Learning Numbers: Introduction to subQuan preK-2nd grade
•
1 like•646 views
NWMC12 K- 2 Number Sense: An introduction to subQuan with the research leading up to our findings. Experience the joy of math to your eyes. It's instinctual! Part 1 of 2.
More Related Content
Recently uploaded
Recently uploaded (20)
Featured
Featured (20)
Learning Numbers: Introduction to subQuan preK-2nd grade
- 2. Learning Numbers: Introduction to subQuan preK-2nd Please contact us if you wish for us to present this class via the internet directly into your classroom. Fee arrangements made via professional development or grants.
- 3. Is counting a culprit?
- 4. Is language a culprit?
- 9. Cubes
- 10. Cubes Squares
- 12. Ones
- 18. Response time in milliseconds per objects
- 21. 2D BNS A – empty to fill video
- 29. What have we done so far? - Subitizing - Organized Subitizing - Ordered Organized Subitizing Too big of a mouthful! subQuan = sudden quantity
- 30. Place Shape Representation subQuan Standard Form 43127
- 31. Forms of subQuans Standard Form 43127 Expanded Form 4(7)3 3(7)2 1(7)1 2 Place Shape Form 4 Cubes, 3 Squares, 1 Seg, 2 Ones base 7 Word Form ! four three one two base seven !
- 37. Exit Quiz: What shape are the 4’s? 3’s? 5’s? 5432x How many Cubes? Squares? Segs? Ones? 1234x
- 38. Enrichment: What quantity of unit cubes are in 32145?
- 39. Learning Numbers: Introduction to subQuan preK-2nd Please contact us if you wish for us to present this class via the internet directly into your classroom. Fee arrangements made via professional development or grants.
- 40. Preview of next sessions: Session 2: Metapatterns & Algebra Today @ 12:45pm (here) Session 3: Differences & Calculus Saturday @ 8:30am Grand Pacific Pender North
- 42. "We are here"Visit us in Second Life to experience the full effect of 3D visualization.
Editor's Notes
- You’re given a deck of cards and asked how many? You count 51. Puzzled, you count again: 51. The person next to you counts 52. You count again: 51. Now you’re frustrated so you turn them over and sort to find the missing card. What other counting strategies do we have?-groups, color, groups of ten
- American students have to learn twenty different number words to count to twenty whereas Chinese children repeat the digits and only have to learn ten number words. The impact is that over 80% of Chinese children can count to 20 while less than 50% of American children cancount to 20 at the same age. It takes American children about three years to catch up to the Chinese. Incidentally, Chinese number words are all mono-syllable. SubQuans use the last syllables of zero and seven to address this.IS THERE AN ALTERNATIVE THAT WOULD HELP LEAP AMERICANS BACK TO THE LEAD?
- StanislasDehaene collected research on animal instinctual number sense.
- He also tested babies and their ability to recognize differences between small quantities.
- First published in 1997, Dehaene went on to prove that number sense is instinctual. We are born with the ability to recognize quantities up to four with very little error.
- “Let’s test our innate ability.”I’m going to show you a set of plates one at a time. See how fast you recognize the number of buttons on the plate. Remember, do not count! Shout out the answer as soon as you know it. **Ready, go. Blue plate 2, pink plate 5, white plate 1, orange plate 4, green plate 3, yellow plate 0.**Let’s continue with shapes. Shout out the number. First, Cubes.
- 4Now, Squares
- 3 Now Segs
- 5And finally the Ones
- 3Let’s act like birds and look at a mixture of shapes. I will call out a shape, you shout back the number of that shape. Ready.
- Ones (2), Squares (4), Segs (3), Cubes (2)These other shapes act as distractors. But we still see that our instinct is not confused by these distractors. We are human after all.But what happens to our number sense as the number of objects increases? How many cubes are on the next picture?
- Were there fewer shout outs? Maybe because many of us resorted to counting to avoid the possibility of errors.Let’s get everybody shouting out this time. How many Squares are there in the next picture? Ready?
- What’s happening? We were really fast and all together with the small numbers.How many Segs are shown here?
- And finally, how many Ones on this next slide?
- Well you probable noted something? We got slower as a corporate body. Some of us were better than others.
- Dehaene noted this slow down too. [whatever else needs to be said]Anyone want to understand one reason why birds fly away from certain food?
- Eek!But what if add some organization.
- Which is easier to quickly recognize quantity of buttons? It’s clear that organization helps. Our test of over 300 subjects including 5ht graders, 8th graders, 11th & 12th graders and others indicates the everyone could recognize organized shapes in less than a second. Well, that’s not exactly true. One student could not. When we inquired about her math grades we were told she was diagnosed with dyscalculia. Hmmm.We searched the researched and found nothing on organized subitizing, but rather a focus on “conceptual subitizing”: composing/decomposing quantities by recognizable patterns. But even these quantities can get too large to recognize and therefore we need containers.You know them as place values: groups of ten.
- Nothing new here.
- Standard place values are very limiting in scope. But the shapes are here, too. See the cubes and the squares. We had no word for the shape of the tens, but ones are last in line. To come up with a shape for the tens, we looked at dimensionality and asked the 300+ students that we were working with. They agreed that cubes are 3-dimensional, squares are 2-dimensional, and tens are 1-dimensional. What is a 1-dimensional shape? A line segment, but to stay with our pattern of one-syllable shape descriptors every student agreed that ‘seg’ was definitive. Remember, even babies can distinguish between word syllables.We have two problems with our 0-9 numbers: anyone know what these are?
- The problem with only looking at groups of ten is that life doesn’t always come in tens.
- Why 2d and 3d?
- Here we have base2 through base 10 or A. The shapes are consistent! We call this a metapattern.
- But the shape still holds for any size container.Foundation for place shape vs. place value: number patternsDifferent bases have the same shapeWhy do we need to learn place shapes in addition to place value? - It connects place value with real world shapes. - Consistent across all container sizes. - And the biggest reason is it translates very easily into algebra and calculus concepts.
- TheHands teach all shapes- maybe
- Let’s go back to subitizing our ordered and organized objects. Here we have a base ten BNS. In relation to the Common Core Standards, we have specific ways of denoting this number: standard, expanded, word, and place value form.Standard = 547Expanded = 500 + 40 + 7Word = Five Hundred Forty SevenPlace Value = 5 Hundreds, 4 Tens, 7 Ones
- But in subQuan these same forms take on different phrasing as we don’t work solely in base ten.Standard = 4312b7Word = Four Three One Two base SevenPlace Value = Four Cubes, Three Squares, One Seg, Two OnesExpanded = +4(7)^3 +3(7)^2 +1(7)^1 +2
- Said as sQ’s in standard, word, place shape, and expanded form.
- g4353b7
- g3265b7
- G3265b9 (same subQuan as the previous slide, but definitely not the same quantity!)
- g5127b8
- g8975bA
- What is the subQuan? [25417]5432x: What shape are the 4’s? 3’s? 5’s?1234x: How many cubes? segs? ones? squares?Enrichment question: What quantity of unit cubes are in 32145 ?
- 434
- Our website at IOT1 allows you to challenge your speed of number and pattern recognition.