it themselves.

Working in a Makerspace means that timelines need to be flexible. This fits in beautifully with Growth Mindsets. Students should not have to feel bad because something wasn’t built by the end of the period – this alone does not prove how much a student learned. What matters is the knowledge built from the experience and the process.

 

 

Consider this example for a moment:

A class is given a design challenge that brings in many elements of structures in science and math concepts with geometry and spatial reasoning. There are multiple entry points, where students can build as simple, or as complex as they would like. Next:

Student A builds a structure in 5 minutes, whereas Student B struggles with the process for an entire learning block, and does not come close to finishing.

The most important questions become: What was learned? What value did each student get out of the process?

Student A feels great because they built something on time. It came fast, and easy. However, student A did not learn anything.

By contrast: Student B doesn’t finish, feels terrible about not finishing. Frustration levels go high. Self-esteem drops.

Both develop a fixed mindset about learning.

What a travesty it would be if Student B did not have the opportunity to understand why there was struggle with the process? What if this student struggled because they were figuring out a very complex piece of learning for them? What if they were taking the risk to learn, even though the stakes might be high?

Student B did not take the easy route. Student B made mistakes. Student B is experiencing frustration which is what happens in learning. Student B doesn’t realise that they are reinforcing an image of not finishing in time as being a bad thing.

Student A doesn’t feel the need to learn anything new. Student A believes that finishing quickly is a good thing. Student A doesn’t have a teacher who will continue to provide opportunities to take the learning even deeper. Student A’s learning stalls, yet Student A benefits from an image of being a model student.

 

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Can you imagine if people were not allowed to change their plans, make mistakes and start fresh? Or worse, what if we as educators are the ones sending these messages to our students that they cannot?

 

I always ask my students, What would happen if an engineer did not ever change plans, make mistakes and even start over?

Now, some students need scaffolding with this – they need to understand what an engineer does, and they need to understand that ‘creating’ and ‘making’ follow a process. They need to understand that we design new ideas and structures to help people.

But when they do understand this, it really seems to click with them. They would WANT an engineer who is designing a bridge, for instance, to stop, revise plans, fix mistakes and start over if necessary. This is far more advantageous than quitting after a mistake, or quitting because work needed to extend past a deadline.

Therefore, working in a Makerspace has to mean becoming flexible with timelines and tasks. It has to be about building knowledge in ways that are very new in our school systems.

My experiences in creating a community atmosphere where students have choice and voice, has taught me a great deal about student learning. It has taught me that I do not have to ‘control’ student learning, yet I can facilitate the learning and help students meet their learning goals in many ways.

This has a huge impact on classroom management as well. In fact, the biggest behaviour issues that surface are the ones directly related to problem solving skills, and from having fixed mindsets. Not from students feeling bored, ‘dumb’, or disconnected from learning.

The fact is, that providing students with different ways of doing things, and providing students with opportunities to learn differently and share their voices in different ways produces greater focus, growth mindsets, and student-centered knowledge building opportunities. In my humble experience, this demonstrates that all students can be successful with opportunities to learn in different ways. It promotes equity.

This takes differentiation and Education for All to a whole new level. We are not differentiating so that students can do what WE want them to do all the time. We are differentiating for them – so that the students can build knowledge in ways that are personally meaningful to them. While still meeting the learning goals. While still learning about the Big Ideas.

What does this look like? 

  • We are facilitating, asking questions, promoting student inquiry.
  • We are starting with the Big Ideas.
  • We are setting key learning goals.
  • We are clustering the specific expectations around them – from many different subjects.
  • We are allowing students to design, plan, construct, and then allowing them to write about it, reflect, problem solve, engage in visual-spatial reasoning. All skills that are proven to increase reading scores and help students to become literate learners.

In addition to problem solving, promoting positive math mindsets, and having the opportunity to build knowledge and understanding in new ways, I believe that Makerspaces have the powerful opportunity to begin to promote equity for students in our school systems.

 

Deborah McCallum

c2016