# Using hands-on materials and manipulatives to deepen students’ levels of mathematical understanding.

## Introduction

The approach to mathematics that speaks loudest to me is the use of hands-on manipulatives. By giving kids visual representations and putting objects in their hands, they develop a concrete mental image of math concepts.

Combined with the auditory and visual pieces, this kinesthetic approach reinforces foundational knowledge and creates the building blocks that allow them to understand how math actually looks and works.

In my classroom, I want my kids to be able to play with math concepts, to experiment with them, and come up with their own conclusions. The way I do that is to provide hands-on materials for every day in a math classroom.

Developing in students this hands-on disposition to mathematical problem solving goes well beyond the math classroom. These direct problem solving skills are transferable and applicable to other subject areas and to life outside of school.

## Reflections

What I did well…

In these sessions, I focused on increasing mathematical understanding by building knowledge through the use of hands-on manipulatives and concrete learning experiences.  I was able to clearly define the rationale and benefits of teaching students in this manner.  Learners were able to not only discuss these benefits, but they were able to experience them as they participated in learning activities and collaborated with partners.  I also believe the final session of the training was important.  Most times, I would be providing professional development of this nature to teachers of mathematics, however, this session was shared with teachers of all levels and all content areas.  In this final session, I asked teachers to reflect and consider how they would apply the concept of taking learners from concrete models to abstract thinking in a variety of settings.

What I would do more of, better, differently . . .

I believe I might have found a better math “problem” to begin our session.  Although I have used a problem like this before, this particular audience did not take the bait as others have in the past.  One of the pieces I would have liked to have brought out was the simple idea that many students (and adults) complete algorithms based on “rules” they learned versus a true and deep understanding of number sense within a base 10 number system.  It would be nice to have also taken a quick moment to allow participants to discuss the disadvantage of “rules and tricks” mathematics teaching and the issues they see in their math classrooms today.  This conversation could have allowed for even greater engagement by participants.

I still want to grow in this practice by . .  .

There are times when teachers believe this style of teaching belongs mainly in a primary classroom.  Teachers share that they see a growing curriculum to “cover”, and they receive pressure for increased rigor within their classrooms.  As such, some teachers feel there is not time for hands-on learning opportunities.  As I continue to provide this type of professional development for staff, I strive to expand my learning examples and activities to reach educators of older students.