The Development Characteristics And Cognitive Neural Mechanisms Of Simple Mental Arithmetic Retrieval

Simple mental arithmetic is a relatively common and widespread thinking activity in daily life,and is a prerequisite for acquiring advanced mathematical knowledge and skills,which is essential for an individual’s later academic and professional success.Strong foundational mathematical problem solving skills acquired in early childhood are critical not only for success in science,technology,engineering,and mathematical(STEM)fields,but also for quantitative reasoning in everyday life.In the rapidly developing modern society of science and technology,the role of mathematical problem solving ability is more obvious.Therefore,the exploration of the mechanism of simple mental arithmetic problem solving process not only helps to understand the development law of simple mental arithmetic problem solving and promote the development of simple arithmetic problem solving ability,but also helps to understand the cognitive processing characteristics of simple mental arithmetic problem solving process of groups with mathematical learning difficulties and developmental dyscalculia,and has an important enlightening role in improving their problem solving.Previous studies have explored the cognitive process of human mental arithmetic,and found that the problem solving process of mental arithmetic includes at least three stages,namely,the encoding stage,the retrieval or calculation stage,and the response stage.However,little is known about the processing of the retrieval stage of simple mental arithmetic.According to retrieval theory,simple arithmetic facts are stored in the brain’s long-term memory association network,and when a problem appears,it automatically activates the correct answer of the problem and the answer of the related problem.However,the mechanism of interference caused by related problems in the retrieval process of simple mental arithmetic is still unclear.At the same time,whether the retrieval process of simple mental arithmetic depends on the numerical format of the problem has always been a controversial topic,and the mechanism of the influence of the numerical format of the problem on the retrieval process of simple mental arithmetic needs to be further explored.Based on this,this study will explore the processing mechanism of simple mental arithmetic retrieval from the two perspectives of problem interference and numerical format through behavioral experiment and event-related potential technology.The study 1 aimed to explore and test whether the process of solving simple mental arithmetic problems involves retrieval,and to examine how the performance of simple mental arithmetic retrieval changes with the increase of age.The study 1 included three experiments.In experiment 1,the association between simple arithmetic problems and answers and the numerical format of the problem were manipulated to examine whether the process of simple mental arithmetic problem solving involved retrieval,and whether interference effect and numerical format effect will occur in the retrieval process.The results showed that simple arithmetic problems were mostly solved by retrieval strategy,and the accuracy of related error answers was lower and the reaction time was longer than that of unrelated error answers but the difference between the two was not significant in the Chinese numerical format problems of single-digit multiplication,and the reaction time of Chinese numerical format problems was longer than that of Arabic numerical format problems.This demonstrates that the solving of simple arithmetic problems is mainly accomplished by retrieval,and interference effect and numerical format effect are observed in the retrieval process of simple arithmetic facts.The experiment 2 and experiment 3 further examined the development characteristics of simple mental arithmetic retrieval from a developmental perspective,as well as the changing characteristics of the role of interference and numeral format of the problem in it.Therefore,in these two experiments,the association between simple arithmetic problems and answers,as well as the numerical format of the problem were manipulated respectively.The results showed that the performance of simple mental arithmetic retrieval had a moderate improvement with the change of age,that is,the reaction time showed a downward trend from the fourth grade to the sixth grade of primary school,but the performance of simple mental arithmetic retrieval was relatively stable from the first grade of middle school to the second grade of high school.Furthermore,the interference effect showed a first decreasing and then increasing trend from the fourth grade to the sixth grade of primary school,but no interference effect was observed in the first grade of middle school,and the interference effect showed a first increasing and then decreasing trend from the second grade of middle school to the second grade of high school.Moreover,the numerical format showed a first increasing and then decreasing from trend fourth grade to sixth grade of primary school and from first grade of middle school to first grade of high school,and the numerical form effect in the second year of high school was slightly larger than that in the first year of high school.This indicates that age plays an important role in retrieval process of simple arithmetic facts,and that the interference effect and numerical format effect change with age.Based on the study 1,the study 2 examined the influence of interference on the retrieval process of simple mental arithmetic.The study 2 included two experiments.In experiment 4,the association type between simple arithmetic problems and answers was manipulated to examine whether there are differences in the performance of simple mental arithmetic retrieval under different association type of problems.The results showed that compared with cross-operation related error answers,operand-related error answers had lower accuracy and longer reaction time.This indicates that operand-related has greater interference than cross-operation.In experiment 5,it was further examined whether operand-related interference would change with the time interval between the problem and the answer(i.e.ISI),and therefore the ISI(150ms,300 ms,500ms)and the association between simple arithmetic problems and answers were manipulated.The results showed that the accuracy of simple mental arithmetic retrieval was lower and the reaction time was longer when the ISI was 150 ms than when the ISI was 500 ms,and the difference in reaction time of simple mental arithmetic retrieval was marginally significant between the ISIs of 150 ms and 300 ms.Furthermore,the interference effect was the most obvious when the ISI was 150 ms,and the interference effect was gradually decreasing with the increased of ISI,but the difference between the related error result and the unrelated error result in one-digit multiplication was slightly larger at 500 ms than at 300 ms.At the same time,the study 3 examined the influence of numerical format on the retrieval process of simple mental arithmetic.The study 3 included two experiments.In experiment 6,the numerical format of operands in the simple arithmetic problems was manipulated to examine whether there are differences in the performance of simple mental arithmetic retrieval under different format of problem operands when the answer format of problems was always an Arabic numerical format.The results showed that the reaction time was longer when the operands before the answers were in Chinese numerical format compared to when the operands before the answers were in Arabic numerical format and Chinese-Arabic numerical format,and the reaction time was also longer when the operands before the answers were in Arabic-Chinese numerical format compared to when the before the answers were in Chinese-Arabic numerical format.But there was no significant difference between all operands format problems in error answers.This demonstrates that the retrieval process of simple mental arithmetic depends on the operands format of the problem when the answer format of the problem is the same.In experiment 7,it was further examined whether the numerical format of the problem would change with the time interval between the problem and the answer(i.e.ISI),and therefore the ISI(500ms,1000ms)and the numerical format of simple arithmetic problems were manipulated.The results showed that in Arabic numerical format problems,the accuracy of simple mental arithmetic retrieval was lower when ISI was 500 ms than when ISI was 1000 ms.Furthermore,the numerical format effect is more obvious when ISI was1000 ms,while the difference between Arabic numerical format problem and Chinese numerical format problem was not significant when ISI was 500 ms.Based on the behavioral studies described above,the study 4 aimed to examine the influence mechanism of interference and numerical format on simple mental arithmetic retrieval from the perspective of brain mechanism.The study 4 included two experiments.In experiment 8,the association between simple arithmetic problems and answers was manipulated to examine whether there were differences in brain components of different association problems during the retrieval process of simple mental arithmetic.The results showed that association between problems and answers would induce N2 b and N400 components,and there were significant differences in N2 b and N400 amplitude between related error answers and unrelated error answers.This indicates that the retrieval process of simple mental arithmetic involves semantic processing and controlled processing.In experiment 9,the numerical format of simple arithmetic problems was manipulated to examine whether there were differences in the brain components of different numerical format problems during the retrieval process of simple mental arithmetic.The results showed that the numerical format of problem could induce P300 and LPC components,and there were significant differences in P300 and LPC amplitude between Arabic numerical format problems and Chinese numerical format problems.This indicates that the retrieval process of simple mental arithmetic involves the allocation of attentional resources.In summary,behavioral studies indicates that simple mental arithmetic problem solving is mainly accomplished by retrieving simple arithmetic facts from long-term memory.Furthermore,there are interference effect and numerical format effect in the retrieval process of simple mental arithmetic,and these two effects were moderated by ISI.Developmental studies indicates that the role of interference and numerical format in the retrieval of simple mental arithmetic changes with age.Brain mechanism studies indicates that interference and numerical format in simple mental arithmetic retrieval are associated with semantic processing and resource allocation.This can not only deepen the understanding of the theoretical model of simple arithmetic processing,but also provide important insights for the practice of mathematics education and teaching,and promotes the improvement of individual’s mathematical problem solving ability.