Mathematical Understanding and Representation Ability of Public Junior High School in North Sumatra

Abstract

This paper is the result of the first phase of the research about the development of students' mathematical understanding and representation ability through Joyful Problem-based Learning (JPBL) at Public Junior High School in North Sumatera, Indonesia. The population is all of the students of public junior high school (PJHS) in North Sumatera. Samples choose based on stratified random sampling. The samples are the students of PJHS 27 Medan, PJHS 1 Percut Sei Tuan, PJHS 1 Tebing Tinggi, and PJHS 2 Pematangsiantar. The techniques used for collecting data is observation, interview, and essay test. The research findings: (1) Based on interview and observation found that conventional approach still uses in all of the class of PJHS, the students engagement in learning activity is very low, and most of the students do not attain minimal mastery achievement. (2) Based on essay test found that performance of the students in mathematical understanding and representation test is categories small.

Analysis Of Eight Grade Students Performance In Solving Mathematical Representation Problems

“…As conclusion, JPBL gives significant effect to the students' MRA achievement. This finding is consistent with the latest research that joyful PBL is effective in improving the ability of mathematical representation of junior high school students [8] [13] Rationale for this achievement is that learning approach based on JPBL has a syntax that allows the students actively engage in constructing their own mathematical concept through solving various mathematical problems. Besides, teacher provides scaffolding gradually to the students who have obstacles in understanding the problem or stuck at any phase before arrived to the solution.…”

“…Whenever the students develop mathematical problem solving, then mathematical understanding and representation will be developed [5] [6]. In turn, the ability of mathematical understanding [7] as well as mathematical representation ability [8] as the prerequisite for the smoothness of problem solving will grow as well. Thus, it is a must to give the opportunity to the students engage in solving problems.…”

“…Thus, it is urgent to implementing student-center learning with constructivism as a theoretical background, because of the principle of this approach is to promote the students to be actively engage in developing their own knowledge and rediscover the concepts of mathematics as well. One kind of such learning is ProblemBased Learning (PBL) [11] Integrating joyful learning [12] into PBL yield effective learning approach, namely Joyful Problem-based Learning (JPBL) [8] [13]. On one side, PBL designed to improve problem-solving skills, integrate learning from different sources and disciplines through synthesis and collaborative inquiry, deals with situations where students are uncertain about data, information, as well as solutions, just as students would face in the real world.…”

Think-Talk-Write Model for Improving Students' Abilities in Mathematical Representation

“…In that way, the mathematical representation enables students in solving an abstract mathematical problems become real. Mathematical representation can be presented in visual (e.g., charts, tables, sketches/drawings, and diagrams) and non-visual representations (e.g., mathematical equations and models) (Minarni at al., 2016;Thompson & Chappell, 2007). Numerous studies related to visual representations have been conducted to discuss various problem solving of the word problem (Epstein at al., 2010;Geeslin & Shavelson, 1975;Güler & Author, 2011;Stylianou & Silver, 2009;Thompson & Chappell, 2007;Webel at al., 2016), with additional studies on the use of technology in mathematical representation (Kendal & Stacey, 2003;Ohlsson, 1998;Reilly at al., 1997) and on the elements used to generate relationships in mathematics learning (Moon International Journal of Instruction, July 2018• Vol.11, No.3 at al., 2013.…”

“…Previous research on mathematical representation has only focused on students' cognition abilities (Minarni at al., 2016). However, numerous studies on students' selfefficacy in mathematics have been conducted, including one that examined their performance experiences (Bandura, 1997).…”