7,918 results
Search Results
2. Tablets Instead of Paper-Based Tests for Young Children? Comparability between Paper and Tablet Versions of the Mathematical Heidelberger Rechen Test 1-4
- Author
-
Hassler Hallstedt, Martin and Ghaderi, Ata
- Abstract
Tablets can be used to facilitate systematic testing of academic skills. Yet, when using validated paper tests on tablet, comparability between the mediums must be established. Comparability between a tablet and a paper version of a basic math skills test (HRT: Heidelberger Rechen Test 1-4) was investigated. Five samples with second and third grade students participated. The associations between the tablet and paper version of HRT showed that these modes of administration were comparable for three arithmetic scales, but unacceptable for a pictorial counting scale. Scores were lower on tablet. Test-retest reliability for arithmetic scales on tablet was satisfactory, but was inferior for a low-performing sample. The overall convergent validity was satisfactory. No effect of test administrator was found. Arithmetic scales can potentially be transferred to tablet with good comparability and maintained test-retest reliability. Precautions are necessary when transferring pictorial scales into tablet. Separate norms for tablet are needed when interpreting scores.
- Published
- 2018
- Full Text
- View/download PDF
3. Rupture or Continuity: The Arithmetico-Algebraic Thinking as an Alternative in a Modelling Process in a Paper and Pencil and Technology Environment
- Author
-
Hitt, Fernando, Saboya, Mireille, and Zavala, Carlos Cortés
- Abstract
Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which underpins the construction of a cognitive structure that links both types of thinking. This paper proposes a theoretical and practical framework for a learning approach that supports the construction of a cognitive structure which fosters arithmetico-algebraic thinking at the beginning of secondary school by means of cultural and technological activities relating to polygonal numbers.
- Published
- 2017
- Full Text
- View/download PDF
4. Finite Field Arithmetic in Large Characteristic for Classical and Post-quantum Cryptography
- Author
-
Duquesne, Sylvain, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Mesnager, Sihem, editor, and Zhou, Zhengchun, editor
- Published
- 2023
- Full Text
- View/download PDF
5. Comparing the Use of the Interpersonal Computer, Personal Computer and Pen-and-Paper When Solving Arithmetic Exercises
- Author
-
Alcoholado, Cristián, Diaz, Anita, and Tagle, Arturo
- Abstract
This study aims to understand the differences in student learning outcomes and classroom behaviour when using the interpersonal computer, personal computer and pen-and-paper to solve arithmetic exercises. In this multi-session experiment, third grade students working on arithmetic exercises from various curricular units were divided into three groups. The first group used personal computers (netbooks), the second group used an interpersonal computer (ie, one projector with a screen, one computer and one mouse per child) and the third group used pen-and-paper. The results of the experiment indicate that all three groups achieved an increase in learning, as shown by the pretest and posttest scores. No significant difference was found between the interpersonal computer and personal computer groups. This suggests that the key characteristic shared by the two groups is the provision of feedback. The format that such feedback takes, either private (through a personal screen) or public (through a shared screen), is shown to make no difference. However, the results significantly favour groups that are provided with instant feedback (interpersonal computer and personal computer) as opposed to delayed feedback (pen-and-paper).
- Published
- 2016
- Full Text
- View/download PDF
6. Extendible functions and local root numbers: Remarks on a paper of R. P. Langlands.
- Author
-
Koch, Helmut and Zink, Ernst‐Wilhelm
- Subjects
- *
SOLVABLE groups , *SET functions , *ARITHMETIC , *L-functions , *ARTIN algebras , *PROFINITE groups - Abstract
This paper refers to Langlands' big set of notes devoted to the question if the (normalized) local Hecke–Tate root number Δ=Δ(E,χ)$\Delta =\Delta (E,\chi)$, where E is a finite separable extension of a fixed nonarchimedean local field F, and χ a quasicharacter of E×$E^\times$, can be appropriately extended to a local ε‐factor εΔ=εΔ(E,ρ)$\varepsilon _\Delta =\varepsilon _\Delta (E,\rho)$ for all virtual representations ρ of the corresponding Weil group WE$W_E$. Whereas Deligne has given a relatively short proof by using the global Artin–Weil L‐functions, the proof of Langlands is purely local and splits into two parts: the algebraic part to find a minimal set of relations for the functions Δ, such that the existence (and unicity) of εΔ$\varepsilon _\Delta$ will follow from these relations; and the more extensive arithmetic part to give a direct proof that all these relations are actually fulfilled. Our aim is to cover the algebraic part of Langlands' notes, which can be done completely in the framework of representations of solvable profinite groups, where two modifications of Brauer's theorem play a prominent role. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Visualizing Math: How Number Lines Can Empower Problem-Solving
- Author
-
Tiffany Berman and Casey Hord
- Abstract
Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships between mathematical operations. These strategies are helpful for the development of addition, subtraction, multiplication, division, and later, fractional mathematics. In this article, we describe the progression of number lines as a supportive strategy for elementary students and those with developmental delays in mathematics to improve mathematical understanding. This strategy is based on students being able to show their work and think about what they have written on paper or how they have used manipulatives.
- Published
- 2024
8. Relative Reasoning and the Transition from Additive to Multiplicative Thinking in Proportionality
- Author
-
Jérôme Proulx
- Abstract
Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work on proportional reasoning has pointed to a type of strategy, called "relative", that appears to be lodged right between additive and multiplicative ways of thinking. This sort of "in-between" strategy raises significant interest and motivates further analysis. In this paper, I explore several of these relative strategies engaged in by a 13-year-old student, Marie, during a series of individual interviews. The analysis outlines several dimensions that can inform as much the transition from additive to multiplicative thinking than proportional reasoning itself. [For the complete proceedings, see ED658295.]
- Published
- 2023
9. A New Classification of Semantic Structures of One-Step Word Problem Situations
- Author
-
Oh Hoon Kwon
- Abstract
A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in Lakoff et al. (2000). The classification identifies two main classes: action on/change of an initial quantity and coordination/comparison of two quantities, providing a unifying characteristic of basic operations of quantities. This classification is more comprehensive and differentiated than the classification of CCSSM (2010) and Polotskaia et al. (2021), as it emphasizes conceptual demands of children's mathematics, coherence and continuity of progressions, and consistency with thinking modes and/or problem-solving strategies. [For the complete proceedings, see ED658295.]
- Published
- 2023
10. Mismatch of the South African Foundation Phase Curriculum Demands and Learners' Current Knowledge
- Author
-
Fritz, Annemarie, Long, Caroline, Herzog, Moritz, Balzer, Lars, Ehlert, Antje, and Henning, Elizabeth
- Abstract
Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners' developmental trajectories. Given the hierarchical structure of mathematics, the curricular requirements should pay attention to learners' current knowledge of mathematical concepts. The aim of this study was to compare the curricular requirements as defined by the CAPS with the conceptual current knowledge of South African learners. South African Grade 1 learners (N = 602) were assessed on a test of numeracy concepts, based on a theoretically informed and empirically validated model of developing mathematical proficiency. The content of the CAPS for Grade 1 was aligned to the model levels by two experts (Cohen's [kappa] = 0.753, p < 0.001). Results show that the curricular requirements go far beyond the current knowledge required to engage with these new concepts of the vast majority of South African Grade 1 learners. The mismatch may to some extent be responsible for the unsatisfactory results in international comparison studies. These results show that the intended curriculum is beyond the grasp of most South African Grade 1 learners. These children are unlikely to develop new arithmetic concepts based on their lack of required foundation knowledge. We therefore argue that the intended curriculum for Grade 1 should focus more on counting skills, ordinal relations between numbers and--most importantly--set-based number representations and part-part-whole relations.
- Published
- 2020
- Full Text
- View/download PDF
11. Extending VIAP to Handle Array Programs
- Author
-
Rajkhowa, Pritom, Lin, Fangzhen, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Piskac, Ruzica, editor, and Rümmer, Philipp, editor
- Published
- 2018
- Full Text
- View/download PDF
12. The Prime Number Theorem as a Mapping between Two Mathematical Worlds
- Author
-
Norton, Anderson and Flanagan, Kyle
- Abstract
This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two mathematical worlds: an additive world and a multiplicative world. Understanding how children might map between their additive and multiplicative worlds provides insights into the prime number theorem. It also helps us appreciate the power of children's mathematics, constructed through the coordination of their own mental actions. [For the complete proceedings, see ED630210.]
- Published
- 2022
13. Fraction Addition through the Music
- Author
-
Maria T. Sanz, Carlos Valenzuela, Emilia López-Iñesta, and Guillermo Luengo
- Abstract
This study examined the effects of an academic intervention, associated with music, on the conceptual understanding of musical notation and arithmetic of fractions of first-year students of high school from a mixed Spanish multicultural and socioeconomic public school. The students (N = 12) had previous concepts about musical instruction, as well as operations with fractions, particularly addition. This is an observational study in which a battery of four tasks was administered before and after an instruction based on a musical environment, music being a semiotic function. The instruction included 9 sessions of 50 minutes each. The results prior to the intervention show deficiencies in a concept that was not new to the students, however, after the intervention the students were competent in addition with fractions. [For the complete proceedings, see ED657822.]
- Published
- 2023
14. 'Leave No One Behind': A Systematic Literature Review on Game-Based Learning Courseware for Preschool Children with Learning Disabilities
- Author
-
Zolkipli, Nurzamila Zasira, Rahmatullah, Bahbibi, Mohamad Samuri, Suzani, Árva, Valéria, and Sugiyo Pranoto, Yuli Kurniawati
- Abstract
The rapid growth of multimedia pedagogy in the education sector has brought about a game-based technological approach that is shaping the learning of children nowadays. The focus of the approach is to encourage active participation from children; the effect can be seen in their interaction, involvement, and engagement throughout the learning content. Active participation in a learning environment would have a substantial impact on children's self-development and academic achievement, particularly for those with learning disabilities (LD). Therefore, the purpose of this paper is to systematically analyze research conducted on Game-Based Learning (GBL) courseware to support the education of children with LD. A systematic literature review was undertaken, following the PRISMA framework for paper selection. A total of 109 articles were retrieved from the Scopus and Science Direct databases by using a specific keywords search. 14 articles were finalized at the end of the screening based on the inclusion and exclusion criteria. Results reveal the trend of publications, approaches used, and research themes of the selected papers, which include the courseware requirement, student adaptation, and impact of the implementation. The findings demonstrate that GBL is one of the effective methods to be applied in preschool education. It has a significant impact on the development of cognitive skills and assists children who have difficulty in reading, writing, and arithmetic. The findings in this paper can be used as a guide in developing GBL courseware that is developmentally appropriate and effective for children with LD.
- Published
- 2023
15. Gender Differences in How Students Solve the Most Difficult to Retrieve Single-Digit Addition Problems
- Author
-
Mathematics Education Research Group of Australasia (MERGA), Russo, James, and Hopkins, Sarah
- Abstract
Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that students preference the near-doubles strategy when the difference between the addends was one, the bridging-through-10 strategy when one of the addends was a nine, and the count-on-from-larger strategy when a derived strategy was more effortful. Moreover, whereas boys were more inclined to use derived strategies, girls were almost three times more likely to use the count-on-from-larger strategy.
- Published
- 2023
16. Tap or Swipe: Interaction's Impact on Cognitive Load and Rewards in a Mobile Mental Math Game
- Author
-
Jost, Patrick, Rangger, Sebastian, and Künz, Andreas
- Abstract
With the growing prevalence of mobile apps for self-directed learning, educational games increasingly find their place in everyday routines, becoming accessible to a broad audience. Despite the growing ease of content creation by artificial intelligence computing, the challenge of designing effective and engaging Serious Games remains, particularly in managing cognitive resources and ensuring quality engagement, notably influenced by the game's interaction modalities. This study explores these challenges within the context of a casual mobile mental arithmetic game, investigating the differential impacts of tap and swipe interaction variants on cognitive load and reward-based engagement. The study presents the findings of an international field study on Google Play. In a between-group design, the two casual interaction paradigms were compared regarding their impact on practice performance, cognitive load and effect on classic casual game rewarding represented through points, leaderboards and badges. The findings show that tap interaction can optimise cognitive load with a better mental math practice performance than the more indirect swipe gesture. A combination of elementary tap interaction with point rank and interaction precision badges indicates to enhance practice motivation. The results are synthesised into interaction design recommendations for casual mental math mobile games. [For the full proceedings, see ED636095.]
- Published
- 2023
17. Effects of an Adaptive Math Learning Program on Students' Competencies, Self-Concept, and Anxiety
- Author
-
Hilz, Anna and Aldrup, Karen
- Abstract
Studies on math learning programs are lacking that consider a wide set of outcome variables, and students' practice behavior. Therefore, we investigated whether an adaptive arithmetic learning program fosters students' math performance (addition and subtraction), math self-concept, and a reduction of math anxiety, and how practice behavior (practiced tasks and practiced weeks) affect the investigated variables. We used a pre-post control group design with a total of 366 fifth grade German students. Randomization took place on the class level. Students in the experimental condition used the program for 22 weeks. Math self-concept only improved in the experimental group. Students' subtraction performance improved as a function of practiced tasks, and addition performance improved as a function of practiced weeks.
- Published
- 2023
- Full Text
- View/download PDF
18. Exploring Insights from Initial Teacher Educators' Reflections on the Mental Starters Assessment Project
- Author
-
Rosemary D. L. Brien and Sharon M. Mc Auliffe
- Abstract
Background: The Mental Starters Assessment Project (MSAP) seeks to address poor performance in Grade 3 mathematics. The programme focusses on eliminating inefficient counting methods and promoting strategic mathematical skills, including numerical sense, mental calculation and rapid recall skills. Additionally, MSAP supports teachers' professional growth by providing them with a toolkit of effective calculation strategies to bridge the performance gap and enhance mathematical education. Aim: This paper explores the insight gained from reflections of final year Bachelor of Foundation Phase (FP) initial teacher educators (ITE) students in South Africa. Setting: Grade 3 classrooms. Methods: The ITE students were given training and materials to implement the MSAP, and this occurred over a 4-week teaching practicum, after which they completed a reflective task on the implementation. A total of 20 students were selected from a cohort of 138 based on their academic performance. Results: The analysis of the reflections showed that ITE students benefitted from reflecting on their practice and highlighted important elements of their professional learning. The reflections raised issues related to challenges in their pedagogical content knowledge (PCK) as well as their confidence and competence to teach mathematics and manage the classroom context. Conclusion: With a multi-dimensional model of reflection, ITE students can achieve a deeper understanding of mathematics teaching and learning when building learners' mental strategies, fostering professional growth and elevating the overall quality of mathematics education. Contribution: Overall, the findings provide insight into the benefits of reflective practices for ITE students' professional development and the improvement of mathematics education.
- Published
- 2024
19. Using Interviews with Non-Examples to Assess Reasoning in F-2 Classrooms
- Author
-
Mathematics Education Research Group of Australasia (MERGA) and Copping, Kate
- Abstract
The development of mathematical reasoning is a key proficiency for mathematics within the Australian Curriculum. However, reasoning can be difficult for teachers to assess, particularly with pen and paper tests. In this study, interview tasks were designed across three curriculum areas at three different levels to assess student reasoning through the use of examples and non-examples. Non-examples can be used to assist in building boundaries and deepening conceptual understanding. Through the interview, teacher and student dialogue can help students to demonstrate reasoning and clarify concepts through explanation and justification.
- Published
- 2021
20. Construction of Arithmetic-Algebraic Thinking in a Socio-Cultural Instructional Approach = Construction d'une pensée arithémico-algébrique dans une approche socioculturelle de l'enseignement
- Author
-
Hitt, Fernando
- Abstract
We present the results of a research project on arithmetic-algebraic thinking that was carried out jointly by a team in Mexico and another in Quebec. The project deals with the concepts of variable and covariation between variables in the sixth grade at the elementary level and the first, second, and third years of secondary school--namely, children from 11 to 14 years old. We target secondary students (first year or K7) in this article. Our objective relates to the development of a gradual generalization in arithmetic-algebraic thinking in a socio-cultural approach to the learning of mathematics. We experimented with investigative situations using a paper-and-pencil approach and technology. We analyze the emergence, in this context, of a visual abstraction, the production of institutional and non-institutional representations, a sensitivity to contradiction, and, finally, the concepts of variable and of covariation between variables. [For the complete proceedings, see ED629884.]
- Published
- 2020
21. Kripke Models Built from Models of Arithmetic
- Author
-
Henk, Paula, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Aher, Martin, editor, Hole, Daniel, editor, Jeřábek, Emil, editor, and Kupke, Clemens, editor
- Published
- 2015
- Full Text
- View/download PDF
22. Justifications Students Use when Writing an Equation during a Modeling Task
- Author
-
Roan, Elizabeth and Czocher, Jennifer
- Abstract
Literature typically describes mathematization, the process of transforming a real-world situation into a mathematical model, in terms of desirable actions and behaviors students exhibit. We attended to STEM undergraduate students' quantitative reasoning as they derived equations. Analysis of the meanings they held for arithmetic operations (+, -, ·, ÷) provided insight into how participants expressed real-world relationships among entities with arithmetic relationships among values. We extend the findings from K-12 literature (e.g., using multiplication to instantiate a rate) to STEM undergraduates and found evidence of new ways of justifying the usage of arithmetic operations (e.g., using multiplication to instantiate an amount). [For the complete proceedings, see ED630210.]
- Published
- 2022
23. Middle School Students' Mature Number Sense Is Uniquely Associated with Grade Level Mathematics Achievement
- Author
-
Kirkland, Patrick K., Guang, Claire, Cheng, Ying, Trinter, Christine, Kumar, Saachi, Nakfoor, Sofia, Sullivan, Tiana, and McNeil, Nicole M.
- Abstract
Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014), students' mature number sense and its nomological network are not yet well specified. For example, how does students' mature number sense relate to their knowledge of fractions and their grade-level mathematics achievement? We analyzed 129 middle school students' scores on measures of mature number sense, fraction and decimal computation, and grade-level mathematics achievement. We found mature number sense to be measurably distinct from their fraction and decimal knowledge and uniquely associated with students' grade-level mathematics achievement. [For the complete proceedings, see ED630210.]
- Published
- 2022
24. The Evolution from 'I Think It plus Three' towards 'I Think It Is Always plus Three.' Transition from Arithmetic Generalization to Algebraic Generalization
- Author
-
María D. Torres, Antonio Moreno, Rodolfo Vergel, and María C. Cañadas
- Abstract
This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its continuity in the generalization process are important for this transition. We are presenting a case study with a semi-structured interview where we proposed a task of contextualized generalization involving the function y = x + 3. Special attention was given to the structures evidenced and the type of generalization expressed by the student in the process. We noted that the student identified the correct structure for the task during the interview and that he evidenced a factual type of algebraic generalization. Due to the student's identification of the appropriate structure and the application of it to other different particular cases, we have observed a transition from arithmetic thinking to algebraic thinking.
- Published
- 2024
- Full Text
- View/download PDF
25. Short Paper: XOR Arbiter PUFs Have Systematic Response Bias
- Author
-
Nils Wisiol and Niklas Pirnay
- Subjects
050101 languages & linguistics ,Computer science ,05 social sciences ,Short paper ,Physical unclonable function ,Arbiter ,Hardware_PERFORMANCEANDRELIABILITY ,02 engineering and technology ,ComputerSystemsOrganization_PROCESSORARCHITECTURES ,Response bias ,ComputingMilieux_MANAGEMENTOFCOMPUTINGANDINFORMATIONSYSTEMS ,0202 electrical engineering, electronic engineering, information engineering ,ComputerSystemsOrganization_SPECIAL-PURPOSEANDAPPLICATION-BASEDSYSTEMS ,020201 artificial intelligence & image processing ,0501 psychology and cognitive sciences ,Arithmetic ,Hardware_REGISTER-TRANSFER-LEVELIMPLEMENTATION - Abstract
We demonstrate that XOR Arbiter PUFs with an even number of arbiter chains have inherently biased responses, even if all arbiter chains are perfectly unbiased. This rebukes the believe that XOR Arbiter PUFs are, like Arbiter PUFs, unbiased when ideally implemented and proves that independently manufactured Arbiter PUFs are not statistically independent.
- Published
- 2020
26. Going Online: A Simulated Student Approach for Evaluating Knowledge Tracing in the Context of Mastery Learning
- Author
-
Zhang, Qiao and Maclellan, Christopher J.
- Abstract
Knowledge tracing algorithms are embedded in Intelligent Tutoring Systems (ITS) to keep track of students' learning process. While knowledge tracing models have been extensively studied in offline settings, very little work has explored their use in online settings. This is primarily because conducting experiments to evaluate and select knowledge tracing models in classroom settings is expensive. To fill this gap, we introduce a novel way of using machinelearning models to generate simulated students. We conduct experiments using agents generated by the Apprentice Learner Architecture to investigate the online use of different knowledge tracing models (Bayesian Knowledge Tracing, the Streak model, and Deep Knowledge Tracing). An analysis of our simulation results revealed an error in the initial implementation of our Bayesian knowledge tracing model that was not identified in our previous work. Our simulations also revealed a more fundamental limitation of Deep Knowledge Tracing that prevents the model from supporting mastery learning on multi-step problems. Together, these two findings suggest that Apprentice agents provide a practical means of evaluating knowledge tracing models prior to more costly classroom testing. Lastly, our analysis identifies a positive correlation between the Bayesian knowledge tracing parameters estimated from human data and the parameters estimated from simulated learners. This suggests that model parameters might be initialized using simulated data when no human-student data is yet available. [For the full proceedings, see ED615472.]
- Published
- 2021
27. Measuring Mental Computational Fluency with Addition: A Novel Approach
- Author
-
Mathematics Education Research Group of Australasia, Russo, James, and Hopkins, Sarah
- Abstract
Measuring computational fluency, an aspect of procedural fluency, is complex. Many attempts to measure this construct have emphasised accuracy and efficiency at the expense of flexibility and appropriate strategy choice. Efforts to account for these latter constructs through assessing children's computational reasoning using structured interviews (e.g., MAI), are necessarily time-intensive. In this paper, we introduce a novel measure of Mental Computational Fluency with Addition (MCF-A) that attempts to incorporate these aspects by requiring children to reason from the perspective of another child. We describe results of a pilot study using the MCF-A with 169 Year 3 and 4 students.
- Published
- 2018
28. Rote versus Rule: Revisiting the Role of Language in Mathematical Thinking
- Author
-
Qin, Jike and Opfer, John
- Abstract
Language is often depicted as the sine qua non of mathematical thinking, a view buttressed by findings of language-of-training effects among bilinguals. These findings, however, have been limited to studies of arithmetic. Nothing is known about the potential influence of language on the ability to learn rules about the relations among variables (e.g., algebra). To test whether arithmetic and algebraic thinking differ, Chinese-English bilinguals were trained to solve arithmetic and algebra problems in either Chinese or English and then tested on new and old problems in both languages. For arithmetic problems, solution times were always longer for English than Chinese; in both languages, solution times dropped during training; after training, solution times continued to drop for old problems, but returned to pre-training levels for new problems. In contrast, for algebra problems, solution times did not differ across language; solution times dropped during training; after training, gains in speed were preserved for both old and new problems. These findings suggest that the contribution of language to mathematical thinking may be limited to the areas of mathematics that are learned by rote and not by rule. [This paper was published in: "Proceedings of the 40th Annual Conference of the Cognitive Science Society," edited by T. T. Rogers et al., Cognitive Science Society, 2018, pp. 918-923.]
- Published
- 2018
29. Productive Seeds in Preservice Teachers' Reasoning about Fraction Comparisons
- Author
-
Whitacre, Ian, Findley, Kelly, and Atabas, Sebnem
- Abstract
Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers' (PSTs) knowledge of fractions and has given little attention to the productive resources that PSTs bring to teacher education. We surveyed 26 PSTs using a set of 9 fraction-comparison tasks. We report the frequency of complete strategy-arguments and the perspectives (ways of reasoning) used for each item. We further examine incomplete strategy-arguments, noting substantial evidence for productive seeds of reasoning. Using data from interviews with 10 of these PSTs, we identify evidence suggesting these seeds are, in fact, productive in that they provide foundations for further development. We argue that this type of research is needed in order to further mathematics teacher education. [For the complete proceedings, see ED629884.]
- Published
- 2020
30. An Approach to Density in Decimal Numbers: A Study with Pre-Service Teachers = Un acercamiento a la densidad en los números decimales: un estudio con profesores en formación
- Author
-
Suárez-Rodríguez, Mayra and Figueras, Olimpia
- Abstract
Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense". This report presents evidence from ten pre-service teachers from Mexico City that this change can initiate through the implementation of a didactic sequence. The pre-service teachers managed to visualize that a decimal number can be found in an interval. Consequently, they were able to conceive an infinity. However, several of them persisted with the idea of the existence of a successor in the set of decimal numbers. [For the complete proceedings, see ED629884.]
- Published
- 2020
31. Teaching Redundant Residue Number System for Electronics and Computer Students
- Author
-
Somayeh Timarchi
- Abstract
This paper describes a study for teaching number system in a computer arithmetic course and addresses the existing gap in the current course by focusing on the characteristics of applications. A redundant residue number system (RRNS) is an efficient and innovative number system that inherits the interesting properties of both residue number system (RNS) and redundant number systems. It breaks the operands into residues by considering a moduli-set and then signifies the residues by a redundant representation. So, by limiting the carry propagation chain inside and outside the moduli, RRNS proposes more efficient arithmetic units which could be employed in digital signal processing (DSP) applications. Despite the applicability of RRNS, there is not well-organized teaching on RRNS covering the recent achievements. Besides, there is an important question for students and researchers what is the most appropriate number representation for each application category? In this paper, we present a step-by-step education process for RRNS that includes basic concepts of RNS and the redundant number system. Then we address characteristics of different applications that RRNS is suitable to be employed for them. So, the method gives a well-organized proceeding to computer arithmetic designers and students.
- Published
- 2023
- Full Text
- View/download PDF
32. Moving beyond Test Scores: Analyzing the Effectiveness of a Digital Learning Game through Learning Analytics
- Author
-
Nguyen, Huy Anh, Hou, Xinying, Stamper, John, and McLaren, Bruce M.
- Abstract
A challenge in digital learning games is assessing students' learning behaviors, which are often intertwined with game behaviors. How do we know whether students have learned enough or needed more practice at the end of their game play? To answer this question, we performed post hoc analyses on a prior study of the game "Decimal Point," which teaches decimal numbers and decimal operations to middle school students. Using Bayesian Knowledge Tracing, we found that students had the most difficulty with mastering the number line and sorting skills, but also tended to over-practice the skills they had previously mastered. In addition, using students' survey responses and in-game measurements, we identified the best feature sets to predict test scores and self-reported enjoyment. Analyzing these features and their connections with learning outcomes and enjoyment yielded useful insights into areas of improvement for the game. We conclude by highlighting the need for combining traditional test measures with rigorous learning analytics to critically evaluate the effectiveness of learning games. [For the full proceedings, see ED607784.]
- Published
- 2020
33. Towards a Critical Mathematics
- Author
-
Savich, Theodore Michael
- Abstract
The goal of this paper is to express necessary conditions for arithmetic in ways that are compatible with the unity of being and knowing understood within first-person experience. In psychological literature, this experience of unity is discussed as flow, but the epistemological and ontological unity is prior to the observer's position from which psychology unfolds, making this project essentially non-psychological. Instead of an externalized psychological conceptualization of mind, the idea explored is internal to first-person experience that experiences consciousness as movement, with key elements of that movement explicable as inference and algorithm. The notion of first-person experience is often taken to be transparent and irrelevant, so an exercise for orienting readers to the I-feeling and its connection to movement is elaborated. A mathematical notion of history as algorithmic elaboration is introduced in order to explicate how to move from talk about judgments in general to doing arithmetic. In this preliminary and exploratory paper, I forgo many possible linkages with modern mathematics education research literature to focus on articulating what I think are some of the foundational elements of a critical mathematics. The purpose of this preliminary work is to orient readers to an ongoing project in critical mathematics, not to provide instrumental notions of how one might improve teaching or research, though brief discussions of how this mathematical theory could be applied in mathematics education research and practice are included.
- Published
- 2020
34. A Conceptual Analysis of the Equal Sign and Equation -- The Transformative Component
- Author
-
Ying, Yufeng
- Abstract
Mathematics education scholars have generally classified students' conception of the equal sign as either operational or relational. Adding to these conceptions, Jones (2008) introduced the idea of substitutional conception. Building off these scholars, I introduce a form of understanding the equal sign that includes a transformative equivalence component and extends the conceptions of the equal sign to conceptions of equations. [For the complete proceedings, see ED629884.]
- Published
- 2020
35. Strategies Used by Grade 6 Learners in the Multiplication of Whole Numbers in Five Selected Primary Schools in the Kavango East and West Regions
- Author
-
Ilukena, Alex Mbonabi, Utete, Christina Nyarai, and Kasanda, Chosi
- Abstract
This research paper reports strategies used by Grade 6 learners in multiplying whole numbers in five selected primary schools in Kavango East and West regions. A total of 200 learners' mathematics exercise books were analysed in order to identify the commonly used strategies by learners in multiplying whole numbers. A total of ten teachers teaching grade 6 mathematics were also requested to complete a questionnaire which required them to indicate the strategies that they employed in class when teaching multiplication of whole numbers. The teachers indicated that they used a variety of strategies including repeated addition, complete-number (including doubling), partitioning and compensation to teach multiplication of whole numbers. The results also disclosed that the majority of the learners' mathematics exercise books reflected the use of the traditional method of repeated addition contrary to the teachers' claims. It was also found that a few of the learners used other strategies such as long method, short method and learner "invented" strategies. Additionally, the mathematics curriculum for upper primary learners (Grade 4-7 mathematics syllabus) requires learners to use paper and pencil algorithms to carry out multiplication of whole numbers without calculators (Ministry of Education, Arts & Culture [MoEAC], 2015, p. 2). However, at Grade 6, learners were expected to use paper and pencil algorithms to multiply numbers within the range 0-100000. Analysis of the learners' exercise books indicated that the majority were not able to multiply a two digit by a single digit, a two digit by a two digit and a three digit by a two digit number.
- Published
- 2020
36. Investigating the Variety and Usualness of Correct Solution Procedures of Mathematical Word Problems
- Author
-
Samková, Libuše
- Abstract
The contribution focuses on issues related to the implementation of formative assessment methods into inquiry based teaching, by means of issues related to solving twelve multiple-step arithmetic word problems based on operations with natural and rational numbers. These word problems have multiple correct solution procedures and the presented qualitative exploratory empirical study investigates how varied and how usual might be correct solution procedures provided by diverse groups of solvers -- future primary school teachers attending diverse university mathematics courses of diverse forms and/or time extent. According to written data collected from 149 solvers, six notions are introduced in the paper: majority, minority and even solution procedures, and majority, minority and mixed solvers. Issues regarding minority solvers are recognized as an important element for implementing formative assessment methods. All the six notions are illustrated in the paper by samples of solution procedures and diagrams of relative frequency. Implications are given for formative assessment within any kind of education involving multiple-step word problems, regardless of the extent of implemented inquiry.
- Published
- 2020
37. THE EFFECT OF ONE MINUTE PAPER AND ROUND TABLE STRATEGIES IN ACADEMIC ACHIEVEMEN
- Author
-
Mahabad Abdul Kareem Ahmed
- Subjects
Round table ,Computer science ,Arithmetic - Published
- 2020
38. Are Approximate Number System Representations Numerical?
- Author
-
Pickering, Jayne, Adelman, James S., and Inglis, Matthew
- Abstract
Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by amalgamating perceptual features confounded with the set's cardinality. In this paper, we approach the question of whether ANS representations are numerical by studying the properties they have, rather than how they are formed. Across two pre-registered within-subjects studies, we measured 189 participants' ability to multiply the numbers between 2 and 8. Participants completed symbolic and nonsymbolic versions of the task. Results showed that participants succeeded at above-chance levels when multiplying nonsymbolic representations within the subitizing range (2-4) but were at chance levels when multiplying numbers within the ANS range (5-8). We conclude that, unlike Object Tracking System (OTS) representations, two ANS representations cannot be multiplied together. We suggest that investigating which numerical properties ANS representations possess may advance the debate over whether the ANS is a genuinely numerical system.
- Published
- 2023
39. Varieties of Numerical Estimation: A Unified Framework
- Author
-
Qin, Jike, Kim, Dan, and Opfer, John
- Abstract
There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing symbol (symbolic, non-symbolic) and boundedness (bounded, unbounded) on free number-line tasks (Experiment 1) and crossing the same factors on anchored number-line tasks (Experiment 2). This strategy yielded 4 novel tasks to assess the generalizability of the models. Across all 8 tasks, 90% of participants provided estimates better fit by a mixed log-linear model than other cognitive models, and the weight of the logarithmic component ([lambda]) decreased with age. After controlling for age, the weight of the logarithmic component ([lambda]) significantly predicted arithmetic skills, whereas parameters of other models failed to do so. Results suggest that the logarithmic-to-linear shift theory provides a unified account of numerical magnitude estimation and provides uniquely accurate predictions for mathematical proficiency. [This paper was published in: "Proceedings of the 39th Annual Meeting of the Cognitive Science Society," edited by G. Gunzelmann et al., Cognitive Science Society, 2017, pp. 2943-2948.]
- Published
- 2017
40. The Development of Addition and Subtractions Strategies for Children in Kindergarten to Grade 6: Insights and Implications
- Author
-
Mathematics Education Research Group of Australasia, Gervasoni, Ann, Giumelli, Kerry, and McHugh, Barbara
- Abstract
This paper provides insight about the development of addition and subtraction strategies for nearly 22,000 Australian primary school children in 2016. The children were each assessed by their teacher using a task-based assessment interview that identified the strategies they used to mentally perform addition and subtraction, and matched these to a growth point framework. The findings highlight the broad distribution of strategies used by children in each grade level and suggest that few children, including those in Grade 6, reach Growth Point 6 that involves the mental calculation of two-digit and three-digit numbers. These findings have important implications for classroom teaching and professional learning.
- Published
- 2017
41. Hypothesis of Developmental Dyscalculia and Down Syndrome: Implications for Mathematics Education
- Author
-
Mathematics Education Research Group of Australasia and Faragher, Rhonda
- Abstract
In this paper, the hypothesis that Developmental Dyscalculia (DD) is a characteristic of Down syndrome (DS) is proposed. Implications for the hypothesis are addressed: If it were to be confirmed that DS implies DD, what would be the consequences for the mathematics education of learners with DS? The use of prosthetic devices to overcome the impaired calculation capabilities of the brain is essential. Fortunately, electronic calculating devices are readily available. Their routine use opens the possibility of studying areas of mathematics that were once inaccessible.
- Published
- 2017
42. Paper-based vs computer-based exams in CS1
- Author
-
Harri Högmander, Antti-Jussi Lakanen, and Vesa Lappalainen
- Subjects
Division by zero ,Computer science ,05 social sciences ,Rework ,Computer based ,050301 education ,02 engineering and technology ,Paper based ,Test (assessment) ,020204 information systems ,0202 electrical engineering, electronic engineering, information engineering ,Test suite ,Mode effect ,Arithmetic ,0503 education ,Simulation - Abstract
In this study, we examine the "test mode effect" in CS1 exam using the Rainfall problem. The participants started working with pen and paper, after which they had access to a computer, and they could rework their solution with a help of a test suite developed by the authors. In the computer- based phase many students were able to fix the errors that they had committed during the paper-based phase. These errors included well-known corner cases, such as empty array or division by zero.
- Published
- 2016
43. The Strategy the Use of False Assumption and Word Problem Solving
- Author
-
Eisenmann, Petr, Pribyl, Jirí, and Novotná, Jarmila
- Abstract
The paper describes one problem solving strategy -- the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual difficulties when solving word problems using linear equations, namely construction of the equations. The paper presents the outcomes of a study conducted on three lower secondary schools in the Czech Republic with 147 14-15-year-old pupils. Pupils from the experimental group were, unlike pupils from the control group, taught the strategy the Use of false assumption before being taught the topic Solving word problems. The tool for the study was a test of four problems that was sat by all the involved pupils three weeks after finishing the topic "Solving word problems" and whose results were evaluated statistically. The experiment confirmed the research hypothesis that the introduction of the strategy the Use of false assumption into 8th grade mathematics lessons (14-15-year-old pupils) helps pupils construct equations more successfully when solving word problems.
- Published
- 2019
44. Students' Mental Model in Solving the Patterns of Generalization Problem
- Author
-
Prayekti, N., Nusantara, T., Sudirman, and Susanto, H.
- Abstract
Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This study was conducted using the qualitative descriptive method to investigate students' mental model during the process of solving the problem of generalization patterns. Students were required to speak aloud what he or she was thinking about solving problems ("think-aloud"). Based on the data obtained, the students' mental models in solving the patterns of generalization problem can be classified into two kinds of mental models, namely: (1) direct mental model and (2) indirect mental model. Students classified using direct mental model were using the only generalization of algebraic in solving the problem. Meanwhile, students classified using indirect mental model were using a combination of both generalizations of algebraic and arithmetic. Based on the results of the study, teachers are required to take into account students' mental model in solving the generalization patterns problem to achieve better learning process. [Paper presented at ICEGE 2018.]
- Published
- 2019
45. Three Ages of FPGAs: A Retrospective on the First Thirty Years of FPGA Technology: This Paper Reflects on How Moore's Law Has Driven the Design of FPGAs Through Three Epochs: the Age of Invention, the Age of Expansion, and the Age of Accumulation
- Author
-
Stephen M. Trimberger
- Subjects
Moore's law ,Computer science ,Fpga architecture ,media_common.quotation_subject ,020208 electrical & electronic engineering ,0202 electrical engineering, electronic engineering, information engineering ,Technology scaling ,02 engineering and technology ,Electrical and Electronic Engineering ,Arithmetic ,Field-programmable gate array ,020202 computer hardware & architecture ,media_common - Abstract
Since their introduction, field programmable gate arrays (FPGAs) have grown in capacity by more than a factor of 10 000 and in performance by a factor of 100. Cost and energy per operation have both decreased by more than a factor of 1000. These advances have been fueled by process technology scaling, but the FPGA story is much more complex than simple technology scaling. Quantitative effects of Moore?s Law have driven qualitative changes in FPGA architecture, applications and tools. As a consequence, FPGAs have passed through several distinct phases of development. These phases, termed "Ages" in this paper, are The Age of Invention, The Age of Expansion and The Age of Accumulation. This paper summarizes each and discusses their driving pressures and fundamental characteristics. The paper concludes with a vision of the upcoming Age of FPGAs.
- Published
- 2018
46. Kindergarten children's symbolic number comparison skills relates to 1st grade mathematics achievement: Evidence from a two-minute paper-and-pencil test.
- Author
-
Hawes, Zachary, Archibald, Lisa, Ansari, Daniel, and Nosworthy, Nadia
- Subjects
- *
MATHEMATICS , *MATHEMATICAL ability in children , *MATHEMATICAL ability testing , *LONGITUDINAL method , *SYMBOLISM of numbers , *ARITHMETIC , *KINDERGARTEN , *CHILDREN - Abstract
Abstract Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (M age = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance. Highlights • We tested the validity and reliability of a recently developed Numeracy Screener. • Performance on the symbolic comparison task predicted kindergarten children's arithmetic performance. • Performance on the symbolic comparison task in kindergarten predicted school mathematics achievement one year later. • The Numeracy Screener may be a useful tool for early mathematics researchers and educators alike. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
47. Learning from Lessons: Teachers' Insights and Intended Actions Arising from Their Learning about Student Thinking
- Author
-
Roche, Anne, Clarke, Doug, Clarke, David, and Chan, Man Ching Esther
- Abstract
A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. We are studying the knowledge construction of mathematics teachers utilising multi-camera research techniques during lesson planning, classroom interactions and reflection. This paper reports on the learning of two Year 7 teachers, one in Melbourne and one in Chicago, teaching the same initial lesson focusing on division, remainders and context. Both teachers claimed to have learned about their students' mathematical thinking after teaching the initial lesson, but found planning a second lesson to accommodate this learning challenging.
- Published
- 2016
48. Improvement of Paper Properties Using White Ledger CNF
- Author
-
Jong Myoung Won, Jin Mo Kim, Im-Jeong Hwang, and Yong-Kyu Lee
- Subjects
White (horse) ,Ledger ,Media Technology ,General Materials Science ,General Chemistry ,Arithmetic ,Mathematics - Published
- 2018
49. The Brave New Digital World: The Value of Published Work Today is Multifactorial; it is in the Heart of the Paper, not an Abstract Meaningless Single-Digit Number
- Author
-
Mutaz B. Habal
- Subjects
Otorhinolaryngology ,Work (electrical) ,business.industry ,Publications ,Digit number ,Humans ,Medicine ,Surgery ,General Medicine ,Arithmetic ,business ,Value (mathematics) - Published
- 2021
50. Validation and Comparison of a Digital Digit Symbol Substitution (DSST) Task Performed on Smart Phones With a Traditional Paper-Pencil Version
- Author
-
Luke Allen, Emily Thorp, Jenny Barnett, Nathan Cashdollar, Kiri Granger, Daniel Thorpe, Miriam Evans, Francesca Cormack, and Elizabeth A. Baker
- Subjects
Computer science ,Substitution (algebra) ,Arithmetic ,Biological Psychiatry ,Pencil (mathematics) ,Symbol (chemistry) ,Numerical digit ,Task (project management) - Published
- 2021
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.