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Basic Facts

Basic Facts. Basic Facts. What are they? Why should students memorize basic facts?. Why Basic Facts Instruction?. Frees up working memory to master algorithms and math applications. Cognitive psychology research points to the value of automatic recall of facts.

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Basic Facts

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  1. Basic Facts

  2. Basic Facts • What are they? • Why should students memorize basic facts?

  3. Why Basic Facts Instruction? • Frees up working memory to master algorithms and math applications. • Cognitive psychology research points to the value of automatic recall of facts. • Students who do not memorize facts flounder when more complex math is introduced—progress for these student can end at elementary school.

  4. Math Wars(Strauss, Washington Post, Jan. 05) • Among the topics the NCTM and the mathematicians said they agreed on: • Heavy reliance on calculators in the early elementary grades is a bad idea. • Elementary school children must have automatic recall of number facts, meaning that, yes, they have to memorize multiplication tables. • Children must master basic algorithms. The meeting participants spent time defining the word "algorithm,"which means a set of rules for solving a problem in a finite number of steps.

  5. Teaching Math Facts • Three types of instructional activities: • Understanding • Relationships • Memorization • What are these activities? Why?

  6. Relationship Activities • Exercises based on a series (e.g., 3x1, 3x2, 3x2) • Exercises based on fact families and inverse operations (e.g., 5-2=3, 5-3=2, 2+3=5, 3+2=5) • Purpose of these exercises is to make memorization easier

  7. Preskill for Relationships • Plus-one Facts—Format 6.1, page 90 • Teaches facts and relationships. • Rule: When you plus one you say the next number. • Model Part A and B.

  8. Plus-one Facts Part C 8 + 1 4 + 1 7 + 1 5 + 1 9 + 1 (Your turn—format practice!)

  9. Series Saying Prompts students to notice the counting relationship: 6 + 2 = 8 5 x 2 = 10 7 + 2 = 9 5x 3 = 15 8 + 2 = 10 5x 4 = 20 5 x 5 = 25

  10. Series Saying • Format 6.2 Model and Practice • Part A: Reading the Statements • Part B: Reading the Statements with the Answer Erased • Part C: Saying the Statements (No visual prompts) • Part D: Random Fact Drill

  11. Series Saying Format 6.2 Model and Practice Teaching behaviors: • 3-2 seconds per statement • Timing for each statement • Practice, practice, practice and make it fun! • Correction for slow pace—lead and work on increasing the pace • Correction for statement error?

  12. Three Number Fact Families • Sets of three numbers from which students can create 4 statements. • Either—addition and subtraction or multiplication and division. • Teach commutative property of addition (a + b = c and b + a = c) and multiplication (a x b = c and b x a = c). • Why is the commutative property important?

  13. Three Number Fact Families • Format 6.3 • Part A—how to construct pairs (big number introduced) • Part B—oral test on the “reverse” fact • Part C—worksheet, filling in the big number and generating the two facts

  14. Three Number Fact Families • Format 6.4 • Family of Facts for Subtraction and Division. Teaches students how to generate 4 statements (2 addition and 2 subtractions or 2 multiplication and 2 division).: • 2 x 5 = 10, 5 x 2 = 10, 10/5 = 2, 10/2 = 5 • Students learn the rule: when you subtract (or divide), you always start with the big number.

  15. Three Number Fact Families: Model and Practice  ____ + ____ = _____ ____ + ____ = _____ ____ - ____ = _____ ____ - ____ = _____

  16. Sequencing Introduction of Facts • Systematic, cumulatively introduction of facts—Figures 6.2, 6.3, 6.4, and 6.5. • Separate similar facts • Teach easier facts first • Teach related facts together • Reverse of specific series taught soon after initial series

  17. Sequencing Introduction of Facts • Systematic, cumulatively introduction of facts—Figures 6.2, 6.3, 6.4, and 6.5. • Figures indicate the order in which to teach facts and the format to use for each set. • A set is presented for several days then included on memorization worksheets.

  18. Sequencing Introduction of Facts • Addition facts are introduced first. • Little research is available to guide us regarding when to introduce subtraction facts—after addition is completed—after part of addition is mastered and extend to subtraction? • Recommendation—delay subtraction until students have learned about half of the addition facts (Sets a-m addition mastered). Then alternate—Subtraction A, Addition N, Subtraction B, Addition O, etc.

  19. Sequencing Introduction of Facts • When to start multiplication? • Start in third grade even if students are still working on addition and subtraction. • Provide a “double dose” of facts instruction for students who need it.

  20. Mastery Activities Programs for Fact Memorization include: • A specific performance criterion • Intensive practice on new facts • Systematic practice on previously introduced facts • Adequate allotted time • A record keeping system • A motivation system

  21. Performance Criterion • Oral criterion: saying an entire fact every 2 seconds • Written criterion: 2/3 rate at which student is able to write digits • How do you determine students’ writing rate?

  22. Performance Criterion • 40 facts per minute is the low end of fluent performance. • However, common expectation around the country is100 facts in five minutes. Otter Creek Institute (Don Crawford)

  23. Intensive Practice • Instruction of new facts using relationship activity • Oral practice on new facts • Written practice on new facts and old facts

  24. Adequate Allotted Time • Approximately 10-15 minutes per day • Preferably, time in addition to math instructional time • Before school, during lunch recess, after school etc.

  25. Record Keeping System • Purpose: monitor student progress • Recommendation: keep paperwork at minimum—see Student Record Form on page 86

  26. Motivation • Integrate with record keeping system • Motivation comes with SUCCESS • Teacher’s responsibility to set students up for success: Must teach facts

  27. Two Fact Mastery Programs • Homogeneous Group Program • Teacher Led – Group Oral Practice • Materials • Pretesting • Timed test • Record keeping/Motivation

  28. Materials • Written fact practice worksheet divided in half • Smaller number of facts to master at once • One minute timings (more than once?) • Top half: Practice on new facts – current set and two previously introduced sets • Bottom half: Current fact set presented twice; practice on previously introduced sets

  29. Pretest • Develop a written pretest with all 100 facts of one operation. • Allow the students 2 minutes to work as many problems as they can. • 30 facts per minute—start at set G • 45 facts per minute—start at set M • 60 facts per minute—start at set R • >85 test on next operation

  30. Oral Group Practice • Using the worksheets—oral drill of top part saying the problem and answer in unison • Repeat the first line until students can answer correctly at with about 2 seconds think time • Model and Practice

  31. Timed Test • Bottom half of the worksheet • About 1 min. 15 seconds

  32. Mastery Criteria • If ¾ or more of the students got 28 of 30 facts correct go on to the next worksheet. • If not, repeat the same worksheet.

  33. Two Fact Mastery Programs • Heterogeneous Group Program • Partner Practice • Materials: folders for each student with their level of worksheet (one folder with answers and one without) • Pretesting: same • Timed Test • Record keeping/Motivation • Modifications

  34. Two Fact Mastery Programs Heterogeneous Group Program • Daily Routine: • Pairs at same level, one with answers • Each student practices the worksheet twice, saying the problem and the answer • If student makes an error the partner with the answer sheet corrects • Teacher times for 1 ½ minutes on the top and one minute on the bottom • Written test—Bottom half of worksheet

  35. Compare/Contrast Traditional Programs • Not teacher-directed • Length of time to mastery • Not cumulative Effective Programs • Teacher-directed (Oral practice) • Quicker mastery of smaller sets • Cumulative introduction and review

  36. Resources • Math facts at: http://depts.washington.edu/facts/ (files are huge but free) • Otter Creek Institute • Mastering Math Fact Families • http://www.oci-sems.com/home.htm

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