Identification and Remediation of Systematic Error Patterns in Subtraction

2005 ◽  
Vol 28 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Paul J. Riccomini
Keyword(s):  
Systematic Error ◽  
Math Performance ◽  
Math Instruction ◽  
Subtraction Problem ◽  
Error Type ◽  
Error Patterns ◽  
Instructional Focus ◽  
Basic Facts ◽  
Subtraction Facts ◽  
Specific Error

The present study investigated 90 elementary teachers' ability to identify two systematic error patterns in subtraction and then prescribe an instructional focus. Presented with two sets of 20 completed subtraction problems comprised of basic facts, computation, and word problems representative of two students' math performance, participants were asked to examine each incorrect subtraction problem and describe the errors. Participants were subsequently asked which type of error they would address first during math instruction to correct students' misconceptions. An analysis of the data indicated teachers were able to describe specific error patterns. However, they did not base their instructional focus on the error patterns identified, and more than half of the teachers chose to address basic subtraction facts first during instruction regardless of error type. Limitations of the study and implications for practice are discussed.

Quantitative and qualitative analyses of clock drawing in frontotemporal dementia and Alzheimer's disease

2006 ◽  
Vol 12 (2) ◽  
pp. 159-165 ◽  
Author(s):  
MERVIN BLAIR ◽  
ANDREW KERTESZ ◽  
PAUL MCMONAGLE ◽  
WILDA DAVIDSON ◽  
NIKOLETTA BODI
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Frontotemporal Dementia ◽  
Control Group ◽  
Cognitive Screening ◽  
Focal Lesions ◽  
Error Type ◽  
Clock Drawing Test ◽  
Clock Drawing ◽  
Specific Error

The clock drawing test (CDT) is a widely used cognitive screening test. It is useful in identifying focal lesions and cognitive deficits in dementia groups. Lately, several studies attempted its use to differentiate between dementia subtypes. Although many studies have examined the CDT in dementia populations, research into the use of clock drawing in frontotemporal dementia (FTD) is limited. We examined quantitative (global) and qualitative (specific error type) differences on the CDT between FTD (n = 36) and Alzheimer's disease (AD; n = 25) patients and controls without dementia (n = 25). Results showed significantly lower overall scores in the dementia groups compared to the control group, whereas FTD patients scored significantly higher than the AD group. On qualitative analysis, the FTD group had fewer stimulus bound responses, conceptual deficits, and spatial or planning errors compared to the AD group. In conclusion, both global and error analysis of the CDT helped discriminate the FTD group from controls and AD patients. (JINS, 2006, 12, 159–165.)

Learning Strategies for Addition and Subtraction Facts: The Road to Fluency and the License to Think

2004 ◽  
Vol 10 (7) ◽  
pp. 362-367
Author(s):  
Lisa Buchholz
Keyword(s):  
Learning Strategies ◽  
First Grade ◽  
Second Grade ◽  
First Year ◽  
Mental Computation ◽  
The Road ◽  
Finger Counting ◽  
Addition And Subtraction ◽  
Basic Facts ◽  
Subtraction Facts

Teaching the basic facts seemed like the logical thing to do. Wouldn't a study of the basic facts make mathematics computation much easier for my students in the future? How could I help my students memorize and internalize this seemingly rote information? How could I get rid of finger counting and move on to mental computation? As I embarked on my first year of teaching second grade following many years of teaching first grade, these questions rolled through my head.

scholarly journals A mixture of generative models strategy helps humans generalize across tasks

2021 ◽  
Author(s):  
Santiago Herce Castañón ◽  
Pedro Cardoso-Leite ◽  
Irene Altarelli ◽  
C. Shawn Green ◽  
Paul Schrater ◽  
...  
Keyword(s):  
Sequence Learning ◽  
Learning Strategy ◽  
Generative Models ◽  
Separate Study ◽  
Error Patterns ◽  
Task Learning ◽  
Learning Tasks ◽  
Gating Mechanism ◽  
Past Experiences ◽  
Specific Error

AbstractWhat role do generative models play in generalization of learning in humans? Our novel multi-task prediction paradigm—where participants complete four sequence learning tasks, each being a different instance of a common generative family—allows the separate study of within-task learning (i.e., finding the solution to each of the tasks), and across-task learning (i.e., learning a task differently because of past experiences). The very first responses participants make in each task are not yet affected by within-task learning and thus reflect their priors. Our results show that these priors change across successive tasks, increasingly resembling the underlying generative family. We conceptualize multi-task learning as arising from a mixture-of-generative-models learning strategy, whereby participants simultaneously entertain multiple candidate models which compete against each other to explain the experienced sequences. This framework predicts specific error patterns, as well as a gating mechanism for learning, both of which are observed in the data.

Division by zero

1971 ◽  
Vol 18 (6) ◽  
pp. 381-382
Author(s):  
Hilda F. Duncan
Keyword(s):  
Multiplication Facts ◽  
Basic Facts ◽  
Subtraction Facts ◽  
Addition Facts

In the teaching of elementary arithmetic we introduce the students to 100 addition facts, 100 subtraction facts, and 100 multiplication facts. When it comes to division, however, most teachers and books present or discuss only 90 basic facts. Many children will not think to question this nonsymmetric arrangement, but what about those who do? What explanation can we give the alert and inquisitive child who wants to know why we have omitted 10 division facts from our list?

Systematic Errors in the Four Vertical Algorithms in Normal and Handicapped Populations

1975 ◽  
Vol 6 (4) ◽  
pp. 202-220 ◽  
Author(s):  
L. S. Cox
Keyword(s):  
Systematic Error ◽  
Systematic Errors ◽  
Random Errors ◽  
Computational Process ◽  
Middle Income ◽  
Adequate Knowledge ◽  
Basic Facts ◽  
One Year ◽  
Computational Skill ◽  
Computational Processes

In a two-year study, frequencies and descriptions of systematic errors in four algorithms in arithmetic were studied in upper-middle income regular and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the computational processes. Systematic errors contained a recurring incorrect computational process and were differentiated from careless errors and random errors. Errors were studied within levels of computational skill for each algorithm. Results showed that 5-6% of the children made systematic errors in the addition, multiplication, and division algorithms. The figure was 13% for the subtraction algorithm. One year later 23% of the children were making either the identical systematic error or another systematic error.

scholarly journals The thin ret(raction) line: biomedical journal responses to incorrect non-targeting nucleotide sequence reagents in human gene knockdown publications

2021 ◽  
Author(s):  
Jennifer A. Byrne ◽  
Yasunori Park ◽  
Rachael A. West ◽  
Amanda Capes-Davis ◽  
Bertrand Favier ◽  
...  
Keyword(s):  
Nucleotide Sequence ◽  
Scientific Literature ◽  
Human Gene ◽  
Editorial Staff ◽  
Negative Control ◽  
Gene Knockdown ◽  
Error Type ◽  
Biomedical Journals ◽  
Specific Error ◽  
Specific Reagent

AbstractThe capacity of the scientific literature to self-correct is of vital importance, but few studies have compared post-publication journal responses to specific error types. We have compared journal responses to a specific reagent error in 31 human gene knockdown publications, namely a non-targeting or negative control nucleotide sequence that is instead predicted to target a human gene. The 31 papers published by 13 biomedical journals generated 26 published responses (14 retractions, 5 expressions of concern, 7 author corrections which included one resolved expression of concern) as well as 6 stated decisions to take no action. Variations in published responses were noted both between journals and by 4 journals that published different responses to at least 2 papers. A subset of published responses revealed conflicting explanations for the wrongly identified control reagent, despite 30/31 papers obtaining their gene knockdown reagents from the same external supplier. Viewed collectively, different journal responses to human gene knockdown publications with a common reagent error type suggest that editorial staff require more support to interpret post-publication notifications of incorrect nucleotide sequence reagents. We propose a draft template to facilitate the communication, interpretation and investigation of published errors, including errors affecting research reagents.

scholarly journals Mastery of Basic Mathematics Facts in Slow Learner Children

2021 ◽  
Vol 8 (8) ◽  
pp. 80
Author(s):  
Bambang Wahyu Nugroho ◽  
Ikrar Pramudya ◽  
Sri Subanti
Keyword(s):  
Opportunity To Learn ◽  
Slow Learner ◽  
Research Subjects ◽  
Validation Data ◽  
Multiplication Facts ◽  
Advanced Phase ◽  
Analysis Technique ◽  
Fourth Level ◽  
Basic Facts ◽  
Subtraction Facts

As one of the mathematics objects, the basic facts of mathematics are the primary material that students must master. The facts of addition and subtraction should have been taught in the first level and mastered by the end of the second level. The multiplication and division facts should have been taught at the third level and could be mastered at the fourth level. The primary fact mastery phase consists of a counting phase, a reasoning phase, and a mastering/advanced phase. Mathematics as science should also be accepted by all students regardless of their characteristics, background, or physical needs. They must have the opportunity to learn and be supported to learn mathematics, one of which is a child with special needs slow learner. This research aims to describe the mastery of basic math facts in slow learner children. This is qualitative research, with research subjects totaling three slow learner students of Melana Junior Hight School, Semarang. Subjects are selected by purposive sampling. Data are collected through tests. Time triangulation is used for data validation. Data collection is carried out three times with a gap of 2-3 weeks. The data analysis technique in this research is data reduction, data presentation, and concluding. The research results conclude that the slow learner children are not yet proficient in mastering the basic facts of mathematics. There are slow learner children who can reach the reasoning stage in mastering basic facts, but more are still in the counting stage. Slow learner children who have good basic fact skills have better grades in mathematics. The addition facts are the most effortless facts to master, while the division facts are the most difficult facts to master. Some students can master multiplication facts better than subtraction facts, but some can master subtraction facts more than multiplication facts.

scholarly journals Jugando con números 2: el software complementario a la instrucción matemática temprana / Playing with Numbers 2: Complementary Software to Early Math Instruction

2013 ◽  
Vol 2 (2) ◽  
Author(s):  
Estíbaliz L. Aragón Mendizábal ◽  
Gonzalo Ruiz Gagigas ◽  
Manuel Aguilar Villagran ◽  
Antonio Araújo Hoyos ◽  
José I. Navarro Guzmán
Keyword(s):  
Secondary School ◽  
Mathematical Knowledge ◽  
Educational Software ◽  
Mathematical Thinking ◽  
Math Performance ◽  
Math Instruction ◽  
Math Learning ◽  
Improve Performance ◽  
Educación Primaria ◽  
Primary And Secondary School

ABSTRACTThe interest to improve math performance involves people in different areas of life therefore may be useful for the progress of society. Frequently efforts are focused in order to obtain an ideal performance in math during Primary and  Secondary  school.  But  the  bases  for  learning  are  acquired  earlier  (Clements  &  Sarama,  2007).  It  is  importantidentify  and  overcome  difficulties  to  improve  performance  at  children  in  kindergarten  and the  first  school  grades (Gersten,  Jordan,  &  Light,  2005). This  research  attempted  to  link  current  Educational  Sciences  knowledge  and Psychology,  connecting  them  with  educational  software  that  can  be  applied  in  math  learning  difficulties  during  the earlier  school  years.  Using  computer  as  an  educational  tool,  students  make  activities  based  on  tangible  situations contributing  to  understand  the  environment  and  allowing  them  to  start  acquisition  of  mathematical  knowledge  and building the logical and mathematical thinking on motivating and effective way.RESUMENEl interés por mejorar el rendimiento en matemáticas puede ser útil para el progreso de la sociedad ya que afecta a las personas en diversas áreas de la vida. Normalmente se dirigen esfuerzos a la obtención de un óptimo rendimiento en matemáticas durante las etapas de Educación Primaria y Secundaria, pero los pilares en los que se asientan los aprendizajes se adquieren antes (Clements & Sarama, 2007). Por esta razón es importante identificar y superar los obstáculos que impiden un buen rendimiento en Educación Infantil y los primeros cursos de Educación Primaria (Gersten, Jordan, & Flojo, 2005). Nuestro trabajo ha tratado de conjugar los conocimientos existentes sobre las ciencias de la educación y la psicología, plasmándolos en un software didáctico con posibilidad de aplicación en el ámbito de las dificultades de aprendizaje matemático durante los primeros cursos escolares. A través del uso del ordenador como herramienta educativa podemos lograr que el alumnado realicen actividades basadas en situaciones reales que contribuyan a la comprensión del mundo que le rodea y, en última instancia, que les permitan iniciarse en la adquisición del lenguaje matemático, y la construcción del pensamiento lógico-matemático de una manera atractiva y eficaz.

scholarly journals Multidimensional cerebellar computations for flexible kinematic control of movements

2022 ◽  
Author(s):  
Akshay Markanday ◽  
Sungho Hong ◽  
Junya Inoue ◽  
Erik De Schutter ◽  
Peter Thier
Keyword(s):  
Purkinje Cells ◽  
Mossy Fibers ◽  
Error Feedback ◽  
Error Type ◽  
Kinematic Control ◽  
Flexible Control ◽  
Feed Forward Network ◽  
Saccade Task ◽  
Movement Parameters ◽  
Specific Error

Both the environment and our body keep changing dynamically. Hence, ensuring movement precision requires adaptation to multiple demands occurring simultaneously. Here we show that the cerebellum performs the necessary multi-dimensional computations for the flexible control of different movement parameters depending on the prevailing context. This conclusion is based on the identification of a manifold-like activity in both mossy fibers (MF, network input) and Purkinje cells (PC, output), recorded from monkeys performing a saccade task. Unlike MFs, the properties of PC manifolds developed selective representations of individual movement parameters. Error feedback-driven climbing fiber input modulated the PC manifolds to predict specific, error type-dependent changes in subsequent actions. Furthermore, a feed-forward network model that simulated MF-to-PC transformations revealed that amplification and restructuring of the lesser variability in the MF activity is a pivotal circuit mechanism. Therefore, flexible control of movement by the cerebellum crucially depends on its capacity for multi-dimensional computations.

Using Hand Signs to Teach Basic Facts

1983 ◽  
Vol 31 (1) ◽  
pp. 38-41
Author(s):  
Carol LaSasso ◽  
Philip L. Mackall
Keyword(s):  
Deaf Children ◽  
Deaf Student ◽  
Addition And Subtraction ◽  
Basic Facts ◽  
Subtraction Facts

The procedure that is described in this article was developed several year ago for use with 12-to-15-year-old deaf student who could not remember basic addition and subtraction facts. Since its development, the procedure has been used successfully with numerous deaf children between the age of 8 and 17 years.

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