Hands On Math Activities

Have you ever had a student be able to seamlessly recite their multiplication facts, but are unable to 1) explain how they solved it and 2) apply it to a real world problem?  This student lacks a conceptual understanding of multiplication.  Conceptual understanding has become an essential component of best practice teaching since the Common Core was adopted, as it expects students to do more than rote memorization.  Instead, it demands students be active participants in real-world learning and application to prepare them for college and careers in the twenty-first century.  Read to learn more about what conceptual understanding is, the difference between conceptual understanding and procedural fluency, why conceptual understanding is important, and what it looks like in an elementary classroom.



WHAT IS CONCEPTUAL UNDERSTANDING?
The National Research Council identified five strands that define math proficiency in 2001: Conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.  Conceptual understanding, one of the five strands, is the “comprehension of math concepts, operations, and relationships” to the extent that a student can transfer and apply what they know to new situations and contexts.

Conceptual Understanding IS:
  • Understanding why we are learning about a concept or skill
  • Applying prior learning to a new situation
  • Explaining and justifying
  • Reasoning
  • Comparing and contrasting math concepts
  • Generating new ideas
  • Thinking flexibly
  • Utilizing models and manipulatives

Conceptual Understanding IS NOT:
  • Simply being fluent in procedures and facts
  • Rote memorization

WHAT IS THE DIFFERENCE BETWEEN CONCEPTUAL UNDERSTANDING AND PROCEDURAL FLUENCY?
Prior to 2001, the emphasis in math instruction was on procedural fluency, which was referred to as procedural knowledge at the time.  Procedural fluency is the ability to follow a sequence of steps “flexibly, accurately, efficiently, and appropriately.”  Students were expected to learn procedures (procedural fluency), like how to regroup, but were not necessarily expected to have a deep understanding (conceptual understanding), like why they are regrouping and what it means.  In recent years, recommendations of effective math instruction have transitioned to a more balanced approach to learning.  Conceptual understanding and procedural fluency are equally important. They are both part of five strands that define math proficiency according to the National Research Council.  As a result, it is essential for educators to support students in developing both abilities.


4 REASONS CONCEPTUAL UNDERSTANDING IS IMPORTANT
  1. Prepares them to solve problems in the real world.
  2. Equips them with the ability to make connections and solve more complex math.
  3. Gives them the skills to deeply understand and transfer knowledge.
  4. Develops them into individuals who are math proficient.


4 WAYS TO BEGIN BUILDING CONCEPTUAL UNDERSTANDING IN YOUR CLASSROOM
  1. Using manipulatives and pictures to teach concepts, solve problems, and explain thinking.
  2. Creating opportunities to discuss math concepts and strategies with peers and the teacher (number talks).
  3. Representing and solving problems in different ways.
  4. Solving real-world problems.


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