Strategies
In order to approach the geometric concepts of perimeter, area, and volume, I will be certain to provide my students with the following:
Manipulatives
Students must use and become familiar with plane figure and solid figure manipulatives, as well as tiles (activities using manipulatives and tiles are identified in various locations within this unit paper), and geoboards (see figure H) to create objects for calculating perimeter, area, and volume. My students will create (paper creation –see figure C1- or manipulatives, or other resource already mentioned) a shape and subsequently they will identify facts about the shape and provide its perimeter, area, or volume, as well as answer questions in which there are several answer choices. By providing several choices students will become involved in reasoning in order to identify the answer. “Educational research indicates mathematical achievement increases when manipulatives are put to good use”.15
Anchor charts and Journal writing
Anchor charts are valuable to students. A best practice, is to create the chart during the mini lesson as the students watch. I will write the concept and the important, detailed information as well as examples as I teach the lesson. I will then hang the chart in the classroom in order for the students to refer back to it as needed. “Anchor charts build a culture of literacy in the classroom by making thinking—both the teacher’s and students’—visible”.16 Similarly, there are also benefits from participating in the journal writing assignment. This is an opportunity for the student to write down in his/her own words and thoughts that he/she recalls about the concepts. This strategy is essential.
“Assumptions about mathematics communication via writing include: (a) students possess writing skill, (b) students can transfer this writing skill to mathematics writing, and (c) mathematics writing is representative of a mathematics knowledge”.17
Other forms of visual aids
Rulers are good tools to use since the student can refer to the numbers on the tool and the numbers will correspond to various sections on the object so it is visually helpful to the students. “It has been concluded that there is considerable evidence of a relationship between the Approximate Number System (in this case the ruler) and symbolic math that is meaningful”.18
Other tools & Methods
Use of online game play to explore and solidify understanding during play is beneficial. In terms of intellectual and expressive motivations, researchers found that,
“Children enjoy video games because of the challenges involved in achieving mastery, the opportunities to express one’s creativity, and the make-believe and discovery moments that happen during game play”.19
Since students are interested in achieving mastery, when using video games, the students will still have the same agenda (to achieve mastery), however, now within the school setting, the games are academically based and used to support the lesson. Based on the determination of the student, the goal of mastery will be attempted and possibly achieved and consistent with that feat. The student will simultaneously achieve academic gains as well. The use of the online games will subtly push the student to master the concepts that they have been taught while using the game. This is a winning combination! The technology game that is similar to the above mentioned can be seen in figure D (this game explores volume), and other technology games are: perimeter shape digital game practice, figure I and splash math area digital game practice, figure J.
Figure I. (technology enhanced perimeter game)
Figure J. (technology enhanced area game)
Use of online story books and songs to introduce the concepts also works well to capture the students’ attention.
“A basic reason for using stories is to utilize them as a means of entertainment and having fun since they inject lots of amusement and interest. Another goal is to instruct, for example, stories are meant to give moral lessons, whereas the good people are rewarded and those that are bad are punished”.20
Peer tutoring is an effective method. Students will also participate in whole group discussions wherein they will be required to participate in deductive reasoning. During deductive reasoning, the students are responsible for arriving at a conclusion based on the information that they are given. Discussions that take place whether with the teacher or peers is also recommended so that the students can practice defining various concepts. When you are able to verbally discuss facts about a given topic, then you are proving that you know and understand the topic. During the whole group discussions, students will be given a few choices and asked to arrive at the best answer based on their abilities to refer back to previous discussions, concepts, and game concept- focused activities that they recall, as well as their own journal notes.
It is common knowledge that children often confuse perimeter and area. Teachers must ensure that they,
“Give students many opportunities to solve problems in meaningful contexts. We must also give children strategies for making sense of the mathematics in problem-solving situations to help them connect the situations with the appropriate computational processes. This teaching strategy requires the appropriate use of representations that support such connections for children in meaningful problem contexts. Children also need opportunities to use both concrete and pictorial representations that support this sense-making process and to share their thinking strategies with peers”.21
Educational leaders commonly advocate that children should not just learn one method to arrive at an answer, but quite the opposite, data exists that supports the fact that students should be given a plethora of tools to use (use of rulers, manipulatives, and opportunities to count independently). When it is necessary, they can pull which tool they want to use from their resources according to what they need.
“Chinese students have advantageous knowledge on how to think and solve the same problem from different perspectives, which will be helpful for them to switch to different strategies once they get stuck”.22
Often times what matters is that you have a resource to reach for when working through math activities, as opposed to the necessity of the resource that you access, being identified as innovative or one of popular use. At times, good old- fashioned rote and/or memorization techniques that are still useful and more importantly, are handy for the student tend to work wonders. This is what is best!
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