Teaching Measurement

One of the major things that I have learned so far this semester is the importance of explaining why. Far too often students are given busy work and complete repetitive tasks that fail to deepen understanding. Measurement is another topic that is often taught at a basic level that students fail to apply correctly in later grades. Measurement of Length by Constance Kamii explains how many third graders and even seventh graders fail to correctly answer what appears to be a basic measurement problem. This leaves teachers stunned and wondering what is ineffective about measurement education. From this article, I took away an understanding that teachers are failing to implement activities that force comparison and connections.

As a student, I recall being tested on measurement even on standardized exams such as the ACT. I wondered why something so simple would be included on an exam like that, but in reality, it is not all that simple. Yes we are taught at a young age, however, were we shown how to use a ruler in multiple ways? From the instruction that I remember, I was only ever told to measure from the end of the ruler, but never told that I can start at the two and count up how many inches the object is. In a way, this relates to what we have been talking about with addition and subtraction. Students are commonly instructed with a set method and fail to see numbers in multiple ways. A majority of the time kids only know one way to solve a problem and if they are given a task that does not appear in the standard way, they are confused and feel that they are unable to solve it. The same happens with measurement. If a ruler is presented with a starting point other than zero, students even as old as seventh grade cannot answer correctly.

As I said before, another issue is the lack of comparisons that is typical of teaching measurement. How many times can you remember measuring an object printed off on a piece of paper? I can recall countless cases of this. To make matters worse, there typically was nothing to compare that measurement to. The number we got was just a number with really no meaning. We did not use it for anything other than to write it on the line provided. So what is the point?

When a task is presented as a problem that needs to be solve, connections are made and the numbers they find from measuring are meaningful. Comparing two or more objects is exactly what measurement is used for. For example, we need to measure the length of a wall and a picture so that we can hang a picture in the exact middle, or one may need to bring a couch into a room and they have to measure the couch and doorway to make sure that the couch would fit. Measuring is not finding the length the object and not using it to make a comparison or to solve a problem.

I recently found a lesson plan for a kindergarten measurement unit, titled Measurement–Length. The ideas include spanned over several days and gave younger children an understanding of measurement before being given a ruler. Students are required to compare objects, such determining what things are bigger or smaller than others. What I enjoyed most about this lesson plan was that students are developing the foundations necessary to indirectly compare two objects. Also, the common core standards of measurement in kindergarten are met by this series of instruction. By lining up markers and miscellaneous classroom items, students are directly comparing objects and placing them in between items that are slightly smaller and larger. After working as a class, children are asked to complete the same task individually on a smaller scale. Therefore, students are exploring the concept of comparison that sets them up for success when it comes to indirect comparison in later grades. Eventually these students are required to measure with different units such as paper clips, shoes, and blocks. This provides an opportunity for the teacher to explain units and their importance.

As I mentioned earlier, giving students a reason why they are completing a task is essential and motivating. Measurement is a math topic that has a clear purpose in life and should be taught as such. This class constantly challenges me to put myself in the teacher mindset and really try to understand student thinking. I strive to challenge and question why in a way that I will be able to answer the same questions for my future students. Measurement is a necessity and the way it is taught should be directed towards the real ways that it is used.




Teaching Intentionally

Each time that the topic of division comes up, memories of minute quizzes make me cringe. I know that I am not alone in this feeling either, so why were “Mad Minutes” so terrible? I’d like to think that it might have been the mad scramble to write an answer to each problem. Maybe it was the frustration of forgetting an answer to a problem that you had seen on a flashcard what must have been a thousand times. I remember my parents testing me the night before until I completed each fact without hesitation. I also recall thinking, why am I doing this? We have talked in class about the importance of fluency and efficient methods. There is no doubt that straight memorization of facts provides fast recall, but as a kid was I fully understanding what each fact represents? Honestly, I believe that I was more focused on memorizing facts of one category so that I could move onto the next the following week.

Last year I volunteered at Wyoming West Elementary School in a kindergarten classroom and a fourth grade class. The majority of my time spent with the fourth graders was holding up flashcards for them to tell me their best guess at the answer. It is true to say that many of the kids really were guessing. Most of them did not understand how to estimate, so when I asked 3 x 5= ? they did not understand that they could count by 5 three times in order to get the answer they need. This poses a major problem to them because they are failing to understand what multiplication is and they are failing to make connections.

We have been talking in class about the importance of connections in math. Without them, students are failing to make sense of math and solve problems in a way that is meaningful to them. From class the last few weeks, there is one phrase in particular that has stood out to me.

Be intentional.

This may sound simple and obvious, but I have recently become more aware of the impact elementary math has on people. All of the foundations students learn are typically followed with memories of frustration, thus turning people away from math as they grow older. In my opinion, math should be supported by real-life problems that prompt problem solving skills and persistence. Too often math is seen as memorization of facts and equations, while understanding how they can be applied is less frequently known. As a recent assignment, I asked two of my friends to complete a long division problem. Both remember the steps and arrived at the correct answer. However, when I asked specific questions about why a certain step was important, they responded with, “Because that is what you do.” If we only know the steps to an algorithm but cannot understand why they are done, are we really improving our knowledge of math?

So, as a future teacher, I hope to encourage understanding with a variety of methods that we have discussed as a class. I want to provide students with methods that make sense to them. It is a clear fact that all people do not learn the same way, so teaching in different ways will support more students in a class. Creating lessons and activities that challenge all students and also give them the new knowledge they need to gain better mathematical understanding are essential to promoting long-term learning. When I think back to my own elementary experiences and how I wondered why we memorized countless math facts, I now know that we need effective strategies. However, before efficiency and speed comes understanding. I see a great importance of teaching realistic division problems, estimations, and easier to understand methods before long division. Yes, long division is effective but students need to understand why we need the algorithm. More importantly, we need to give them a why in math. There should be less “It is just what you do,” and more “I am doing this because…” As teachers, we need to be intentional in a way that we have more than just the next test in mind. We should be considering the importance of providing students with tools and understanding that will benefit them for their entire lives.