Mathematical Strategies Research Articles

Effect of the teaching and learning mathematics strategy based on metacognitive scaffolding on instructional efficiency

Metacognitive scaffolding (MS) with self-questioning is helpful in promoting student problem solving skill and independent learning. MS deals with the process of learning which helps the students to think, control, and monitor their learning. The instructional condition will be more efficient if the performance of student achievement in problems solving needs less than mental effort invested or equivalent. Therefore, the purpose of this paper was to examine the effect of the scaffolding metacognitive strategy on instructional efficiency. The results of quasi-experiments indicated that the MS strategy fulfilled the direct effect to instructional efficiency. This data provide support for the claim that MS strategy is superior in comparison to the conventional teaching. Students in the experimental group showed an overall favorable view towards the implementation of MS strategy. They viewed that the MS strategy is an interesting, new, simple, and easy instructional format to use in mathematics learning.

Function2Form Bridge-Toward synthetic protein holistic performance prediction.

Protein engineering and synthetic biology stand to benefit immensely from recent advances in silico tools for structural and functional analyses of proteins. In the context of designing novel proteins, current in silico tools inform the user on individual parameters of a query protein, with output scores/metrics unique to each parameter. In reality, proteins feature multiple "parts"/functions and modification of a protein aimed at altering a given part, typically has collateral impact on other protein parts. A system for prediction of the combined effect of design parameters on the overall performance of the final protein does not exist. Function2Form Bridge (F2F-Bridge) attempts to address this by combining the scores of different design parameters pertaining to the protein being analyzed into a single easily interpreted output describing overall performance. The strategy comprises of (a) a mathematical strategy combining data from a myriad of in silico tools into an OP-score (a singular score informing on a user-defined overall performance) and (b) the F2F Plot, a graphical means of informing the wetlab biologist holistically on designed construct suitability in the context of multiple parameters, highlighting scope for improvement. F2F predictive output was compared with wetlab data from a range of synthetic proteins designed, built, and tested for this study. Statistical/machine learning approaches for predicting overall performance, for use alongside the F2F plot, were also examined. Comparisons between wetlab performance and F2F predictions demonstrated close and reliable correlations. This user-friendly strategy represents a pivotal enabler in increasing the accessibility of synthetic protein building and de novo protein design.

The Engineering Tools That Shaped the Rational Expectations Revolution

The rational expectations revolution was not based only on the introduction of Muth’s idea of rational expectations to macroeconomics; this introduction alone cannot explain the more drastic changes to the mathematical toolbox, concepts, and research strategies since the 1980s. The shift from “Keynesian economics” to “new classical economics” is based on a shift from a control engineering approach to an information engineering methodology. This “revolution” was even more radical; it also changed the epistemology and ontology of macroeconomics. The ontology of information engineering, and hence of new classical economics, is a world populated by machines that communicate by the exchange of noisy information. The decisions these machines make are conditioned on the (noisy) information they have about the current state of the world but which at the same time will affect future states. Policy in this world therefore means tracing an optimal trajectory taking all these issues into account. To show this shift in epistemology and ontology, the history of economics is interwoven with the history of mathematics, which cannot be detangled from the emergence of the digital computer. The computer changed the nature of mathematics in a specific way by adopting a new concept of solution, namely the algorithm.

Mathematical strategies for base unit allocation in unequally spaced DWDM systems

Abstract Existing unequally spaced channel allocation in Dense Wavelength Division Multiplexed systems involves use of recurring, Fixed Size Base units (FS-BUs) which has been demonstrated as a solution for reduction of Four Wave Mixing. In this paper, a novel, Variable Sized Base Units (VS-BUs), channel allocation strategy is proposed and analysed, which involves the mapping of Fibonacci, Triangular and Lazy Caterer’s (LC) mathematical series used in the construction of BUs. It is shown that the best, LC based VS-BU, substantially reduces the number of generated FWM products by 59.68%. A reduction of approximately 19 dBm FWM intensities and maximum SNR of 35 dB is also reported which further supports the proposed methodology. To ascertain the new strategy, a Performance Index is defined, which relates the percentage change in size of adjacent BUs, to the decrease in number of FWM components generated. Performance trade-off factors are discussed following which LC’s mapping is observed to be the superior channel allocation strategy in DWDM systems.

Mental mathematics under the lens: Strategies, oral mathematics, enactments of meanings

This article is in continuation of previous work reported in Proulx (2013a, 2015a). It is part of a wider research programme oriented toward scrutinizing the nature of the mathematical activity generated in mental mathematics contexts about various mathematical themes (from numbers, algebra, geometry, to statistics and functions). The main intention in this article is to study solvers’ strategy processes in mental mathematics contexts for developing a better understanding of what doing mental mathematics entails. This issue is first addressed through Nunes et al. (1993) distinction between oral and written mathematics; and second through building on distinctions about solving processes outlined from the enactivist theory of cognition. These combined conceptualizations are then reinvested empirically to analyze several examples and illustrations of strategies taken from mental mathematics studies. These analyses enable the drawing out of issues of meaning-preservation, meaning-making, and good-enough as ways of understanding mental mathematics strategies and their specific space of mathematical exploration.

OPTIMISING TRAFFIC FLOW AT A SIGNALISED INTERSECTION USING SIMULATION

Traffic signal lights system is a signalling device located an intersection or pedestrian crossing to control the movement of traffic. The timing of traffic signal lights has attracted many researchers to study the problems involving traffic light management and looking for an inexpensive and effective solution that requires inexpensive changes in the infrastructures. A simple traffic lights system uses a pre-timed control setting based on the latest traffic data, and the setting could be manually changed. It is a common type of signal control and sometimes the setting was not correctly configured with the traffic data, thus leading to congestion at an intersection. Many mathematical strategies were applied to get an optimal setting. This study aims to model the traffic flow at Persiaran Kayangan and Persiaran Permai Intersection, Section 7, Shah Alam, as the case study, by using AnyLogic simulation software. The model was used to determine the best timings of traffic green lights that minimise the average time at the intersection and reduce traffic congestion. The findings showed that the best timings of traffic green lights for four directions at the intersection are 120 seconds, 75 seconds, 130 seconds and 100 seconds, respectively. These timings of green lights produced the lowest average time at the intersection (55.65 seconds).

فاعلیة برنامج قائم على حلّ المشکلات فی تنمیة التفکیر التباعدی لدى طلبة الصف العاشر فی ضوء تباین مفهوم الذات الریاضیّ لدیهم

هدفت هذه الدراسة إلى تقصى فاعلية برنامج قائم على حل المشکلات في تنمية التفکير التباعدي لدى طلبة الصف العاشر في ضوء تباين مفهوم الذات الرياضي لديهم. اختيرت عينة مکونة من (89) طالبا وطالبة من مدرستي وادي بني خروص للتعليم الأساسي وأم حکيم للتعليم الأساسي في سلطنة عمان. وتم توزيع العينة إلى مجموعتين: تجريبية وعدد أفرادها (48) طالبا وطالبة ، وضابطة وعدد أفرادها (41) طالبا وطالبة. وتم إعداد المادة التعليمية لوحدتي الحدوديات والدوال الجبرية و الدوال المثلثية للصف العاشر الأساسي وفق البرنامج القائم على حل المشکلات. کما تم إعداد اختبار التفکير التباعدي، ومقياس مفهوم الذات الرياضي، وقد تمتعت الأدوات بدلالات صدق وثبات مقبولة. أظهرت النتائج وجود فروق ذات دلالة إحصائية لصالح المجموعة التجريبية في اختبار التفکير التباعدي. وأظهرت النتائج وجود فروق ذات دلالة إحصائية في اختبار التفکير التباعدي يعزى لمفهوم الذات الرياضي، کما اظهرت عدم وجود فروق ذات دلالة إحصائية في اختبار التفکير التباعدي يعزى إلى التفاعل بين طريقة التدريس ومفهوم الذات الرياضي. وفي ضوء هذه النتائج أوصت الدراسة بعدة توصيات، أهمها: أهمية إثراء المناهج الرياضية باستراتيجيات حل المشکلات الرياضية، وضرورة عقد دورات تدريبية لتدريب المعلمين على استخدام استراتيجيات حل المشکلات وحثهم على توظيفها في تدريس الرياضيات. This study aimed at investigating the impact of a problem solving based program in Developing Divergent Thinking among 10th grade students in the light of the variance of their mathematical self-concept. The purposive sample of this study consisted of (89) male and female students from Wadi Bani Kharous Basic Education School and Om Hakeem Basic Education School at Sultanate of Oman. The sample were divided into experimental group, consisted of (48) students, and control group, consisted of (41) students. The instructional materials of Polynomial and Algebraic Functions Unit and Trigonometric Functions Unit for Grade 10th were designed based on the problem solving program. The Divergent Thinking test and mathematical self-concept scale were developed and both were valid and reliable. The findings showed that there were significant statistical differences in Divergent Thinking test in favor of the experimental group. The findings indicated that the significant statistical differences in the Divergent Thinking test is due to the mathematical self-concept and the absence of statistical significance differences in Divergent Thinking test is due to the interaction between teaching methods and mathematical self-concept. In light of the findings, the study suggested some crucial recommendations including the importance of enriching mathematics curricula with mathematical problem-solving strategies, and having professional development workshops to train teachers on how to use mathematical problem-solving strategies and urge them to use these strategies in teaching Mathematics.

After eliciting: Variation in elementary mathematics teachers’ discursive pathways during collaborative problem solving

Mathematics teachers are called on to craft instruction that centers students’ mathematical ideas and creates consistent, pervasive opportunities for meaning-making through discourse. In the context of collaborative problem solving, teachers can use eliciting and probing to uncover student thinking while students work together to develop mathematical ideas and strategies. After eliciting and probing, teachers can further respond to the student thinking that has been revealed. This study explored the discursive pathways two fourth grade mathematics teachers used after eliciting student thinking, when their aim was to be responsive to and advance student thinking. Drawing on interactions (n = 97) from nine lessons, qualitative analysis identified five distinct discursive pathways after eliciting, two of which, praise and funneling, were associated with the nature of student understanding uncovered during eliciting. Implications for future research and professional development on teacher-student discourse are discussed.

Merging of Metacognitive Regulation Strategies and Activity Based Learning through Best Seller Mathematical Learning Activities to Enhance Student's Mastery of Mathematics

Metacognitive Regulation Strategies (MRS) and Activity Based-Learning (ABL) is a learning strategy that is significant and have proven to effect student’s mastery. The student’s ability to plan, monitor and evaluate the learning process and their thinking process, known as metacognitive regulation, can strengthen the understanding. ABL also has significant positive effects on students’ level of interest, engagement and performance. Through the activity, students developed their communication skills, self-regulation and the learned knowledge has positive effects on retention due to learning by doing and having fun while learning. In fact, Best Seller Mathematical Learning Activities (Apm-BS) merges principles and strategies from the activity during learning and metacognitive regulation skills. This conceptual paper tries to discuss the potential of merging activity based learning and metacognitive regulation learning strategies as an intervention to the problem of mastering the mathematical concept of students. This activity was designed and created based on the basic of the concept of entrepreneurship, which involves buying and selling activities among students during the learning process. Students communicate and interact with peer to practice the metacognitive behavior and improve metacognitive skills in order to enhance their understanding.

Emotional intelligence in the initial teacher training

The objective of the article is to evaluate emotional intelligence in the initial teacher training of the mathematics bachelor program at the “Universidad Francisco de Paula Santander”, San José de Cúcuta, Colombia. The methodology is framed in the qualitative approach with some complementary aspects of the quantitative approach, the applied technique is the interview and the trait meta-mood scale instrument. The results describe that the impacts of integrating the emotive dimension in the learning strategies of mathematics is a greater resilience in the teachers in formation, since thanks to the contact with their emotions through introspection and reflection they manage to draw plans and alternatives that help them to devote more time, ask more and study better, especially in those aspects that cause them difficulty.

A review on control-relevant glucose–insulin dynamics models and regulation strategies

This article presents a state-of-the-art review on automated control of blood sugar, especially for Type 1 diabetic patients. A brief introduction is provided so as to justify how this biomedical issue proves to be a control system problem in sense of blood glucose regulation. Various mathematical models and control strategies that have been used in recent research work for automated insulin delivery are discussed. An attempt has been made to provide a structural survey of research done till date in the development of artificial pancreas system. At the end, a general idea is presented on how control system can be designed for this biomedical control problem by employing Bergman’s minimal model for blood glucose regulation and an internal model–based proportional–integral controller is designed. The controller exhibits faster response in maintaining the blood glucose when compared with other existing techniques.

Application of Vee Diagram as a Problem-Solving Strategy in Developing Students’ Conceptual and Procedural Knowledge

Vee diagram is a constructivist approach to teaching and learning, to help students understand the relevant principles and concepts of mathematical problem-solving. This study aimed to investigate the development of students’ conceptual and procedural knowledge after the Vee diagram is introduced as a problem-solving strategy in learning a topic in mathematics. This study used a quasi-experimental research design, which involved 48 lower secondary school students selected through purposive sampling. Data were collected using a set of pre-test and post-test that consists of 5 mathematical problem-solving questions. Data were analysed using Statistical Package for Social Science version 23. Findings of this study showed that the application of Vee diagram as a mathematical problem-solving strategy has significantly developed students’ conceptual and procedural knowledge.

Optimization of grooved klystron collector design for efficient heat transfer

Klystron microwave amplifiers play a vital role in addressing the increasing demands of high-average microwave power for strategic applications such as linear accelerators, active denial technologies, radar, and so forth. Typically, klystrons have an efficiency of 50%-60% that demands an efficient thermal design for dissipating the unused DC power in the form of spent electron beam in collector. Hence, thermal modeling of the collector for efficient heat dissipation is highly critical in design of high average power klystrons. Of several types of design, grooved collector design is widely employed so as to increase the surface area between the collector and coolant and thereby enhance heat transfer. In this article, a mathematical model and design strategy have been demonstrated to obtain the optimum dimensions, that is, height, depth, and width of fins based on film coefficient and Reynolds number. For validation, the dimensions are then simulated in a computational fluid dynamics software (ANSYS-Fluent) demonstrating excellent agreement with the mathematical modeling. In addition, the optimum choice of grooving method (longitudinal or crossed) for the given power level has also been provided. The demonstrated strategy can also potentially be employed to other devices, which uses groove based design with water as coolant medium such as gyrotrons, plasma devices, and so forth.

A hybrid mathematical modeling strategy for controlling the mechanical performance of polyethylene/poly(ethylene-co-vinyl acetate)/Nanoclay cast films

Abstract A two-stage mathematical modeling/optimization approach on the ground of response surface methodology (RSM) and desirability function (DF) was applied here to imitate and optimize the mechanical properties of polyethyelene (PE)/ethylene-vinyl acetate copolymer (EVA)/nanoclay (NC) nanocomposite cast films. First, a series of experiments were designed by the use of RSM so as to assess the effects of material parameters as well as processing temperature profile on the Young's modulus, tensile strength and strain at break of the nanocomposite films. Applying RSM statistical analysis, regression functions were examined and the best reduced interpolating functions were subsequently identified and transformed into the DF to optimize the desired responses concurrently. The findings unravelled that the PE/EVA/NC films with optimum elastic modulus, tensile strength and toughness are attainable by extruding the PE-rich blends at higher processing temperatures, preferably without the use of NC platelets. The multiple optimization strategies revealed the significance of the extruder temperature profile on mechanical properties as a key controlling factor governing the phase behavior of the PE/EVA blends.

A mathematical method to realize complex poles in a high‐order passive switched‐capacitor filter

SummaryA high‐order discrete‐time IIR low‐pass with complex poles using charge sampling is presented in a single‐stage structure by using a mathematical strategy. In comparison with the analog complex‐poles Gm‐C filters, the proposed filter consumes lower power and has good linearity, and all of the tunings are implemented only by capacitor sizes. The proposed filter is a seventh‐order Butterworth, but this method can be generalized to implement other complex pole filters like Tchebyshev and Elliptic. Post‐layout simulation results in 130‐nm complementary metal‐oxide‐semiconductor (CMOS) show an IIP3 of +18 dBm and a noise figure of 5 dB. The filter has a rejection of more than 110 dB in its stop band and consumes 1.5 mW with a 1.6‐V supply voltage, and circuit occupies an about 0.12 mm2 of silicon.

Kaedah Pembelajaran Matematika dan Kaitannya dengan Kecerdasan Interpersonal Siswa SMA Kota Makassar

This study aimed to examine the links between mathematical learning strategy and interpersonal intelligence of high school students at Makassar. The research method used is explorative and quantitative research. The population of this study is Makassar high school students, and the sample is students of class XI SMAN 8 Makassar and SMAN 22 Makassar. The data analysed by using descriptive and inferential statistics with analysis of variance (ANOVA). The results obtained were descriptions of students’ interpersonal intelligence in experimental class is in the high category, while the descriptions of students’ interpersonal intelligence in control class is in the low and middle category. The results of inferential statistical analysis shows that students’ interpersonal intelligence at Makassar high school in experimental class is better than the students’ interpersonal intelligence in control class, this means there is a link between mathematical learning strategy and interpersonal intelligence of high school students at Makassar.

Developing, mature, and unique functions of the child’s brain in reading and mathematics

Cognitive development research shows that children use basic “child-unique” strategies for reading and mathematics. This suggests that children’s neural processes will differ qualitatively from those of adults during this developmental period. The goals of the current study were to 1) establish whether a within-subjects neural dissociation between reading and mathematics exists in early childhood as it does in adulthood, and 2) use a novel, developmental intersubject correlation method to test for “child-unique”, developing, and adult-like patterns of neural activation within those networks. Across multiple tasks, children’s reading and mathematics activity converged in prefrontal cortex, but dissociated in temporal and parietal cortices, showing similarities to the adult pattern of dissociation. “Child-unique” patterns of neural activity were observed in multiple regions, including the anterior temporal lobe and inferior frontal gyri, and showed “child-unique” profiles of functional connectivity to prefrontal cortex. This provides a new demonstration that “children are not just little adults” – the developing brain is not only quantitatively different from adults, it is also qualitatively different.

Studying drugs and diseases with “body-on-a-chip” models

Authors summarize mathematical modeling strategies used to design and analyze multi-organ microphysiological systems.

Pengaruh Model Pembelajaran Treffinger Berorientasi Kearifan Lokal Berbantuan Tugas Berjenjang Terhadap Self Efficacy Dan Kompetensi Strategis Matematika Siswa Sekolah Menengah Pertama (SMP)

This study aims to find out whether: (1) self efficacy mathematics of students who are taught by the learning model of Treffinger oriented local wisdom with better-tiered assignment or not from self efficacy of students receiving conventional learning, (2) students' mathematics student competence taught by model Lessons are used to perform better or better tasks from students receiving conventional learning, (3) there is some self-efficacy and simultaneous mathematical strategies between students who are taught by Treffinger-aided learning model with tiered assignments conventional learning. This research type is quasi experiment with posttest only control group design. Data in this research is self efficacy mathematics used by using questionnaire and data required by student. The data obtained were analyzed descriptively on the basis of t-test 1 for hypothesis 1 and hypothesis 2, and MANOVA test for hypothesis 3. Characteristics of the teaching-oriented model of Treffinger oriented local wisdom with the help of this tiered function are: (1) student involvement in the problem and they as participants active in problem solving, (2) the science of cognitive dimension and student affectivity to seek the direction of problem solving provided, (3) the students do group analysis to explore ideas, and (4) the students use the acquired understanding to solve other related problems with everyday life. In addition, by delivering advice sourced from Bali's reliable local wisdom and making the process more enjoyable. Given tiered tasks in learning mathematics such as practice questions that can be done effectively. Through the learning model oriented Treffinger local wisdom assisted by this tiered task is expected students are able to solve problems in a way with their own. The process of thinking to discuss mathematical problems and will foster confidence in students to solve problems related to other terms for the next. To complete the problem of tiered training well, also required good students also.

Mathematical Creative Thinking Ability for Students Through REACT Strategies

The ability to think creatively is important to create students who can use mathematical mindset in their daily activities, and in various sciences. The conditions at school this time show us that students still run into problems in resolve math questions which related to mathematical creative thinking ability that finally impact on the result is low for this ability. Therefore, we need strategy for mathematics learning so it can improve mathematical creative thinking ability for students. The strategy that can be applied are through Relating, Experiencing, Applying, Cooperating, dan Transferring (REACT). This research aims to know the improvement creative thinking mathematical ability for students through react strategy. The type of this research is experimental research with a quantitative approach. The populations in this study are students in class X SMAN 1 Banda Aceh. The sample in this study is students in class X MIA-3 as an experimental class that gets learning with REACT’s strategy, and students in class X MIA-1 as a control class that has conventional learning. The instrument of this research is the questions of pretest and post-test. The quantitative analysis using a test independent sample t-test. Based on the results of data analysis it can be concluded that improvement creative thinking mathematical ability for students by teaching with REACT’s strategy is better than improvement of students' creative thinking skills by teaching conventionally.