Abstract
When teaching elementary children remotely, it is imperative that they are provided with an opportunity to thoughtfully evaluate mathematical concepts. Learning must go beyond rote memorization and the recalling of information. Rather, there needs to be a focus on discovery of connections and concepts. The focus of this chapter is guiding students to discover features of shapes using tools and technology through remote instruction with an emphasis on problem posing. Activities are provided to help intermediate elementary students explore the impact that doubling or tripling dimensions has on perimeter and area for two-dimensional shapes and surface area and volume for three-dimensional shapes. Activities that increase in difficulty as well as extensions are provided to differentiate instruction. Lessons are designed to use technology to promote discovery of mathematical relationships using technology. Strategies for remote lesson plan design in mathematics are provided.
TopIntroduction And Background
In mathematics, technology has a tremendous potential to support the understanding of concepts and ideas and enhance student learning. The power of technology can support deeper and quicker explorations compared to more traditional methods using just paper and pencil (Engelbrecht et al., 2020). Technology can enhance learning by providing opportunities to investigate mathematics on a more significant, conceptually based level (Dockendorff, 2020; Ozel et al., 2008) and has the potential to support the testing of conjectures by providing immediate feedback (Cullen et al., 2020; Korenova, 2017). It can help students visualize changes and how those changes impact mathematical structures and connections.
While technology can enhance student learning in the elementary classroom, it is often not used in ways that promote thoughtful evaluation of concepts. Applications and games can be used to support the critical analysis of mathematical ideas. For example, referencing geometry and measurement, students can discover how changes in dimensions of rectangles can impact other features of the shapes like perimeter and area or surface area and volume for prisms. Building and discovering these features using paper and pencil can be challenging because of the time it takes to construct and test. Using technology, dimensional changes can be made quickly and efficiently so students can focus more on understanding relationships rather than computing and constructing. Students can simply build shapes, quickly change dimensions and then evaluate how changes in dimension impacted calculations like perimeter, area, surface area or volume. In contrast, a direct instruction lesson may include the teacher solving formulas on perimeter, areas, surface area and volume in a whole class setting, seen in Table 1. Then, the teacher may ask the students to perform 20 more problems using the same procedure. With direct instruction approaches, there is little thought or evaluation, just computation. Problem posing provides an opportunity to critically evaluate relationships moving beyond simple calculations.
Table 1. Standard formulas for rectangles and rectangular prisms.
| Formula |
| Perimeter, Rectangle | P = 2l + 2w
l = length of the rectangle
w = width of the rectangle |
| Area, Rectangle | A = lw
l = length of the rectangle
w = width of the rectangle |
| Surface Area, Rectangular Prism | S.A. = 2lw + 2lh + 2wh
h = height of the rectangular face
l = length of the rectangular face
w = width of the rectangular face |
| Volume, Rectangular Prism | V = lwh
h = height of the rectangular face
l = length of the rectangular face
w = width of the rectangular face |
Key Terms in this Chapter
Differentiation: In education, the process of modifying or altering instruction or lessons to more successfully teach diverse learners.
Problem Posing: In mathematics, the process of presenting a problem to students that has multiple entry points and requires critical thinking to answer.
Surface Area: The calculated and summed area for each face in a polyhedron.
Isometric Paper: A special form of graph paper made of equilateral triangles or dots that can form equilateral triangles that is used to assist in drawing dimensions of shapes.
Color Tiles: Plastic or wooden manipulatives measuring 1 in by 1 in usually colored blue, green, red, and yellow. They are often used to teach mathematical concepts in measurement, geometry, and probability.
Area: The amount of surface a polygon occupies.
Perimeter: The continuous line forming the border around a polygon.
Volume: The amount of space that a polyhedron (or other three-dimensional shape like a sphere) occupies.