The Training and Technical Assistance Center (T/TAC) at the College of William and Mary (W&M) provides free Considerations Packets on a variety of educational topics. Considerations Packets provide brief overviews of user-friendly, research-based strategies that educators can incorporate into their instruction. Considerations Packets may be ordered at the T/TAC W&M website, http://education.wm.edu/centers/ttac/resources/considerations/index.php. Packets can be delivered by mail or downloaded free of charge.
This article contains an excerpt from Geometry Strategies for Middle School written by Elizabeth M. O'Brian. The complete packet may be ordered from the link above.
The geometry Considerations Packet provides strategies that address teaching middle school students at their developmental level of geometric reasoning. Understanding these levels allows teachers to differentiate instruction based on student readiness.
The geometry strategies in the complete packet address teaching perimeter and area, geometric solids, and transformations. This excerpt highlights methods for teaching plane figures.
Strategies for Teaching Plane Figures
The following strategies have been used effectively to teach plane figures to middle school students. Research has shown that when teachers incorporate the following four strategies in their instruction, retention is increased (Marzano, Pickering, & Pollock, 2001).
When parallelograms are first introduced to the class, it is helpful for the students to have a manipulative to explore. Geo strips, which can be made of varying-size strips of tag board and brat fasteners, help students discover the properties of parallelograms.
Once students have been introduced to parallelograms and their basic properties, the jigsaw method may be used to further explore special types of quadrilaterals. Teachers can follow these steps:
- Divide the class into groups of four. Within each group, assign a student to be a rectangle, square, rhombus, or trapezoid.
- Ask the "expert" from each group to leave the home group and meet with the experts from the other teams. For example, all the rectangles meet in one corner, the rhombi in another, and so on.
- Provide each group with a guided activity that allows members to explore their shape and learn its properties. Group members must come to a consensus on the properties and feel confident that they can teach these properties to their home teams.
- Ask the "expert" for each figure to prepare examples, diagrams, properties, and three quiz questions to share with their home teams.
- After the allotted time, have students return to their home teams to share their knowledge with their respective groups (Posamentier, Hartman, & Kaiser, 1998).
As students further study the properties of different types of parallelograms, they need to learn how to compare and contrast the properties of these shapes. Venn diagrams are an excellent method for displaying the shared as well as unique properties of each type of parallelogram (Marzano et al., 2001).
Venn Diagram Comparing Parallelograms
Finally, to reinforce new vocabulary explored in the unit, students can participate in a group game that focuses on the properties of each quadrilateral. The teacher can do the following:
- Divide the class into groups of four students.
- Provide each group with a "construction bag" containing items such as straws, toothpicks, tiles to show right angles, and play dough.
- Provide each student with a card that contains the description of one of the quadrilaterals studied.
- Ask students to use the items in the bag to construct the quadrilateral on their card, making it identifiable to others in their group.
- Using their definitions, have students justify the construction of the figures (National Council of Teachers of Mathematics, 2000).
If you are interested in accessing additional math strategies, please visit http://education.wm.edu/centers/ttac/resources/considerations/index.php for a complete list of Considerations Packets.
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Reasearch-based strategies for increasing student achievement. Alexandria,VA: Association for Supervision and Curriculum Development.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
O'Brian, M. E. (2004), Geometry strategies for middle school. (Available here for download)
Posamentier, A. J., Hartman, H. J., & Kaiser, C. (1998). Tips for the mathematics teacher: Research-based strategies to help students learn. Thousand Oaks, CA: Corwin Press.