Beyond Cookies: Understanding Various Division Models (Teaching Children Mathematics)
The
instruction of division in today’s classrooms generally deemphasizes the
relationships that the operation of division has between multiplication,
fractions, and algebraic concepts. Teachers often provide students with one
type of division problem that asks students to determine the number of items in
a particular group when provided with the whole and the number of groups. This
type of problem is known as partitive division. The authors of the article
encourage educators to also include measurement division problems in which the
number of groups is unknown but the whole and the equal number of items is
provided in the problem. This type of division problem requires students to be
more flexible in their thinking and encourages them to make connections to
multiplication. Additionally, the article discusses the importance of creating
clearly written story problems. Teachers need to keep in mind these three
criteria: 1) questions should be clear, 2) all groups should be equal and the
equality should be emphasized in the problem, and 3) problems should include a
variety of contexts. Teachers should avoid only creating problems that involve
the division of food items and instead should include several real-world
situations that students can relate to. It is also suggested for teachers to
ask students to create their own story problems to help expand their understanding
of how division works. When applicable, teachers are encouraged to provide
students with manipulatives to work through division problems as well.
The
discussion of creating clearly written story problems was the section of the
article that I gained the most from. As a result of being extremely busy during
the school year, it is easy for a teacher to find a pre-made worksheet online
and use it for the next day’s lesson without thoroughly reviewing the provided
problems for the three criteria listed above. I think it is important for
teachers to take the time to analyze their worksheets and story problems or ask
other to review them in order to ensure that the wording of the problem is not
confusing for students. If students are not provided with adequate information
or are confused what the problem is asking them to do, they are inevitably
going to struggle and do poorly on assignments. It is also important for
teachers to create multiple versions of division problems to hold student
interest and to avoid simple memorization of the process of solving the problem.
Technology Helps Students Transcend Part-Whole Concepts (Mathematics Teaching in the Middle School)
Most
American students learn fractions through a part-whole concept. Students are
provided with a section of an object and asked to identify how many parts of
the whole object is that section. This is the most common method for teaching
fractions in the United States, but it comes with certain limitations
especially concerning more complex fractions such as improper fractions. The
author s of the above article stress the importance of including partitioning
and iterating in the instruction of fractions. Partitioning is similar to the
part-whole concept such as how to divide a food item equally among a specified
number of friends. Iterating, on the other hand, is using multiplication to
understand fractions. For example, students can understand that 3/5 is the same
as 1/5 x 1/5 x 1/5. Using this strategy, students are more likely to be able to
perform more advanced fraction problems in the classroom.
The
authors of the aforementioned article suggest an iPad application to help
students with both partitioning and iterating fractions called the Candy
Factory App. In this game, students serve as employees in a candy factory
helping to serve customers with their candy orders. The customers ask for a
specific size of candy bar and students are expected to use their knowledge of
fractions in order to accurately cut the appropriate size the customer asked
for. There are three levels to the game that increasingly get more difficult
and the student continues playing. This application enables students to be
engaged and interested in learning more about fractions and provides them with
essential practice.
Teachers
have to be extremely careful when selecting games to use in the classroom. On
the surface a game may seemed to provide the needed practice for a particular
kind of skill, but upon further notice, the teacher may find that the game is
more flashy and colorful than educational. The Candy Factory app, since it was
created by The Learning Transformation Group in Virginia, is more than likely an
appropriate and effective game for students to use in learning fractions. Games
and applications not created by credible institutions should be explored
thoroughly before being used in the classroom. Student engagement and interest
is not the same as student learning and understanding of mathematical concepts.
Thanks Sara!
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