Making Math Make Sense

This week we discussed an important question. We were asked if it is more important to know/do math, or to understand it. As much as we want our students to do math, as it is required, it is more important that our students understand what they are doing. Often times, students will memorize information, and only retain it for as long as they need it, like a test for instance. However, this is not what we should strive for. It is much more beneficial for students to understand what they are doing, in order to retain in within their long-term memory, which will allow students to come back to their learning at any point in the future. How do we go about doing this though? How do we truly get our students to understand math? Simply put, we have them practice, practice, practice.

As educators, we need to differentiate the instruction in all subjects. One way to do this is through visual aids. Regardless of what a student’s learning style is, visual aids can be beneficial to all students in math class. If you are working through a math problem, odds are it will be quicker and easier to solve if you have the problem right in front of you to work with. For instance, when we were asked to count to 1000 on our fingers starting at the thumb, on one hand, we had to conclude what finger we would finish on. Rather than students counting to 1000, there are ways you could come up with to speed up the process. For instance, I drew my hand on a sheet of paper. I noticed that my pointer finger and my ring finger were always even numbers. Therefore, every time I went up another 10, I wrote that number above the finger it landed on. Once I got to 20, I kept jumping back and forth between the two fingers until I got to 100. When I found out what finger 100 landed on, I knew that would be the same finger that 1000 landed on. As a result, 1000 fell on my ring finger. This is a visual of what it would look like:

 Einar Jorgen Haraldseid. (October 4, 2006). My hand. Retrieved from: https://www.flickr.com/photos/ejh/260959129/in/photolist-p4u4k-fZL6AG-fn8ZQK-DkL-hu399v-2gmPu-cftf7w-dcxmXb-99sLpa-4ji5Lv-5uh8Jv-aRzMCi-2T6KoD-eWKQtL-HmGB7-NoNmb-bqWDkG-84WcqY-oPgLGj-prRbCC-hu1MSi-hu1Pmk-5XRxkZ-8QyBGF-an69JF-djYDXd-34WfVK-62w2QS-5XRHPr-cvUW9h-ciHSTy-bcsP8X-hu1PKM-rnpSoc-d7hvry-5XW1e3-e1GnbW-ehTDCD-5wjKQt-34km4-eWgczG-5uh41F-2gny7-eW3yMX-4CdoFR-98ALqu-9VV5yq-5XS6bF-5XSgyn-4AcQZm

Lastly, an important thing to remember is that when asking any question, it has to make sense. For instance, one of the questions that students were asked was about a shepherd having 125 sheep and 5 dogs in a flock, how old is the shepherd? As educators, we know this question does not make sense because there is no way a student can find out the shepherd’s age based on this question. One proper way to word this question could be:

At 20 years old, a shepherd inherits 25 sheep and 1 dog for his flock. Every 2 years, the shepherd adds 25 more sheep and 1 more dog to the flock. How old will the shepherd be when his flock has 125 sheep and 5 dogs?

This question makes much more sense because it gives students enough information to do the math to solve the problem. This is just an example that demonstrates how a math problem must make sense so that students can solve it. I give credit to the students that still attempted to solve the problem because you could see where their thought process was.

To summarize, I would hope that you take three things from this post:

1.      Make sure your students UNDERSTAND the math

2.      Visual aids in mathematics are beneficial for ALL students, regardless of their learning style

3.  If you ask student to solve a math question, make sure the question makes sense! 

Thanks for reading!