The aim of this study is to analyze whether there is enhancement difference of student mathematical problem solving ability (MPSA) taught by guided discovery learning model (GDLM) and direct learning model (DLM). This study is quasi experiment study. The population of this study is seventh grade student of junior high School (SMP N 2 Kutalimbaru). The sample of this study is two classes of seventh grade of junior high School (SMP N 2 Kutalimbaru) which is taken randomly. The experiment class is taught by GDLM and the control class is taught by DLM. The result of this study shows that there is enhancement difference of student MPSA taught by GDLM and taught by DLM. N-gain of student taught by GDLM is higher than student taught by DLM.

The objectives of this study are: (1) Analyzing the presence or absence of differences in mathematical solving abilities between students taught using the scientific approach and the scientific approach assisted by software Autograph, (2) Testing statistically whether or not there is interaction between learning approaches (scientific, scientific assisted Autograph software) and mathematical initial ability (high, medium, low) to mathematical problem solving abilities. The study population is all students of class X Public Senior High School 1 Medan with a total of 464 people who have been distributed into 13 parallel classes, while the research sample is class X students of Mathematics and Natural Sciences-5 as Experiment-I Class and class X Mathematics and Natural Sciences-6 as Experimental Class-II as many as 68 people. The instrument used is a test of mathematical problem solving abilities. Hypothesis testing uses two-way variant analysis techniques with 2x3 factorial design. In this study using two factors, namely: 1) The learning approach consists of two levels (scientific, scientific assisted software Autograph) and 2) initial mathematical abilities consisting of three levels (High, Medium and Low). The results of the study show: (1) there are significant differences in mathematical problem solving abilities between students taught using a scientific approach and a scientific approach assisted by software Autograph with a difference of = 0.0704, so the use of software Autograph contributes to improving students' mathematical problem solving abilities in the material of equations and inequalities of absolute linear values of one variable. (2) There is no interaction between the learning approach (scientific, scientific assisted Autograph software) and the initial ability (high, medium, low) on students' mathematical problem-solving abilities, so that the effect of the second factor of learning contributes to improving mathematical problem solving skills students and students' initial mathematical abilities only have a very small effect on improving problem solving abilities.