Although we do
not have to try to focus on making a connection between the reading we pick
from this week and then last week, I wanted to try to make a connection as best
I could. The first reading I wanted to focus on is from last week from Siebert &
Gaskin’s “Creating, Naming, & Justifying Fractions”. Most of my
concentration went into one of the figures in this article, figure 3. This
figure stood out to me most for two reasons, connection with my field placement
and connection with measurement. In my placement, my students are very stuck on
trying to understand the concept of a “whole”. Several students don’t realize
that when you have a fraction the denominator equals the number of total parts
in the whole. I liked this figure 3 because I feel like this would be a picture
or diagram I would bring into the classroom to try to reiterate that concept. I
really liked how the authors showed 1/8 in two different ways as well as
partitioning the fraction and iterating the fraction. The picture shows area
model and set model allows students to see a fraction being used in different
types of criteria. In my placement showing this picture would be so key because
I think my students need to see how a fraction is not “what is the shaded part
of the object OVER how much is left over” like a subtraction problem, they need
to see fractions as a whole. This cannot only help them understand wholes but
also measurement.
I believe this figure effectively displays the use of
fractions in terms of measurement especially when they show the partitioning
portion of HOW 1/8 fits into a whole. The figure for the area model displays
the notches in the “whole” to show how many 1/8s are in that whole. I believe
this can help students understand the concept of measurement and how you have
different units of different sizes in different “wholes” or even the same
whole. This would be a good figure to show struggling students who cannot
understand the concept of measurement maybe due to lack of understanding the
concept of a whole. In the set model example we see how you can group this
whole into 1/8 groups. This would definitely help students recognize the
significance of determining a certain measurement based on the whole quantity.
Next I want to focus on one of this weeks reading by Van
DeWalle “Developing Measurement Concepts”. I believe this further establishes
the need to make connections between fractions and measurements because it
effectively supports students learning of both concepts. Although DeWalle was
talking about the integration of science and mathematics curriculums I felt
this quote was also relevant to fractions for math. Measurement should be
connected with fractions because of “the need for increased precision leads to
fractional parts of units.” From my understanding of this point, DeWalle is
saying that the importance of measurement is not only important for that
subject alone but also can be an educational advantage to incorporate
measurement into other subjects like fractions so the students can further
benefit from a more integrative lesson.
Kate, I definitely agree with your ideas on Figure 3 from the Siebert and Gaskin article. The students in my field placement are older than yours and they still do not fully understand the concept of fractions and whole numbers. I think that once teachers find a way to help students memorize information, they stick with it, instead of helping them understand exactly why certain concepts make sense. In my field placement, any phrases are used to help students remember how to find equivalent fractions or perform operations using fractions. Since all students learn in different ways, it's important to incorporate different means of presentation to help students understand these concepts fully. In figure 3 in the Siebert and Gaskin article, they show two ways to represent 1/8. Like you said, this is beneficial because it shows how partitioning and iterating of 1/8 as well as two different ways to model this fraction. I think that if the students in my class saw this, they would be able to understand at least one of these representations, helping them develop a deeper understanding of a whole. Although my MT does do a great job of trying to incorporate different materials to represent fractions, sometimes connections are not made so the use of these materials does not serve her intended purpose. If the concepts in Figure 3 were tied in to the clock method my MT tried to use to teach operations with fractions, then the students would have understood how to use the clock without her giving them step-by-step directions each time they were used.
ReplyDeleteThis transitions over to your idea that fractions and measurement are related to one another and that understanding that fractions are a part of a whole can help students understand measurement as well. In the Van de Walle article, he discusses time measurement. Van de Walle states, "many hcildren who caan read a clock at 7:00 or 2:30 are initially challenged by 6:58 or 2:33." He was using this to describe 1st graders and their clock-reading skills; however, I did notice that with the clock activities used to teach operations with fractions, many of the 5th graders were also struggling with this issue. Without the fundamental knowledge of how to read a clock, this automatically put those students further behind than the students who did have fully-developed clock reading skills. Van de Walle further discussed that students should be knowledgeable of how many minutes are within an hour and have a perception of what a minute feels like. With this knowledge, it becomes easier for students to fully understand how to measure time. Since the students used clocks to add and subtract fractions, knowing the value of a minute would have helped them make sense of exactly how big their answer would be in fraction form. For example, if a student was going from 12:50 to 1:10, then the fraction should be no larger than 1 whole since an hour had not passed. Again, this example shows the significance of understanding what 1 whole is.
When you mentioned how Van de Walle mentioned the integration of curriculum, this made me think of the math lesson the students had today. Many of the students talked about measurement and 2D shapes and my teacher was able to show real-life examples of some of the ideas the students shared. I thought it was beneficial when the students brought up measuring angles in 2D shapes and my teacher tied in the idea of carpentry. When one student brought up right angles, my MT pointed out the angle in the window frame. She stated that the angle was 90 degrees and that carpenters referred to this as "square." She told the students that the 90 degrees made up part of the total sum of all the angles of a quadrilateral, which is always 360 degrees. Although it may have been more beneficial to have the students discover this on their own, I think it was helpful that she did tie in real-life examples to help the students make connections to new knowledge. Even in this example, my MT was able to exhibit the significance of 1 whole.
Fractions have always been a challenge for me, growing up. Most of my experiences with them were of me not understanding the concept of fractions, and my inability to add and subtract them. Surprisingly, I found I easier to multiply and divide them, than to add and subtract them. Now that I think about it, though, I think most of that was a result of there being more work involved in adding and subtracting them. Before you can do anything, the denominators had to be the same. This was the very thing I struggled with.
ReplyDeleteNow that I have had the time to improve my mathematical skills, I thought that it would be beneficial to choose fractions as my lesson plan topic. Siebert and Gaskin's article focused a lot on teaching students what fractions were and, more specifically, the difference between the numerator and denominator. I thought the content was wonderful, but I do not feel that my students are experienced enough with partitioning, to focus on these aspects of fractions, just yet. Therefore, I chose to introduce fractions by incorporating shape divisions and partitioning.
In the Van DeWalle (Pt. 2) article, there were several activities that focused on teaching measurement topics. What I really liked, was that the differences between certain units and categories were thoroughly explained. For example, I always had a hard time distinguishing what the difference was between weight and mass. None of my teachers were able to give me a good explanation as to why they were different. So, I was forced to enter college not being able to tell the difference. After reading this article, I feel like I finally understand what these different units represent, even though the purpose was for me to learn ways of TEACHING about measurement. I think that it is imperative for us, as teachers, to know and understand topics that we teach to our students. If we are not able to thoroughly define these concepts, then we need to challenge ourselves by learning more about the given topic. OUR experiences can help create new, fun, and exciting experiences for our students. We just need to take all we can from them.
The two articles I have chose to discuss is the Clark article on Practical tips for making fractions come alive and make sense, and VandeWalle Developing Measurement concepts article. Both of these articles stood out to me because they address issues that are apparent in learning theses concepts. Fractions are difficult for students because most times they do not understand the meaning of them or why they are important. Students need to understand that fractions are an important part of our everyday lives. In the Clarke article it mentions that students need to concentrate on developing reasoning proportions so that they may understand the size of a fraction. I remember in grade school when learning fractions I had a hard time because I did not understand this concept. I had a common misconception that the fraction size depends on the size of the number in the denominator, the larger the number the larger the fraction. For the fact that my teachers focused on carrying out the four operations of fractions and not the reasoning behind it caused me to fall behind.
ReplyDeleteJust like fractions it is important for students to understand measurement in the same way. Students need to understand the attribute that they are measuring just like they need to know fractional proportions. When this topic was first introduced to me it was easy when we worked with measurement units that I used often, such as feet, inches, liters, etc. When we began using units that were unfamiliar to me such as area, volume, mass, etc it became difficult because I was not able to make comparison to something that was familiar. The different teaching strategies shown in this article really helped me see how to use measurement in the classroom.