The Application of the Accelerated Learning Cycle, Brain-based Learning Model, and Direct Instruction Model toward Mathematical Reasoning in Terms of Mathematical Communication

*Correspondence:arie_pk@stkipkusumanegara.ac.id The students' mathematical reasoning and mathematical communication abilities are influenced by several factors such as the use of learning models used by teachers in learning. The use of appropriate learning models can increase students' mathematical communication abilities and reasoning. This study aims to determine the effect of the Accelerated Learning Cycle, Brain-based learning model and Direct Instruction learning models on students' mathematical reasoning abilities seen from their communication abilities. This is a quasi-experimental research. The data were analyzed using analysis of variance with unequal cells. This study concludes that, first, Accelerated Learning Cycle provides better mathematical reasoning abilities than the Brain-based learning model and the Direct Instruction learning model and Brain-based learning model provide better mathematical reasoning abilities than the Direct Instruction learning model. Second, students who have high mathematical communication abilities have better mathematical reasoning than students with moderate or low mathematical communication abilities, students who have medium communication abilities have better mathematical reasoning than students with low mathematical communication abilities.


Introduction
Mathematics is one of the subjects taught from primary, secondary, and tertiary education (Syazali, 2015). Mathematics has become an important element in developing science and technology (Wulandari, Mujib, & Putra, 2016). However, students still think that learning mathematics is boring (Sari, Farida, & Syazali, 2016). The teacher-centered learning process does not provide an opportunity for students to be active in teaching and learning activities (Badrun & Hartono, 2013). Difficulties in learning mathematics are seen when students are given questions in the form of reasoning. The level of mastery of the material regarding reasoning is still categorized as low. This means that mathematics lessons related to the ability to recognize and communicate still need special attention because students can exchange ideas and at the same time clarify the understanding and knowledge they gain in learning.
In building reasoning and strategic thinking, teachers must pay attention to in learning mathematics, namely: the type of mathematical thinking must be relevant to the students, the type of teaching materials, class management, the role of the teacher, as well as student autonomy in thinking and doing activities. The application of an appropriate learning model is possible to improve the reasoning ability of students. Currently, the learning model used at the schools known as the direct learning model (Direct Instruction). Using this model, teacher activities dominate the teaching and learning activities while students tend to be passive. Cooperative learning is a learning model based on students actively involved in sharing ideas and working together to complete academic tasks (Zakaria & Ihsan, 2007). The cooperative models used in this research were Accelerated Learning Cycle, Brain-based learning model, and Direct Instruction. Accelerated Learning Cycle has the principle that learning also involves the whole mind and body, learning is creative not consuming, cooperation can help the learning process well, learning takes place at many levels simultaneously, learning comes from doing the work itself, supporting positive emotions that help to learn, as well as the brain that can absorb information directly and automatically. This is the principle of a good learning model to apply. This study aimed to describe which is better between the Accelerated Learning Cycle, Brain-based learning model, and Direct Instruction on students' mathematical reasoning in terms of mathematical communication.
The research method used was quasi-experimental research. This study used a 3x3 factorial design through a two-way ANAVA technique with unequal cells because this study intended to examine simultaneously the 3 treatments of learning models in groups that were different in terms of mathematical communication abilities levels. The research design can be seen in Table 1.

the Research Methods
With xyij is the value of the learning model (i) and the mathematical communication ability (j), i = 1, 2, 3 and j = 1, 2, 3. The documentation method was used to investigate the students' mathematics data in the previous year. The test was also used to collect reasoning ability data and mathematical communication abilities in the form of multiple-choice tests which consisted of 25 items for the mathematical reasoning test and 7 items the mathematical communication test. The mathematical reasoning ability test scores were analyzed using a two-way analysis of variance with unequal cells with an error level of 5%. Hypothesis testing was aimed at finding out whether there is an influence between each learning model, each ability category of students' mathematical communication, and interactions between the two can be seen in the results of mathematical reasoning abilities.
The results of the prerequisite test allowed the use of two-way ANOVA with unequal cells with a significance level of 5%. The result of hypothesis testing can be seen in Table 2. The results of the calculation of Fobs for H0X, H0Y, and H0XY shown in Table 2 can be concluded were rejected. Based on the test decision, it can be concluded that: (1) learning model influences mathematical reasoning ability, (2) mathematical communication ability influences mathematical reasoning, (3) there is an interaction between learning models and mathematical communication ability on mathematical ability. Since the H0X, H0Y, and H0XY were rejected, it is necessary to do a post-ANOVA test using the Scheffe' method, namely inter-row average comparison test, inter-column average comparison test, and inter-cell average comparison test. The results are presented in Table 3. (2) (3.00) = 6.00 0 is rejected 2. = 3. 34.33 (2) (3.00) = 6.00 0 is rejected 1. = 3. 6.20 (2) (3.00) = 6.00 0 is rejected By comparing F obs with critical value, it appears that there are significant differences between the μ 1. and μ 2. , μ 3 and μ 3 . By paying attention to the marginal average, it can be concluded that: (1) the Accelerated Learning Cycle is better than the Brain-based learning model and Direct Instruction and the Brain-based learning model is better than Direct Instruction. The result of the inter-column multiple comparison test is presented in Table 4. Based on the test in Table 5, it can be concluded that: (1) H 0 : μ 11 = μ 21 , H 0 : μ 11 = μ 31 , and H 0 : μ 21 = μ 31 , the test decision declares that H 0 is accepted. This means that at high mathematical communication abilities, the Accelerated Learning Cycle, Brain-based learning model, and Direct Instruction provide equally good mathematical reasoning abilities, (2) at H 0 : μ 12 = μ 22 , H 0 : μ 12 = μ 32 , and H 0 : μ 22 = μ 32 , the test decision declares that H 0 is accepted.