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

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

 

Professional Learning: Does it work?

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I have been doing some research lately into Training Evaluation, and quite unexpectedly have become intrigued at how we measure professional development and whether it really works.

A lot of time, money, effort, resources, blood, sweat, and tears goes into PD. We as educators provide and receive PD regularly, but does it change our learning stances? A learning stance could be viewed as our own theory of learning, which impacts how we will continue to develop professionally. These stances cannot help but impact how we choose to change, or not make changes in our own practice.

Sometimes, educators might believe that we have the ‘right’ way, or that ‘we know what works in education’, or ‘we alone understand what the students need’. I do think that these stances can become problematic, in that they can prevent us from learning, growing and evolving with our students. If we are thinking about student learning, in addition to justifying money spent on PD, then we need to think about this uncomfortable area.

Also, in education we may focus more on the design of the Professional Learning, including learning principles, sequencing of training material, and job relevance. However, one area where we may be able to improve includes an increased emphasis on trainee characteristics including ability, skill, motivation and personality factors. In addition to work-environment characteristics including supervisory and peer support. All of which have tremendous impacts on learning, and perhaps this is a reason why schools tend to maintain their ‘culture’ over time. It becomes more of a situation where the learning gets changed to fit in with the culture, versus the culture changing to retain new learning. I think that this embodies a ‘transfer problem’. Can we truly transfer our learning from our professional development, and if so, how would we measure that?

Some interesting information that I have processed include 3 prevailing strategies that can be used used that could prevent us from making substantial changes to learning. (I will need to re-evaluate where I found similar information).

I have re-applied them with my own questions about how we as educators possibly deal with new information.

3 Strategies to avoid Change:

  1. Finding ways to reject the new content we are being presented with
  2. Modifying any new content to make the changes less demanding. This includes modifying the content as close as possible to current practice so that we can say we already teach that way, and
  3. Pinpointing only the content that we can easily implement. This means that we teachers will use elements of the content that we can easily apply to our teaching without changing it fundamentally.

I can’t help but wonder what this all means for education. Myself, I can see #2 and #3 happening quite unconsciously. After all, learning is very hard. Learning new things is uncomfortable. It can be very easy to look at a new professional development opportunity assume that it is already quite similar to what we already do – thereby missing key information that could be important.

I have many questions regarding the 3 strategies as well.

First, are they merely proof of the human condition and how we want to learn in ways that help us to feel comfortable? If we remain comfortable, what are implications of this for our students?

What about our educational institutions? How can our schools actively create cultures where we teachers value this feeling of being uncomfortable with learning? Does this behoove educational institutions to create new organizational cultures? How can leaders work to shake up learning cultures that need to change? Who, or what variables, decides whether a learning culture needs to change anyway?

At what point can we take a step back, feel confident in what we are doing, and give ourselves that pat on the back for working so hard and having a competent learning stance? Can we do that? Should we do that?

How do motivation and prior experience impact whether we will allow ourselves to become uncomfortable with learning? And finally, how do we accurately measure the transfer of learning in the first place? Can our learning stances change?

Finally, if we knew the answers to these questions, would it change the way we provide Professional Development for educators?

Does PD work and how do we know?

Certainly a lot to think about. Much more than what can realistically be discussed in a small blog post.

What are your personal insights on this? 

 

Deborah McCallum

c 2016

 

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

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

Learn something new each day!

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Learn something new everyday. That is how the old adage goes. But how many of us are actually learning something new each day? Learning something new is uncomfortable. It is a process that cannot be isolated to one day. How many of us are actually learning new things, versus evolving and reinforcing what we already have learned?

As educators, we teach and facilitate learning each day. We understand the processes by which people learn. We understand the importance of introducing new material and concepts. We provide the strategies, feedback and encouragement to promote learning. We gradually release responsibility for students to take ownership of their learning. We even attend regular PD to learn new concepts, ideas, and more. Education is our passion. Our career. We are always learning and adding more to our learning frameworks. Forever thinking about our students and how to help them succeed.

Perhaps our teaching processes become so automatic that we feel like we have the learning process down-pat. However, sometimes I have to stop and think about whether I myself am also engaging in the kind of thinking that we are asking students to do in the 21st century.

Do I truly understand what active learning is, if I have not actively learned something brand new in a long time?

What does it mean to learn something new?

I don’t mean an iteration of the same learning and teaching we have always done. I mean something completely new. Perhaps something we have no background for. No context.

This is the point where so many of our learners are at when they come into our classrooms and learning environments. They are brand new to what is being taught, with no background knowledge, contexts, or strong frameworks to insert new knowledge.

There is danger when we forget what the learning process feels like for new ideas and information.

When we engage in Professional Development – much needed and so important- and we may in fact be learning new things. However, this can be easier than learning something brand new because we already have strong frameworks of learning build from our years as a student and educator.

Learning that fits into existing frameworks can make us stronger and grow. However, it can also make us forget what it is like to be brand new to a topic, idea or subject. We can forget about the power of talk, and forget about the power of visuals and organizers. We can forget that there are multiple points of view on many different topics and ideas. We can forget how lost and lonely it can feel when are forced to struggle with something we have never done before.

Remember what it is really like for our students to learn something completely new. What having a Growth Mindset really feels like, and looks like. What it means to learn something brand new, and at the same time learn how to integrate into new technologies.

So go out and learn something new today!

 

Debbie McCallum

c 2016