Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning. Emphasize the mathematical meanings of ideas, including how the idea, concept or skill is connected in multiple ways to other mathematical ideas in a logically consistent and sensible manner. Create a classroom learning context in which students can construct meaning. Make explicit the connections between mathematics and other subjects. Attend to student meanings and student understandings.
Students can learn both concepts and skills by solving problems.
There is evidence that students can learn new skills and concepts while they are working out solutions to problems. Development of more sophisticated mathematical skills can also be approached by treating their development as a problem for students to solve. Research suggests that it is not necessary for teachers to focus first on skill development and then move on to problem solving. Both can be done together. Skills can be developed on an as-needed basis, or their development can be supplemented through the use of technology.