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The purposes of this research were (1) to study the mathematical problem-solving abilities; and (2) to study mathematical problem-solving behaviors via open approach activities. The research sample included thirty-two Mathayomsuksa III students in the first semester of the 2018 academic year at Suwannaram Wittayakom School, obtained by cluster sampling. They were divided into groups of 4 students which were mixed of the high, medium and low academic achievement. One group was selected as target case to study in depth regarded to the mathematical problem-solving behaviors. The experiment lasted for twelve fifty-minute periods using the one-group pretest - posttest design. The research tools included (1) lesson plans via open approach activities, (2) the mathematical problem-solving ability tests (pre-test and post-test); and (3) the observation forms for mathematical problem-solving behaviors. The data were statistically analyzed using a t-test and a z-test; and the mathematical problem-solving behaviors were analyzed by using the Artzt and Armour-Thomas form. The research findings shown that students who had studied via open approach activities were as follows: (1) had the mathematical problem-solving abilities after learning significantly higher than before learning at the .05 level and were able to solve mathematical problems above the criterion more than sixty percent of Mathayomsuksa III students significantly at the .05 level; and (2) conducted the mathematical problem-solving behaviors follow steps: the posing open-ended problem step, students took more times in reading and participated more in discussing the problems; the student’s self-learning step, students explained the problems using their own language, specified the main variables, planned before solving the problems, explained steps used for solving the problems and verified the answers more before submitted; the discussing and comparing step, students discussed and compared their problem-solving method to the other groups; and the summing-up by interlink the classroom’s concepts step, students gave more answers to interlink to the conclusion.