Creative Mathematical Reasoning: Does Need for Cognition Matter?

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.

Effects on brain activity after creative mathematical reasoning when considering individual differences in cognitive ability

Many learning opportunities of mathematical reasoning in school encourage passive imitative learning procedures (algorithmic reasoning, AR) instead of engaging in more active constructive reasoning processes (e.g., creative mathematical reasoning, CMR). In the present study, we employed a within-subject mathematical intervention in the classroom with pupils in upper secondary schools followed by a test situation during brain imaging with fMRI one week later. We hypothesized that learning mathematical reasoning with the active (CMR) compared to the passive mode (AR) should lead to a CMR-effect, characterized by better performance and higher activity in brain regions related to semantic memory processing one week after learning. Despite controlling for individual differences in cognitive abilities, higher brain activity in key semantic brain regions such as left AG and left IFG was observed on tasks previously learnt with CMR compared to AR. Thus, encouraging pupils to engage in more active constructive processes when learning mathematical reasoning might have beneficial effects on learning and memory.

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.

Exploration of Creative Mathematical Reasoning in Solving Geometric Problems

Reasoning that is constructed from remembering is imitative reasoning, while the opposite is creative reasoning. This study aims to explore creative mathematical reasoning in solving geometric problems. Mathematical creative reasoning is reasoning that contains elements of novelty, plausibility, and mathematical foundation. This type of research is descriptive qualitative, which is explorative. The research subjects were the first-semester student in the mathematics education study program with 32 students. The results showed that from 32 students, there was only one student identified as having creative mathematical reasoning in solving geometry problems. Creative mathematical reasoning can be identified when the subject is able to reason algorithmically but is aware of problems so they cannot be resolved algorithmically so that they must form new reasoning, which consists of novelty, plausibility, and mathematical foundation. Creative mathematical reasoning arises after students make an algorithmic reasoning process, but find no solution. Novelty is the weakest indicator of creative mathematical reasoning, so it requires scaffolding to bring it up.

EXPLORING THE CREATIVE MATHEMATICAL REASONING OF MATHEMATICS EDUCATION STUDENT THROUGH DISCOVERY LEARNING

Discovery learning is a learning model that enhancescreative thinking skill including develops students' creative mathematical reasoning. Creative mathematical reasoning process includes novelty, plausibility, and mathematical foundation. This research aims to describe students’ creative mathematical reasoning of the mathematics education department on Geometry. The data was collected based on the observation and individual evaluation of students.The results showed that Discovery Learning can (1) grow as much as 35.48% of students have complete creative mathematical reasoning (novelty, plausibility, and mathematical foundation), (2) grow as much as 64.52% of students have incomplete creative mathematical reasoning, and (3) grow novelty by 77.42%.

ADVERSITY QUOTIENT DAN PENALARAN KREATIF MATEMATIS SISWA SMA DALAM PEMBELAJARAN ARGUMENT DRIVEN INQUIRY PADA MATERI TURUNAN FUNGSI

This study is designed in the form of experiment with the design of control group and posttest only aimed at investigating the role of learning that Argument Driven Inquiry (ADI) in improving senior high school students’ creative mathematical reasoning ability. The population of this study was senior high school students’ in Cimahi City and the samples were 69 senior high school students’ set purposively and randomly to be included into the experimental class and control class. Based on the results and discussion, it is concluded that: (1) creative mathematical reasoning ability of the students who received Argument Driven Inquiry (ADI) instruction is better than those who received direct instruction is reviewed based on the whole and the type of Adversity Quotient (Quitter / AQ Low, Champer / AQ Medium, and the Climber / AQ High); Learning factors and type of Adversity Quotient (AQ) affect the achievement of creative mathematical reasoning skills students. In addition, there is no interaction effect between learning and AQ together in developing the creative mathematical reasoning ability of students'; (3) creative mathematical reasoning ability of students’ has not been achieved optimally on the indicators novelty.