Parents in a Westchester school were unhappy with the Mathematics Investigations Program being used in an elementary school. They believed the children were falling behind in mathematics because “standard ways” of doing math were improperly expressed. The principles expressed in the MIT program emphasize a “constructivist approach” in order to facilitate children thinking in a mathematical perspective. One parent who objected to the program had to supplement his son’s middle school mathematics with additional instruction. Children incorporate constructivism in mathematics in order to surmise solutions deduced through their own thinking processes, as opposed to first being taught and thereafter using rules or processes. They are supposed to construct their own solutions to the problems. This theory is often attributed in education to Dewey and Piaget.
Mathematical programs in elementary school may appear effective, but this can be deceptive because it is when students enter middle schools from K-5 schools, their achievement drops. A research study from Harvard, The Impact of Alternative Grade Configurations on Student Outcomes through Middle and High School by Guido Schwerdt and Martin R. West. (September 13, 2011) demonstrated that when middle school students scores who entered in either grade 6 or 7 were analyzed they “continue to fall” especially in mathematics in schools throughout Florida.
So while parents can ponder the effectiveness of a mathematics program, they should also remember that students entering grade 6 or 7 from a grade K-5 organization or even Grade 7 from a K-6 school have lower mathematics scores. Worse yet, these middle school students apparently do not regain the math achievement losses in grades 9 and l0. Unfortunately, they found students in the lowest half of achievement scores and ethnic minorities had ” more pronounced” drops in achievement. In contrast, students entering high school from K-8 schools in grade 9 experienced a smaller drop in achievement which improved in the next grade.
There are several scholars who have now decided that K-8 schools are more productive for students. They are suggesting elementary and middle schools should be changed to K-8 schools. This is one area where charter schools may be able to be formed with this configuration without disrupting the public schools.
Schools always grapple with the need to group students in a way that is educationally beneficial. Teachers group students in the classroom, principals group students heterogeneously or homogeneously. But there is little discussion about the best school organization and what grade breakdowns are beneficial for student learning. This Harvard study has examined the important reorganizations that would be necessary to benefit students’ achievement.
Other countries have different configurations. In Germany after grade 4, their students go onto secondary education schools to finish their education. Finland has a grade 1 – 10 configuration. Alternate schools can even have kindergarten to grade 12 configurations. Another study in New York City (Rochoff and Lockwood, 2010) found when students entered middle school there was a dramatic drop in achievement.
Teachers, especially in elementary schools, admit they are spending more time on mathematics and language arts because of the “high stakes” testing in these areas. It has also been confirmed that teachers’ teaching time in other subjects such as as social studies, art, music, and even science in elementary school is being reduced because of testing mandates. So while additional time can be spent teaching mathematics and language arts in elementary grades, when students reach middle or high school this “additional” time may no longer be available during the school day. This could be a contributing factor why middle school mathematics scores drop. Another comparison has been made. In the fourth and eighth grades, no statistical differences was found in the mathematics achievement scores between boys and girls. (Sparks, Education Week, 12/12/11).
Looking objectively at mathematics education can we reasonably conclude that while the programs used are important, there are other considerations, especially the grade organizations of the schools in the system?