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Steve Wyborney's Blog: I'm on a Learning Mission.

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Steve Wyborney's Blog: I'm on a Learning Mission. - Sharing Thoughts About Education

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Steve Wyborney's Blog: I'm on a Learning Mission.

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In my previous post, Provide Massive Space to Notice, I described how to repeatedly use the same dot pattern to promote noticing. In this post, I would simply like to give you 10 pages of dot patterns which you can download and use with your students. The purpose is to promote a wide variety of seeking perspectives, noticing , and recording observations in ways that can be very useful. Simply watch the video and download the pages.

You can download the pages from the video here. Each PDF is an individual file, so feel free to download each one separately.
Page 1, Page 2, Page 3, Page 4, Page 5, Page 6, Page 7, Page 8, Page 9, and Page 10.
Also, in the next post I'll describe how you can use a tool that I've developed to make your own pages in 10 seconds or less.
Other Posts That May Interest You 12 Ideas to Propel Your Growth Journey The Number Concept Map (Video and PDF) The Animated Multiplication Table Finding Bedrock Further Notes
Thanks to Martin Joyce (@martinsean) for sending the following image of student thinking, which he has detailed along with several other idea in his post "Day 83: Number Talk, Transformations, Quadratic Regression Model."

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In my previous post, Provide Massive Space to Notice, I described how to repeatedly use the same dot pattern to promote noticing. In this post, I would simply like to give you 10 pages of dot patterns which you can download and use with your students.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Here is a new resource for you: The Number Concept Map.

While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for connections among the ideas once that have been gathered.

I hope the video and the downloadable Number Concept Map will be helpful in your classroom. I would love to hear about your classroom journey!
You can download the blank number concept map here.
If you are interested in other animated posts, you might want to take a look at " The Animated Multiplication Table."

You may also be interested in Math Imposter Sets (with video and PDF).

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Here is a new resource for you: The Number Concept Map. While there are many different ways this resource could be used in the classroom, I've provided a recording below to detail how you might gather representations in your classroom community, and also to show how you might use those representations to look for connections among the ideas once that have been gathered.

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Explore Nicki Newton's board "REKENREK" on Pinterest. | See more ideas about Teaching math, Teaching ideas and Number talks.

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Ways of Knowing, Knowing Ways: Whitecourt 2017
JULY 10 to 14

Effective instruction encourages students to match, sort, classify and COMPARE. Thinking begins from these simple skills.

As you introduce a new concept be thoughtful. If we only allow one way to build, one way to explain, one way to represent we narrow INTEREST, ENGAGEMENT, UNDERSTANDING and ABILITY.

We make it simple cause we think we are helping. Quite the opposite, we are removing the most important component of learning. COMPARE, describe, explain, discuss, adjust, refine, come to consensus. Once students are willing to engage in learning, you can teach them anything.

We sorted words. This represents a sort. Do you see any reason for the sort as it sits? Look very closely. Using the words, seeing, saying, spelling them is a critical literacy connection. Students cannot understand a concept they cannot communicate around. Knowing and using the language matters.

CONSIDER AND COMPARE THE STUDENT RESPONSES BELOW. We were identifying the equivalence of one tenth to ten hundredths. Each representation contributes to part of the understanding. But what is still missing?

My goal as a teacher is to help students see the connections before we decide how we will as a class represent decimal fractions.

The materials, year plans, lessons and BERCS CARDS I am sharing at this Summer's Institutes are designed around visual spatial models that support and sustain attention to the development of reasoning and problem solving skills AS, not after, students learn, study, & practice in order to efficiently RECALL FACTS.

Isolated practice with individual facts does not generate success with reasoning and problem solving. Facts memorized in isolation lack meaning and so are easily mixed up or even forgotten. Students resort to finger counting when under pressure.

As you preview BERCS materials some imagery will pop out at you. Rectangular arrays are everywhere....

Part whole relationships abound

Imagery linked to symbols prompts and sustains recall.

Student practice is tailored to meet their current physical, emotional and academic levels of development. The cards provide a range of challenges to allow students to progress toward mastery.

BERCS Cards are supported by a variety of practice pieces. Oral and written.

BERCS cards provide you ready made, differentiated independent practice centres. All you do is choose a method or medium through which students will communicate their learning.

Students can work in pairs or alone. They can use all the cards or just a few.

Teachers who "know" mathematics as a way of thinking, reasoning and explaining the world, not as a set of "rules" to memorize or "answers to try to remember.

University of Lethbridge: K to 3 July, 2017

Hilltop School, Whitecourt: K to 6 July, 2017

WECA, Edmonton: K to 3 only August, 2017

Grande Prairie, AB: K to 6 August, 2017

Number One:

If you want to build proficiency with subtraction at any grade, you must not be afraid to move things in your head.

Start by moving things in real time and discuss the affects of the move. So here is a ChunkitZ puzzle. I see 3 and 2. That's 5.

How do I know this is still 5? I turned the 2, (quarter turn left) flipped it over (reflected) and slid it down to match the left hand side.

I see 8 = 8 because I see 6 + 2 in each of them.I turned the 6 (one quarter turn to the left). Then I slid the dot on the far left side of the middle row down below and lined up with the middle bottom dot. I slid the dot on the far right side of the middle row up. It is above and lined up with the middle top dot. It is still 6 and 2.

NUMBER TWO: Subtraction is an action that emerges when you want to make things equal or maintain equality. These are not equal. One way to make them equal is to remove from one side.

IT IS CALLED SUBTRACTING not take away. first I did a quarter turn to the left. Then I removed one dot and pushed the other to the right. Yes, the action was a removing action but the mathematical term is subtract and the sign we use is a subtraction or minus sign. WHEN STUDENTS HAVE THE VOCABULARY, THEY CAN JOIN THE MATH COMMUNITY. Vocabulary is a part of community. You have to speak the language to join the club. we correct DA DA to become daddy or dad or even father but we leave take away??? I do not agree. You do not take away to solve every subtraction problem.

Number 3: Addition and Subtraction are RELATED. Teach them together, first as a relationship.

If you can add, you can subtract. Since 1997, the Western Protocol for Mathematics and the Alberta Program of Studies for mathematics which emerged from it, has stated this as an outcome in mathematics. Students need to know and understand that addition and subtraction are related. In the 2004 revision, the statement think addition for subtraction was used as a strategy. HOWEVER, it is not just a strategy it is an actual property of our number system. The focus is relationships before equations. Understand the relationship, talk, describe explain the relationship. Then introduce the notation. Not the same day, but once they can explain.....

INVERSE OPERATIONS, is a critical understanding students need to be able to apply when they work with integers, rational numbers and algebra.

Number 4: Subtraction is not just a "taking away".

It is a comparison. Taking part of the whole away can reveal the answer but the comparison might be phrased as difference between. In that case you are looking at 2 lengths or heights, or weights or quantities and comparing them.

My sunflower is 4 meters tall. My mom's is 3 metres tall. How much taller is my mother's sunflower. (You do not see taking a sunflower away in your head. You see the space between the sunflowers.)

B.E.R.C.S. cards and tasks were designed to prompt and promote visual spatial reasoning. They focus on the relationships that matter. They prompt communication, problem solving and critical thinking. Use them to support your Guided Math approach. Use them to open lessons as warm-ups or as the introduction to a lesson. Use them with small groups or individuals for added practice. Use them to differentiate so that every student builds his or her full potential.

"WAYS OF KNOWING: KNOWING WAYS"

Thinking101 Institutes are dedicated to fuelling the evolution of learning that is teaching. Every summer, every session deepens the connections between Numeracy, Literacy, Science and Math. The ARTS are INFUSED throughout, a little or a lot. An approach to teaching and assessing that values- no prizes visual/temporal spatial reasoning is an approach that includes EVERY LEARNER, EVERY CULTURE, EVERY BACKGROUND.

It embodies and encompasses a holistic world view, a holistic learning view... we all share the gift of coming to know as a body mind connection... Visual models can bridge any gap be it: Literacy, Numeracy, Remembering or Recall.

Infographics is more than reading graphs and organizing data. It is an approach that makes connections and patterns burst forward as students discuss and COMPARE.

The focus is thinking and comparing: the teacher role is to prompt, probe, prod.... immerse students in the vocabulary, shape and mould the pathway from seeing and experiencing through thinking and doing to understanding the conventions of the discipline. We do not start from memorizing symbols and rules... but we can certainly end up with understandings of the symbols and rules.

How does this:

Link to this:

And to this?:

"WAYS OF KNOWING: KNOWING WAYS"

Thinking101 Institutes are dedicated to fuelling the evolution. Every summer, every session deepens the connections between Numeracy, Literacy, Science and Math. The ARTS are INFUSED throughout, a little or a lot. An approach teaching and assessing that values- no prizes visual/temporal spatial reasoning is the BASIC SKILL for learning, anything even MATH FACTS!

This summer my new word is INFOGRAPHICS. The topic is huge and all encompassing. Making sense of the mathematics that is all around us, often used to influence us, often used to bias our decisions. Infographics refers to an approach to actively, deliberately teaching students to connect and communicate the development of their literacy, numeracy and critical thinking skills through the use of graphics based artifacts. STEM, STEAM with a focus on learning to think, not a focus on making products.

Over the next few weeks I will share samples to demonstrate the breadth and scope of using INFOGRAPHICS as the organizer for curriculum. Here is one:

As a class we looked for connections between the problem told orally and the diagram this student created to share her solution. Here is what we came up with through that discussion. We can now use the information on the diagram to re write the problem or to improve our own solutions.

or to start building the number relationships that will support the kind of number practice Grade twos need to constantly engage in. Do you understand this table that we created from information in the picture?

Can you make a t table? Here is a different problem. Build a t table to show some solutions.

My dad gave me 12 nails. He said I had to let my sister hammer more than 6 into the wood.

How many could I let her hammer? How many will I get to hammer?

This past weekend a phenomenal groups of mathematics educators, researchers and learners met at the BIRS research station, Banff, Alberta for the annual Math Fair Retreat. I share here thoughts and reflections the weekend spawned.....

Traditional cultures, traditional arts, traditional ways of "knowing" ourselves and the world are highly spatial, highly visual and can be used to build, adapt, refine spatial reasoning skills that improve our abilities to reason and think. Why are we not immersing ourselves in the experiences, then noting the "math" connections as they become apparent. Why do we start from "math" first as though the knowing of mathematics is more important than the Coming to Know....

Read the following excerpt that describes the traditional art of bark biting and tell me again about what mathematics and knowing mathematics entails???

As I was when I first heard an interview with a traditional bark biter, I am left breathless in wonder as I consider the incredible skill and knowledge involved in birch bark biting. This is mathematics in our world.

Another of my favourite topics is Knot Theory and for just a few brief moments I got to immerse myself back into the world of knots. Knots are opening the door to math, science pursuits never before dreamed possible. The world awaits and all you need literally is a shoestring!!

This summer we will re enter the world of spatial reasoning with a powerful look at INFOGRAPHICS and how we can use the appeal of the visual spatial temporal world to connect ALL students and ALL cultures to Literacy as Numeracy and Numeracy as Literacy. Ways of Knowing, Knowing Ways....

Here's an article to consider:
order-of-operations-the-myth-and-the-math
The evolution has begun, WE WILL CHANGE THE WORLD... Join me for SUMMER INSTITUTES 2017.... Multiplication is not repeated ADDITION... It is much, much more and our KIDS DESERVE TO KNOW "why?" AND " Why DO they have to learn this?" Make the mathematics they learn meaningful in a way that leaves them wanting to LEARN MORE....

LITERACY IS NUMERACY, NUMERACY IS LITERACY and let's not leave out SCIENCE. Comprehension, reading and writing skills do not grow in a vacuum. We use the content of math and science in engaging, authentic and challenging explorations and experiments to develop the skills that link them all.

IT IS WELL PAST TIME FOR TEACHING TO EVOLVE OR GO EXTINCT.... THE world demands it, our kids deserve it...

MARK THESE DATES:

JULY 10 to 14: WHITECOURT, ALBERTA, CANADA Finding Common Ground: Making the Connections: Literacy, Numeracy, Critical Thinking.... K to 6 Registration is now open

AUGUST 14 to 18: EDMONTON, ALBERTA, CANADA FINDING COMMON GROUND: THE EVOLUTION CONTINUES. Every year adds a new layer

TEACHERS, COACHES, LEADERS who are engaged in change at any grade level... This is the continuing journey. All you need is a mindset not willing to accept the MEDIOCRITY that education contains to MIRE DOWN IN.... and a passion for EXCELLENCE. Every learner deserves to learn.....

How do you think about the link between 21st Century Competencies and the learning of mathematics? The list below sounds suspiciously like the reasons I teach mathematics ergo mathematics is a creative endeavour.... More evidence for why our teaching must EVOLVE or go EXTINCT.... mathematics should make students curious, joyful and excited to discuss, compare and create.....

I would add:

Students composing and decomposing number, space and shape in multiple ways through various mediums.

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JULY 10 to 14 Effective instruction encourages students to match, sort, classify and COMPARE. Thinking begins from these simple skills. As you introduce a new concept be thoughtful. If we only allow one way to build, one way to explain, one way to represent we narrow INTEREST, ENGAGEMENT, UNDERSTANDING and ABILITY.