The purpose of this study is to develop a framework based on a modelling process diagram for designing mathematical modelling tasks using applied problems in math-textbooks. Furthermore, we illustrated the framework with a mathematical problem in a textbook for the 9th grade. Two novel findings have been obtained:
(1) We designed a framework to transform applied problems in math-textbooks to modelling tasks. It was constructed by three methods: (a) selection of the applied problem, (b) analysis of the applied problem, and (c) constructing the mathematical modelling tasks based on the analysis.
(2) We developed a modelling process diagram that is composed of the basic phases of the modelling process, with arrows indicating the interactive activity of each phase.
This study examined the kinds of words children think the term “energy” is linked to with the help of questionnaire surveys (using concept maps) administered to third- to sixth-grade elementary school students. The results revealed the following insights:
1) The children listed many words relating to food, the body, and electricity as words associated with “energy.” In particular, the thought processes that link food and energy tended to be maintained or increased at higher grade levels as well as middle grade levels. 2) There were almost no descriptions of the workings of wind and rubber, and pendulum and leverage, as used in elementary school science. 3) Many children were aware of electricity as a form of energy since third grade in elementary school. 4) The idea of “energy conversion” was limited to the relationship between “energy and electricity” and “energy and foods”, and the children had no awareness of it in other fields. 5) There were no correct responses when it came to “energy conservation.”
The purpose of this research was to study whether students’ solution of the science problem “A graph that is proportional first and then becomes constant after certain amounts are added.” would be promoted by having them solve similar mathematics problems before working on the science problems.
The results show that students achieved higher marks in science tests by taking prior mathematics tests.
Teachers administered the students some easy mathematics problems similar to the science ones, which helped them build inference schema, and lead them to an understanding of the meaning of a graph.
Therefore, science teachers should promote the use of simple analogical problems in order to encourage their students to solve science problems because such instructions help them comprehend the meaning of a graph.
A university collaborated with twelve public schools and the Boards of Education they are affiliated with, for a systemic reform initiative, purposing to improve science education in the schools and their areas. The main approaches are; (1) a core science teacher (CST) serves as a promoter, making efforts to improve lessons in the school, (2) to periodically investigate students’ consciousness (scientific literacy indexes: SLI) on the motivation to learn science in all classes of the participating schools, and use it to further improve the initiative, (3) to hold “Jyugyou Kenkyukai” (lesson study teacher training sessions) for the purposes of transferring the initiative to other schools. In addition, (4) the university provides advice for each school’s efforts, support for the development of lesson environment, and training opportunities for CSTs, and (5) Boards of Education support the review of lesson plans and participation from other schools in the “Jyugyou Kenkyukai”. As a result of two years initiative since FY2016, it was found that the trend toward SLI, which declines with grade level from elementary to junior high school, partly improved during the initiative. It is suggested that a whole school effort for improving SLI will enhance students’ science learning.
This study examines effective instructions for developing a novice science teacher’s ability to plan appropriate lessons in lower secondary school. The connections between support, guidance and advice offered by the teacher’s mentor were considered, as were methods to improve teachers’ ability to plan lessons from the viewpoint of “teacher knowledge”.
As a result, it was found that the novice science teacher did not adequately possess the three sets of mixed teacher knowledge needed in lessons as well as the three sets of single teacher knowledge. Therefore, he was unable to structure them and adequately formulate “teacher knowledge concerning subject matter, pedagogy and students”.
These findings suggest two strategies for developing the ability to plan lessons for novice science teachers. First, mentors need to structure teacher knowledge in a way that allows novice science teachers to consider “teacher knowledge concerning subject matter and pedagogy”,“teacher knowledge concerning subject matter and students” and “teacher knowledge concerning pedagogy and students”, and to blend these into appropriate lessons to formulate “teacher knowledge concerning subject matter, pedagogy and students”. Second, mentors need to reduce guidance and advice gradually, slowly shifting from guidance to advice while encouraging teachers’ independence when planning lessons.