Reasoning is defined by the
Merriam-Webster online dictionary as “the process of thinking about something
in a logical way in order to form a conclusion or judgment”. This logical
thinking is critical in mathematics in both the real world as well as the
educational setting. Ensuring students can think about their answer and
understand if it is right or wrong is critical for student success. As teachers
we need to ensure we are asking students if their answers “make sense”. Do the
answers fit with the question or does there seem to be something that is
backwards or out of place?
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Earlier this week, this concept
of reasoning became apparent in a question presented in my University math class. The question presented an inverse
relationship that discussed a specific number of workers completing a
job in a specific amount of time and asked how long would it take a larger number of workers to complete the same job. When solving this question it was
interesting to hear the logic that was used to explain how we found a solution.
I was intrigued when a member of the class explained that the answer that he
found “was higher than the original time, but that did not make sense since
there were more workers”.
This is a prime example of thinking
about something in a ‘logical way in order to form a conclusion’. Thinking logically allowed
him and many other students in the class to realize that when there are more
workers present, the amount of time should decrease, not increase. As teachers
we must foster this thinking as it can be applied to everyday scenarios. Not
only does logic influence their decisions in the mathematics classroom, but
also when using math in the real world. Using logic will ensure students
connect other pieces of information that they know are true to the problem that
they are attempting to solve. This concept of connecting knowledge to the
current problem is presented in the video below.
https://www.teachingchannel.org/videos/student-self-correction
In the case of the problem
presented in class the students knew that as more people work together the
amount of time spent on that task should decrease, not increase. A real life
example could include as they give the cashier more money for an item they
should receive more money in return for change, or as they work more hours
their pay cheque should increase by a set amount. Students must be encouraged to think about the
answers they are giving, rather than simply writing or responding with the
numbers that the calculator spits out.
Thanks for reading!
Mr. Moore
Hello,
ReplyDeleteVery clever title of your blog, first off. On the notion of self-correction and logical thinking, I find that these formats of teaching and encouragement are very beneficial in the classroom. By using self-correction techniques, students are more drawn to develop self-learning and critical thinking skills as they are solving and learning from their own mistakes. I also agree with your statement, that teacher's need to be asking students if something perhaps in a word problem makes sense, and how can we make sense of it. Through incorporating activities and questions around these questions, their logical and mathematical think skills are sure to develop more rapidly. Overall, very intriguing concepts you bring up.
Mr. Moore,
ReplyDeleteFirstly, your blog is very user-friendly with its pictures and videos and I enjoyed reading it. I also liked your use of the official definition of reasoning as it immediately caught my attention and it helped to introduce the importance of logic. I believe that it is often easy to get caught up in formulas and, consequently, logic is sometimes forgotten. You mentioned hearing one of our colleagues mention that when considering construction worker problem, they found an answer that was higher than the original, and I must admit that I myself had obtained this higher number. As I discussed with my group, we too came to the conclusion that although the method we chose was mathematically well calculated, it was not a logical answer. As such, we reconsidered the problem, thinking logically, and were able to discover the correct answer. This said, I believe that as a future educator, it will be important for me to remember this method of self-correction and the use of logic in real world problems to help my students stray from memorizing formulas and producing illogical answers. I look forward to hearing more from you!