Visualisation and modelling as active thinking maths strategies
Visualisation and modelling is the third and final research-based strategy covered in this series.
When students use or recall objects, pictures, or models during and after their maths study, they are better able to explain their understanding to peers, parents and teachers. Visualisation and models also give students a safe zone to draw upon their own senses in relation to maths, and offer teachers the chance to gain insights into student understanding. It is vitally important to have think-aloud maths discussions about how visual models/mental images enhance student number sense in the same way they do for literacy comprehension. Teachers who demonstrate the use of visualisation and modelling help their students build interest, which then helps students understand how to monitor and adjust those visual models that are most effective for each maths topic they study.
Teachers set the importance for using visualisation and modelling
As with all good instruction, the teacher should be the model for thinking aloud using short examples and a variety of models, drawings, and descriptions of images they have experienced first-hand. This process works particularly well in guided maths or number sense sessions during maths workshop. (If you are unfamiliar with the practice, I have found Math Workshop, by Jennifer Lempp, to be quite teacher-friendly in getting started.) Gradually, students should be invited to share their own use of these models and explain their mental images from their personal senses/experiences. ORIGO Big Books and ORIGO Box and Book of Facts can be used to help with this task.
Students should begin their study of 3D objects and visualisations by interacting with objects in their everyday environment. This allows students to learn how the objects feel and understand the attributes that each possesses. The ORIGO Big Book, Muddy, Muddy Mess is a great resource for this. In the story, the character objects are partially hidden and students have to visualise the footprints of each and match them to the object. As a follow-up activity, students can make their own footprint stamps and describe their objects to their peers.
Addition and Subtraction
Students should use concrete objects to help them grasp addition and subtraction, laying the foundation for later, deeper conceptual understanding. The ORIGO Big Book, The Fun Machines offers a story where the characters are input-output machines following a particular rule. Students are challenged to use strategies such as count-on, doubling, and think-addition. For additional practice, a student might use the visual models in ORIGO Box of Facts cards. Finally, students can attempt a recall activity by creating their own visual to represent their mathematics thinking.
ORIGO Box of Facts cards can used as visual models for maths study.
Add more of these experiences to your classroom repertoire as the year goes on, using concrete objects, student language, and pictures with models, all of which help students progressively become more advanced in using thinking as an active maths strategy.
About the Author
Brian De Moss is the Director of School Partnerships at ORIGO Education and works with some of the largest school districts seeking mathematics improvement (Fairfax County, Hawaii DOE, Fort Worth ISD, and Albuquerque) with the ORIGO Stepping Stones mathematics program. Brian has been involved in mathematics education for over 26 years. He started his career as a kindergarten teacher in Arizona after completing his BA in elementary education at the Center for Excellence at Northern Arizona University in 1992. Brian received his MS from Northern Arizona University in 1998 in Curriculum in Educational Leadership. In 1992, he accepted a position at the Bullhead City School District, Bullhead City, Arizona, where he has been involved in the teaching kindergarten through Grade 2. Brian was formally trained and certified as a multi-age teacher as well as a Project LIFE coach for Clark County School District. Brian is a passionate promoter of the concept of math as a social subject.
About ORIGO Education
ORIGO Education is dedicated to making learning mathematics meaningful, enjoyable and accessible for all, offering primary-level instructional materials, and professional learning.