Multiplication Facts Research Articles

Imagine Math Facts Improves Multiplication Fact Fluency in Third-Grade Students

Math fact fluency is foundational for later mathematics education. Unfortunately, many students across the nation continue to struggle with these core skills. Computer-assisted instruction may be a potentially valuable tool for improving math fact fluency due to its ability to differentiate instruction at the student level, provide added practice opportunities, and improve student interest and motivation. However, research is currently lacking to demonstrate the effectiveness of many computer-assisted interventions. One such program is Timez Attack by Imagine Math Facts, a multiplication fact fluency training program for elementary-age students. Using a multiple baseline across groups design, we sought to determine the effectiveness of Timez Attack in improving math fact fluency in third-grade students. We randomly assigned 63 students to three study groups and regularly assessed for multiplication fact fluency for 12 weeks. Compared to baseline averages, all three study groups demonstrated improved multiplication fact fluency following the onset of the intervention phase. Further, performance during a follow-up maintenance phase demonstrated persistence of learning. The results of this study suggest that Timez Attack may be an effective computer-assisted instruction option for improving multiplication fact fluency in elementary-age students.

Language switching costs in bilingual mathematics learning: Transfer effects and individual differences

There is an implicit assumption in Content- and Language Integrated Learning that the acquired knowledge is represented independently of the language of instruction. However, it could be shown in several experimental intervention studies that cognitive costs (i. e. longer reaction times and lower accuracy) arise when the languages of study and retrieval do not match. In the present study, we focused on arithmetic fact learning and investigated whether these cognitive costs generalize to more complex contexts. In addition, we explored the relationship between the cognitive costs and individual differences in executive functions, intelligence, mathematical competence and second language (L2) proficiency. Participants were 58 German-French bilingual university students (L2 proficiency B2 or above). They studied multiplication facts for 3 consecutive days in either their L1 or L2, followed by a test in both languages on the 4th day. Cognitive costs caused by language switching between training and test were found for both problems requiring simple fact retrieval and problems requiring knowledge application in novel, more complex text problems. The costs were negatively related with L2 proficiency and positively with inhibition. This study shows for the first time that language switching costs can be found in situations when knowledge needs to be applied in a new context, as it is often necessary in classroom learning. Implications of this study will be discussed with regards to bilingual arithmetic learning.

The Effects of Copy, Cover and Compare with and without Additional Error Drill on Multiplication Fact Fluency and Accuracy

Introducción: La utilización de copiar, tapar y comparar se ha señalado cómo un procedimiento de intervención efectivo en el aula. El presente caso examina la utilización de dicha estrategia en relación con hechos matemáticos de un estudiante con dificultades de aprendizaje.Objetivos: El propósito de esta investigación fue incrementar la eficacia y disminuir la tasa de error en la visión/escritura de dígitos utilizados en la multiplicación utilizando la estrategia de copiar, tapar y comparar. Un segundo objetivo fue utilizar un procedimiento de corrección de los errores utilizando dicha estrategia y evaluar los efectos.Método: El participante era un estudiante de cuarto curso con dificultades de aprendizaje que había tenido problemas en el área de matemáticas. Tras el establecimiento de la línea base se implementó el procedimiento de pegar, tapar y comparar. Por último, la corrección del error fue añadida al procedimiento de copiar, tapar y comparar.Resultados: Los resultados generales indicaron un aumento de las respuestas correctas y una disminución de los errores mediante el uso del copiar, tapar y comparar. Cuando copiar, tapar y comparar se combinó con la corrección del error, las respuestas correctas aumentaron y los errores disminuyeron. La facilidad también aumentó con la corrección de errores.Discusión: La evidencia encontrada en el presente informe indica que la eficacia del procedimiento de copiar, tapar y pegar. Cuando se utiliza de forma adicional la corrección de errores, la eficacia del procedimiento se incrementa. Por último, se discuten los beneficios, así como las dificultades, para que profesorado y alumnado utilicen la estrategia de copiar, tapar y comparar con y sin corrección de errores.

The impact of the different types of navigation (hierarchical - list) in the interactive media on the development of academic achievement among primary school students in the mathematics curriculum: أثر اختلاف نمط الإبحار (هرمي – قائمة) في الوسائط المتعددة التفاعلية على تنمية التحصيل الدراسي لدى تلاميذ المرحلة الابتدائية في منهج الرياضيات

Abstract: The current research aimed to identify the effect of the different types of navigation (pyramid-list) in the rich media on the development of the achievement of students in primary school in the mathematics curriculum. The research problem was limited to the following main question: In the interactive media on the development of academic achievement of primary school students? The research was applied to a sample of (60) third grade students randomly selected from Aws Bin Haritha Primary School in Madinah, Saudi Arabia, during the second semester of the second semester. In the 2017 academic year. Students were divided into two experimental groups, 30 of which were students as a first experimental group, which examined the multiplication facts by means of a hierarchical sailing pattern, and 30 students as a second experimental group. The same multiplication facts were examined by the list navigation style, Both groups have been applied The results of the study were found to be statistically significant at (0.05) between the average scores of the students in the two experimental groups. In the learning achievement test, the main effect of the variation of the navigation style (pyramid-list) in the interactive media is to the benefit of the group that implemented the application through the hierarchical navigation style. Therefore, we recommend that the results of the research be used to urge the education professionals to pay attention to the software production Which are designed by means of interactive media according to scientific technical standards and hierarchical navigation patterns to contribute to the achievement of the desired educational objectives.

An evaluation of sex and cultural differences in arithmetic retrieval-induced forgetting

ABSTRACTRetrieval practice of arithmetic facts (e.g. 2 × 3) can interfere with retrieval of other, closely related arithmetic facts (e.g. 2 + 3), increasing response time (RT) and errors for these problems. Here we examined potential sex and culture-related differences in arithmetic retrieval-induced forgetting (RIF). This was motivated by re-analyses of several published arithmetic RIF data sets that appeared to show that the effect occurred for women but not men. Experiment 1 (n = 72) tested for possible sex differences in a diverse but predominantly Canadian university sample. Experiment 2 (n = 48) examined potential sex differences in native Chinese participants, which previous research indicated may not be susceptible to the RIF effect for a particular subset of small addition problems (sum ≤ 10). In Experiment 1, we found no evidence that the addition RIF effect differed between male and female adults. In Experiment 2, the Chinese adults showed RIF for tie problems (e.g. 2 + 2, 3 + 3, etc.) regardless of sex, but neither sex presented RIF for small non-tie addition problems. The results indicated that the RIF effect is not gender specific, and there might not be strong memory retrieval competition between addition and multiplication facts for non-tie problems in Chinese adults.

Involvement of working memory in mental multiplication in Chinese elementary students

ABSTRACTThe authors' aim was to examine the relation between two-digit mental multiplication and working memory. In Study 1, involving 30 fifth-grade students, we used digit span backward as an abbreviated measure of working memory. In Study 2, involving 41 fourth-grade students, working memory comprised measures of phonological loop, visuospatial sketchpad, and central executive (i.e., updating) based on A. Miyake et al. (2000). In Study 1, working memory measured through the use of digit span backward explained unique variance in response time. In Study 2, participants' accuracy and response time were most susceptible to phonological loop influence. The findings support the argument that multiplication facts are stored in a verbal form and the retrieval of multiplication facts relies more on verbal modality. Unique features of Chinese mathematics instruction of mental multiplication were discussed. The findings suggested that the involvement of different subcomponents of working memory in mental arithmetic may be subject to instructional, contextual, and linguistic factors.

초등수학에서의 곱셈구구 지도 순서에 대한 고찰

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students’ mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.

The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing

Three experiments were conducted in which adults practiced complex multiplication problems (e.g., 4 x 17). In Experiments 1 and 2, after practice participants completed a number-matching task in which two digits (cues) were followed by a single digit (probe) and had to determine whether the probe matched either of the cues. In simple arithmetic (e.g., 4 x 3), when the probe is the product of the cues (12), participants are slower/more error prone when determining whether there is a match. Results of Experiment 1 extended this effect to complex multiplication. In Experiment 2, participants practiced problems with the larger operand first (e.g., 17 x 4) or with the smaller operand first (e.g., 4 x 17). The number-matching interference effect from Experiment 1 was replicated, and was equal across the two groups whether cues were presented in their practiced or non-practiced order. Experiment 3 was conducted to determine if two additional simple multiplication effects, consistency and relatedness, could be documented for complex multiplication. After practice, in a verification task (4 x 13 = 56?) it was found that when presented answers shared a digit with the decade digit of the correct answer (consistency) or were a correct answer to another practiced problem (relatedness), participants rejected answers more slowly and/or less accurately. Together, findings from the three experiments support arithmetic models that posit that commuted pairs are not represented in long-term memory independently and that posit representations of two-digit multiplication answers are decomposed into decades and units during arithmetic processing.

Using High-Probability Instructional Sequences and Explicit Instruction to Teach Multiplication Facts

Students with learning disabilities often struggle with math fact fluency and require specialized interventions to recall basic facts. Deficits in math fact fluency can result in later difficulties when learning higher-level mathematical computation, concepts, and problem solving. The response-to-intervention (RTI) and multitiered-systems-of-support (MTSS) approaches for delivering research-based interventions to struggling learners provide educators with the structural frameworks necessary for planning tiered interventions to address skill deficits. Some schools have been implementing RTI/MTSS for years, while others have recently started using these frameworks. Regardless of the number of years delivering tiered interventions, educators benefit from learning about additional interventions they can implement for students requiring tertiary supports (i.e., Tier 3). This article provides readers with a detailed explanation of a Tier 3 multiplication fact fluency intervention that involves the use of high-probability instructional sequences and explicit, systematic, intensive instruction to increase motivation and fluency development.

The role of physical digit representation and numerical magnitude representation in children’s multiplication fact retrieval

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (Mage=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.

Simple arithmetic: electrophysiological evidence of coactivation and selection of arithmetic facts.

This study aimed at exploring the time course of processes underlying the associative confusion effect. We also evaluated the consequences of selecting arithmetic facts to resolve addition problems. We gathered electrophysiological evidence when participants performed a verification task. Simple addition problems were presented in blocks of two trials and participants decided whether they were correct or not. The N400-like component was considered an index of semantic access (i.e., the retrieval of arithmetic facts), and the P200 component was used to determine the difficulty associated with encoding after the answer to an addition problem. When an addition problem was incorrect but the result presented to the participant was that of multiplying the operands (e.g., 2+4=8), N400-like amplitude was reduced relative to an unrelated condition (e.g., 2+4=10). This finding suggested that the coactivation of addition and multiplication facts took place. Furthermore, the P200 amplitude was more positive when participants answered to addition problems whose result was that of multiplying the operands of the previous trial (e.g., 2+6=8). This suggests that irrelevant results were inhibited and it was difficult to encode them later.

The Contribution of Numerical Magnitude Comparison and Phonological Processing to Individual Differences in Fourth Graders’ Multiplication Fact Ability

Although numerical magnitude processing has been related to individual differences in arithmetic, its role in children’s multiplication performance remains largely unknown. On the other hand, studies have indicated that phonological awareness is an important correlate of individual differences in children’s multiplication performance, but the involvement of phonological memory, another important phonological processing skill, has not been studied in much detail. Furthermore, knowledge about the relative contribution of above mentioned processes to the specific arithmetic operation of multiplication in children is lacking. The present study therefore investigated for the first time the unique contributions of numerical magnitude comparison and phonological processing in explaining individual differences in 63 fourth graders’ multiplication fact ability (mean age = 9.6 years, SD = .67). The results showed that children’s multiplication fact competency correlated significantly with symbolic and nonsymbolic magnitude comparison as well as with phonological short-term memory. A hierarchical regression analysis revealed that, after controlling for intellectual ability and general reaction time, both symbolic and nonsymbolic magnitude comparison and phonological short-term memory accounted for unique variance in multiplication fact performance. The ability to compare symbolic magnitudes was found to contribute the most, indicating that the access to numerical magnitudes by means of Arabic digits is a key factor in explaining individual differences in children’s multiplication fact ability.

Magic Finger Teaching Method in Learning Multiplication Facts among Deaf Students

<p>Deaf students face problems in mastering multiplication facts. This study aims to identify the effectiveness of Magic Finger Teaching Method (MFTM) and students’ perception towards MFTM. The research employs a quasi experimental with non-equivalent pre-test and post-test control group design. Pre-test, post-test and questionnaires were used. As many as 70 deaf students from three special education primary schools in Selangor and Federal Territory were gathered as research respondent. Data were analyzed by using descriptive and inferential statistics of t-test. Findings from the t-test analysis showed that MFTM has a significant effect on multiplication facts achievement among deaf students whereas conventional teaching method does not given a significant effect on multiplication facts achievement among them. The findings from questionnaires found that the deaf students have high level of perception towards MFTM in the dimensions of interest, self-confidence, persistence and motivation in learning multiplication facts. The findings serves as an implication towards students, parents, teachers, Special Education Division and Malaysia Education Ministry in terms of awareness, involvement, planning and implementation in the context of diversifying of multiplication facts teaching method, and the suitability of supporting materials in teaching and learning multiplication facts.<strong></strong></p>

Number of repetitions required to retain single-digit multiplication math facts for elementary students.

Computational fluency is an important aspect of math proficiency. Despite widely held beliefs about the differential difficulty of single-digit multiplication math facts, little empirical work has examined this issue. The current study analyzed the number of repetitions needed to master multiplication math facts. Data from 15,402 3rd, 4th, and 5th graders were analyzed using a national database. Results suggested that (a) students with lower math skills required significantly (p < .001) more repetitions than more skilled students; (b) across all students, single-digit multiplication facts with 4s, 5s, 6s, and 7s required significantly (p < .001) more repetition than did 2s and 3s; and (c) the number of practice sessions needed to attain mastery significantly (p < .001) decreased with increase in grade level. Implications for instructional planning and implementation are discussed.

Are Arithmetic Networks Interdependent In Number-Matching Task?

Addition and multiplication facts are retrieved from a network-like structure, as shown by data from number-matching tasks. Even if several evidences (e.g., cross-operation confusion effect) suggest that these networks are interrelated, the interdependency between addition and multiplication networks could be influenced by the type of task used (e.g., verification task). The present study aimed to investigate whether the addition and multiplication networks were interdependent or separate using a number-matching task. Eighty participants were divided in four groups. The Groups A (x, x, x) and B (+, +, +) performed the task in which only one arithmetic interference effect was implemented through three sessions (pure condition). The Groups C (x, x, +) and D (+, +, x) performed the same task in which the same arithmetic interference effect appeared in the first and second sessions, while a different arithmetic problem was presented in the last session (mixed condition). In the last session, the interference effect in the mixed condition was higher than that in the pure condition. The results argued more for an independency of addition and multiplication networks than for their interdependency.

DEVELOPING MULTIPLICATION FACT FLUENCY

Using specific components of three broad learning theories—cognitive, social-interactional, and behavioral—students in 3 rd , 4 th and 5 th grade classrooms were given multiplication fact fluency instruction over a period of five weeks for 10-15 minutes each day. Two different approaches were utilized with two distinct groups of students for the purpose of comparing different approaches to fluency development. Results indicate that students using a strategy-based approach for fluency development by means of instructional tasks emphasizing social-interactional and cognitive theories (particularly Bruner’s theory of Modes of Representation) increased multiplication fact fluency, with a greater degree of consistency, than students using a drill-based approach emphasizing behavioristic techniques such as repetition and memorization.

Effects of a Strategic Intervention With iPad Practice on the Multiplication Fact Performance of Fifth-Grade Students With Learning Disabilities

This study investigated the effects of explicit, strategic intervention with iPad application practice on the multiplication fact performance and strategy use of elementary students with learning disabilities (LD) using a single-case, multiple probe design across participants. Four fifth-grade students with LD received 15 1:1 intervention sessions in multiplication facts. Results indicated that all students made significant growth in multiplication fact performance across the study and maintained the intervention gains 2 weeks following the intervention. Overall, students increased their use of a doubling strategy taught during intervention and were able to retrieve facts automatically after intervention sessions. Social validity interview results indicated that participants had positive perspectives about the intervention. Implications for practice and suggestions for future research are discussed.

Contribution of working memory in multiplication fact network in children may shift from verbal to visuo-spatial: a longitudinal investigation.

Number facts are commonly assumed to be verbally stored in an associative multiplication fact retrieval network. Prominent evidence for this assumption comes from so-called operand-related errors (e.g., 4 × 6 = 28). However, little is known about the development of this network in children and its relation to verbal and non-verbal memories. In a longitudinal design, we explored elementary school children from grades 3 and 4 in a multiplication verification task with the operand-related and -unrelated distractors. We examined the contribution of multiplicative fact retrieval by verbal and visuo-spatial short-term and working memory (WM). Children in grade 4 showed smaller reaction times in all conditions. However, there was no significant difference in errors between grades. Contribution of verbal and visuo-spatial WM also changed with grade. Multiplication correlated with verbal WM and performance in grade 3 but with visuo-spatial WM and performance in grade 4. We suggest that the relation to verbal WM in grade 3 indicates primary linguistic learning of and access to multiplication in grade 3 which is probably based on verbal repetition of the multiplication table heavily practiced in grades 2 and 3. However, the relation to visuo-spatial semantic WM in grade 4 suggests that there is a shift from verbal to visual and semantic learning in grade 4. This shifting may be induced because later in elementary school, multiplication problems are rather carried out via more written, i.e., visual tasks, which also involve executive functions. More generally, the current data indicates that mathematical development is not generally characterized by a steady progress in performance; rather verbal and non-verbal memory contributions of performance shift over time, probably due to different learning contents.

Effect of Modifying Intervention Set Size With Acquisition Rate Data While Practicing Single-Digit Multiplication Facts

Incremental rehearsal (IR) has consistently led to effective retention of newly learned material, including math facts. The number of new items taught during one intervention session, called the intervention set, could be used to individualize the intervention. The appropriate amount of information that a student can rehearse and later recall during one intervention session is called the acquisition rate (AR). The current study taught single-digit multiplication facts with factors of 6, 7, and 8 to 55 third- and fourth-grade students. Each student was randomly assigned to be taught two multiplication math facts, eight multiplication math facts, or a set size determined by each student’s AR. The average AR was 4.05 ( SD = 0.71). Set size led to a significant and large effect on retention, percentage of multiplication math facts retained, and efficiency as computed by math facts retained per minute of intervention time. IR appeared to be an effective intervention when AR data were used to determine the intervention set size, and it was more efficient to do so.

Comparing Two Classwide Interventions: Implications of Using Technology for Increasing Multiplication Fact Fluency

An adapted alternating treatments design with initial baseline and final best treatment phase was used to evaluate and compare the effects of two classwide interventions, detect–practice–repair (DPR), and self-mediated iPad instruction, on the multiplication math facts fluency in an inclusive third-grade classroom. Twelve students participated in both interventions over a 3-week treatment phase. Results showed that although both interventions were effective, in general, students showed greater gains during the iPad intervention compared to the DPR intervention. Intervention acceptability results also revealed that students, teachers, and parents preferred the iPad intervention. The discussion focuses on the benefits and implications of using technology to differentiate instruction in inclusive settings.