Multiplicative Thinking and Proportional Reasoning Assignment Sample

• Subject Name : Science and Maths

Inquiry Based Task in A School Setting

Introduction to Multiplicative Thinking and Proportional Reasoning

While teaching to the students of grade 5 to 7, it becomes important for the teachers to adopt innovative techniques for encouraging creativity in the students. It is also advisable for the teachers to move beyond the academic principles and engage the students in classroom activities for making them understand mathematical concepts and reasoning. The route to engagement is one of the suggested methods by Michell (2017) that can be used for enhancing student experience in the classroom. The teacher can use innovative technology teaching techniques in order to help the students expand their educational potential and also to induce proportional reasoning among the learners (Admiraal et al., 2020). With the method of proportional reasoning, the teachers can help the students in solving the mathematical problems of fractions, rate and decimals without using rule based procedures but with simple logic.

According to the findings of the earlier assessment, it could be understood that in order to teach the mathematical concepts of additional, multiplication and fractions to the students, the teachers need to impart basic knowledge regarding the relationship between all the above mentioned mathematical processes to the students. The findings also depicted the symbolic representation can also be used by the teachers for clearing the concept of mathematical processes (Das, 2020). Before conducting the processes manually, the students can learn to implement the concept using images, objects and diagrams. In order to further facilitate the cognitive processes of the students, the teachers can also utilize software applications in the learning environment (Fadillah & Susiaty, 2019). With the use of software applications and creative methods of role plays and games, teachers can develop basic insights of computation among the students.

The previous assignments also highlighted that students may face difficulties and develop misconceptions in their learning process. In order to avoid the misunderstanding among the students, it is important that the teacher should adopt one computation rule while teaching one mathematical process (Kusmaryono et al., 2020). In the beginning, the teachers should always prefer to adopt pencil to pencil approach in which the students can first write down the entire given data and then try to solve it graphically. Overgeneralization and exaggeration of rules should also be avoided by the teachers.

Based on the above findings of the assessment one, open ended questions will be asked from the students of grade 5 for understanding their knowledge about the mathematical processes. The assessment conducted will focus on identifying the misconceptions that the students usually develop during their learning process. The report will also discuss the solutions through which the possible misunderstandings can be addressed by the teachers in a classroom setting.

Enquiry Regarding Mathematical Processes

2.1 Research Questions

1. What are the categories of misconceptions and misunderstandings that the student may form while learning mathematical concepts in Grade 5?
2. What are the possible explanations for the developed misunderstandings and misconceptions?
3. What can be the possible solutions for addressing the developed misunderstandings and misconceptions effectively?

2.2 Data Sample

In order to investigate regarding the misconceptions that the students usually form while studying mathematical processes, a sample of three students was selected of fifth grade. Open ended questions were asked from the students associated with their learning experience of mathematical processes.

2.3 Data collection

The answer to the first research questions will be found from the interview process conducted with the students of grade 5. The interview questions will target to identify the challenges dealt by the students. The present literature on the topic will be used for identifying the explanations along with the solutions for effectively addressing the challenges dealt by the students.

3.Findings of The Interview Process Along with The Suggestions

 The students were asked regarding the challenges they face during learning mathematical processes. According to the response of one of the students, one of the major obstacles they face is the technical language used by the teachers during instruction. The student stated that it becomes difficult for him to gain the access of mathematical epistemic while negotiating and trying to understand the language used by the teachers. For example, rational number is a precise mathematics term that is not a simple English term and teachers need to comprehend the meaning of the term before they actually use rational numbers in the process of doing mathematical problems (Tabacu et al., 2020). The student further added that if the language used by the teachers is not transparent and clear, it becomes difficult for the learners to construct mathematical meaning of the provided numbers.

It can be easily interpreted from the response of the student that it becomes important for the teachers to adopt transparent language in teaching in order to provide support to the students (Permata & Wijayanti, 2019). It is important to integrate mathematical and English language in a critical manner in order to avoid misconceptions and misunderstandings.

According to the response of the other student, it becomes difficult for the student to divert from the arithmetic schemas taught in the primary school. For example, the student stated that we are taught in primary school that 3 is greater than 9 , therefore it becomes difficult to believe that -9 is smaller than -3. It could be easily understood from the response of the student that the student finds it difficult to adapt to the mathematical procedural knowledge in the process of learning mathematical operations. Therefore, it can be understood that it becomes important for the teachers to develop the ability of mathematical notions among the student first in order to eventually develop the ability of finding solutions to mathematical problems. Considering the example given by the student, wherein the student cannot understand the difference between -9 and 9, it can be understood that the student was only able to gauge the absolute value of both the numbers and unable to understand the relationship between both the above presented numbers (Khalid & Embong, 2019). In order to avoid these situations, it is expected from the teachers to generate mathematical sense among the students through classroom activities in the mathematics class in order to make the student learn mathematical operations.

According to the response of the third student, the premature usage of the technical instruments also becomes difficult for the learners. When the learners are hurried to use the calculators, this demotivates the learners to develop relationship understanding between the numbers. The student states that we know that the answer is right but we do not know what exactly made it right and what would have made the solution incorrect. Therefore, it can be interpreted from the response of the student that the teachers need to utilize graphical representations and symbols for making the student understand the relational relationship between two or more numbers (Rahmawati et al., 2019). It can thus be evaluated that relational understanding between numbers and mathematical processes is important avoiding errors and misconceptions in the learning process. According to the study conducted by Khalid & Embong (2019), the relational understanding of numbers may take time to develop in a student but once developed it becomes easier for the student to understand future mathematical topics. The study also states that the copious time involved in developing the relational understanding may be high but the benefits are applicable throughout the learning process (Waluyo et al., 2019).

4.Conclusion on Multiplicative Thinking and Proportional Reasoning

1.What are the categories of misconceptions and misunderstandings that the student may form while learning mathematical concepts in Grade 5?

One of the categories of misunderstanding is regarding the positive and negative values. The students are unable to gauge the difference between -9 and 9 that is they have limited knowledge of absolute value of the integer. Another category of misconception can be the meaning of mathematical terms. The students can be unclear regarding the mathematical notions which can impact their mathematical problem solving capacity.

2.What are the possible explanations for the developed misunderstandings and misconceptions?

It can be understood from the above conducted inquiry that relational understanding that inadequate understanding of relational understanding between the numbers, usage of arithmetic schemas, use of technical solutions without understanding the basic concepts are some of the possible explanations for the developed misunderstandings and misconceptions.

3. What can be the possible solutions for addressing the developed misunderstandings and misconceptions effectively?

One of the possible solutions can be usage of transparent knowledge by the teachers. The adoption of creative techniques like classroom activities can also be used in order to make the students understand the relational understanding of two or more numbers.

References for Multiplicative Thinking and Proportional Reasoning

Admiraal, W., Vermeulen, J., & Bulterman-Bos, J. (2020). Teaching with learning analytics: how to connect computer-based assessment data with classroom instruction?. Technology, Pedagogy and Education, 1-15.

Das, K. (2020). A Study on Misconception of Using Brackets in Arithmetic Expression. Shanlax International Journal of Education, 8(4), 76-80.

Fadillah, S., & Susiaty, U. D. (2019). Developing refutation text to resolve students’ misconceptions in addition and subtraction of integers. Beta: Jurnal Tadris Matematika, 12(1), 14-25.

Khalid, M., & Embong, Z. (2019). Sources and Possible Causes of Errors and Misconceptions in Operations of Integers. International Electronic Journal of Mathematics Education, 15(2), em0568.

Kusmaryono, I., Basir, M. A., & Saputro, B. A. (2020). Ontological Misconception In Mathematics Teaching in Elementary Schools. Infinity Journal, 9(1), 15-30.

Permata, D., & Wijayanti, P. (2019, July). Students’ misconceptions on the algebraic prerequisites concept: causative factors and alternative solutions. In Journal of Physics: Conference Series (Vol. 1265, No. 1, p. 012005). IOP Publishing.

Rahmawati, R. D., Mardiyana, & Triyanto. (2019, December). Analysis of student misconception on calculus materials based on student mathematical reasoning. In AIP Conference Proceedings (Vol. 2202, No. 1, p. 020046). AIP Publishing LLC.

Tabacu, L. M., Watson, S. M., Chezar, L. C., Gable, R., Oliveira, C. R., & Lopes, J. (2020). Looking for a pattern: Error analysis as a diagnostic assessment for making instructional decisions to promote academic success. Preventing School Failure: Alternative Education for Children and Youth, 1-12.

Waluyo, E. M., Muchyidin, A., & Kusmanto, H. (2019). Analysis of Students Misconception in Completing Mathematical Questions Using Certainty of Response Index (CRI). Tadris Jurnal Keguruan dan Ilmu Tarbiyah, 4(1), 27-39.

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