Design, Implementation & Performance of Vedic Multiplier Based on Look Ahead Carry Adder for Different Bit Lengths

This paper proposed the layout of Vedic Multiplier based totally on Urdhva Trigbhyam approach of multiplication. It is most effective Vedic sutras for multiplication. Urdhva triyagbhyam is a vertical and crosswise approach to discover product of two numbers. Multiplication is an essential quintessential feature in arithmetic logic operation. Computational overall performance of a DSP device is limited via its multiplication overall performance and since, multiplication dominates the execution time of most DSP algorithms. Multiplication is one of the simple arithmetic operations and it requires extensively extra hardware assets and processing time than addition and subtraction. Our work is to compare different bit Vedic multiplier structure using carry look ahead adder technique. Keywords: Carry Look Ahead Adder, Urdhva Trigbhyam, DSP algorithms, Vedic Multiplier

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>

Teaching Students With Mild Intellectual Disability to Solve Word Problems Using Schema-Based Instruction

This study, which used a multiple baseline across students’ design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem-solving performance of three students with mild intellectual disability, two of them with autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent with change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed.

DEVELOPING DIGITAL - BASED COMIC MEDIA IN TEACHING MATHEMATICS FOR ELEMENTARY SCHOOL STUDENTS

This research aims to develop digital-based comic media on addition and subtraction materials of mathematics for elementary school students at grade II. This research was motivated by a lack of knowledge of students on addition and subtraction materials. The novelty of this media is in the form of files without using sheets of paper. This study used ADDIE model (Anlysis, Design, Develop, Implement, and Evaluate). Based on the five stages of development of comic media resulted from the feasibility of 90% while the practicality of teachers obtained a percentage of 90% and practicality of students obtained a percentage of 93%. The use of products gets a percentage of 86% with the category "excellent". This study has an implication that that the use of learning media makes students more actively involved in the learning process especially those in elementary schools. Therefore, teachers are supposed to maintain their creativity in teaching.

Not toeing the number line for simple arithmetic: Two large-n conceptual replications of Mathieu et al. (Cognition, 2016, Experiment 1)

We conducted two conceptual replications of Experiment 1 in Mathieu, Gourjon, Couderc, Thevenot, and Prado (2016, https://doi.org/10.1016/j.cognition.2015.10.002). They tested a sample of 34 French adults on mixed-operation blocks of single-digit addition (4 + 3) and subtraction (4 – 3) with the three problem elements (O1, +/-, O2) presented sequentially. Addition was 34 ms faster if O2 appeared 300 ms after the operation sign and displaced 5° to the right of central fixation, whereas subtraction was 19 ms faster when O2 was displaced to the left. Replication Experiment 1 (n = 74 recruited at the University of Saskatchewan) used the same non-zero addition and subtraction problems and trial event sequence as Mathieu et al., but participants completed blocks of pure addition and pure subtraction followed by the mixed-operation condition used by Mathieu et al. Addition RT showed a 32 ms advantage with O2 shifted rightward relative to leftward but only in mixed-operation blocks. There was no effect of O2 position on subtraction RT. Experiment 2 (n = 74) was the same except mixed-operation blocks occurred before the pure-operation blocks. There was an overall 13 ms advantage with O2 shifted right relative to leftward but no interaction with operation or with mixture (i.e., pure vs mixed operations). Nonetheless, the rightward RT advantage was statistically significant for both addition and subtraction only in mixed-operation blocks. Taken together with the robust effects of mixture in Experiment 1, the results suggest that O2 position effects in this paradigm might reflect task specific demands associated with mixed operations.

Learning Obstacle on Addition and Subtraction of Primary School Students: Analysis of Algebraic Thinking

This study aims at exploring learning obstacles about arithmetic operations, and problems of addition and subtraction of whole numbers in primary schools. This preliminary qualitative research used a didactic research design. The participants of this study were 50 second-grade students at primary schools in three regencies. The instruments used were test and nontest. The test technique was conducted by giving questions about algebra, whereas the nontest technique was in the form of interviews. The data were analyzed using interactive analysis by Miles & Huberman. The findings indicate that there are three types of learning obstacles, namely, (1) ontogenic obstacles with psychological and instrumental types (students feel afraid and do not understand the prerequisite material), (2) epistemological obstacles (students’ experience in working on story problems with the concept of algebraic thinking does not exist), and (3) didactical obstacle (the methods taught tend to focus on the counting process instead of understanding the concept). Learning barriers can be categorized into three types, namely, ontogenic, epistemological, and didactic barriers. With the discovery of these learning barriers, a solution is found in the form of making learning designs that are tailored to the learning obstacles found. One of them is by applying grading questions from story problems into mathematical sentences.

SPECIFICS OF TEACHING THE INVERSE RELATIONS BETWEEN THE ARITHMETIC OPERATIONS ADDITION AND SUBTRACTION DURING THE EDUCATION IN MATHEMATICS IN GRADE 1

One of the fundamental knowledge in mathematics in Primary school is related to the arithmetic operations addition and subtraction. According to the educational programs in mathematics in the Republic of Bulgaria, students start studying these operations in grade 1. The article presents theoretical concepts affecting studying the arithmetic operations addition and subtraction in the education in mathematics at a primary school. The research work identified the specifics of studying the inverse connections between the arithmetic operations addition and subtraction in the education in mathematics for grade 1 are also presented. Some of the significant tasks with importance for discovering the relations between the forward operation addition and the reverse operation subtraction were proposed in the study. A new methodology system of work with tasks where these relations are used was developed and tested. The author studied the knowledge, skills, and competencies of the grade 1 students to solve arithmetic operations addition and subtraction tasks. After the exit diagnostic, it was found out that the students of the class where the new methodology system of work was applied during their education in mathematics have got a higher level of knowledge and skills from competency Cluster Numbers in respect of the arithmetic operations addition and subtraction. The use of mathematical tasks with reverse relations between the arithmetic operations addition and subtraction help the students to develop both the overall mathematical knowledge and the logical thinking of the first-graders.