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DOUBLE TAP TO ZOOM WITH PHONE OR TABLET What Is Mathematizing?   7 mathematics promotes a construction-​of-​meaning pro- cess. Children are provided with real-​life contexts and the materials to make sense of the mathematics found within those experiences. The skills-​based approach to mathematics, on the other hand, focuses on providing children with an accumulation of factual knowledge with the goal of having them repeat the memorized information. Had the Willis Tower study been incorpo- rated using the skills-​based approach, the teacher would have shown the child a photo of the skyscraper and told him everything there was to know about the building. This teacher-​directed approach may help in naming parts of the skyscraper, but it does little to develop chil- dren’s understanding of the mathematics that were in- corporated in the construction of the building. In fact, Douglas H. Clements and Julie Sarama, two well-​known math-​education researchers, state that students may not Figure i.10. A five-​year-​old’s representa- reach the level of understanding needed for future aca- tion of the Willis Tower (twenty-​eight demic success “if children are not helped to mathematize inches tall) with Legos (reflect on, give language to)” (Clements and Sarama 2014). Mathematizing a tall building and pro- viding the students with many opportunities to create a model of the skyscraper with different MATHEMATIZING PROBABILITIES materials can help develop a student’s under- FOR TREE STUDY standing of how math is integrated within our environment. Angles Great mathematizing opportunities also Tall/Short occur when teachers use children’s environ- Wide/Narrow ments to promote mathematical learning. Take for example an exuberant tree I photo- Far/Near graphed in California (fig. i.12). The natural More/Less beauty of this tree embodies the essence of rich Shapes/Forms mathematics existing within living things. At first glance, some of the mathematical Patterns concepts that are visible in the photograph Quantities include angles, length, height, and quantity Proportions (fig. i.11). A mathematizing teacher interprets the kinds of math concepts that can be investi- Etc. gated with this photograph and plans learning Figure i.11. COPYRIGHTED MATERIAL