Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

<p>Mathematical achievement may impact on outcomes in later life; thus, identifying and improving key mathematical skills is a focus of a large body of educational research. Both additive reasoning, and knowledge of addition and subtraction facts, appear to predict later mathematical achievement. The current study explores the impact of a short intervention with a small group of year 7 and 8 students working at lower than expected academic levels. The current study is based on Cognitive Load Theory and research suggesting that counting strategies overload working memory. A mixed-methods approach was used to identify whether structured manipulatives improved the additive reasoning and, addition and subtraction fluency in a sample of ten participants. Participants attended after-school intervention sessions of 45 minutes for seven weeks. The intervention focused on teaching additive reasoning and fluency using structured manipulatives. Inferential statistical analysis showed a statistically significant mean improvement in participants’ ability to answer simple addition and subtraction questions. Tests constructed to operationalise additive reasoning also showed statistically significant mean improvement. Participants answered diagnostic questions operationalising various aspects of additive reasoning. Individual differences in understanding of additive reasoning were observed, and the inverse relationship between addition and subtraction proved to be a challenging concept. Semi-structured interviews provided themes of valuing the intervention and the manipulatives used. Due to the size and design of this study, it is not possible to extrapolate findings to other learners. However, the study may provide directions for future research. Structured manipulatives may have a role to play in enabling learners to begin to learn additive relationships and further securing recall of addition and subtraction facts. Students at years 7 and 8 may still need considerable exposure to additive concepts; moreover, returning to manipulatives may develop this knowledge. Finally, the findings from the diagnostic questions help show the complexity of additive reasoning. Classroom practitioners may need to further develop their knowledge of additive reasoning, its importance, and the individual differences and misconceptions that learners hold in order to provide considered learning experiences.</p>

Do structured manipulatives aid understanding of additive reasoning, and addition and subtraction fluency in a sample of Year 7 and 8 students?

<p>Mathematical achievement may impact on outcomes in later life; thus, identifying and improving key mathematical skills is a focus of a large body of educational research. Both additive reasoning, and knowledge of addition and subtraction facts, appear to predict later mathematical achievement. The current study explores the impact of a short intervention with a small group of year 7 and 8 students working at lower than expected academic levels. The current study is based on Cognitive Load Theory and research suggesting that counting strategies overload working memory. A mixed-methods approach was used to identify whether structured manipulatives improved the additive reasoning and, addition and subtraction fluency in a sample of ten participants. Participants attended after-school intervention sessions of 45 minutes for seven weeks. The intervention focused on teaching additive reasoning and fluency using structured manipulatives. Inferential statistical analysis showed a statistically significant mean improvement in participants’ ability to answer simple addition and subtraction questions. Tests constructed to operationalise additive reasoning also showed statistically significant mean improvement. Participants answered diagnostic questions operationalising various aspects of additive reasoning. Individual differences in understanding of additive reasoning were observed, and the inverse relationship between addition and subtraction proved to be a challenging concept. Semi-structured interviews provided themes of valuing the intervention and the manipulatives used. Due to the size and design of this study, it is not possible to extrapolate findings to other learners. However, the study may provide directions for future research. Structured manipulatives may have a role to play in enabling learners to begin to learn additive relationships and further securing recall of addition and subtraction facts. Students at years 7 and 8 may still need considerable exposure to additive concepts; moreover, returning to manipulatives may develop this knowledge. Finally, the findings from the diagnostic questions help show the complexity of additive reasoning. Classroom practitioners may need to further develop their knowledge of additive reasoning, its importance, and the individual differences and misconceptions that learners hold in order to provide considered learning experiences.</p>

Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children. Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or a procedure. We analyzed these four problem categories (retrieved multiplications, retrieved subtractions, procedural multiplications, and procedural subtractions) in our study. In summary, we found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed neurophysiological differences between multiplications and subtractions within retrieval problems. Although there were no response time or accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Mastery of Basic Mathematics Facts in Slow Learner Children

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.

Oscillatory Electroencephalographic Patterns of Arithmetic Problem Solving in Fourth Graders

Numerous studies have identified neurophysiological correlates of performing arithmetic in adults. For example, oscillatory electroencephalographic (EEG) patterns associated with retrieval and procedural strategies are well established. Whereas fact retrieval has been linked to enhanced left-hemispheric theta ERS (event-related synchronization), procedural strategies are accompanied by increased bilateral alpha ERD (event-related desynchronization). It is currently not clear if these findings generalize to children.Our study is the first to investigate oscillatory EEG activity related to strategy use and arithmetic operations in children. We assessed ERD/ERS correlates of 31 children in fourth grade (aged between nine and ten years) during arithmetic problem solving. We presented multiplication and subtraction problems, which children solved with fact retrieval or via a procedure. Based on both problem size and verbal strategy reports, we analyzed these problem types separately for each operation.We found similar strategy-related patterns to those reported in previous studies with adults. That is, retrieval problems elicited stronger left-hemispheric theta ERS and weaker alpha ERD as compared to procedural problems. Interestingly, we observed differences between multiplications and subtractions within retrieval problems. Although there were no response time and accuracy differences, retrieved multiplications were accompanied by larger theta ERS than retrieved subtractions. This finding could indicate that retrieval of multiplication and subtraction facts are distinct processes, and/or that multiplications are more frequently retrieved than subtractions in this age group.

Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them

How children learn the basic addition and subtraction facts, why many have difficulty mastering these basic skills, and what teachers can do to prevent or overcome these learning difficulties.

Identification and Remediation of Systematic Error Patterns in Subtraction

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.

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

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.