I have been teaching mathematics for 15 years and during that time I have developed an understanding of two different approaches to teaching mathematics. One involves conceptual learning and the other procedural learning.

The Jasper Woodbury Problem Solving Series provides students with experiences that help develop a conceptual understanding of mathematical concepts. Students work cooperatively to generate and solve math problems using realistic narratives and scenarios. Teachers encourage students to exercise critical and flexible thinking skills and to recognize connections between mathematics and various other areas of the curriculum. This approach to mathematics requires higher order thinking skills including analysis, evaluation, and creation of new ideas or problems.

This approach differs from lessons that focus on procedural math skills. Procedural math lessons can often have a particular focus that includes knowing the language, rules, algorithms, and symbols of mathematics. The aim of many of these lessons is to support students becoming proficient in the skills needed to be able to problem solve.

Both these approaches are important when developing a learning environment that will meet learners’ needs. The Jasper series provide beneficial opportunities for students who can connect with open ended problem-solving experiences. However, it is equally important to recognize the needs of students who benefit from a more hands on and teacher directed approach. According to Gersten, Chard, Jayanthi, Baker, Morphy & Flojo (2009), students with LD’s do not always benefit from environments from peer assisted learning environments and benefit from being provided with a step by step strategy provided through explicit instruction by a teacher. It is important to keep in mind who the learners are and to provide them with the tools they need for success. It is only through ongoing assessment and consultation with students that teachers can determine when and how to introduce new concepts that will move students forward in their learning.

References:
Cognition and Technology Group at Vanderbilt. (1992). The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design. Educational Technology Research and Development, 40(1), 65–80.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics Instruction for Students With Learning Disabilities: A Meta- Analysis of Instructional Components. Review of Educational Research, 79(3), . 1202–1242.