Mathematical Inquiry and Hands-On Manipulatives

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Concept by: Natalie Croome


This course is an invitation to explore the research-based rationale for bringing a spirit of inquiry to the teaching and learning of mathematics. Participants will discover and use a range of hands-on materials to actively solve mathematical problems while deepening their knowledge of key aspects of mathematical inquiry. Teachers will learn how to transform mathematics lessons into powerful learning experiences, full of enjoyment!

Learning Outcomes

The course will help the participants to:

  • Define Mathematical Inquiry;
  • Explore possible inquiry structures;
  • Describe teaching and learning practices in an inquiry classroom;
  • Explore the benefits of using manipulatives to support students in developing conceptual understandings of Mathematics;
  • Experiment and become familiar with a range of mathematical manipulatives;
  • Experience and participate in mathematics lessons designed to develop an understanding of mathematical concepts, using manipulatives;
  • Use a written curriculum to inform inquiry-based planning and teaching of mathematics, using manipulatives;
  • Designing and planning for mathematical inquiry tasks.

Tentative Schedule

Day 1 – Introduction to the course and to Mathematical Inquiry

  • Introduction to the course, the school, and the external week activities;
  • Icebreaker activities;
  • Presentations of the participants’ schools;
  • Mathematical Inquiry…What it is and What it isn’t.

Day 2 – Mathematical Inquiry in Action

  • A sample lesson;
  • Reading and discussion: Becoming an Increasingly Inquiry-based Teacher;
  • Increased / decreased emphasis for Mathematical inquiry practices;
  • Exploring and critiquing a range of hands-on manipulatives.

Day 3 – Exploring hands-on manipulatives

  • A Carousel of Mathematical Inquiry Stations;
  • Exploring with a range of hands-on manipulatives;
  • Four Inquiry Structures: From guided to free inquiry: The where, why and how of using manipulatives;
  • Mathematical Inquiry in Action;
  • Adapting tasks according to identified inquiry structures;
  • Planning for Mathematical Inquiry: Collaborative design of four inquiry tasks for your students.

Day 4 – Making connections

  • Making connections with your written curriculum: Big ideas & understandings for the teaching and learning of mathematics;
  • Choosing the right manupulative/s for the right inquiry;
  • Designing & Planning for Inquiry: Preparing for new teaching and learning strategies in your classroom;
  • Free-choice time to explore, write, design and plan.

Day 5 – A Student-designed Carousel

  • Sharing designs for inquiry with manipulatives.

Day 6 – Excursion & Course closure

  • Course evaluation: round-up of acquired competencies, feedback, and discussion;
  • Awarding of the course Certificate of Attendance;
  • Excursion and other external cultural activities.


  • Teachers & school staff: pre-school level;
  • Teachers & school staff: primary level;
  • Teachers & school staff: special needs.


  • Activities: All courses include at least one guided city tour and one full-day excursion (usually on Saturday).
  • Certificate: Certificate of Attendance guaranteed for participants who attend at least 80% of the course.
  • Lessons: Classes take place in the Morning (9:00 – 13:45) or in the Afternoon (14:00 – 18:45).
  • Price: 480 €

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