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I’ve found that math confidence often starts at a young age and develops over time. Starting on a positive note can instill in students an appreciation for math. Encouraging students to perceive and experience math in a positive light is important. Elementary students typically experience math through a variety of hands-on experiences/manipulatives (base-ten blocks, geometric solids, counters, etc…) and then eventually progresses to the abstract. The more time spent using engaging manipulatives often builds confidence, enabling the students to transfer their math understanding to abstract problems. Building a solid mathematical foundation at the elementary level can lead to an enriching and encouraging math experience in the upper grades. If you teach a form of math at the elementary level this concept shouldn’t be unfamiliar. Most math in the K-5 curriculum is unveiled in a specific instructional order, as federal/state benchmarks indicate. Publishers may suggest that math is linear, although many experts in the field disagree. I assume that most teachers agree with a concrete/manipulative (visual representation) –> abstract (print) type of instruction model.
I’d like to recommend an edit in this process. Not necessarily a change, but an addition. Before moving straight onto the abstract, teachers should encourage students to reflect on their learning experience using manipulatives to solve math problems. When given an opportunity to reflect on their learning, students often begin to become more responsible for their own learning. Utilizing self-reflection math journals also allows students opportunities to connect their effort and achievement. It may also give the teacher insight in how a particular student understands a specific concept and plan for formative assessments. I’m not suggesting that the transfer from manipulatives to abstract should occur during the same day. Giving ample time for math connections to fuse is important and will build a solid mathematical foundation. I’ve found that the more engaged students are in their own learning the more opportunities that they will have to retain and apply their mathematical knowledge. I believe the process below assists in building math confidence which will enable students to become more responsible for their own learning. I have provided two flow charts below that may be helpful in explaining this process.