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Teaching Maths

Pedagogical Content (Early Number and Place Value)

To teach early numbers and the place value, it is important to make the students understand the positioning of the number. Place value is important as it helps to understand how and why the number can be placed with the depiction of the number (Sutopo 2017). For example, if the number would be choosing the number and how to denote the meaning of a number (Vijayan, 2018). The used numbers can be picked randomly, then there is no relevancy of the known numbers and what it means actually. It has to be out on the place value to note the order of numbers as well (Sonnenschein, et al, 2018).

Good Teaching Strategy

The good teaching strategy is to use the Bean Bag Number Toss, and then give each student, the 1, 2, 3 bean bags and to throw different numbers that would be helpful to create the number (Rittle‐Johnson, 2017). Such as, if a student would have to throw the bags from 2 and a 3, then the student is asked to combine and form the number 23. Write the same onboard and then ask them to read it, then add zero's or other numbers to team them how it is adding on the places such as now 2300 is two thousand and three hundred instead of simple twenty-three (Lee, 2018).

Explain and Give Examples of Appropriate Tasks

Some of the teaching tricks are the use of bean bag number or the Abacus, such as if it is the 6578, what is in the thousand places which are "6", then understand the hundred place which is 5, then tens place which is the 7 and finally the unit place 8. It can be done through the Abacus device and making the kids with the colorful slide rods and using the beads to interpret the value (Carlson, 2019). With the place value and the early number understanding, it would be helpful to add, subtract, multiply, and even divide (Angeli, 2016).

Appropriate Resources

The use of the appropriate resources is the placards, the use of the blackboards, any bean bags as used as the props or simply to use the Abacus (Elofsson, 2018). Each of the ways is different in helping to identify the relevancy of the number and the working of it (Gess-Newsome, et al, 2019). Each resource has its significance and it has drawn to the relevancy and choosing the appropriate can help the students to learn the concept theoretically and even practically apply it. It would help the students to rightfully place on the values and recognize the place (Herring, 2016).

Areas of Mathematics

In the area of the Mathematics, the skill set required are the critical thinking, involves an active problem solving, requires analytical thinking, would aim for the quantitative reasoning, to cross-check the ability to manipulate precise along with including the intricate ideas and to develop a construction of the logical arguments that can analyze the illogical arguments (Iserbyt, 2017). Further, the areas of Mathematics would involve communication, time management, aim at the skills management to be used independently (Johnson, 2020). The application of the Mathematics requires the analysis, in-depth evaluation, and requires a time-based step by step approach (Koh, 2016). For example, if it is simple 24 + 86 then, first te students should know how to place the numbers one after the other as per the place value and recognize how to add 24 on to the 86 and what would be the additional carry forward number and final result. In the end, the answer also requires to read it carefully and constructively. Mathmathetical concepts during the early years help in identifying the complexity of the problem solving and would require to use the process of evaluating options and how to proceed with the implemented solutions (Kilpatrick, 2017). the next step would be the critical thinking, requires logic and the step by step reasoning along with finding appropriate alternative solutions. Critical Thinking is by using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems (Rittle‐Johnson, 2017). Subsequently requires arranging the findings, understanding the values, implications, and helps in the future course of the decision making. The subsequent findings of the Mathematical concepts involve the mathematical reasoning, would help to choose the right mathematical methods or formulas, helps in the number facility, and would help in the deductive reasoning along with the inductive reasoning. Through the information order, it would help to arrange the patterns and ideas (Lee, 2018).

Conclusion on Effects of Improved Content Knowledge

To conclude, Mathematical concepts involve a high degree of competency and would require to include skills and concepts. Through the extensive ability that can exercise information would help to check for the ordering, inductive reasoning, and even help to draw rationality of the mathematical reasoning that can help in structuring and drawing decision-making abilities. Math skill aims to help and acquire a sharp orientation towards alertness and requires a high brainstorming to draw relevant answers. Mathematical concepts help in drawing relevant abstract concepts and deliver concepts accurately.

References for Effects of Improved Content Knowledge

Angeli, C., Valanides, N., & Christodoulou, A. (2016). Theoretical considerations of technological pedagogical content knowledge. Handbook of technological pedagogical content knowledge (TPACK) for educators11.

Carlson, J., & Daehler, K. R. (2019). The refined consensus model of pedagogical content knowledge in science education. In Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 77-92). Springer, Singapore.

Elofsson, J., Englund Bohm, A., Jeppsson, C., & Samuelsson, J. (2018). Physical activity and music to support pre-school children’s mathematics learning. Education 3-1346(5), 483-493.

Gess-Newsome, J., Taylor, J. A., Carlson, J., Gardner, A. L., Wilson, C. D., & Stuhlsatz, M. A. (2019). Teacher pedagogical content knowledge, practice, and student achievement. International Journal of Science Education41(7), 944-963.

Herring, M. C., Koehler, M. J., & Mishra, P. (Eds.). (2016). Handbook of technological pedagogical content knowledge (TPACK) for educators. Routledge.

Iserbyt, P., Ward, P., & Li, W. (2017). Effects of improved content knowledge on pedagogical content knowledge and student performance in physical education. Physical Education and Sport Pedagogy22(1), 71-88.

Johnson, K., & Olanoff, D. (2020). Using transformative learning theory to help prospective teachers learn mathematics that they already “know”. The Mathematics Enthusiast17(2), 725-769.

Koh, J. H. L., & Chai, C. S. (2016). Seven design frames that teachers use when considering technological pedagogical content knowledge (TPACK). Computers & Education102, 244-257.

Kilpatrick, S., & Swafford, J. (2017). Findell. (2001). Adding it up: Helping children learn mathematics. Mathematics Learning Study Committee: National Research Council.

Lee, Y., Capraro, R. M., & Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education13(2), 75-90.

Rittle‐Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives11(3), 184-190.

Salomonsen, T. (2019). What does the research tell us about how children best learn mathematics?. Early Child Development and Care, 1-9.

Sonnenschein, S., Galindo, C., Simons, C. L., Metzger, S. R., Thompson, J. A., & Chung, M. F. (2018). How Do Children Learn Mathematics? Chinese and Latina Immigrant Perspectives. In Parental Roles and Relationships in Immigrant Families (pp. 111-128). Springer, Cham.

Sutopo, H., & Pamungkas, W. (2017, July). Developing mathematics mobile games to enhance learning for children. In 2017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC) (Vol. 1, pp. 191-197). IEEE.

Vijayan, K. (2018). Unit-3 How Children Learn Mathematics. IGNOU.

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