Download - Basic Facts Understanding and Automaticity
![Page 1: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/1.jpg)
Basic Facts Understanding and Automaticity
John SanGiovanni
http://jsangiovanni.hcpss.wikispaces.net
![Page 2: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/2.jpg)
Let’s Take a Test…
![Page 3: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/3.jpg)
Traditionally, how have we taught (or learned) basic facts?
![Page 4: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/4.jpg)
They don’t know their facts.
![Page 5: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/5.jpg)
![Page 6: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/6.jpg)
Drill on arithmetic facts does not necessarily lead to recall…….
Drill must be preceded by sound instruction.- Brownell and Chazal,
19351935
![Page 7: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/7.jpg)
Has our approach to teaching basic facts met the needs of
all of our students?
![Page 8: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/8.jpg)
Has our approach met the needs of ANY of our students?• Understanding• Number sense
Has it aligned with our ideas of good teaching?
![Page 9: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/9.jpg)
Why hasn’t memorization worked?
![Page 10: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/10.jpg)
Turn to a “shoulder buddy” and identify all of the skills
needed for this everyday task.
![Page 11: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/11.jpg)
![Page 12: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/12.jpg)
In math…
2 + 4
½ + ¾ 2y + 4y
0.2 + 0.462 + 34
![Page 13: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/13.jpg)
Have we confused memorization with
AUTOMATICITY?
![Page 14: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/14.jpg)
Processing of new information makes heavy use of working memory.
As skills are repeated, the brain recognizes the information and can process it more quickly and with less effort.
Automaticity reduces the load of working memory by as much as 90% (Schneider, 2003)
![Page 15: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/15.jpg)
Computation in the “real world” is done mentally 84.6% of the time.
- Northcote and McIntosh 1999
With this in mind…
![Page 16: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/16.jpg)
Solve the next in problem mentally.
![Page 17: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/17.jpg)
49 + 27
![Page 18: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/18.jpg)
![Page 19: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/19.jpg)
![Page 20: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/20.jpg)
![Page 21: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/21.jpg)
Does memorization contribute to
understanding?
![Page 22: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/22.jpg)
Does knowing your facts mean you
understand?
![Page 23: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/23.jpg)
If our approach that uses memorization doesn’t help kids develop number sense
and/or computational fluency?
When do they develop it?
![Page 24: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/24.jpg)
If we memorize 6 + 8…
Will it help with 56 + 38?
![Page 25: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/25.jpg)
If I understand…
Multiplying by 5 is the same asMultiplying by ½ of 10 4 x 5 is the same as ½ of 4 x 10
I know 68 x 5
![Page 26: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/26.jpg)
If I understand…
Multiplying by 9 is the same asMultiplying by 1 group less than 10
8 x 9 is the same as(8 x 10) – (8 x 1)
I know 37 x 9
![Page 27: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/27.jpg)
New Tricks for an Old Dog orOld Tricks for a New Dog
• Foundational Understanding• Instruction in Context• Intentional Practice• Independent Practice• Assessment
![Page 28: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/28.jpg)
•What +/-/x/÷ means..•Commutative property•Associative property *
Foundational Understanding
Picture Removed
![Page 29: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/29.jpg)
![Page 30: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/30.jpg)
FoundationalUnderstanding
Picture Removed
Picture Removed
![Page 31: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/31.jpg)
Pictures Removed
![Page 32: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/32.jpg)
![Page 33: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/33.jpg)
Patterns andThe Beauty of Mathematics
![Page 34: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/34.jpg)
Develop Understanding+1/+2 (counting on)
38 + 1
74 + 2
![Page 35: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/35.jpg)
Develop Understanding+1/+2 (counting on)+0
198 + 0
0 + 56
![Page 36: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/36.jpg)
Develop Understanding+1/+2 (counting on)+0+10
10 + 23
45 + 10
![Page 37: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/37.jpg)
Develop Understanding+1/+2 (counting on)+0+10Doubles
33 + 33
45 + 45
![Page 38: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/38.jpg)
Develop Understanding+1/+2 (counting on)+0+10DoublesMake ten
4 + 66
53 + 7
![Page 39: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/39.jpg)
Develop Understanding+1/+2 (counting on)+0+10DoublesMake ten
+8/+9 (Using Ten)
38 + 7
59 + 4
![Page 40: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/40.jpg)
Develop Understanding+1/+2 (counting on)+0+10DoublesMake ten
+8/+9 (Using Ten)Using Doubles
33 + 34
45 + 46
![Page 41: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/41.jpg)
Develop Understanding+1/+2 (counting on)+0+10DoublesMake ten
+8/+9 (Using Ten)Using DoublesUsing Knowns
![Page 42: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/42.jpg)
Develop Understandingx 2 (doubles)
12 x 2
210 x 2
![Page 43: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/43.jpg)
Develop Understandingx 2 (doubles)x 10
12 x 10
![Page 44: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/44.jpg)
Develop Understandingx 2 (doubles)x 10x 5 (1/2 of x10)
33 x 5
(33 x 10) ÷ 2
![Page 45: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/45.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1
14 x 1
![Page 46: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/46.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
![Page 47: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/47.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)
6 x 3 (12 + 6)
14 x 3 (28 + 14)
![Page 48: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/48.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)x 4 (x2)(x2)
7 x 4(7 x 2) x 2
23 x 4(23 x 2) x 2
![Page 49: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/49.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)x 4 (x2)(x2)x 6 (x3)(x2)
7 x 6(7 x 3) x 2
42 x 6(42 x 3) x 2
![Page 50: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/50.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)x 4 (x2)(x2)x 6 (x3)(x2)x 8 (x2)(x2)(x2)
8 x 5(5 x 2) x 2 x 2
31 x 8(31 x 2) x 2 x 2
![Page 51: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/51.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)x 4 (x2)(x2)x 6 (x3)(x2)x 8 (x2)(x2)(x2)x 9 (x10) – (x9)
6 x 9(6 x 10) – (6 x 1)
18 x 9(180) - 18
![Page 52: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/52.jpg)
Develop Understandingx 2 (doubles)x 10 (double x5)x 5x 1x 0
x 3 (x2 + x1)x 4 (x2)(x2)x 6 (x3)(x2)x 8 (x2)(x2)(x2)x 9 (x10) – (x9) x 7 ---- just one
![Page 53: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/53.jpg)
Good Mathematics Teaching
ContextProblem Solving
PracticeAssessmentPicture Removed
![Page 54: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/54.jpg)
Draw 10 meatballs on one of your paper plates.
Draw 9 meatballs on your other paper plate.
![Page 55: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/55.jpg)
Picture Removed
![Page 56: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/56.jpg)
![Page 57: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/57.jpg)
Intentional Practice
Picture Removed
![Page 58: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/58.jpg)
Intentional Practice
1.Fold a piece of paper in half and then in half again.
2.Label your columns a number, double it, double it again, double it again.
3.Write some numbers in the first column and complete the other columns.
![Page 59: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/59.jpg)
Intentional Practice
![Page 60: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/60.jpg)
Engaging Practice: Games
Picture Removed
![Page 61: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/61.jpg)
Engaging Practice: Games
![Page 62: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/62.jpg)
Engaging Practice: Games
Match ‘Em Up
![Page 63: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/63.jpg)
Assessment
What is our purpose?
Picture Removed
![Page 64: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/64.jpg)
Traditional Tests
• Negative impact• They don’t teach
anything• Can reinforce
inefficient strategies• Avoid overuse Picture Removed
![Page 65: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/65.jpg)
Picture Removed
![Page 66: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/66.jpg)
![Page 67: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/67.jpg)
![Page 68: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/68.jpg)
Data from Observation
Picture Removed
![Page 69: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/69.jpg)
Student Progress
![Page 70: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/70.jpg)
Positive Attitudes
• Recognize progress• Provide support• Reasonable
expectationsPicture Removed
![Page 71: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/71.jpg)
All students are able to master the basic facts-including children with learning disabilities. Children simply need to construct efficient MENTAL tools that will help them. - Van de Walle, 2005
![Page 72: Basic Facts Understanding and Automaticity](https://reader036.vdocuments.net/reader036/viewer/2022062521/56816643550346895dd9b5dd/html5/thumbnails/72.jpg)
All students are able to master the basic facts-including children with learning disabilities. Children simply need to construct efficient MENTAL tools that will help them. - Van de Walle, 2005
But we have to:• teach them in context with problems. • practice them in an intentional and engaging way.• assess them in a fair way that promotes growth.• believe that they can.