Research study conducted by Elida V. Laski†, Marina Vasilyeva, and Joanna Schiffman

Boston College

Ensuring that children acquire basic numerical understanding in early childhood is central to improving mathematics achievement. Early mathematical knowledge predicts rate of growth in mathematics as well as mathematics achievement test scores as late as high school. Specifically, place-value and arithmetic knowledge are foundational for later mathematics learning. The present study examined whether the Montessori approach promotes a better understanding than other public-school approaches of three foundational aspects for later mathematics learning: (a) base-10 and place-value understanding, (b) ability to accurately solve arithmetic problems, and (c) use of base-10 decomposition, an efficient arithmetic strategy.

……

The results from this longitudinal study indicate that the Montessori approach may offer an early advantage over non-Montessori programs in helping children understand critical math concepts, but this gain does not translate into a long-term advantage. The findings raise at least two questions for Montessori educators to consider.

First, as children transition to elementary programs, what can be done to maintain and build on the advantage kindergartners demonstrate in base-10 understanding? Children from Montessori schools did not demonstrate improvement on base-10 understanding between kindergarten and first grade, despite not being at ceiling in kindergarten. In contrast, children in non-Montessori programs demonstrated substantial improvement between kindergarten and first grade. Further, it is important to note that the advantage did not re-emerge at the end of the three-year cycle: no difference remained in place-value understanding between Montessori and non-Montessori children in third grade. A better understanding of what happens when children transition from the Children’s Garden to the elementary program is needed. There may be unnecessary repetition in lessons; alternatively, the transition to abstract representations could occur more rapidly.

Second, how can instruction help children generalize and transfer their understanding of bead bars and units to arithmetic tasks and strategies? Previous research has demonstrated that kindergartners’ representation of base 10 contributes to the frequency with which they attempt to solve arithmetic problems with base-10 decomposition.

There is increasing evidence that children require explicit guidance and instruction to abstract concepts from concrete materials or to see connections between two concepts. According to the cognitive-alignment framework, a theoretical framework for instructional design, even if the concrete materials are ideally designed, learning is unlikely to occur if procedures and didactic statements do not direct children’s attention to the relevant features. Thus, educators should consider how to explicitly show children that their base-10 knowledge is beneficial in the use of decomposition for mentally solving addition problems.

You can read the research here: Longitudinal Comparison of Place-Value and Arithmetic Knowledge in Montessori and Non-Montessori Students