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http://www.therecoveringtraditionalist.com/fact-fluency/

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What is Mastery? (+Developmental Phases)

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What is Mastery? (+Developmental Phases)

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Mastery of a basic fact means that a student can give a quick and accurate response (in about 3-5 seconds) without resorting to inefficient means, such as counting by ones.

Teaching Student Centered Mathematics by John Van de Walle

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Cognitively Guided Instruction- Progression of Fact Fluency

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Cognitively Guided Instruction- Progression of Fact Fluency

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http://www.therecoveringtraditionalist.com/fact-fluency/

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Elementary & Middle School Mathematics by John Van de Walle

1. Ask students to self-monitor.
2. Focus on self-improvement.
3. Drill in short time segments.
4. Work on facts over time.
5. Involve families.
6. Make drill enjoyable.

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Drill refers to repetitive, non-problem based exercises designed to improve skills or procedures already acquired.
Benefits of drill:  increased facility with a procedure but only with a procedure already learned.
Limitations of drill:  a focus on a singular method and an exclusion of flexible alternatives; a false appearance of understanding
Drill is appropriate, for short periods of time (5-10 minutes) when an efficient strategy for the skill is already in place.

Practice refers to different problem-based tasks or experiences, spread over numerous class periods, each addressing the same basic idea.
Benefits of practice: an increased opportunity to develop conceptual ideas and an opportunity to develop alternative and flexible strategies and make useful connections
John Van de Walle, 2010, Elementary and Middle School Mathematics
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 Memorizing facts without strategies is not enough

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 Memorizing facts without strategies is not enough

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"Some textbooks and teachers move from presenting concepts of addition and multiplication straight to memorization of facts, skipping the process of developing strategies. This means that students have 100 separate addition facts (0-9) and 100 separate multiplication facts.  They may even have to memorize subtraction and division separately.  However, the reality that many students in the fourth and fifth grades have not mastered addition and subtraction facts, and that students in middle school and beyond do not know their multiplication facts strongly, suggests that this method simply does not work well."

Elementary & Middle School Mathematics by John Van de Walle, 2010

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"Automaticity is the quick and effortless recall of math facts.  No need to count, no need to think about related facts. The answer is automatically known. Automaticity with basic facts is a goal for our students, but alone it is not enough.  Students must also understand the facts that they are being asked to commit to memory.” (source:  O’Connell and SanGiovanni 2011, Mastering the Basic Math Facts)

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Teaching Student Centered Mathematics by John Van de Walle

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What Not to Do When Teaching Basic Facts

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What Not to Do When Teaching Basic Facts

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Elementary & Middle School Mathematics by John Van de Walle
1. Don't use lengthy timed tests.
2. Don't use public comparisons of mastery.
3. Don't proceed through facts in order from 0 to 9.
4. Don't move to memorization too soon.
5. Don't use facts as a barrier to good mathematics.