They will learn arithmetic faster, more fluently, with confidence, speed and accuracy.
Here’s an article to consider:
DO YOU UNDERSTAND NUMBER PROPERTIES??? Then how can you teach NUMBER SENSE?
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.
I do not and will not support DreamBox or any other on line platform for teaching and learning mathematics but this is one of the components that we really really need to learn from…. Christopher writes a great blog, thanks
Here is an email that a friend of mine—father of a first grader in the Minneapolis Public Schools, and math-teacher-on-parental-leave—received from DreamBox, an “adaptive learning platform” for K—8 math.
Congratulations! [Child] successfully completed a group of DreamBox Learning lessons.
Are you familiar with the concept of compensation? This is a strategy that can be used to make addition problems “friendlier”. To use it, just subtract a “bit” from one number and add that same “bit” to the other to create two new numbers that are easier to add mentally.
[Child] learned this strategy by completing a series of lessons using the special DreamBox tool, Compensation BucketsTM. For example, when shown the problem 29 + 64, [Child] turned it into 30 + 63. Towards the end of this unit, [Child] was adding 3-digit numbers with sums up to 200!
On the Run: Friendly Numbers
Take turns supplying two numbers to add. The other player has…
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This is how too many students respond when we ask them to create their own problems. No understanding, no knowledge and no confidence.
This is Grade 4… Where will this student be by Grade 6? The research says we never fill the gaps… I say because we still refuse to attend to what we know now to be true: VISUAL, SPATIAL, TEMPORAL REASONING matters….. especially in math. The numbers make sense when you learn to build them, compare them and then image them as related parts and wholes….
If this student had imagery for number and words, she would make sense of the problem, then be able to set up a mental image for what has to happen with the numbers. She still might make a computational error but she would at least understand what the problem is actually asking her to figure out. I cover this in Thinking 101, place value 101…. book a session, workshop or private tutoring session… You will be amazed at how quickly we can turn this student ON, by engaging her in the learning.
I will be all over the province this year, join me for a day of learning…..
fixed my spleling (ha,ha)
Teach kids to think & reason, then teach “math” or “science” or “socials” or..
So here’s my point folks. We present math ideas with a perspective that pushes students’ focus to the wrong place in the picture or in the manipulative. Then we say see that didn’t work and go back to telling them what to think. Instead, I want you to get rid of “fill in the blank math sheets.” Start giving students fully finished equations and have them learn to read, demonstrate and compare them. What can you change and not affect the outcome.
3 + 6 = 9 is true. No argument.
Now look at my collection of 9 and tell me what else is true?
What happens if you move the collection around? Knowing 9 is the answer is not the same knowledge as “knowing” 9. Think about it. We have to do the right job in…
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What is this grade one telling me about his knowledge of number?
Flash Math is a term I use for the exercises I do with students to support the development of automatic recall with quantity.
Subitizing, conserving number, developing imagery for commutative property, inverse operations, associative property, making sense of one more, one less, hierarchical inclusion are put a few of the concepts that can be developed with flashmath tasks. In the early stages I use dot collections and ChunkitZ.
Students look for 3 seconds, then the image is covered and students are asked to recall the image in their mind. Another 3 second look, cover, recall in their mind. On the last 3 second some students are noting a different way to confirm how many, while others are finally sure they know what they saw. There are 2 goals on flashmath: how many in the set, what parts are related to make the set. So some students say I saw 5 and 3 while others say I saw 8.
The intent is not to match my arrangement,the intent is to know how many you saw and why you are sure of the total without counting. So this boy drew an arrangement he liked better for 8, circled 5 to tell me he saw the five and the three and knew it was 8.
This young man asked me if he could use pictures numbers and words to explain what he saw, then proceeded to show all 3 on each collection.
What collection do you think this boy saw?
Did you note his turned down corner?
Here’s another Grade one spatial reasoner… How do teachers recognize, capture and build on spatial reasoning??
When he saw what everyone around him was drawing he changed it to this,
What happens with these students if we do not?
When students use the materials at hand as thinking tools they demonstrate how they are making sense and constructing meaning. Both these students were quite clear how to explain the number they were dealing with and both had no trouble explaining overall how many tens are in their number. 551 has 55 tens, but 50 of them are packed into hundreds. So you can also say 5 hundreds.
This student drew it first, then separated out the pieces in the second part of the drawing to be sure I understood 294 is composed of 2 hundreds, 9 tens ten less than a hundred, so easy to draw) and 4 ones. Again this student had no trouble explaining there are 29 tens in this 3 digit number.
The struggles I see for students when it comes to place value are all built around a lack of imagery due to lack of experience with the BUILD. We must take time to allow students to build the units, right from the 10 to the 10 000, then backwards to the thousandth. When we do, the pay-offs are immense. Students understand the positions are based on a proportional growth change. They learn to think before they calculate. They make sense of the “zeroes” and are not forced to “line up” the digits, when they add.
You cannot learn this BUILD on a computer. You have to experience first hand with concrete materials. Every classroom Grade 1, 2 and 3 needs to be equipped with snap cubes ( I like “unifix”). Enough for every student to build to the thousand. Not “base ten” blocks. Snap cubes… Base ten blocks should only come out once students have demonstrated they can be flexible with the units…
When students are challenged to visualize, imagine and then build with snap cubes and paper models they experience how numbers are related and the power of trusting units. The experiences support their understandings of magnitude, density, direction, proportional growth. Linear, vs area, vs volume. Making one thousand with strips of ten is incredibly different than making the thousand with squares of one hundred. And the thousand cube is impossible with a flat model.
This picture shows the thousand being constructed 3 different ways. Most adults are astounded to see the difference with the linear thousand. The picture only captured to the first 300.
This is only one hundred in blocks, can you imagine the length for 1000?
Spatial skills and spatial reasoning engage students in the learning. Flexible thinking, mental fluency, confidence, risk taking, these are the skills that student’s develop. If you want students to build and apply common sense, to develop a foundation of practical math skills engage them spatially.
I hear adults says kids do not “know” or “remember” or “recall” but I wonder when we actually actively engage in teaching them how to learn, how to know they are learning, and how to remember what they supposedly learned. Do you agree with the statement below?
Dr. Barbara Oakley, A Mind for Numbers, “unless you can prove that the material is moving into your brain by recalling the main ideas without looking at the page: you are not learning.”
This is why I use BUILD EXPLAIN REPRESENT COMPARE.
Active engagement in your own learning. The teacher’s role is to make sure kids know they are learning … sometimes it is just the exercise of learning itself. So you engage students by having them tell you how they are going to accomplish “learning this”. Make it a challenge, a puzzle to solve… you will be amazed at the difference in attitude and ability….
What is this girl telling me about the task I gave her? About her current knowledge, ability to learn, preferences for tasks, tools and contexts that support learning? About her knowledge of herself as a learner?