The purpose of this mixed-method study is to investigate and compare students' problem-solving and higher order thinking skills. This study involves two contexts: a traditional teaching program and a Lesson Study program. In qualitative phase, seven mathematics lecturers, a physics lecturer and the researcher forms the Lesson Study group and they collaboratively design five research lessons on functions topics. Also, the researcher collects all the materials taught by the lecturers individually in their classes on these topics. These topics in the textbook, individual lecturers' lessons and research lessons analyse descriptively using document analysis technique to find some understanding on the emphasis on problem-solving and higher order thinking skills. In quantitative phase, two classes choose randomly as experimental and control groups. The lecturers' developed tests use to compare the ability of students in problem-solving and higher order thinking. Data was analysed using independent samples t-test. The results of this mixed-method study show that, lecturers were teaching exactly contents of the textbook and focusing more on solving of routine exercises. Whereas, in Lesson Study program, collaborative work among lecturers in preparing suitable problem-solving activities not only improved lecturers' knowledge tremendously but also enhanced the ability of students in problem-solving and higher order thinking skills.