# Three Ways to Deepen Math Understanding in Elementary Schools

Written By in Math Learning on September 11th, 2013

Elementary school is a critical time for learning to think mathematically because it is when students build the foundational number sense and critical reasoning habits that will help them comprehend increasingly complex concepts as they get older. Numeracy and algebraic thinking are becoming ever more important as we move further into the 21st century. Many careers (particularly those in the critical STEM fields of science, technology, engineering and mathematics) rely on quantitative and abstract reasoning.

To improve mathematical understanding and thinking in young students, teachers and administrators must go beyond assigning pages of factual recall to be completed with a paper and pencil. Given how much access students have to free tools such as calculators and Wolfram|Alpha that are capable of solving many math problems, we have the opportunity and obligation to engage students in mathematics problems and experiences that can’t simply be solved with a graphing calculator. Elementary school students are curious learners who enjoy being engaged in authentic tasks with challenging purposes. To give your students the experiences they need in the classroom, try these approaches for improving math performance:

1. Make use of manipulatives (both tangible and digital) Concrete manipulatives in math classrooms are nothing new. Many adults will tell you they most enjoyed math when it was “hands on.”  The reason they liked “hand on” learning is because manipulatives are designed to help students make sense of concepts and ideas.  Learning improves when students can make sense of things. Here’s a demo.

By reasoning with concrete tools in quantitative ways, students have a stronger foundation from which to develop more abstract reasoning.  From a learning standpoint, student interactions and thinking with manipulatives are what support cognitive development.  Because there are limitations to what concrete manipulatives can be built, new digital technologies enable the creation of virtual manipulatives that help students interact with concepts in new ways. Virtual manipulatives shouldn’t just act as a substitute for concrete ones; they should empower new learning tasks that wouldn’t be possible without a digital environment. DreamBox virtual manipulatives are designed to engage student thinking in new ways, and students individually use these tools to make sense of things for themselves while receiving the unique differentiation and scaffolding they need.

2. Use meaningful situations and contexts Just as a digital or virtual manipulative helps students make sense of a math concept, strategic situations and contexts also enable student sense-making. It might be a real-life situation such as a “fair sharing” problem for division and fractions, or perhaps it’s a mathematical context such as making jumps on a number line.

Such contexts give students a point of reference for understanding and engaging in critical thinking. The scenarios in which students are thinking mathematically are critical to helping them make connections, understand what they are learning in a deeper way, and retain acquired knowledge and skills. Teachers know their students, school, and community well enough to find situations to which students can relate – whether it be a baking situation, sports context, or an actual math problem the principal is trying to figure out to help the school.

3. Develop a community of mathematicians

Professional mathematicians are continually engaged in constructing proofs and solutions to problems, publishing those proofs and solutions, and critiquing the work of others. Students who are working on the type of authentic problems mentioned earlier should be expected to share their ideas and publish them in the classroom for a wider audience.  Their work could be presented on a poster or classroom blog.

The important point is that students are learning to prove or solve something mathematically, communicate effectively, and submit their work to a community of other young mathematicians for their review and critique.  If you’re in a state that has adopted the Common Core State Standards, then developing this type of community will ensure that students are continually engaged in Standard for Mathematical Practice 3: “Construct viable arguments and critique the reasoning of others.” This practice is a standard for all grades and will help students become great thinkers in a safe community of their peers.

To find more tips for helping elementary school students be successful in math, check out DreamBox’s free whitepaper.

### Tim Hudson

Senior Director of Curriculum Design for DreamBox Learning, Inc., Hudson is a learning innovator and education leader who frequently writes and speaks about learning, education, and technology. Prior to joining DreamBox, Hudson spent more than 10 years working in public education, first as a high school mathematics teacher and then as the K–12 Math Curriculum Coordinator for the Parkway School District, a K–12 district of over 17,000 students in suburban St. Louis. While at Parkway, Hudson helped facilitate the district’s long-range strategic planning efforts and was responsible for new teacher induction, curriculum writing, and the evaluation of both print and digital educational resources. Hudson has spoken at national conferences such as ASCD, SXSWedu, and iNACOL.