The Science of Math

The "Science of Math*," involves using research-based methods to teach mathematical concepts effectively. This approach emphasizes understanding how children learn math, diagnosing their needs, and implementing instructional strategies that are proven to work. Read more here.
PictureFive Strands of Math Proficiency (Codding, R. S., Peltier, C., & Campbell, J. (2023). Introducing the Science of Math. TEACHING Exceptional Children, 56(1), 6-11. https://doi.org/10.1177/00400599221121721)

Aligning Current Research with the Traditional Montessori Curriculum

​The strength of the Montessori method lies in its ability to make abstract mathematical concepts tangible and accessible for children. The latest research in math education supports this hands-on approach, highlighting the importance of concrete experiences in developing a deep understanding of mathematical principles. By leveraging new insights into how children learn math, Montessori educators can refine and expand the use of Montessori materials to better support cognitive development and mathematical thinking. ​This section provides suggestions for incorporating the latest findings into the classroom, ensuring that students benefit from a robust and dynamic math education.
1. Foundational Numeracy Skills 
  • Number Sense: Materials like the Number Rods and Sandpaper Numerals help children understand number relationships and quantities.
  • Counting and Cardinality: The Spindle Box and Cards and Counters support counting and one-to-one correspondence.
  • Subitizing: While Montessori materials inherently encourage subitizing, additional activities could be incorporated to explicitly teach this skill.
Updates to Consider:
  • Introduce specific subitizing activities and games to enhance instant number recognition skills.
2. Conceptual Understanding
  • Place Value: The Golden Beads are excellent for teaching place value, showing the significance of units, tens, hundreds, and thousands.
  • Operations: Montessori materials like the Addition Strip Board and Multiplication Bead Board provide concrete experiences of arithmetic operations.
Updates to Consider
  • Emphasize conceptual understanding before procedural fluency by incorporating visual models and diagrams (Concrete-Pictoral-Abstract approach) that show the "why" behind operations.
  • Integrate digital tools that allow for interactive exploration of these concepts.
3. Procedural Fluency
  • Efficient Calculation: Materials like the Stamp Game and Bead Frames encourage practice and understanding of calculations.
  • Algorithm Understanding: Montessori methods ensure children understand the rationale behind algorithms.
Updates to Consider
  • Incorporate more explicit instruction on efficient calculation strategies.
  • Provide practice with both Montessori materials and standard algorithms to build a bridge to traditional methods.
4. Strategic Competence 
  • Problem Solving: The use of story problems and real-life scenarios helps develop problem-solving skills.
  • Flexibility: Montessori encourages using various methods and tools, like the Checkerboard for multiplication and Division Charts.
Updates to Consider:
  • Introduce a wider range of problem-solving strategies and encourage children to discuss and compare different methods.
  • Use digital resources and games that promote strategic thinking and flexibility.
5. Mathematical Reasoning
  • Logical Thinking: Materials like the Binomial Cube and Geometric Solids foster logical reasoning and spatial awareness.
  • Pattern Recognition: Bead chains and color-coded materials help with recognizing and understanding patterns.
Updates to Consider:
  • Incorporate more explicit teaching of logical reasoning and pattern recognition, including the use of pattern blocks and puzzles.
  • Use technology to create dynamic visual patterns and interactive reasoning activities.
6. Use of Manipulatives and Visual Aids
  • Concrete Representations: Montessori’s use of manipulatives is foundational, with materials like the Pink Tower and Brown Stair.
  • Visual Models: Tools like the number line and Fraction Circles provide visual representations of abstract concepts.
Updates to Consider:
  • Enhance the use of visual models by incorporating modern visual aids like interactive whiteboards and apps that allow manipulation of virtual objects.
​7. Instructional Practices
  • Explicit Instruction: Montessori emphasizes self-directed learning but can include more explicit instruction for clarity.
  • Guided Practice: Teachers offer guidance through the three-period lesson and individual presentations.
Updates to Consider:
  • Increase the use of explicit instruction for introducing new concepts, followed by guided practice with Montessori materials.
  • Incorporate formative assessments to provide ongoing feedback and tailor instruction
​8. Multisensory Learning
  • Engaging Multiple Senses: Montessori materials are inherently multisensory, involving touch, sight, and sometimes sound.
  • Interactive Activities: Activities like sorting, matching, and sequencing engage children in interactive learning.
Updates to Consider:
  • Expand multisensory learning with auditory and kinesthetic activities, such as clapping rhythms for counting or movement-based math games.
  • Integrate technology to create engaging, interactive learning experiences.
9. Differentiation
  • Addressing Diverse Needs: Montessori’s individualized learning plans cater to the unique needs of each child.
  • Supporting Struggling Learners: Use of concrete materials helps those who struggle with abstract concepts.
Updates to Consider
  • Enhance differentiation by using adaptive learning technologies that provide personalized practice and feedback.
  • Offer more targeted interventions for students who need additional support or challenges.
10. Mathematical Language
  • Vocabulary Development: Montessori materials come with specific terminology that children learn and use.
  • Communication: Children are encouraged to discuss their work and explain their thinking.
Updates to Consider:
  • Place a greater emphasis on teaching and reinforcing precise mathematical vocabulary.
  • Use collaborative activities and discussion-based lessons to encourage mathematical communication and reasoning.
*The Science of Math is currently in its beginning phases. While the foundational concepts and initial research are promising, they are still under development. As such, the application of these ideas should be approached with flexibility and an open mind. Educators and practitioners are encouraged to adapt and adjust methodologies to best suit their specific contexts and the individual needs of their students. Continuous feedback and iterative improvements are essential as we collectively explore and refine these innovative approaches to mathematics education and their application to the Montessori Method.