Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

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Creative Mathematical Reasoning: Does Need for Cognition Matter?

Frontiers in Psychology ◽

10.3389/fpsyg.2021.797807 ◽

2022 ◽

Vol 12 ◽

Author(s):

Bert Jonsson ◽

Julia Mossegård ◽

Johan Lithner ◽

Linnea Karlsson Wirebring

Keyword(s):

Problem Solving ◽

Conceptual Understanding ◽

Mathematical Reasoning ◽

Need For Cognition ◽

Math Performance ◽

Equation Modeling ◽

Positive Effects ◽

Cognitive Motivation ◽

Solution Methods ◽

Creative Mathematical Reasoning

A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning (CMR), a method that in previous studies has been contrasted against algorithmic reasoning (AR) with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition (NFC), and working memory capacity (WMC). Two independent groups, consisting of upper secondary students (N = 137, mean age 17.13, SD = 0.62, 63 boys and 74 girls), practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding.

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Creative Mathematical Reasoning of Prospective Teachers in Solving Problems Reviewed Based on Working Memory Capacity

Journal of Physics Conference Series ◽

10.1088/1742-6596/1417/1/012055 ◽

2019 ◽

Vol 1417 ◽

pp. 012055 ◽

Cited By ~ 1

Author(s):

I Palengka ◽

D Juniati ◽

Abadi

Keyword(s):

Working Memory ◽

Prospective Teachers ◽

Mathematical Reasoning ◽

Working Memory Capacity ◽

Memory Capacity ◽

Creative Mathematical Reasoning

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Dispersive evaluation and surface chemistry of advanced, multifunctional silica/lignin hybrid biomaterials

Open Chemistry ◽

10.2478/s11532-013-0322-4 ◽

2013 ◽

Vol 11 (11) ◽

pp. 1860-1873 ◽

Cited By ~ 6

Author(s):

Magdalena Nowacka ◽

Łukasz Klapiszewski ◽

Małgorzata Norman ◽

Teofil Jesionowski

Keyword(s):

Zeta Potential ◽

Surface Charge ◽

Electrochemical Sensors ◽

Relevant Information ◽

Structural Features ◽

Kraft Lignin ◽

Morphological Properties ◽

Wide Range ◽

Hybrid Biomaterials

AbstractAdvanced silica/lignin hybrid biomaterials were obtained using hydrated or fumed silicas (Aerosil®200) and Kraft lignin as precursors, which is a cheap and biodegradable natural polymer. To extend the possible range of applications, the silicas were first modified with N-2-(aminoethyl)-3-aminopropyltrimethoxsysilane, and then with Kraft lignin, which had been oxidized with sodium periodate. The SiO2/lignin hybrids and precursors were characterised by means of determination of their physicochemical and dispersive-morphological properties. The effectiveness of silica binding to lignin was verified by FT-IR spectroscopy. The zeta potential value provides relevant information regarding interactions between colloid particles. Measurement of the zeta potential values enabled an indirect assessment of stability for the studied hybrid systems. Determination of zeta potential and density of surface charge also permitted the quantitative analysis of changes in surface charge, and indirectly confirmed the effectiveness of the proposed method for synthesis of SiO2/lignin hybrid materials. A particularly attractive feature for practical use is their stability, especially electrokinetic stability. It is expected that silica/lignin hybrids will find a wide range of applications (polymer fillers, biosorbents, electrochemical sensors), as they combine the unique properties of silica with the specific structural features of lignin. This makes these hybrids biomaterials advanced and multifunctional.

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Strategy use moderates the relation between working memory capacity and fluid intelligence: A combined approach

Intelligence ◽

10.1016/j.intell.2022.101627 ◽

2022 ◽

Vol 91 ◽

pp. 101627

Author(s):

Chenyu Li ◽

Xuezhu Ren ◽

Karl Schweizer ◽

Tengfei Wang

Keyword(s):

Working Memory ◽

Fluid Intelligence ◽

Working Memory Capacity ◽

Memory Capacity ◽

Strategy Use ◽

Combined Approach

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Dyscalculia and pedagogical intervention

International Research Journal of Management IT and Social Sciences ◽

10.21744/irjmis.v6n5.710 ◽

2019 ◽

Vol 6 (5) ◽

pp. 95-100

Author(s):

Mariela Alexandra Calderón Delgado ◽

Ronald Iván Zamora Delgado ◽

Raphael Palma Palma ◽

María Elena Moya

Keyword(s):

Teaching And Learning ◽

Mathematical Reasoning ◽

Collaborative Work ◽

Relevant Information ◽

Intervention Strategies ◽

Long Term Results ◽

Learning Disorder ◽

Pedagogical Intervention ◽

Teaching Learning

The acquisition of knowledge in the area of mathematics, generally requires a series of numerical competencies that are strengthening as school-age progress, this process is sometimes affected by a learning disorder called dyscalculia that it causes severe difficulties in understanding or internalizing arithmetic contents that lead to mathematical reasoning. The objective of this article is to provide relevant information on the causes of dyscalculia, repercussions on learning and the importance of early pedagogical intervention, through a descriptive study, a bibliographic review of the topic and analysis of various sources have carried out, which allowed formulating conclusions regarding the teaching and learning of mathematics. These data provided the necessary information to determine that dyscalculia is a condition that requires treatment that includes collaborative work between specialists, parents, and teachers. Early diagnosis and the use of appropriate pedagogical intervention strategies and the incorporation of innovative methodologies in the teaching-learning process will allow effective long-term results.

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Understanding the Relationship Between Rationality and Intelligence: A Latent-Variable Approach

10.31234/osf.io/ns9ky ◽

2021 ◽

Author(s):

Alexander P. Burgoyne ◽

Cody Mashburn ◽

Jason S. Tsukahara ◽

Zach Hambrick ◽

Randall W Engle

Keyword(s):

Working Memory ◽

Latent Variable ◽

Fluid Intelligence ◽

Working Memory Capacity ◽

Memory Capacity ◽

Attention Control ◽

Equation Modeling ◽

General Intelligence ◽

Variable Approach ◽

The Relationship

A hallmark of intelligent behavior is rationality—the disposition and ability to think analytically to make decisions that maximize expected utility or follow the laws of probability, and therefore align with normative principles of decision making. However, the question remains as to whether rationality and intelligence are empirically distinct, as does the question of what cognitive mechanisms underlie individual differences in rationality. In a large sample of participants (N = 331), we used latent variable analyses to assess the relationship between rationality and intelligence. The results indicated that there was a common ability underpinning performance on some, but not all, rationality tests. Latent factors representing rationality and general intelligence were strongly correlated (r = .54), but their correlation fell well short of unity. Indeed, after accounting for variance in performance attributable to general intelligence, rationality measures still cohered on a latent factor. Confirmatory factor analysis indicated that rationality correlated significantly with fluid intelligence (r = .56), working memory capacity (r = .44), and attention control (r = .49). Structural equation modeling revealed that attention control fully accounted for the relationship between working memory capacity and rationality, and partially accounted for the relationship between fluid intelligence and rationality. Results are interpreted in light of the executive attention framework, which holds that attention control supports information maintenance and disengagement in service of complex cognition. We conclude by speculating about factors rationality tests may tap that other cognitive ability tests miss, and outline directions for further research.

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Early Auditory Evoked Potential Is Modulated by Selective Attention and Related to Individual Differences in Visual Working Memory Capacity

Journal of Cognitive Neuroscience ◽

10.1162/jocn_a_00684 ◽

2014 ◽

Vol 26 (12) ◽

pp. 2682-2690 ◽

Cited By ~ 28

Author(s):

Ryan J. Giuliano ◽

Christina M. Karns ◽

Helen J. Neville ◽

Steven A. Hillyard

Keyword(s):

Working Memory ◽

Individual Differences ◽

Selective Attention ◽

Working Memory Capacity ◽

Relevant Information ◽

Auditory Evoked Potential ◽

Control Mechanisms ◽

Auditory Selective Attention ◽

Visual Change Detection ◽

Listening Task

A growing body of research suggests that the predictive power of working memory (WM) capacity for measures of intellectual aptitude is due to the ability to control attention and select relevant information. Crucially, attentional mechanisms implicated in controlling access to WM are assumed to be domain-general, yet reports of enhanced attentional abilities in individuals with larger WM capacities are primarily within the visual domain. Here, we directly test the link between WM capacity and early attentional gating across sensory domains, hypothesizing that measures of visual WM capacity should predict an individual's capacity to allocate auditory selective attention. To address this question, auditory ERPs were recorded in a linguistic dichotic listening task, and individual differences in ERP modulations by attention were correlated with estimates of WM capacity obtained in a separate visual change detection task. Auditory selective attention enhanced ERP amplitudes at an early latency (ca. 70–90 msec), with larger P1 components elicited by linguistic probes embedded in an attended narrative. Moreover, this effect was associated with greater individual estimates of visual WM capacity. These findings support the view that domain-general attentional control mechanisms underlie the wide variation of WM capacity across individuals.

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