The manipulative that I will be creating will be a tool for students to think, learn and solve problems about time. I will be using the same concept of fraction circles, yet instead of labeling them with a fraction, they will be labeled with minutes. For instance, a whole circle will be labeled “1 hour”, while two half circles will be labeled “30 minutes”. I will also have circles fractions for 15 and 5 minutes. Though I thought about doing 1 minute pieces, I would fear that they would be too small and for the purposes of teaching young children, may also not be safe.
The main goal of this projects is to give a concrete representation of the relationship between hours and minutes. Using manipulatives is especially important when exploring new concepts, and sense time is a very abstract concept, it is especially pertinent that students have something concrete to work with (Van de Walle et al., 2014). With these manipulatives, students will be better able to solve addition, subtraction, multiplication and division problems relating to time. For instance a child may be confronted with a problem such as this:
Bob has four homework assignments. It will take him 45 minutes to finish each assignment. How many hours of homework does Bob have in total?
As stated in Teaching Student-Centered Mathematics, a study by Blume, Galindo and Walcott found that on the 2003 NAEP assessment, “only 26 percent of fourth graders and 55 percent of eighth-grade students could solve a problem involving the conversion of one measurement of time to another” (2014). With Minute Minis, students would theoretically be able to make this conversion by using the pieces to model and solve the problem. A potential way this could be modeled would be using one 30 minute piece and a 15 minute piece to show 45 minutes, then replicating this 3 other times to show 4×45. A child might then notice that they can make 2 wholes – hours in this case – using 4 of the 30 minute pieces and 1 whole/hour using the four 15 minute pieces, leading them to an answer of 3 hours.
Another potential use for Minute Minis is to use them to introduce clock reading. According to the Common Core, students are only exposed to clocks to the hour or half hour in 1st grade and then later exposed to the nearest 5 minutes in 2nd (2016). As Van de Walle et al. explains, a student who can identify 2:30 may initially be challenged by 2:33 (2014). Likely, this is because students don’t know what 2:30 means; they might not be able to make the connection that 2:30 is 30 minutes past 2:00 or have any concept of how minutes relate to hours. The reason why I decided to design my manipulatives in likeness of fraction circles was to ensure that they could easily translate to the face of a clock. It is my hope that students would be able to use the Minute Minis directly on the face of a clock provided by the teacher to explore the relationship between where the minute hand is pointing and the number of minutes past the hour. In other words, students can use the pieces to help them count, i.e. “I know that when the minute hand is pointing at the 4, it is 20 minutes past the hour because 15+5=20. I started at the 12 on the clock and put a 15 minute and a 5 minute piece to get to 4.” I also wanted to ensure that I used fractions that would equate to important benchmark times (15 minutes, 30 minutes), something that Van de Walle states is important in becoming a proficient clock reader (2014).
Overall, Mini Minutes would allow students to work with time in a concrete fashion using their own uniques strategies. If Mini Minutes is a success, students would be able to begin reading time and solve problems involving time, though not without proper support. Students need to have a thorough understanding of the concept of time to be able to effectively work with manipulatives (Van de Walle et al., 2014). For example, if a student were to use these manipulatives to read the time on a clock, they would first have to understand the different parts of a clock, what direction the clock spins in, etc. If they did not, using the manipulatives would likely fail to help the child understand and solve problems with time.
As for how I intend on testing this, I happen to be giving a lesson on reading clocks in my placement in a few weeks and – if my cooperative teacher allows it – I would love to somehow incorporate my manipulatives in the classroom as a way to gage what my students know about time. Currently, most of the 2nd graders in my class can tell time to the nearest half hour, yet I am unsure of how they know how to do this. Is it just because they know that when the minute hand is pointing at the 6 I say _:30 and when it’s pointing at the 12 I say _:00? Or do they have a more deeper understanding of time and how a clock works? For example, a child in my placement who did not know the direction an analog clock goes, might use the pieces to count the minutes by starting at the 12, but going the opposite direction. This may lead them to believe that when the minute hand is pointing at the 9, that is 15 minutes past the hour. However, a child who has a deeper understanding, may be able to use the manipulatives to tell time to the nearest 5 minutes, even when they have only been taught to read time to the nearest half hour. This will help me craft a lesson plan that will build on what they know.
Standards for Mathematical Practice. Common Core State Standards Initiative. (2016).
Retrieved October 27, 2016, from http://www.corestandards.org/Math/Practice/
Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for
Grades 3–5, 2nd Edition. Van de Walle, J., Karp, K., LouAnn, L., & Bay-Williams, J.
(2014). Boston, MA: Pearson. [ISBN-13: 978-0132824876]