1	What do we really mean by Computational Fluency?
2	What is your definition?
3	A Traditional Definition. A person who is computationally fluent is able to compute the exact answer accurately, using paper and pencil, to an arithmetic problem involving whole numbers with all four operations: addition, subtraction, multiplication, and division
4	Too Narrow a View The problem is that this definition is too narrow in scope. It only takes into account one facet of computational fluency. In fact, it ignores the method that is used most often by adults.
5	A six-month survey involving 200 individuals found: • 84.6% of all calculations involved some form of mental mathematics. • 11.1% involved written mathematics. • 6.8% involved the use of calculators. • 19.6% used other physical objects. Total is not 100% because some instances used more than one method.
6	1 Shirt costs $37 1 pair of Shorts costs $38 How much would you spend if you bought one of each?
7	"A computational child" A computational child is automatic with the basic facts understands our number system.
8	"A computationally fluent child" A computationally fluent child makes a conscious effort to complete calculations using prior knowledge and simpler calculations.
9	Is this Numerically Powerful?
10	Important Qualities of Algorithms Efficiency Accuracy Flexibility
11	"A computationally fluent child is..." A computationally fluent child is Accurate and Efficient. The child chooses appropriate calculation methods to obtain exact answers and to estimate, and he/she performs those calculations accurately, and with relative efficiency.
12	"A computationally fluent child" A computationally fluent child can perform the steps in an algorithm correctly and can discuss the underlying ideas and important relationships used.
13	A student is given the task 140 - 85 How could they compute the exact answer? Traditional Algorithm- Focused on the digits. 140 - 85
14	Two alternate methods
15	Adjust the numbers to make the computation more friendly.
16	Adjust the numbers to make the computation more friendly.
17	Left to Right The most common method used without teaching. This makes sense because we read left to right and kids work with manipulatives from big to small (left to right).
18	That leaves 60. Take away 5 more.
19	That leaves 55.
20	"A computationally fluent child" A computationally fluent child is flexible. He/She typically uses a variety of calculation strategies, even when completing calculations involving the same operation.
21	For the problem 53 - 27 = A student might add 3 to both sides making a new sentence 56 - 30 =
22	The same child might use a different method for 53 - 29 Get to a decade number using chunks. Add one to 29 to get 30. Add 20 to 30 to get to 50. Add 3 to 50 to get to 53. What’s the total of the chunks? 29 + 1 + 20 + 3 = 53 - 29 = 24
23	He/She may use yet another method for 53 - 25 53 - 23 = 30 and 30 - 2 = 28 This break apart method involves the understanding of numbers to realize that 25 = 23 + 2 and that fact is useful in this situation. Could also be done 50 - 25 + 3
24	"The student that uses a..." The student that uses a flexible approach to computation is much more powerful than one that only uses the traditional column algorithms.
25	So why do kids latch onto the Traditional Algorithms? There is a proven link between smoking and lung cancer and yet despite that Each day, nearly 6,000 children under 18 years of age start smoking; of these, nearly 2,000 will become regular smokers. That is almost 800,000 annually. Why? Various forms of pressure and tradition keep the habit alive.
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27	Four Arguments in favor of this proposal:
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31	Classroom Flexibility Classes have different needs so one size does not fit all. Teachers need to have the professional discretion to decide what their kids need to learn and how to best teach it. However, we also need to agree to have all our kids reach expected standards no matter how we strive to achieve those goals. And we have to accept that there will be outside assessments for which we must prepare our kids.
32	What should I be doing in my classroom to foster fluency? Mini-lessons Activities Problem Solving
33	Mini-Lessons This is a short lesson that is similar to Daily Tune-Ups. The difference is mini-lessons are focused on one big idea for a period of time. This long window of learning allows time for fluency to develop.
34	Focus for Grade Levels
35	Activities Activities are a form of repetitive practice - like flash cards; but kids like activities more than paper and pencil drill. They will practice more and longer in this format. Once an activity is introduced, it can be played in small groups with differentiation that allows time to re-teach those kids that need it.
36	Work to Do We need to have a more coherent view of what each grade level is expected to accomplish in terms of computational fluency (see Frameworks as guideline). Then each grade level must take ownership for making sure all students are computationally fluent to that standard.
37	My biggest fear By establishing these standards, my biggest fear is that I will set in motion a swing back to a system of teaching that is based on a series of procedures. Nothing could be further from my intent. I want students who are Numerically Powerful and everything that implies: accurate, efficient, flexible, with understanding.
38	How can we meet these standards and have students retain their number sense? We must build from the conceptual to the math notation in a systematic manner. Concrete Mathematical Models Math Notation
39	The goal is to move from the fingers to fluency but to not lose the number sense. If we stay at the concrete level too long we do not foster fluency. Manipulatives can keep us at the counting stage.
40	A study was done on how one child solved this problem over time: 32 - 19 =
41	Be Careful- We tend to go too quickly to paper! We need to build the transition from concrete to math notation in a way that builds on the student’s understanding. If we go too quickly, they just rely on procedures: a set of rules.
42	Concrete Kids physically interact with the tools. Counters Snap Cubes Money Base 10 Blocks
43	Mathematical Models Kids represent the concrete manipulative or a problem situation with a diagram.
44	Math Notation Students learn to label their mathematical models using numerals and math symbols.
45	Activities also give us the opportunity to teach math notation with context One of my favorite activities is, “What’s Hidden?” It is a part-part-whole activity and teaches addition and subtraction concepts.
46	How you play Students take some counters. They determine how many there are. Their partner then hides some of them. They must figure out What’s Hidden?
47	Students can draw what they saw and then label with numbers.
48	This can grow into math notation.
49	Older kids might record like this (moving to numbers) :
50	When presented with 34 - 17 the student might be thinking
51	How would you solve it? 17 + c = 34 or 34 - 17 = c What algorithm would you use? Would you do it in your head, on paper, or with a calculator? How do you know your answer is correct? How sure are you?
52	If we have students that ask themselves questions like these when presented with a problem like 34 - 17 =
53	I think it would be time to celebrate!