People are different, and learn things differently. That is
and definitely should be a huge focus for prospective teachers all over the
world. Recognizing that there will be
more than one type of learner in a room, will help teachers to provide lessons
that are inclusive and meaningful. In class this week, we were asked a simple
math problem, and we were asked to show how we knew we were correct. The
question was:
Which is bigger- 6/10 OR 5/8
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| "Which Is Bigger". Anna Laman. September, 2015 |
Although I was pretty certain that I would be able to
successfully answer the question without doing the extra work of showing my
work, I began the process of answering the question by drawing the fractions.
In my mind, I assumed that this was what everybody would do. It did not even
cross my mind that another way would be easier or more direct, but when the
teacher asked us to explain our answers, I was shown so many other ways to come
to the same answer.
One way of arriving at an answer is not necessarily better
than another, instead, they are all equally valid ways of arriving at an
equally correct answer. All three of the ways depicted involved a process, some
being more or less complex than others, but all useful and indicatory of
mathematical understanding.
It is important that students are given the tools and
opportunity to learn more than one way of answering any math question in order
to accommodate the many learners in a classroom. There is a time for heavily
structured procedures, but students should be given some independence in the
process of choosing what process speaks to them, and which they would rather
stay away from.
Allowing students to be the masters of their own destiny in
the sense that they are encouraged to experiment, and told that there are ways
to succeed that do not necessarily mirror the standard procedures is an aspect
of a growth mindset. A growth mindset refers to the idea that a person is able
to work hard and succeed in their own way, rather than the idea of a fixed
mindset; that a person is born with an intelligence that cannot be changed. Where
a fixed mindset would credit only certain types of achievements, a growth
mindset is concerned with the process that went into a correct (or incorrect)
answer. It recognizes and appreciates hard work, rather than inherited intelligence
Validating a natural intelligence MORE than hard work can be
dangerous in students, as it leads them to believe that a mistake or a failure
is undoubtedly bad, and to be avoided at all costs. This is one way in which a
closed mindset is propagated within education systems, and allows students to
believe that hard work is less important than correct answers. For this reason,
they tend to be less adventurous in expanding their math skills in order to
maintain correct answers as much as possible.
Although it is important that students are taught to have
growth mindsets by all of the people who influence them, it is especially important
that their teachers, regardless of the grade level, propagate this view.
Hi Anna,
ReplyDeleteI also appreciated the opportunity we were given in class to figure out the math problem involving fractions and to see that we all came up with answer through various methods. Like you mentioned it is important that we provide students with the opportunity to learn more than one way of "doing math". I think that when we provide students with the opportunity to take ownership of how they will solve a problem they can have a better understanding of why it worked. This also helps students from believing that math is a mundane, black and white subject, with no room for fun or exploration. We now know that math is filled with room for exploration through methods such as inquiry based learning and I am happy that we can be apart of this change in how math is taught.
Lindsey
Hi Anna,
ReplyDeleteI thoroughly enjoyed your post and reflection regarding how important it is for students to be able to explore multiple ways to arrive at the same answer for math problems. Just as you stated above, it is critical for our students to be given those tools that will allow all them to be successful, and those types of accommodations come from us! As a student, I wish I had been given more opportunities to explore multiple ways to arrive at the same answer as maybe then one procedure would have spoken to me, however, in Elementary School we were taught the old school method where there was one right way to arrive at the right answer and this was the only way. Due to our experiences and reflections during our time here, I do believe that we'll both make insightful teachers as we recognize the importance of allowing our students to explore math without fear of repercussions. Great post overall!
- Kathlene
Hi Anna,
ReplyDeleteI really enjoyed reading your post this week on your blog. Like you, when it came to the fractions question we worked through this week in class, I too thought I didn't need to work the problem out. However, when I looked over to see how my partner solved the problem, I noticed that she had used an entirely different approach than me. While I changed the fractions into decimal figures, she drew pictures to explain. We both were right. That being said, it is here that I realized that even "teachers in the making" use different approaches. There is not just one way to learn, or teach for that matter. I think this is very important to express to our students. They need to know that they are free to use manipulative, ask questions, use different approaches , etc as a way to understand in a meaningful manner. By having a growth mindset themselves, they persevere and understand any challenge that comes their way. Teachers too must be willing to adopt this state of mind. After all, we are the role models for these students! Great post Anna!
-Jessica Scozzari
Hi Anna,
ReplyDeleteIt is so important to realize that there is more than one way to accomplish something. Especially as teachers, we need to be accepting of differences. Some teachers, particularly in math class, teacher their students a formula, and expect them to always use this one specific process to find the answer to a problem. It shows that you have a growth mindset when you say that there is more than one way of solving a problem. You recognize that people learn and think in different ways, and you are willing to help your students learn in these ways. This is so important to do to encourage students to succeed. Good thinking!
Hi Anna,
ReplyDeleteThank you for reiterating the fact that it is important to keep in mind the different type of learns we will have in our classrooms. We as teachers need to create inclusive lessons that will hit the needs of all the types of learners in our classrooms. I also approached the "Which one is bigger" questions using a visual drawing. I did not bother to think of a alternative method of approaching the question, because my chosen approach worked best for me. I found it very interesting to see how others in the class approached the same problem. Most of the approaches I would have never thought of, and some methods I adopted as a more efficient way of solving the problem. You are right, one method is not better than another. What is best is what works better for the individual student. The teacher does not need to be the keeper of all knowledge, allow the students to share and learn form each other. Thank you Anna for highlighting this point in your post.
Hi Anna!
ReplyDeleteGreat post. I am also glad we were given the opportunity to compare methods of solving the same question: very eye opening! As educators, it is especially important to realize there is more than one way of arriving at the answer. I know that during my placement, I was often guilty of only demonstrating one way of arriving at the correct answer, when I should've had other students explain their thinking as well. I wonder, is there ever a time during your academic career when you needed to possess a growth mind set?