Mathematics teachers require to have the mathematical understanding to ensure that they engage in the teaching process effectively. Mathematical understanding focuses on the conceptual knowledge of ideas, facts, and methodologies associated with different concepts regarding mathematics. Gaining mathematical understanding helps to ensure that a teacher can transfer knowledge to the students efficiently without the distortion of main concepts and ideas. Considering that mathematics involves specific concepts and ideas, the teachers should focus on having an understanding that goes beyond the understanding of facts and ideas to ensure that the knowledge is applicable in different situations. Mathematical understanding enables the teachers to connect with students and identify their weaknesses in relation to mathematical ideas and concepts. Mathematics teachers should focus on the implementation of strategies and measures that helps towards gaining mathematical understanding, which is a factor that enhances the learning process of the students.
Dual Nature of Teachers’ Mathematical Understanding
The mathematical understanding of the teachers exists in a dual nature, which is an aspect that broadens the understanding of the specific concepts and ideologies regarding mathematical problems. The first nature of teacher’s mathematical understanding is the instrumental understanding. The instrumental understanding involves learning the basic concepts and procedures used to perform different mathematical problems (Afgani, Suryadi, & Dahlan, 2019). Teachers with instrumental understanding tend to have basic knowledge and information that enables the students to only pass the examination. The second nature of mathematical understanding is the rational understanding. Rational understanding refers to knowledge obtained from a deeper analysis of mathematical concepts to understand the applicability in real-life situations. Teachers with rational understanding ensure that the students gain adequate knowledge that helps to appreciate concepts relating to mathematics (Chapman, 2017).
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Importance of Teachers’ Mathematical Understanding
Mathematical understanding is an important aspect that the teachers should have to ensure that they enable students to gain relevant skills associated with mathematics (Kaya & Aydın, 2016). The first importance of teachers’ mathematical understanding includes enabling students to appreciate the subject and have effective problem-solving skills. Considering that mathematics is regarded as a complex subject to understand, students tend to shy off from the subject by developing negative attitudes. Cai & Ding (2017) maintain that a teacher with effective mathematical understanding helps to ensure that the students develop positive attitudes regarding the subject by appreciating concepts and mathematical ideas. The second importance of teachers’ mathematical understanding involves the ability to achieve national educational goals. Mathematical understanding among the teachers helps to enhance effectiveness in the learning process thereby leading to the achievement of the set goals and objectives.
Influences of Mathematical Understanding on Teachers’ Instruction and Beliefs
Mathematical understanding of the conceptual analysis of the subject thus impacting the strategies and techniques implemented by the teachers. The first impact of mathematical analysis involves increasing expertise in mathematics, which is a factor that impacts on the teacher's instruction. Masingila, Olanoff, & Kimani (2018) argue that teachers with a mathematical understanding tend to focus on instructions that are easy to understand and comprehend to ensure that the students appreciate the concepts. Increased expertise in mathematics results in a situation where the teachers’ beliefs are impacted resulting in changed mentality regarding the importance of mathematics in life (Beswick, 2019). Additionally, the mathematical understanding enables the teachers to focus on simplified instructions based on the ideas and concepts provided.
Conclusion
Mathematical understanding is a vital aspect that broadens knowledge and ideas regarding the subject. The key elements necessary to understand the concepts of mathematical understanding include the instrumental and rational understanding, which are necessary to define the nature of information obtained. Mathematics teachers should focus on bettering their mathematical understanding to help in overcoming challenges and barriers associated with the subject. Although mathematical understanding benefits the teachers, there is a benefit among the student, which include the ability to appreciate the subject and earning effective skills to solve a wide range of problems.
References
Afgani, M. W., Suryadi, D., & Dahlan, J. A. (2019). The Enhancement of Pre-Service Mathematics Teachers' Mathematical Understanding Ability through ACE Teaching Cyclic. Journal of Technology and Science Education , 9 (2), 153-167.
Beswick, K. (2019). The role of knowledge and beliefs in helping learners to progress their mathematical understanding. Journal of Mathematics Teacher Education , 22 (2), 125-128.
Cai, J., & Ding, M. (2017). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teacher Education , 20 (1), 5-29.
Chapman, O. (2017). Attending to mathematics teacher thinking. Journal of Mathematics Teacher Education , 20 (1), 1-4.
Kaya, D., & Aydın, H. (2016). Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication. Eurasia Journal of Mathematics, Science & Technology Education , 12 (6), 1-11.
Masingila, J. O., Olanoff, D., & Kimani, P. M. (2018). Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem-solving. Journal of Mathematics Teacher Education , 21 (5), 429-450.
