Editor’s Note: “Direct retrieval” is when you automatically remember something without having to stop and think about it.<\/em><\/p>\n Some educational researchers consider facts to be automatic when a response comes in two or three seconds (Isaacs & Carroll, 1999; Rightsel & Thorton, 1985; Thorton & Smith, 1988).\u00a0 However, performance is not automatic, direct retrieval when it occurs at rates that purposely \u201callow enough time for students to use efficient strategies or rules for some facts (Isaacs & Carroll, 1999, p. 513).\u201d<\/p>\n Most of the psychological studies have looked at automatic response time as measured in milliseconds and found that automatic (direct retrieval) response times are usually in the ranges of 400 to 900 milliseconds (less than one second) from presentation of a visual stimulus to a keyboard or oral response (Ashcraft, 1982; Ashcraft, Fierman & Bartolotta, 1984; Campbell, 1987a; Campbell, 1987b; Geary & Brown, 1991; Logan, 1988).\u00a0 Similarly, Hasselbring and colleagues felt students had automatized math facts when response times were \u201cdown to around 1 second\u201d from presentation of a stimulus until a response was made (Hasselbring et al. 1987).\u201d\u00a0\u00a0 If however, students are shown the fact and asked to read it aloud then a second has already passed in which case no delay should be expected after reading the fact.\u00a0 \u201cWe consider mastery of a basic fact as the ability of students to respond immediately to the fact question. (Stein et al., 1997, p. 87).\u201d<\/p>\n In most school situations students are tested on one-minute timings.\u00a0 Expectations of automaticity vary somewhat.\u00a0 Translating a one-second-response time directly into writing answers for one minute would produce 60 answers per minute.\u00a0 However, some children, especially in the primary grades, cannot write that quickly.\u00a0\u00a0 \u201cIn establishing mastery rate levels for individuals, it is important to consider the learner\u2019s characteristics (e.g., age, academic skill, motor ability).\u00a0 For most students a rate of 40 to 60 correct digits per minute [25 to 35 problems per minute] with two or few errors is appropriate (Mercer & Miller, 1992, p.23).\u201d\u00a0\u00a0 This rate of 35 problems per minute seems to be the lowest noted in the literature.<\/p>\n Other authors noted research which indicated that \u201cstudents who are able to compute basic math facts at a rate of 30 to 40 problems correct per minute (or about 70 to 80 digits correct per minute) continue to accelerate their rates as tasks in the math curriculum become more complex….[however]…students whose correct rates were lower than 30 per minute showed progressively decelerating trends when more complex skills were introduced.\u00a0 The minimum<\/em> correct rate for basic facts should be set at 30 to 40 problems per minute, since this rate has been shown to be an indicator of success with more complex tasks (Miller & Heward, 1992, p. 100).\u201d\u00a0\u00a0 Rates of 40 problems per minute seem more likely to continue to accelerate than the lower end at 30.<\/p>\n Another recommendation was that \u201cthe criterion be set at a rate [in digits per minute] that is about 2\/3 of the rate at which the student is able to write digits (Stein et al., 1997, p. 87).\u201d\u00a0 For example a student who could write 100 digits per minute would be expected to write 67 digits per minute, which translates to between 30 and 40 problems per minute.\u00a0\u00a0\u00a0 Howell and Nolet (2000) recommend an expectation of 40 correct facts per minute, with a modification for students who write at less than 100 digits per minute.\u00a0 The number of digits per minute is a percentage of 100 and that percentage is multiplied by 40 problems to give the expected number of problems per minute; for example, a child who can only write 75 digits per minute would have an expectation of 75% of 40 or 30 facts per minute.<\/p>\n If measured individually, a response delay of about 1 second would be automatic.\u00a0 In writing 40 seems to be the minimum, up to about 60 per minute for students who can write that quickly.<\/strong>\u00a0 Teachers themselves range from 40 to 80 problems per minute.\u00a0 Sadly, many school districts have expectations as low as 50 problems in 3 minutes or 100 problems in five minutes.\u00a0 These translate to rates of 16 to 20 problems per minute.\u00a0 At this rate answers can be counted on fingers.\u00a0\u00a0 So this \u201cpasses\u201d children who have only developed procedural knowledge of how to figure out the facts, rather than the direct recall of automaticity.<\/p>\n References<\/strong><\/p>\n Ashcraft, M. H. (1982).\u00a0 The development of mental arithmetic: A chronometric approach.\u00a0 Developmental Review<\/em>, 2, 213-236.<\/p>\n Ashcraft, M. H. & Christy, K. S. (1995).\u00a0 The frequency of arithmetic facts in elementary texts:\u00a0 Addition and multiplication in grades 1 \u2013 6.\u00a0 Journal for Research in Mathematics Education<\/em>, 25(5), 396-421.<\/p>\n Ashcraft, M. H., Fierman, B. A., & Bartolotta, R. (1984). The production and verification tasks in mental addition: An empirical comparison.\u00a0 Developmental Review<\/em>, 4, 157-170.<\/p>\n Ashcraft, M. H. (1985).\u00a0 Is it farfetched that some of us remember our arithmetic facts?\u00a0 Journal for Research in Mathematics Education<\/em>, 16 (2), 99-105.<\/p>\n Campbell, J. I. D.\u00a0 (1987a).\u00a0 Network interference and mental multiplication.\u00a0 Journal of Experimental Psychology: Learning, Memory, and Cognition<\/em>, 13 (1), 109-123.<\/p>\n Campbell, J. I. D.\u00a0 (1987b).\u00a0 The role of associative interference in learning and retrieving arithmetic facts.\u00a0 In J. A. Sloboda & D. Rogers (Eds.) Cognitive process in mathematics: Keele cognition seminars, Vol. 1.<\/em>\u00a0 (pp. 107-122). New York: Clarendon Press\/Oxford University Press.<\/p>\n Geary, D. C. & Brown, S. C. (1991).\u00a0 Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children.\u00a0 Developmental Psychology<\/em>, 27(3), 398-406.<\/p>\n Hasselbring, T. S., Goin, L. T., & Bransford, J. D. (1987).\u00a0 Effective Math Instruction: Developing Automaticity.\u00a0 Teaching Exceptional Children<\/em>, 19(3) 30-33.<\/p>\n Howell, K. W., & Nolet, V.\u00a0 (2000).\u00a0 Curriculum-based evaluation: Teaching and decision making.<\/em>\u00a0 (3rd Ed.)\u00a0 Belmont, CA: Wadsworth\/Thomson Learning.<\/p>\n Isaacs, A. C. & Carroll, W. M. (1999).\u00a0 Strategies for basic-facts instruction. Teaching Children Mathematics<\/em>, 5(9), 508-515.<\/p>\n Logan, G. D. (1988).\u00a0 Toward an instance theory of automatization.\u00a0 Psychological Review<\/em>, 95(4), 492-527.<\/p>\n Mercer, C. D. & Miller, S. P. (1992).\u00a0 Teaching students with learning problems in math to acquire, understand, and apply\u00a0 basic math facts.\u00a0 Remedial and Special Education<\/em>, 13(3) 19-35.<\/p>\n Miller, A. D. & Heward, W. L. (1992).\u00a0 Do your students really know their math facts?\u00a0 Using time trials to build fluency.\u00a0 Intervention in School and Clinic<\/em>, 28(2) 98-104.<\/p>\n Rightsel, P. S. & Thorton, C. A. (1985).\u00a0 72 addition facts can be mastered by mid-grade 1.\u00a0 Arithmetic Teacher<\/em>, 33(3), 8-10.<\/p>\n Stein, M., Silbert, J., & Carnine, D.\u00a0 (1997)\u00a0 Designing Effective Mathematics Instruction: a direct instruction approach<\/em> (3rd Ed).\u00a0 Upper Saddle River, NJ: Prentice-Hall, Inc.<\/p>\n Thorton, C. A. & Smith, P. J. (1988).\u00a0 Action research: Strategies for learning subtraction facts.\u00a0 Arithmetic Teacher<\/em>, 35(8), 8-12.<\/p>\n <\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Students should be automatic with the facts. \u00a0How fast is fast enough to be automatic? Editor’s Note: “Direct retrieval” is when you automatically remember something without having to stop and think about it. 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