An in depth study that shows how web-based instruction using visuals in fractions leads to gains in student knowledge and problem solving ability. Software or web-based programs allow manipulation or experimentation of visual representations of fractions. The program was successful in raising math scores in our weakest students. The district then bought SuccessMaker which allowed us to weekly track improvements.
Creating pictures in the mind or drawing representations with my students took up a major part of my teaching. Students who have trouble in math often do not have a picture in the mind of quantity or size or measurement. Page 12 is especially helpful, and shows the different visual representations for fractions.
Teachers need better training in the deep knowledge of what methods to use to teach fractions. This paper and video explain the problems with the American methods of teaching fractions, and lists what students lack.
Looking at page 18 it becomes of this report, obvious math has been an obstacle to graduating from high school. At 9th grade level, being able to master Algebra I and Geometry assures graduation. Other countries are more successful in mathematics teaching than the United States, especially with females. For my at-risk students it meant the difference between a satisfying life or a life in poverty.
The development of thinking approaches that allow processing of operations on fractions serve to develop advanced math thinking. Two processes worked with my at-risk students. The first was doing intensive questioning about the vocabulary and phrasing in word problems. The second piece was using hands on materials such as fraction circles, or fraction bars to create a visual representation in the mind.
Learning the math of fractions begins with language. My students did not have fraction vocabulary. Parents, unless they have math jobs, do not speak those terms and media only has a few shows that do. at-risk students have academic language deficits to begin with because of poverty, so specialized vocabulary such as math has to be specifically and intentionally taught.
This site has resources, videos, and methods proven to improve fraction instruction from the teacher end. Teacher training has to improve before student scores can come up. Lead teachers show how to use materials and how to teach the concepts in a way that takes students to Jr. High level thinking, or at least lays the foundation for it.
For at-risk students, its extremely important to find something they know well and attach new learning to it. Students have the times table chart in their schema. Certain sets of equivalent fractions in pattern form are apparent. It makes a good basis to start the process rather than going to abstract calculations.